Tao Song
email: songtao@mail.iee.ac.cn

Changyou Chen

Linjie Chen

Pingping Wang

Long-Fei Wu

Steering of magnetotactic bacterial microrobots by focusing magnetic field for targeted pathogen killing

Keywords: Magnetotactic bacteria, Microrobot, Focusing magnetic field, Targeted Therapy, Staphylococcus aureus

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Introduction

Numerous advances in the development of microrobots with various architectures have been described [START_REF] Schwarz | Hybrid BioMicromotors[END_REF][START_REF] Ceylan | Mobile microrobots for bioengineering applications[END_REF][START_REF] Ricotti | Biohybrid actuators for robotics: A review of devices actuated by living cells[END_REF]. Some microrobots with a targeting ability are essential for the noninvasive targeted therapy of diseases, such as tumor or infection in deep tissues [START_REF] Belharet | Simulation and Planning of a Magnetically Actuated Microrobot Navigating in the Arteries[END_REF][START_REF] Arcese | Endovascular Magnetically Guided Robots: Navigation Modeling and Optimization[END_REF]. Magnetotactic bacteria show potential as actuators for the construction of microrobots with targeting abilities owing to their special characteristics. They are a unique group of bacteria that swim along magnetic field lines because of their intracellular magnetic crystals called magnetosomes [START_REF] Blakemore | Magnetotactic Bacteria[END_REF][START_REF] Blakemore | Magnetotactic bacteria[END_REF][START_REF] Frankel | Magnetosomes and magneto-aerotaxis[END_REF][START_REF] Faivre | Magnetotactic Bacteria and Magnetosomes[END_REF]. Some of these bacteria are autotrophic which can supply energy by themselves; and their motile speed can reach 300 μm/s [START_REF] Lefevre | Isolation and characterization of a magnetotactic bacterial culture from the Mediterranean Sea[END_REF][START_REF] Frankel | Magneto-aerotaxis in marine coccoid bacteria[END_REF]. As a result, the motile direction of magnetotactic bacterial microrobots can be easily controlled by magnetic fields. These characteristics endow them with many biomedical applications, for example, pathogen target [START_REF] Stanton | Magnetotactic Bacteria Powered Biohybrids Target E. coli Biofilms[END_REF], cargo delivery [START_REF] Martel | Controlled manipulation and actuation of micro-objects with magnetotactic bacteria[END_REF][START_REF] Ma | Construction and operation of a microrobot based on magnetotactic bacteria in a microfluidic chip[END_REF], and drug transport [START_REF] Alsaiari | Magnetotactic bacterial cages as safe and smart gene delivery vehicles[END_REF][START_REF] Taherkhani | Covalent Binding of Nanoliposomes to the Surface of Magnetotactic Bacteria for the Synthesis of Self-Propelled Therapeutic Agents[END_REF][START_REF] Felfoul | Magneto-aerotactic bacteria deliver drug-containing nanoliposomes to tumour hypoxic regions[END_REF].

One of the key points in these applications is the magnetic control of magnetotactic bacteria to reach a target. In general, a static magnetic field adjusted in real time can provide directions for magnetotactic bacteria because they can sense geomagnetic fields. Thus, guiding these bacteria is easily achieved via a static magnetic field if the swimming route and location of magnetotactic bacteria could be tracked in real time in a microfluidic chip under a microscope [START_REF] Chen | A compound magnetic field generating system for targeted killing of Staphylococcus aureus by magnetotactic bacteria in a microfluidic chip[END_REF]. However, real-time monitoring of the location of magnetotactic bacteria is difficult in complicated environments, such as the human body, despite the availability of information about the pattern of a flowing passageway. Thus, a simple magnetic field cannot be adjusted momentarily. Therefore, three groups of Maxwell coils were used.

Each group of Maxwell coils consist of two identical coils with a certain distance and could produce two magnetic fields of opposite direction, respectively. The two magnetic fields were superposed to form a gradient magnetic field. The three groups of Maxwell coils were modulated by a time-sequencing program to produce a focusing magnetic field equivalent to a magnetic field whose directions in the space point to or are oriented away from the focusing center. This focusing magnetic field can guide magnetotactic bacteria and induce their aggregation in a precise location [START_REF] Felfoul | Assessment of navigation control strategy for magnetotactic bacteria in microchannel: toward targeting solid tumors[END_REF]. On the basis of Maxwell coil groups, the introduction of multiple focusing points within the motion path was proposed to navigate magnetotactic bacteria to successively reach the targets [START_REF] Felfoul | Assessment of navigation control strategy for magnetotactic bacteria in microchannel: toward targeting solid tumors[END_REF][START_REF] Loghin | Exploiting the responses of magnetotactic bacteria robotic agents to enhance displacement control and swarm formation for drug delivery platforms[END_REF]. Maxwell coil method with a given control tactics is independent of the location of magnetotactic bacteria and can consequently avoid difficulties in detecting the position of these bacteria in vivo at all times [START_REF] De Lanauze | Three-dimensional remote aggregation and steering of magnetotactic bacteria microrobots for drug delivery applications[END_REF]. Therefore, how to set and optimize focusing points in the complicated channels needs to be further investigated.

Another key point in targeted therapy is the execution of functions when magnetotactic bacterial microrobots arrive at the target. Magnetotactic bacteria can be constructed as drug-carrier microrobots [START_REF] Alsaiari | Magnetotactic bacterial cages as safe and smart gene delivery vehicles[END_REF][START_REF] Taherkhani | Covalent Binding of Nanoliposomes to the Surface of Magnetotactic Bacteria for the Synthesis of Self-Propelled Therapeutic Agents[END_REF]. Applying an alternating magnetic field to induce magnetic hyperthermia of magnetotactic bacteria is an alternative [START_REF] Alphandery | Preparation of chains of magnetosomes, isolated from Magnetospirillum magneticum strain AMB-1 magnetotactic bacteria, yielding efficient treatment of tumors using magnetic hyperthermia[END_REF][START_REF] Chen | Killing of Staphylococcus aureus via Magnetic Hyperthermia Mediated by Magnetotactic Bacteria[END_REF]. However, these applications generally needs two sets of independent devices that can generate guiding and alternating magnetic fields respectively. The heat effect may also damage the surrounding healthy cells in clinical applications. Thus, real-time temperature measurement is needed. However, detecting and regulating the temperature at deep target locations are difficult when applying an alternating magnetic field.

In view of these challenges, the navigation of magnetotactic bacterial microrobots without real-time monitoring and targeted killing by applying different magnetic fields in an integrated device may be the new trends. In previous reports, we demonstrated that magneto-ovoid strain MO-1, a kind of magnetotactic bacteria, are coated by a MO-1 specific antibody to be microrobots and then can attach to Staphylococcus aureus (S. aureus) that was killed by applying a swinging magnetic field (Fig. 1a,b) [START_REF] Chen | Construction of a microrobot system using magnetotactic bacteria for the separation of Staphylococcus aureus[END_REF][START_REF] Chen | Magnetically-induced elimination of Staphylococcus aureus by magnetotactic bacteria under a swing magnetic field[END_REF]. The device used to produce a swinging magnetic field is similar to that used to generate a focusing magnetic field. In the present study, we conducted the targeted killing of S. aureus by using magnetotactic bacterial microrobots in a magnetic target device, which could produce focusing, rotating, and swinging magnetic fields (Fig. 1c). We optimized the control strategy and investigated the possibility of targeted navigation and aggregation of magnetotactic bacteria in the microchannel of microfluidic chip within the magnetic target device. Once the magnetotactic bacterial microrobots arrived at the target, rotating magnetic field assisted the mixing of microrobots and S. aureus for their attachment, and then swinging magnetic fields generated by the device under different control circuits were applied to kill S. aureus. aureus under rotating MF for their attachment, and then killed S. aureus under swinging MF.

Theory

We expect that a focusing magnetic field B could be applied to steer magnetotactic bacteria to reach the target area without knowing the location information. A plane focusing magnetic field is produced through two orthogonal coil groups. One group called x-coil produces an x-directional gradient magnetic field, while the other group named y-coil generates a y-directional gradient magnetic field. X-and y-directional gradient magnetic fields are alternately produced, thereby generating a focusing magnetic field in a time scale, as shown in Fig. 2. Fig. 2. Principle for production of focusing magnetic field. X-and y-directional gradient magnetic fields are alternately produced, finally generating a focusing magnetic field. Red, yellow, green and blue note the magnitude of magnetic field in descending order.

In a plane, the width of the microchannel in a microfluidic chip is ignored. The microchannel height is not considered either in a two dimension as microchannel height in each microfluidic chip is same and does not affect the theoretical results.

Then the shape of the microchannel in a microfluidic chip can be expressed by the following function/curve:

. Here, we assumed that the friction coefficient between the microchannel wall and magnetotactic bacteria is large enough. We could obtain the following theories:

Theorem The necessary and sufficient condition for guiding magnetotactic bacteria from the initial point P 0 to destination P 1 (focusing center) when an applied focusing magnetic field is generated by independently using x-and y-coils is that the function for the microchannel shape is a monotone function.

When the function for the microchannel shape is a monotone function, we can easily prove that the focusing magnetic field can navigate magnetotactic bacteria (Fig. 3a). X-coils produce an x-directional gradient magnetic field that steer magnetotactic bacteria to swim in the x-direction, and y-coils generate a y-directional gradient magnetic field that control their motion in the y-direction. Therefore, magnetotactic bacteria could be guided finally to the focusing center through alternated usage of x-and y-coils.

If the function is not a monotone function, then two cases will be analyzed. For the case where the function is a monodrome but not a monotone function (Fig. 3b), a point of x 0 corresponding to maximum or minimum value y 0 can be observed. At the two sides of x 0 , the direction of the focusing magnetic field that navigates magnetotactic bacteria to P 1 is the opposite. So it is impossible to achieve the aggregation of magnetotactic bacteria. For the case where the function is multivalued, x-directional magnetic field is balanced at an x point corresponding to multivalued y (y 1 and y 2 ) (Fig. 3c). As a result, the focusing magnetic field cannot navigate magnetotactic bacteria to the destination (focusing center) either.

Corollary 1

The necessary and sufficient condition for guiding magnetotactic bacteria from the initial point P 0 to destination P 1 (focusing center) under the control of the focusing magnetic field produced by the combination of x-and y-coils is the presence of a Cartesian coordinate transformation A that makes the function transform to a monotone function .

At the moment, applying a focusing magnetic field on the microchannel can be achieved by combining x-and y-coils, as shown in Fig. 3d.

Corollary 2 Finite points that make the subsection of the function monotone are present. Thus, the application of a focusing magnetic field successively on these points could steer magnetotactic bacteria.

Thus, the method of applying a focusing magnetic field can be found from the theorem (Fig. 3e).

Material and methods

Design and fabrication of magnetic target device

A magnetic target device consisting of power supplies, magnetic field coils, a control circuit, and a control program was designed and fabricated, as shown in Fig. 4a. Two power supplies (P 1 and P 2 ) (model number: DH1765-5, Beijing Dahua Radio Instrument co. LTD, China) provide current for magnetic field coils. The magnetic field coils were designed by using Maxwell (Ansoft Inc., PA, USA), and was fabricated by ourselves. Currents in coils were adjusted through the control program according to the requirement. The control program was compiled in a Microsoft

Visual Studio (community 2010) using C++ scripting language. The control circuit was established by solid-state relays whose states were set by the control program through the on-off output of the data acquisition card; the switchover of solid-state relays modulates the current state. According to the size of the objective table of an inverted microscope (IX70, Olympus co., Japan), we designed magnetic field coils that consist of two orthogonal coil groups, and these coils can be fixed on the objective table (Fig. 4b,c). Each coil group contains two identical coils placed in parallel: one group called x-coil (x 1 and x 2 coils) produces an x-directional gradient magnetic field, and the other group named y-coil (y 1 -and y 2 -coils) generates a y-directional gradient magnetic field.

The control program was used to choose the corresponding circuit. P 1 and P 2 supplied currents for the x 1 -and x 2 -coils, respectively. We set the currents in the x 1and x 2 -coils with the same magnitude in opposite directions. The x 1 -and x 2 -coils produced a gradient magnetic field in the x-axis pointing toward the geometric center of

x-coil, and this phenomenon maintained a period of T/2. Then, the control program was utilized to choose another circuit. As a result, P 1 and P 2 provided currents for the y 1and y 2 -coils, respectively, with the same magnitude in opposite directions. A gradient magnetic field in the y-axis pointing toward the geometric center of the magnetic field coils was also generated by the y 1 -and y 2 -coils. This phenomenon sustains another period of T/2. Within a period of T, gradient magnetic fields in the x-and y-axes overlaid, thereby generating a focusing magnetic field (Fig. 2). We implemented the focusing magnetic field on a time scale by continuing the repetition of this process. The location of the focusing center of focusing magnetic field could be adjusted by changing the current magnitude of each coil in the x-or y-coils to steer magnetotactic bacteria flexibly. The amplitude of the magnetic field on the axis of a rectangular coil is described in Eq. ( 1) [START_REF] Grant | Electromagnetism[END_REF]:

, ( 1
)
where B is the amplitude of the magnetic field on the axis of a rectangular coil, a and b are the two rectangular side lengths, h is the distance from one point on the axis of a rectangular coil to the center of the rectangular coil, μ 0 is the permeability of the vacuum, and I is the current. In addition, (1) the currents in a coaxial coil pair

For the square coil, a is equal to b, and a 2 /4 is equal to A. Eq. ( 3) can be written as follows [START_REF] De Lanauze | Three-dimensional remote aggregation and steering of magnetotactic bacteria microrobots for drug delivery applications[END_REF]:

.

Therefore, two sets of currents satisfying Eq. ( 4) can cause the location of the focusing center to diverge a distance of δ from the geometric center of the coaxial coil.

In addition to the focusing magnetic field, rotating and swinging magnetic fields can be generated using the magnetic target device fabricated here. In the generation of rotating and swinging magnetic fields, P 1 provides currents with the same magnitude and direction for the x 1 -and x 2 -coils by choosing the corresponding circuit under the setting of the control program, thereby creating a magnetic field in the x-axis. P 2 also supplies currents for the y 1 -and y 2 -coils, thereby producing the other magnetic field in the y-axis. A rotating magnetic field can be generated in a discrete mode by controlling the power supply and circuit in accordance with the program. When P 1 and P 2 yield currents according to a certain frequency, the magnetic target device can generate a swinging magnetic field with the corresponding frequency in a space enclosed by magnetic field coils.

Fabrication of microfluidic chip

To test our analyses, we developed three types of glass microfluidic chips: Z-chip with a monotonic channel, U-chip with a nonmonotonic channel, and M-chip with a piecewise monotonic channel. Each type of glass microfluidic chips was characterized by a width of 200 μm and a height 20 μm, and comprised sample and target holes with 400 μm in diameter. The three chips were fabricated by photomasking, lithography

                                                     4 1 4 1 4 4 4 1 4 1 4 4 2 2 2 2 2 2 2 2 0 2 2 2 2 2 2 2 1 0 b h a h b a h ab nI b h a h b a h ab nI                       4 1 4 1 4 1 4 1 4 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 b h a h b h a h b a h b a h I I                                 A h A h A h A h I I           2 2 2 2 2 1 2 2    
exposure, film development, chrome removal, etching, chip cutting and drilling, and hot compaction. In brief, a photomask was prepared using a PET film according to the designed shape of the microfluidic chip. A Cr plate was aligned to the mask and exposed using a lithography machine. Afterward, the Cr plate was placed with its light rubber oriented in a forward direction and imaged in 0.5% NaOH for 40 s to rinse the part of the imaged light rubber. The Cr plate was fixed with water for 1 min. After drying, its light rubber was positioned in a forward direction in an oven at 110 °C for 15 min to solidify the remanent light rubber. After cooling to room temperature, the Cr plate with its photoresist surface upward was enchased in Cr removal solution to remove naked Cr by shaking gently for 40 s. A glass substrate with a shape of a transparent channel was formed after water cleaning and drying. Adhesive tapes were pasted to the back and edge of the substrate as a protective layer, and the pasted substrate with the channel side upward was etched by immersing it in an etchant at 40 °C with slow shaking. The etched substrate was rinsed in water, and the adhesive tapes were removed. Then, the glass substrate was punched by a straight-handle twist drill in the micropores. Finally, the glass substrate was bound with coverslips at a high temperature. The chips can be placed on the center of the magnetic field coils and fixed to the objective table of the microscope.

Preparation of magnetotactic bacteria MO-1 and S. aureus

Magneto-ovoid strain MO-1 was grown in EMS2 medium at room temperature and collected until the exponential phase was reached [START_REF] Lefevre | Isolation and characterization of a magnetotactic bacterial culture from the Mediterranean Sea[END_REF]. A permanent magnetic block made of Nd-Fe-B was placed around 2 mL Eppendorf tubes containing MO-1 solution to enrich the MO-1 cells. To determine the cell concentration, some solution containing the enriched MO-1 cells was mixed with 4% formaldehyde to let MO-1 cells lose the motility. Then the number of MO-1 was counted using a hemacytometer under a microscope and the original concentration of MO-1 was further determined.

S. aureus (ATCC25923) was grown on blood LB agar plates (Land Bridge

Technology Co., Ltd., Beijing, China) in an incubator at 37 °C. Bacterial cells were harvested and suspended in normal saline buffer containing 0.9% NaCl. Their concentration was measured through conventional plate counting.

Navigation of magnetotactic bacteria MO-1 in microfluidic chips

Navigation experiments were carried out in the three types of microfluidic chips.

1.5×10 7 MO-1 was injected into the sample hole of microfluidic chips. Through the adjustment of electric current in the x-and y-axes, the focusing magnetic field was produced to cover the chips, and its focusing center was set. The time sequence of the focusing magnetic field was set to 10 s. Considering that MO-1 is a North-Seeking magnetotactic bacterium which preferentially swims parallel to the magnetic field, we used the focusing magnetic field equivalent to a magnetic field whose directions in the space point to the focusing center for navigation. When a focusing magnetic field was applied, the movement of MO-1 was monitored under the brightfield of the microscope (objective: 40×; light source: mercury lamp) to validate the aggregation effect and not to provide positional information for magnetic field control. The videos are recorded by using a camera (EOS 500D, Canon Inc., Japan) connected to the microscope. The relative position between the magnetic field coils and the microfluidic chip remained unchanged when the objective table of the microscope was shifted because the chip, the magnetic field coils, and the objective table were fixed to one another.

Targeted killing of S. aureus by magnetotactic bacterial microrobots

S. aureus was subjected to targeted killing in M-chip. Magnetotactic bacterial microrobots were first constructed according to our previous study [START_REF] Chen | Construction of a microrobot system using magnetotactic bacteria for the separation of Staphylococcus aureus[END_REF]. Briefly, magnetotactic bacteria MO-1 was first incubated with rabbit anti-MO-1 polyclonal antibodies for 30 min at room temperature; rabbit anti-MO-1 polyclonal antibodies specifically react with MO-1 surface antigens to construct MO-1 microrobots; after that, MO-1 microrobots of good activity were enriched by a permanent magnetic block for the following experiment. Then, 1.5×10 7 microrobots were injected into the sample hole, and 1.5×10 6 S. aureus was simultaneously injected into the target hole.

When the microrobots were guided to arrive at the target hole, a rotating magnetic field was exerted to induce the intensive mixing between S. aureus and MO-1 microrobots. Then, S. aureus was incubated for 30 min at room temperature for their attachment to MO-1 microrobots through antibody-protein A interaction [START_REF] Chen | Killing of Staphylococcus aureus via Magnetic Hyperthermia Mediated by Magnetotactic Bacteria[END_REF][START_REF] Chen | Construction of a microrobot system using magnetotactic bacteria for the separation of Staphylococcus aureus[END_REF]. A swinging magnetic field with an intensity of 10 mT and a frequency of 2 Hz was applied for 40 min. After the application of swinging magnetic field, the S. aureus solution in the target hole was diluted by 100-fold, and 50 μl dilution was spread on blood LB agar plates. The number of S. aureus clones was counted after the plates were incubated overnight in a thermostatic incubator at 37 °C. Meanwhile, the case in the absence of the swinging magnetic field was used as its control group. Besides, S. aureus alone group (SA) and the simple mixture group (SA + MO-1) where MO-1 cells which is not coated by a MO-1 specific antibody were also guided to the target hole of M-chip containing S. aureus were also performed in the presence and absence of swinging magnetic field.

Statistical analysis

Data for S. aureus clone was acquired by averaging clone number of three plates in each experiment. Data were expressed as mean ± standard deviation (SD). Each killing experiment was independently performed thrice. Student's t-test was applied to compare the difference. Differences with a P value of < 0.05 were considered significant in the statistical test.

Results

Movement of magnetotactic bacteria MO-1 in Z-and U-chips under the control of focusing magnetic field

The control effect of the focusing magnetic field on magnetotactic bacteria MO-1 was first observed in the Z-(Fig. 5a) and U-chips (Fig. 5b). The Z-chip channel can be expressed as a monotone function, whereas the U-chip channel can be expressed as a nonmonotonic and multivalued function. According to theory, the magnetotactic bacteria would aggregate at the target hole in the Z-chip (Fig. 5c) and not in the U-chip (Fig. 5d) when the focusing center was set on the target holes of the two chips. Fig. 6a shows the movement of MO-1 in the Z-chip under the control of the focusing magnetic field. MO-1 cells in the sample hole initially sensed the rightward direction of the focusing magnetic field at site I located in Fig. 5c and consequently swam away from the sample hole along this magnetic field (Fig. 6a). After 5 s in the rightward magnetic field, the direction of the focusing magnetic field changed upward, which caused MO-1 aggregation in the wall of the microfluidic chip (Fig. 6a). After 5 s in the upward magnetic field, the direction of the focusing magnetic field was rightward again, which guided the MO-1 cells to move continuously. When the MO-1 cells arrived at the first turn shown in site II, the change in the magnetic field direction from rightward to upward guided them to pass the turn, and the focusing magnetic field continuously assisted these cells. The same scenario was observed in the second turn in site III, that is, MO-1 passed through the turn. Finally, magnetotactic bacteria MO-1 reached the target hole (site IV) controlled by the focusing magnetic field (Fig. 6a). Fig. 6b illustrates the movement of MO-1 cells from the sample hole of the U-chip under the focusing magnetic field. The MO-1 cells at the sample hole initially perceived the rightward direction of the focusing magnetic field. As a result, they swam away from the sample hole for 5 s at site I of the U-chip, as shown in Figs. 5d and6b. As the direction of the focusing magnetic field changed upward, the MO-1 cells moved to and aggregated on the channel wall at site I. Under the control of the focusing magnetic field, the MO-1 cells continuously swam in the channel, such as at site II, until they reached the P site (Figs. 5d and6b). At the P site, the MO-1 cells perceived only the gradient magnetic field in the y-direction because the x-directional magnetic field was balanced dynamically. Therefore, they swam back and forth at the P site (site III) (Fig. 6b). The target hole (focusing center) over the P site was observed by moving the microscopic objective table (Fig. 6b). We did not find any magnetotactic bacteria in the target hole, suggesting that the bacteria in the U-chip could not reach the target hole. Hence, our experimental results in the Z-and U-chips were consistent with the theorem.

Guiding magnetotactic bacteria MO-1 in M-chip by using the focusing magnetic field

The schematic of M-chip fabrication is shown in Fig. 7a. In an orthogonal plane coordinate system, the channel of the M-chip was expressed as a nonmonotonic function. If the focusing center O of the focusing magnetic field was set directly on the target hole, then the magnetotactic bacteria aggregated at site II (Fig. 7b) and cannot arrive at the target hole. According to Corollary 2, the shape of the M-chip could be segmented as a piecewise continuous function by point IV. Thus, we chose point IV as the first focusing center (O 1 ) ( Fig. 7c) and then set the center on the target Fig. 8. Swimming of Magnetotactic bacteria MO-1 in M-chip under the control of focusing magnetic field. Microrobots MO-1 images depict the detailed status of magnetotactic bacteria MO-1 movement under the focusing magnetic field control. Their locations are corresponding to the site I, II, III, IV in Fig. 7c, V and VI in Fig. 7d, respectively. Red and blue arrows note the direction of focusing magnetic field. A video is available as additional material.

Targeted killing of S. aureus by magnetotactic bacteria MO-1 microrobots

The guidance provided by the focusing magnetic field demonstrated the potential of the magnetotactic bacteria for targeted therapy, even in deep tissues. We previously showed that MO-1 can kill S. aureus under either alternating [START_REF] Chen | Killing of Staphylococcus aureus via Magnetic Hyperthermia Mediated by Magnetotactic Bacteria[END_REF] or swinging magnetic fields [START_REF] Chen | Magnetically-induced elimination of Staphylococcus aureus by magnetotactic bacteria under a swing magnetic field[END_REF] and that bacterial MO-1 microrobots can be fabricated by coating MO-1 cells with their antibodies [START_REF] Chen | Construction of a microrobot system using magnetotactic bacteria for the separation of Staphylococcus aureus[END_REF]. Basing from these findings, we used MO-1 microrobots to target S. aureus under the control of the focusing magnetic field and eradicated this pathogen under a swinging magnetic field. In M-chip, 1.5×10 7 MO-1 microrobots and 1.5×10 6 S. aureus were injected into the sample and target holes, respectively. The MO-1 microrobots successfully arrived at the target hole in M-chip after about 80 s when the focusing magnetic field was applied by the magnetic target device. A rotating magnetic field (1 mT) was exerted to induce an intensive mixing between MO-1 microrobots and S. aureus for their attachment. A swinging magnetic field with a frequency of 2 Hz and an intensity of 10 mT was subsequently applied for 40 min after the MO-1 microrobots conjugated to S. aureus. As shown in Fig. S1 in the supplementary material, the union body swung due to the oscillation of MO-1 microrobots along with swinging magnetic field (black ellipses). As a result, S. aureus attached to MO-1 microrobots was driven by the motion of the microrobots and consequently swung (shown as red dashed ellipses in Fig. S1 in the supplementary material). Then, the effect of the swinging magnetic field on S. aureus was evaluated (Fig. 9). When the MO-1 microrobots conjugated to S. aureus, the applied swinging magnetic field induced a significant decrease in S. aureus viability (P<0.01).

Discussion

Steering of magnetotactic bacterial microrobots to the target area is an important step for the targeted killing of harmful cells. In this work, strategies to control magnetotactic bacterial microrobots under a focusing magnetic field was analyzed, and an integrative targeted killing of S. aureus was verified in a microfluidic chip. In a two dimensional space, a focusing magnetic field can be generated via a simple method of applying currents to the x-and y-coils simultaneously [START_REF] Jürgen Rahmer | Spatially selective remote magnetic actuation of identical helical micromachines[END_REF]. The focusing magnetic field used in the present study was generated in a time-sequencing manner with the fabricated device (Fig. 4). Compared with the simultaneous application of a gradient magnetic field, the time-sequencing manner is more propitious for magnetotactic bacteria to overcome the restraint of the pipe wall and subsequently aggregate [START_REF] Loghin | Exploiting the responses of magnetotactic bacteria robotic agents to enhance displacement control and swarm formation for drug delivery platforms[END_REF].

To overcome the influence of tortuous channels, we confirmed that the application of focusing centers on specific points to steer magnetotactic bacteria was feasible. This approach did not require real-time imaging and monitoring, and importantly, the focusing center can be set in a small range to navigate microrobots and not necessarily restricted to specific points. This trait may play a critical role especially when a vascular shape may be obtained incompletely. Although our analyses and experiments were carried out in two dimensional space, the case in three dimension is similar. In general, acquiring a vascular shape in the human body is feasible by means of some techniques, including magnetic resonance imaging [START_REF] El-Merhi | Peripheral vascular tumors and vascular malformations: imaging (magnetic resonance imaging and conventional angiography), pathologic correlation and treatment options[END_REF][START_REF] Do | Simultaneous Variable-Slab Dual-Echo TOF MR Angiography and Susceptibility-Weighted Imaging[END_REF], computed tomography [START_REF] Heo | Computed Tomography-Based Thrombus Imaging for the Prediction of Recanalization after Reperfusion Therapy in Stroke[END_REF], and angiography [START_REF] Gillmann | Tumor Blood Vessel Visualization[END_REF]. In a three dimensional environment, the guidance of magnetotactic bacterial microrobots could also be achieved if three dimensional channels are content with the similar monotonic functions (i.e. the projections of three dimensional channels on the three planes of XYZ coordinate system are all monotonic functions.). In this case, the focusing center can be set directly on the targeted hole, and the gradient magnetic fields along x-, y-and z-axes are applied in a time-sequencing way to guide magnetotactic bacterial microrobots. If they're more complicated channels, for example the vascular network, we could also steer magnetotactic bacterial microrobots in a way similar to Corollary 2. We can first identify a series of specific points which are used as focusing centers and then the blood vessel could be divided into many segments. After that, magnetotactic bacterial microrobots could be steered to reach each specific point by applying a time-sequencing gradient magnetic field along x-, y-and z-axes and finally arrive at the target. Moreover, the time for changing the focusing center should also be considered during the guiding of magnetotactic bacterial microrobots. In the study, the focusing center could be changed quickly by microscope.

When in the invisible case, we are able to acquire the path length of a channel by imaging; and then the time to arrive at the given focusing center for microrobots could be estimated as the velocity of magnetotactic bacterial robot is known. Considering other factors(i.e. blood flow, bacteria individual difference, curve of the actual path), we may set up a suitable time for bacterial microrobots to reach the focusing center and then change to the next one.

As for three kind of microfluidic chips, the walls of the channel are straight, which does not trap the motile of bacterial microrobots. But the friction coefficient of microchannel is supposed to be large enough in our analysis. If the friction coefficient is very small and the time sequence of the focusing magnetic field sustains slightly longer, the steering of the magnetotactic bacteria or their microrobots to aggregate might also be realized. However, the accumulation of most bacteria or microrobots could not be achieved in this case. In addition to magnetotaxis, magnetotactic bacteria also have the aerotaxis that they are able to sense the oxygen concentration and swim toward the direction of low oxygen. Since deep area of tumor is a hypoxic region due to the consumption of oxygen by rapidly growing tumor cells, the hypoxic status could also assist MTB to guide tumor, which is complementary with magnetotaxis [START_REF] Felfoul | Magneto-aerotactic bacteria deliver drug-containing nanoliposomes to tumour hypoxic regions[END_REF]. Other electron acceptors and chemicals in the blood should also be considered when steering magnetotactic bacteria.

As the next step, killing target cells is the ultimate goal. Previously, we have performed the killing experiments by using magnetotactic bacteria MO-1 under the swinging magnetic field and calculated the mechanical force, which decreased the viability of S. aureus [START_REF] Chen | Magnetically-induced elimination of Staphylococcus aureus by magnetotactic bacteria under a swing magnetic field[END_REF]. In the present study, the used guiding magnetic field coils (Fig. 4c) was also able to produce the swing magnetic field which was similar to the results by Chen et al [START_REF] Chen | A compound magnetic field generating system for targeted killing of Staphylococcus aureus by magnetotactic bacteria in a microfluidic chip[END_REF]. The swinging of MO-1 microrobots with the swinging magnetic field was also found here. This result suggests that a mechanical force was particularly exerted on S. aureus, which was then killed. These experiments also suggested that the integration of target navigation and therapy was essential for applications involving magnetotactic bacteria. We also aimed to address this issue in the study. On the one hand, focusing, rotating, and swinging magnetic fields were produced in one system by using different control programs and circuits. It should be noted that the steering strategy is different. The present study proposed the controlling method which does not need a real time monitoring, whereas the steering was performed under a microscope in the literature by Chen et al [START_REF] Chen | A compound magnetic field generating system for targeted killing of Staphylococcus aureus by magnetotactic bacteria in a microfluidic chip[END_REF]. In the complex vascular network, the presented steering strategy may be more advantageous. On the other hand, the flow of targeted killing pathogens in vivo with magnetotactic bacterial microrobots and magnetic fields was simulated by completely conducting target aggregation, mixing, and targeted killing in one microfluidic chip.

Conclusions

In the study, we reported the targeted aggregation of magnetotactic bacterial microrobots by using a focusing magnetic field to avoid difficulty in real-time monitoring and targeted therapy for killing S. aureus. The focusing magnetic field was generated in a time-sequencing manner within the magnetic target device fabricated in the study. The strategy of focusing magnetic field was feasible in steering of magnetotactic bacterial microrobots. Finally, we successfully decreased S. aureus viability by using magnetotactic bacteria MO-1 microrobots under the control of focusing, rotating, and swinging magnetic fields generated in the magnetic target device. The combination of focusing magnetic field and controllable magnetotactic bacteria in the magnetic target device showed potential for targeted killing and drug delivery. However, effects from pulsating blood flow, red blood cells, friction on the control of magnetotactic bacterial microrobots and the safety of magnetotactic bacteria in human need further investigations for the future application.

Fig. 1 .

 1 Fig. 1. Schematic of targeted killing of Staphylococcus aureus by magnetotactic bacterial microrobots. (a) Magnetotactic bacteria (MTB) MO-1 with a chain of magnetosome and two bundles of flagella [24]. (b) Attachment of magnetotactic bacteria MO-1 to S. aureus [24]. Antibody-coated magnetotactic bacteria MO-1 (microrobots) could attach to S. aureus via the affinity between MO-1 specific antibody and Protein A expressed in the surface of S. aureus. Black arrows noted MO-1 microrobot and red arrows indicated Staphylococcus aureus. (c) MO-1 microrobots was first navigated to the target by focusing magnetic field (MF), mixed with S.

Fig. 3 .

 3 Fig. 3. Effect of microchannel shape on the control of magnetotactic bacteria under the focusing magnetic field. (a) A monotone function for a microchannel shape. (b) A non-monotone but monodrome function for a microchannel shape. It generally has a point of x 0 corresponding to maximum or minimum value y 0 . (c) The multivalued microchannel function where some x points correspond to multivalued y (y 1 and y 2 ). (d) The non-monotone microchannel function could be transformed to a monotone function by a Cartesian coordinate transformation A. (e) Finite points make the subsection of the microchannel function monotone.

8 / 22 Fig. 4 .

 8224 Fig. 4. Fabrication of a magnetic target device. (a) Schematic of magnetic target device. The device mainly consists of power supplies, magnetic field coils, control circuit as well as control program. (b) The embedded magnetic field coils into the objective table. (c) The magnetic field coils. The coils consist of two orthogonal coil groups

comprising I 1

 1 and I 2 coils are I 1 and I 2 , respectively;[START_REF] Ceylan | Mobile microrobots for bioengineering applications[END_REF] the distance between the coil pair is 2h; and (3) the distance covered by the focusing center diverging from the central point of the coaxial coil is δ. The distances from the focusing center to I 1 and I 2 coils are h + δ and h -δ, respectively. The offset of the gradient magnetic field produced by I 1 and I 2 coils can be determined by the following: I 2 in the two coils satisfy the following equation:.

Fig. 5 .

 5 Fig. 5. Movement analysis of magnetotactic bacteria MO-1 under the control of focusing magnetic field in Z-chip and U-chip. (a) Z-chip. (b) U-chip. (c) Schematic movement of magnetotactic bacteria MO-1 in Z-chip when the focusing center O (four red counter-arrows) was fixed directly on the target hole. (d) Schematic movement of magnetotactic bacteria MO-1 in U-chip when the focusing center O (four red counter-arrows) was fixed directly on the target hole. Black arrows in the microchannel in (c) and (d) note the direction of focusing magnetic field magnetotactic bacteria MO-1 felt during their movement.

Fig. 6 .

 6 Fig. 6. Swimming of magnetotactic bacteria MO-1 under the control of focusing magnetic field in Z-and U-chips. (a) Movement of MO-1 microrobots in the Z-chip. Robot images shows their movements in different location in sites of Fig. 5c under the control of focusing magnetic field. (b) Movement of MO-1 microrobots in U-chip. Robot images shows their movements in different location in sites of Fig. 5d under the control of focusing magnetic field. Red and blue arrows note the direction of focusing magnetic field. Two videos are available as additional material.

Fig. 9 .

 9 Fig. 9. Targeted killing of S. aureus by magnetotactic bacteria MO-1 microrobots. The suspensions of S. aureus alone (SA), simple mixture (SA + MO-1) and the conjugated form that MO-1 microrobots combined to S. aureus (SA + microrobots) were exposed to a swinging magnetic field (sMF: 2 Hz, 10 mT) for 40 min. Then the number of CFU for S. aureus was counted to quantify the cell viability. **P < 0.01, n=3.

Acknowledgements

We thank Dr. Haiying Shen (National Center for Nanoscience and Technology of China) and Xiaofei Zhang (Wenhao Co., Ltd., Suzhou, China) for help to the fabrication of

Funding

This work was supported by the National Key Research and Development Program of China (Grant NO. 2017YFC0108501), the National Youth Foundation of China (Grant NO. 31300689) and the National Foundation of China (Grant NO. 81871488).

hole (O 2 ) after the magnetotactic bacteria arrived at the first focusing center (Fig. 7d). Black arrows in the microchannel note the direction of focusing magnetic field in a time sequence that magnetotactic bacteria exposed to during their movement.

The experimental demonstration of MO-1 movement under the control of the focusing magnetic field is shown in Fig. 8. Similar to the condition in Z-chip, MO-1 cells were controlled to swim at site I, moved across the two turns at sites II and III, and arrived at the first focusing center O 1 at site IV (Fig. 8). If the focusing center was maintained at site IV, then the magnetotactic bacteria persistently aggregated. Then, we changed the focusing center to the target hole. As a result, the direction of the magnetic field in the y-axis was downward ( Fig. 7d). MO-1 cells consequently swam downward shown as blue arrows at site IV (Fig. 8), went through the curve channel at site V, and finally arrived at the target hole at site VI (Fig. 8). These results demonstrated that the magnetotactic bacteria could be steered in complex flows by choosing and setting some specific points under the focusing magnetic field.

Supplementary data

Supplementary data associated with this article can be found, in the online version.


Xue-Gong Li
email: xuegongli@idsse.ac.cn

Wei-Jia Zhang

Xiao-Qing Qi

Long-Fei Wu

Genome analysis of Crassaminicella sp. SY095, an anaerobic mesophilic marine bacterium isolated from a deep-sea hydrothermal vent on the Southwest Indian Ridge

Keywords: CDS, coding sequence, COG, clusters of orthologous groups, GO, gene ontology, KEGG, Kyoto Encyclopedia chemoheterotroph, chemoorganotroph, extreme environment, genome sequencing, prophage, sporulation

Crassaminicella sp. strain SY095 is an anaerobic mesophilic marine bacterium that was recently isolated from a deep-sea hydrothermal vent on the Southwest Indian Ridge. Here, we present the complete genome sequence of strain SY095. The genome consists of a chromosome of 3,046,753 bp (G+C content of 30.81%) and a plasmid of 36,627 bp (G+C content of 31.29%), encodes 2966 protein, 135 tRNA genes, and 34 rRNA genes. Numerous genes are related to peptide transport, amino acid metabolism, motility, and sporulation. This agrees with the observation that strain SY095 is a spore-forming, motile, and chemoheterotrophic bacterium. Further, the genome harbors multiple prophages that carry all the genes necessary for viral particle synthesis. Some prophages carry additional genes that may be involved in the regulation of sporulation. This is the first reported genome of a bacterium from the genus Crassaminicella, providing insights into the microbial adaptation strategies to the deep-sea hydrothermal vent environment.

Introduction

Deep-sea hydrothermal vent environment is characterized by steep temperature and geochemical gradients, which provide a large range of habitats for chemotrophic microorganisms [START_REF] Dick | The microbiomes of deep-sea hydrothermal vents: distributed globally, shaped locally[END_REF]. Chemosynthetic bacteria and archaea utilize chemical energy to fix inorganic carbon into organic carbon for microbial growth, and form the foundation of vent ecosystems [START_REF] Mcnichol | Primary productivity below the seafloor at deep-sea hot springs[END_REF][START_REF] Nadine | Hydrothermal energy transfer and organic carbon production at the deep seafloor[END_REF]. Chemotrophs are an important component of the microbial community in the deep-sea hydrothermal vent, and play critical roles in deep-sea carbon, nitrogen and sulfur cycling [START_REF] Ding | Microbial Community Structure of Deep-sea Hydrothermal Vents on the Ultraslow Spreading Southwest Indian Ridge[END_REF][START_REF] Cao | Microbial Sulfur Cycle in Two Hydrothermal Chimneys on the Southwest Indian Ridge[END_REF].

The genus Crassaminicella is affiliated with Clostridiales and was first reported in 2015 [START_REF] Lakhal | Crassaminicella profunda gen. nov., sp. nov., an anaerobic marine bacterium isolated from deep-sea sediments[END_REF]. It represents a novel type of mesophilic chemoorganotrophic bacteria from the deep-sea hydrothermal environment. Cells from this genus are gram stain-positive, motile, straight or curved rods, and form terminal endospores. Crassaminicella is an obligate anaerobic and heterotrophic bacterium that ferments carbohydrates and proteinaceous substrates [START_REF] Lakhal | Crassaminicella profunda gen. nov., sp. nov., an anaerobic marine bacterium isolated from deep-sea sediments[END_REF]. To date, this genus contains only one species, Crassaminicella profunda, the sole strain Ra1766HT, as the type strain of this species, was isolated from sediments of the Guaymas Basin at a depth of 2002 m [START_REF] Lakhal | Crassaminicella profunda gen. nov., sp. nov., an anaerobic marine bacterium isolated from deep-sea sediments[END_REF]. During the recent cruise, we have isolated an anaerobic mesophilic marine bacterium, strain SY095, from a deep-sea hydrothermal vent on the Southwest Indian Ridge. Phylogenetic analysis based on 16S rRNA gene sequences indicated that strain SY095 was most closely related to the type strain of C. profunda Ra1766HT (96.05% similarity). Notably, the reported bacteria from the deep-sea hydrothermal vent environment mainly represent gram-negative bacteria. Only a few represent gram-positive bacteria, e.g., Clostridium tepidiprofundi SG 508 T [START_REF] Slobodkina | Clostridium tepidiprofundi sp. nov., a moderately thermophilic bacterium from a deep-sea hydrothermal vent[END_REF], Vulcanibacillus modesticaldus BR T [START_REF] L'haridon | Vulcanibacillus modesticaldus gen. nov., sp. nov., a strictly anaerobic, nitrate-reducing bacterium from deep-sea hydrothermal vents[END_REF], and Sulfobacillus acidophilus NAL T [START_REF] Norris | Characteristics of Sulfobacillus acidophilus sp. nov. and other moderately thermophilic mineral-sulphide-oxidizing bacteria[END_REF]. Here, we report the first genome of a bacterium from the genus Crassaminicella. The availability of genome sequence will promote the understanding not only of bacteria from this genus but also the adaptation strategies of gram-positive bacteria to the deep-sea hydrothermal vent.

Data description

General features of this strain and the MIGS mandatory information are shown in Table 1. High-quality total genomic DNA was extracted using a MagAttract DNA kit (Qiagen, USA) according to the manufacturer's instructions. Whole genome sequence was obtained by sequencing using GridION platform (Nextomics, China). Over 3 Gb of processed reads were generated for an approximately 950-fold depth of coverage.

Clean reads were assembled using Canu v1.7 to generate the complete genome sequence [START_REF] Koren | Canu: scalable and accurate long-read assembly via adaptive k-mer weighting and repeat separation[END_REF], and the results were corrected using Pilon v1.22 (https://github.com/broadinstitute/pilon) based on the MGI-SEQ 2000 sequence. Gene predictions were made using Prodigal v2.6.3 (https://github.com/hyattpd/Prodigal).

Functional information for each predicted gene was obtained based on sequence-similarity search against the non-redundant protein database available from the National Center for Biotechnology Information, Clusters of Orthologous Groups (COG) database [START_REF] Galperin | Expanded microbial genome coverage and improved protein family annotation in the COG database[END_REF], Gene Ontology (GO) database [START_REF] Ashburner | Gene Ontology: tool for the unification of biology[END_REF], and Kyoto Encyclopedia of Genes and Genomes (KEGG) [START_REF] Kanehisa | Data, information, knowledge and principle: back to metabolism in KEGG[END_REF]. tRNA genes were predicted by using tRNA scan-SE v2.0 (http://lowelab.ucsc.edu/tRNAscan-SE). rRNA genes were predicted by Viruses, especially phages, are the most abundant life forms in the deep-sea hydrothermal vent ecosystems, and have been proposed to play a pivotal role in the regulation of microbial abundance and metabolism, thus driving the biogeochemical cycles [START_REF] Rastelli | High potential for temperate viruses to drive carbon cycling in chemoautotrophy-dominated shallow-water hydrothermal vents[END_REF][START_REF] Castelan-Sanchez | Extremophile deep-sea viral communities from hydrothermal vents: Structural and functional analysis[END_REF]. In addition to acting as microbial predators, phages might confer an enhanced level of fitness to the microbial host, enhancing host survival in the extreme environment [START_REF] He | Deep-sea hydrothermal vent viruses compensate for microbial metabolism in virus-host interactions[END_REF]. In the strain SY095 genome, four putative prophages were identified, named CTV1 to CTV4. CTV1, CTV2, and CTV3 are integrated into the chromosome, while CTV4 exists in the form of an extrachromosomal plasmid (Table 2). The four prophage genomes contain all the genes necessary for viral particle synthesis and have similar gene organization. The prophage attachment sites (attL and attR) were detected at the ends of proviral sequences. In addition, large numbers of genes coding for functionally unknown proteins were identified in the prophage genomes, whose functions in phage-host interaction or adaptation of the host cells to extreme environments require further investigation. an aspartyl-phosphate phosphatase that controls the precise timing and progression of sporulation [START_REF] Dubey | Comparative genomic study of spo0E family genes and elucidation of the role of Spo0E in Bacillus anthracis[END_REF]. Seven spo0E genes harboring a classical conserved motif were identified in the SY095 genome. Three of them were carried by chromosomal prophages CTV1, CTV2, and CTV3, while none was identified in the CTV4 prophage.

It is therefore likely that auxiliary spo0E genes of prophages are involved in the sporulation of the host cell. However, the interaction among the prophages and their relationship with the host cell remains largely unknown. Further efforts will be required to elucidate their biological function and ecological roles, especially in the deep-sea hydrothermal vent environment.

Collectively, the complete genomic data of strain SY095 provides additional genetic information for bacteria from the genus Crassaminicella and also contributes to the expansion of knowledge on microbial adaptations to the deep-sea hydrothermal vent environment.

Genome sequence accession numbers

The

Fig. 1 .

 1 Fig. 1. Schematic representation of the Crassaminicella sp. SY095 genome. The

Table 1 .

 1 using RNAmer 1.2 (http://www.cbs.dtu.dk/services/RNAmmer). Prophages were predicted by using PHASTER web server (http://phaster.ca/). Presence of genomic General features and genome sequencing project information for

	islands	was	investigated	by	using	Islander	v1.2	program
	(https://bioinformatics.sandia.gov/islander) and CRISPR arrays were analyzed by
	using the Minced program v0.3.0 (https://github.com/ctSkennerton/minced). Circular
	representations of the SY095 genome were prepared by using Circos v1.7.11
	(http://circos.ca/).
	Item			Description
	MIGS data
	Project_name		Crassaminicella sp. SY095 genome sequencing
	Geographic location	Indian Ocean
	Latitude and longitude	37° 46 58.69 S, 49° 38 59.96 E
	Water depth		2730 m
	Collection date		12-2018
	Environment (biome)	Ocean biome ENVO:01000048
	Environment (feature)	Marine hydrothermal vent ENVO:01000122
	Environment (material)	Marine hydrothermal vent chimney ENVO:01000129
	Observed biotic		Free living
	relationship
	Trophic_level		Chemoheterotroph
	Sequencing method	Oxford Nanopore GridION
	Assembly method		Canu version 1.7
	Coverage			950.0x
	Finishing_strategy	Complete
	General feature
				Domain Bacteria
				Phylum Firmicutes
	Classification		Class Clostridia Order Clostridiales
				Family Clostridiaceae
				Genus Crassaminicella
	Gram stain		Positive
	Cell shape		Rod
	Motility			Motile

mechanisms (7.76%); general function prediction only (7.04%); transcription (6.99%); cell wall/membrane/envelope biogenesis (6.33%); coenzyme transport and metabolism (5.97%); carbohydrate transport and metabolism (5.87%); and energy production and conversion (5.72%).

Table 2 .

 2 Predicted prophage clusters in Crassaminicella sp. SY095.

	Prophage	Size(kb)	GC content	ORFs	Location
	CTV1	60.5	31.66%	96	chromosome
	CTV2	56.6	31.53%	93	chromosome
	CTV3	48.0	31.09%	91	chromosome
	CTV4	36.6	31.28%	59	plasmid
	Strain SY095 forms terminal endospores at late stage of growth. Spo0E gene encodes

  complete genome sequence of Crassaminicella sp. SY095 is available in the Genbank database (https://www.ncbi.nlm.nih.gov/genbank/) under the accession number CP042243 (Chromosome) and CP042244 (Plasmid). BioSample data is available in the NCBI BioSample database (http://www.ncbi.nlm.nih.gov/biosample/) under accession number SAMN12368985. The data have been deposited with links to BioProject accession number PRJNA556796 in the NCBI BioProject database (https://www.ncbi.nlm.nih.gov/bioproject/). The strain is available at Marine Culture Collection of China, MCCC (http://www.mccc.org.cn/) with accession number MCCC 1K04191. and the pilots of the Shen Hai Yong Shi for their professional service during this cruise. The LABGeM (CEA/Genoscope & CNRS UMR8030), the France Génomique and French Bioinformatics Institute national infrastructures (funded as part of Investissement d'Avenir program managed by Agence Nationale pour la Recherche, contracts ANR-10-INBS-09 and ANR-11-INBS-0013) are acknowledged for support within the MicroScope annotation platform.

	Declarations of interest: none

Acknowledgements

This work was supported by grants from the National Key R&D Program of China (2018YFC0309904, 2016YFC0304905, and 2016YFC0302502), the National Natural Science Foundation of China (NSFC 41806174, 91751202, and 91751108), and a grant for LIA0858-MagMC from the Centre National de la Recherche Scientifique.

We are very grateful to all the participants of the TS10 cruise of R/V Tan Suo Yi Hao


D Hurther

Ulrich Lemmin
email: ulrich.lemmin@epfl.ch

Lrh-Dgc

A Correction Method for Turbulence Measurements with a 3D Acoustic Doppler Velocity Profiler

A method is proposed to reduce the noise contribution to mean turbulence parameters obtained by 3D acoustic Doppler velocity profiler measurements. It is based on a noise spectrum reconstruction from cross-spectra evaluations of two independent and simultaneous measurements of the same vertical velocity component over the whole water depth. The noise spectra and the noise variances are calculated and removed for the three fluctuating velocity components measured in turbulent, open-channel flow. The corrected turbulence spectra show a Ϫ5/3 slope over the whole inertial subrange delimited by the frequency band of the device, while the uncorrected turbulence spectra have flat high-frequency regions typical for noise effects. This method does not require any hypothesis on the flow characteristics nor does it depend on device-dependent parameters. The corrected profiles of turbulence intensities, turbulent kinetic energy, shear stress, and turbulent energy balance equation terms, such as production, transport, and dissipation, are in better agreement with different semitheoretical formulas and other measurements from the literature than those from the uncorrected data. Combined with the use of a phase array emitter, the proposed correction method allows measurements with a relative error under 10% in the outer flow region. The corrected inner flow region measurements are still affected by errors that may originate from spatial averaging effects within the sample volume due to the high local velocity gradient or the lack of validity of the universal laws concerning turbulence quantities over a rough bed.

Introduction

Over the past decades, high-resolution multistatic ultrasonic velocity profilers working with coherent demodulation of the backscattered Doppler phase have been of increasing interest in the fields of fluid dynamics, physical oceanography, and, more recently, sediment transport and river hydrodynamics. They have shown their advantage particularly in field applications where the presence of particulate matter often does not allow measurements by other techniques.

In all turbulent flows the precision and the identification of noise sources are of great importance. In this respect, the mean flow can be treated separately from the turbulent component. When classical hydraulic mean flow characteristics are estimated from high-resolution sonar data, the precision of the measurements is typically better than 4% [START_REF] Rolland | De ´veloppement d'une instrumentation Doppler ultrasonore adapte ´e a `l'e ´tude hydraulique de la turbulence dans les canaux[END_REF][START_REF] Lemmin | An acoustic velocity profiler for laboratory and field studies[END_REF] confirming their high reliability. The remaining error is mainly due to the precision of positioning the sensors.

Noise effects are of particular importance if turbulence measurements are evaluated because they are directly based on the fluctuating quasi-instantaneous velocity field estimation. In that case several mechanisms inherent to the measurement technique may reduce the precision. Several authors, [START_REF] Garbini | Measurement of fluid turbulence based on pulsed ultrasound techniques[END_REF], [START_REF] Lhermitte | Open-channel flow and turbulence measurement by high-resolution Doppler sonar[END_REF], [START_REF] Voulgaris | Evaluation of the acoustic Doppler velocimeter (ADV) for turbulence measurements[END_REF], have worked on the theoretical and experimental identification of the noise sources affecting the turbulence measurements with ultrasonic Doppler velocity profilers. These undesired physical processes can be classified as follows: 1) the Doppler ambiguity process that is characterized by the amplitude modulation of the backscattered signal related to the transit time of the acoustical targets through the measurement volume. 2) The spatial averaging of the instantaneous velocity field (a large number of targets are present instantaneously), which is taken over the sample volume weighted by the directivity function of the emitter. 3) The effect of the mean flow shear stress present within the sample volume. 4) The phase distortion effect of the emitted front wave. 5) The effect of those turbulent scales that are of the same order of magnitude or smaller than the sample volume's transverse size. 6) The electronic circuitry's sampling errors linked to the A/D conversion. Except for the spatial averaging process (process 2), all other noise sources enter as additional variance terms in the measured fluctuating velocities variances and therefore are statistically inde-pendent. Due to the geometrical configuration of the sensors these noise variances have different values dependent on which component (longitudinal, vertical, or transverse) is measured. This relates to different weighting factors for the total noise variance common to all components, as will be shown later.

Correction methods for the mean turbulence measurements expressed as additional variances broadly fall into two different categories, described in the next two subsections.

a. Indirect correction method

This method is most frequently used [START_REF] Lhermitte | Open-channel flow and turbulence measurement by high-resolution Doppler sonar[END_REF][START_REF] Zedel | Performance of a single beam pulse-to-pulse coherent Doppler profiler[END_REF]. The different noise variance terms are estimated as a function of the sample volume's distance from the sensors (processes 1, 3, 4, 5 above). They are added together to form the total noise variance, and a factor is applied to each component to remove the corresponding term from the measured variance. Three main disadvantages can be identified: R The evaluation of the different noise variances is based on assumptions about specific flow conditions. Variance 3 is calculated by assuming the logarithmic distribution of the mean longitudinal velocity profile.

Variance 5 requires the knowledge of the turbulence dissipation rate [START_REF] Cabrera | Development of a practical coherent acoustic Doppler current profiler[END_REF], computed from expressions valid for isotropic turbulence. R The transverse size of the sample volume has to be known [START_REF] Voulgaris | Evaluation of the acoustic Doppler velocimeter (ADV) for turbulence measurements[END_REF] to calculate variances 1, 4, and 5. It can either be estimated from acoustical beam approximations or be measured directly [START_REF] Lhermitte | Open-channel flow and turbulence measurement by high-resolution Doppler sonar[END_REF]. The noise term related to process 6 also has to be evaluated from additional measurements [START_REF] Zedel | Performance of a single beam pulse-to-pulse coherent Doppler profiler[END_REF]) because an expression for the phase resolution uncertainty cannot be established. R No direct correction of the turbulence power spectral density is possible even if the noise variances are evaluated correctly.

b. Correction method based on two point cross correlation

This method, proposed by [START_REF] Garbini | Measurement of fluid turbulence based on pulsed ultrasound techniques[END_REF] assumes that the noise signals (variances 1, 3, 4, and 5) between two points in the velocity profile are uncorrelated. It should be noted that [START_REF] Garbini | Measurement of fluid turbulence based on pulsed ultrasound techniques[END_REF] used a monostatic acoustic Doppler velocity profiler (ADVP), where one transducer serves as emitter and receiver. In that case the cross correlation has to be applied to two spatially separated volumes in the velocity profile to ensure that the noise processes are uncorrelated.

The advantage is that it can directly be applied to measured data and does not require any prediction as does the indirect correction method. The disadvantage is that the target population in the two sample volumes, to which the cross correlation is applied, has to be different to ensure the decorrelation. The existence of overlapping regions between two consecutive volumes in the profiles, which have to be inclined with respect to the flow direction, limits the decorrelation of the noise part. The method is applied to two volumes separated by one measuring volume, which decreases the noise but in turn also attenuates the desired velocity signal. Our experience has shown that this method cannot be used with multistatic Doppler systems.

In the present paper, a correction method is presented to reduce the effects of variances 1, 3, 4, 5, and 6. The main contribution to noise reduction presented here concerns a direct treatment of the data similar the one proposed by [START_REF] Garbini | Measurement of fluid turbulence based on pulsed ultrasound techniques[END_REF]. The essential difference is that it can be used with a multistatic 3D-ADVP sensor configuration. We will discuss the efficiency of the method as a function of the flow depth in boundary layer applications such as open-channel flow where the improvement can be compared against the exsisting universal laws.

Description of the 3D-ADVP

a. General principle

The 3D-ADVP is composed of the 1-MHz focused phase array emitter (TRA), discussed in [START_REF] Hurther | A constant beamwidth transducer for 3D acoustic Doppler profile measurements in open channel flows[END_REF], which is installed vertically in the center. This is an ultrasonic constant beamwidth transducer system, which is capable of generating an extended focal zone by electronically focusing the beam over the desired water depth range. The sample volume has a constant width (ϳ7 mm from Ϫ6 dB acoustic beam measurements) over a range of 60 cm. Due to this configuration, the effects of process 2 and variance 4 cited in the introduction can be significantly reduced.

Four 1-MHz large angle receivers are placed symmetrically around the emitter (Fig. 1a). They are used to obtain the velocity components in the tilted directions, TRB, TRC, TRD, and TRE. For the data analysis, the system is divided into two independently working multistatic subsystems (each multistatic system is composed of two bistatic configurations). The first subsytem is oriented in the longitudinal plane (TRA, TRB, TRC) of the flow, and measures the vertical and longitudinal instantaneous velocity profiles over the whole water depth. The second one is oriented in the transverse direction (TRA, TRD, TRE) of the flow, and allows the vertical and transverse instantaneous velocity profiles to be measured simultaneously with the longitudinal plane.

Five sinusoidal sound pulses of identical duration are emitted by the elements of the focused transducer at a fixed pulse repetition frequency (PRF). PRF is chosen to cover the investigated water column and also to ensure a high temporal resolution. Between two pulses, TRB, TRC, TRD, and TRE receive the sound scattered from the same volume in the beam generated by TRA. All signals are simultaneously digitized and gated into M consecutive sample volumes to provide, after processing, two quasiinstantaneous local velocity profiles in the two planes and over the whole insonified water depth.

The 3D velocity vector components are shown in Figs. 1b and1c. The Doppler frequency corresponding to each sample volume R j (j ϭ 1, . . . , M) is calculated using the pulse-pair algorithm [START_REF] Lemmin | An acoustic velocity profiler for laboratory and field studies[END_REF]. For each of the two multistatic subsystems, the two local Doppler frequencies ( f d1,j and f d2,j for the longitudinal system, f d3,j and f d4,j for the transverse system) are:

2 f 2 f 0 0 f ϭ cos(␣ /2)V f ϭ cos(␣ /2)V d1, j 1, j 1, j d 3, j 3, j 3, j c c 2 f 2 f 0 0 f ϭ cos(␣ /2)V f ϭ cos(␣ /2)V d2, j 2, j 2, j d 4, j 4, j 4, j c c (1)
where V i,j are the projections of the local instantaneous velocity V j on the Bragg wavenumber vectors K Bi,j with i ϭ 1, . . . , 4 and j ϭ 1, . . . , M. From these Doppler frequencies we can determine the longitudinal, transverse, and two vertical components of the quasi-instantaneous velocity vector over the whole insonified water column as

c u ϭ [ f Ϫ f ] j d 1, j d 2, j 2 f sin␣ 0 1 , j c ϭ [ f Ϫ f ] j d 3, j d 4, j 2 f sin␣ 0 3 , j c w ϭ [ f ϩ f ] j,t d3, j d 4, j 2 f (1 ϩ cos␣ ) 0 3 , j c w ϭ [ f ϩ f ],
(2)

j,l d1, j d 2, j 2 f (1 ϩ cos␣ ) 0 1 , j
where subscript l denotes the longitudinal tristatic sub-system and t the transverse one. Here f 0 is the emitted sound wave frequency and c the speed of sound for our water condition. It is noted that two independent estimates of the vertical velocity are obtained simultaneously with this system. The temporal resolution is fixed by PRF and by the number N pp of consecutive samples needed to estimate a quasi-instantaneous velocity by the pulse-pair algorithm. The corresponding Nyquist frequency is PRF/ (2N pp ) [in our case equal to 666.67/(2 ϫ 16) ഡ 20.84 Hz].

b. Expression of mean turbulence characteristics in terms of geometrical configuration and noise

The measured mean turbulent characteristics that can be expressed as a function of the bistatic configuration (subscript i) and as a function of the measurement position (subscript j) can be written as the sum of the true quantity and the noise contribution. The measured fluctuations of the radial velocities can be composed as

͗ ͘(t) ϭ ͗ ͘(t) ϩ ͗n i,j ͘(t). ṼЈ VЈ i,j i,j (3)
All terms are quasi-instantaneous quantities. The fluctuating quantities are noted by a prime. Here ͗ ͘ indicates spatial averaging weighted by the transducer's directivity function. The tilde denotes the true flow quantities. The term n i,j (t) is the instantaneous noise signal for component i at location j.

As suggested by [START_REF] Lohrmann | Direct measurements of Reynolds stress with an acoustic Doppler velocimeter[END_REF], the following assumptions are made concerning the noise signal: R the noise signal has a flat power spectral density over the investigated frequency band PRF/(2N pp ) (white noise) R it is unbiased R it is statistically independent of the velocity fluctuations TABLE 1. Constants depending on the geometrical configuration. The first three columns are the normalized water depth, the distance from the emitter (TRA, see Fig. 1a), and the Doppler angle, respectively. The last three columns are the noise weighting factors for the vertical, horizontal turbulence variances, and the turbulence kinetic energy, respectively. R it is uncorrelated between the different radial components i.

z/h d j (cm) ␣ j (Њ) a j b j a j ϩ b j /2 0.
The validity of these assumptions will be demonstrated as part of the verification of the method.

1) VARIANCES

The variance of the radial velocity components is given by

2 2 2 ͗VЈ ͘ ϭ ͗VЈ ͘ ϩ ͗ ͘, (4) i, j i, j i, j
where the second term of the right member of Eq. ( 4) is the variance of the noise signal. The velocity variances can then be written as 1

2 2 2 ͗uЈ ͘ ϭ (͗VЈ ͘ ϩ ͗VЈ ͘ Ϫ 2͗VЈ ͗͘VЈ ͘) j 1, j 2, j 1, j 2, j 2 4 sin (␣ /2) j 1 2 2 ϭ ͗u ˜Ј ͘ ϩ ͗ ͘ j j 2 2 sin (␣ /2) j 1 2 2 2 ͗Ј ͘ ϭ (͗VЈ ͘ ϩ ͗VЈ ͘ Ϫ 2͗VЈ ͗͘VЈ ͘) j 3, j 4, j 3, j 4, j 2 4 sin (␣ /2) j 1 2 2 ϭ ͗ ˜Ј ͘ ϩ ͗ ͘ j j 2 2 sin (␣ /2) j 1 2 2 2 ͗wЈ ͘ ϭ (͗VЈ ͘ ϩ ͗VЈ ͘ Ϫ 2͗VЈ ͗͘VЈ ͘) j,l 1, j 2, j 1, j 2, j 2 4 cos (␣ /2) j 1 2 2 ϭ ͗w ˜Ј ͘ ϩ ͗ ͘ j j 2 2 cos (␣ /2) j to obtain 2 2 2 2 2 2 ͗uЈ ͘ ϭ ͗u ˜Ј ͘ ϩ a ͗ ͘ ͗Ј ͘ ϭ ͗ ˜Ј ͘ ϩ a ͗ ͘ j j j j j j j j 2 2 2 ͗wЈ ͘ ϭ ͗w ˜Ј ͘ ϩ b ͗ ͘, (5)
j,l j j j assuming that ␣ 1,j ϭ ␣ 2,j ϭ ␣ 3,j ϭ ␣ 4,j ϭ ␣ j and ͗ ͘ 2 i,j ϭ ͗ ͘. This implies that the receiver transducers are 2 j identical and ideal. This hypothesis will be verified in section 5a. The coefficients a j and b j are related to the geometrical configuration of the 3D-ADVP (Fig. 1; Table 1).

In Table 1, the variables d j and ␣ j represent the distances of the measurement point j from the emitter and the Doppler angle at measurement point j, respectively. The horizontal velocity components are much more affected by noise (due to the geometrical configuration) than the vertical component. Furthermore, the weighting factors for the vertical component are nearly independent of location j, while the factors affecting the variances of the horizontal components change strongly.

2) KINETIC ENERGY

The kinetic energy can be expressed as

2 ͗K ͘ ϭ ͗K ͘ ϩ (a ϩ b /2)͗ ͘ with j j j j j 1 2 2 2 ͗K ͘ ϭ (͗uЈ ͘ ϩ ͗Ј ͘ ϩ ͗wЈ ͘). (6) j j j j , l 2
3) REYNOLDS STRESS TERMS AND TRICOVARIANCES With the same approach as outlined above, we obtain the Reynolds stress and tricovariance terms entering in the turbulent energy balance equation for a 2D mean flow:

1 2 2 ˜͗uЈwЈ ͘ ϭ (͗VЈ ͘ Ϫ ͗VЈ ͘) ϭ ͗uЈwЈ ͘, ( 7
) j j,l 1, j 2, j j j , l 2 sin(␣ ) j 1 3 3 3 2 ˜˜˜͗ uЈ ͘ ϭ (͗VЈ ͘ Ϫ VЈ ͘ ϩ 3͗VЈ ͗͘VЈ ͘ j 1, j 2, j 1, j 2, j 3 8 sin (␣ /2) j 2 3 ˜Ϫ 3͗VЈ ͗͘VЈ ͘) ϭ ͗uЈ ͘ 2, j 1, j j 1 3 3 3 2 ˜˜˜͗ Ј ͘ ϭ (͗VЈ ͘ Ϫ ͗VЈ ͘ ϩ 3͗VЈ ͗͘VЈ ͘ j 3, j 4, j 3, j 4, j 3 8 sin (␣ /2) j 2 3 ˜Ϫ 3͗VЈ ͗͘VЈ ͘) ϭ ͗Ј ͘ 3, j 4, j j 1 3 3 3 2 ˜˜˜͗ wЈ ͘ ϭ (͗VЈ ͘ Ϫ ͗VЈ ͘ ϩ 3͗VЈ ͗͘VЈ ͘ j,l 1, j 2, j 1, j 2, j 3 8 cos (␣ /2) j 2 3 ˜ϩ 3͗VЈ ͗͘VЈ ͘) ϭ ͗wЈ ͘, 2, j 1, j j , l (8) 1 2 ͗uЈ wЈ ͘ ϭ j j , l
4 sin(␣ ) sin(␣ /2)

j j 3 3 2 2 ˜˜˜˜˜ϫ (͗VЈ ͘ ϩ ͗VЈ ͘ Ϫ ͗VЈ ͗͘VЈ ͘ Ϫ ͗VЈ ͗͘VЈ ͘) 1, j 2, j 1, j 2, j 1, j 2, j 2 ϭ ͗u ˜Ј w ˜Ј ͘ j j , l 1 2 ͗Ј wЈ ͘ ϭ j j , t
4 sin(␣ ) sin(␣ /2)

j j 3 3 2 2 ˜˜˜˜˜ϫ (͗VЈ ͘ ϩ ͗VЈ ͘ Ϫ ͗VЈ ͗͘VЈ ͘ Ϫ ͗VЈ ͗͘VЈ ͘) 3, j 4, j 3, j 4, j 3, j 4, j 2 ϭ ͗ ˜Ј w ˜Ј ͘. j j , t (9)
There are no contributions from noise signals to the Reynolds stress [Eq. ( 7)] and all tricovariances terms [Eqs. ( 8) and ( 9)]. Equations ( 8) and ( 9) are found by taking the skewnesses equal to zero under the white noise assumption. Therefore the probability density function of the noise is symmetrical. Only the effect of spatial averaging is still present in the measured quantities.

As [START_REF] Garbini | Measurement of fluid turbulence based on pulsed ultrasound techniques[END_REF] have shown, the ambiguity induced by the spatial averaging process can be neglected as long as the sample volume size is sufficiently small to avoid large spatial averaging in the spectrum. For nonfocused piston emitters, the size of measurement volume changes along the beam axis and the averaging effect varies in rapport. The phase array emitter used here ensures a constant sample volume size over the entire ensonified water depth. Thus, variations in spatial averaging contributions will result from changes of the flow characteristic only. Effects of this process will be found most likely in the near wall region of the flow where strong gradients occur.

Principle of correction method

The aim of the correction method is to eliminate the noise terms from the above equations. These contain the additional and undesirable variances discussed in the introduction. For the correction, use will be made of the fact that the configuration of the 3D-ADVP provides a redundant and independent measurement of the quasi-instantaneous vertical velocity component in the longitudinal and transverse planes. All quantities in the following are considered spatially averaged over the sampling volume. Based on Eqs. ( 5) and ( 6) the vertical velocities can be rewritten including the noise signal term as ͗wЈ ͘(t) ϭ ͗w ˜Ј ͘(t) ϩ ͗n*͘(t)

͘( f ) ϭ b j ͗N j ͘( f ) ϭ ͗S xx, j ͘( f ) Ϫ ͗S xy, j ͘( f ) ͗N* j ϭ ͗S yy, j ͘( f ) Ϫ ͗S xy, j ͘( f ), ( 14
)
where b j is the geometrical weighting factor for the vertical component defined in section 2b. Here ͗S xx,j ͘( f ) and ͗S yy,j ͘( f ) are the power spectral densities of the fluctuating vertical velocity components measured in the longitudinal and transverse plane, respectively. The power spectral density and the related noise variance that appears in Eq. ( 5), common to all measured velocity components, is then

1 ͗N ͘( f ) ϭ [͗S ͘( f ) Ϫ ͗S ͘( f )] j x x , j x y , j b j 1 ϭ [͗S ͘( f ) Ϫ ͗S ͘( f )] xx,j xy,j b j ϩϱ 1 2 ͗ ͘ ϭ [͗S ͘( f ) Ϫ ͗S ͘( f )] df j ͵ xx,j xy, j b j Ϫϱ ϩϱ 1 ϭ [͗S ͘( f ) Ϫ ͗S ͘( f )] df . ( 15
)
͵ xx,j xy, j b j Ϫϱ It has to be emphasized that, for this method to work, the spectra need to be robustly estimated from long time series with high degrees of freedom, or the statistical uncertainty will result in negative variances. It is now possible to verify the above assumptions on the noise signal if the following relations are valid:

2 2 ͗wЈ ͘ ϭ ͗wЈ ͘ j,l j,t ͗S ͘( f ) Ͻ ͗S ͘( f ) for all f (16) xy, j xx, j ͗S ͘( f ) ϭ ͗S ͘( f ) for all f. xx, j yy, j
The first relation in Eq. ( 16) indicates that the receivers can be considered as identical due to the same noise contribution in terms of their energy. The last two relations show that the magnitude of the cross-sprectrum is lower than the power spectral densities of the vertical velocity component calculated from the longitudinal and

Experimental setup

Experiments were carried out in a laboratory open channel (29 m long, 2.45 m wide, 75 cm deep) under uniform flow conditions over a rough bed. The measurement section is placed 12 m downstream from the entrance where turbulent flow is well developed. All velocity data presented here were taken at the center of the channel with the transducers mounted in a separate chamber above the flow as indicated in Fig. 1.

The experiments were conducted in clear water conditions where particles do not contribute significantly to backscattering [START_REF] Shen | Ultrasonic scattering in highly turbulent clear water flow[END_REF]. All measurements presented here are extracted from datasets acquired over 600-s intervals in order to minimize the statistical uncertainty (less than 5% with the present device bandwidth). The spatial and temporal resolutions are dependent of the settings of the instrument and are equal to ϳ3 mm and 0.024 s, respectively, in the present case.

The hydraulic parameters that indicate a subcritical highly turbulent flow are given in Table 2. The variables u * ,m and u * ,s represent the friction velocities obtained from linear extrapolation of the mean Reynolds stress at the wall and from the energy line slope formula for uniform flow, respectively. The relative errors (relative to u * ,s ) are less than 3%, which shows that uniform flow conditions are established. The roughness Reynolds number is evaluated from the standard roughness of ϩ k s the sand (d 50 ϭ 2.1 mm) and is equal to 36, which indicates an incompletely rough channel bed.

Figure 2 shows results for the mean longitudinal velocity measurements. They agree well with theoretical estimations (wall-law, velocity-defect law, and Coles wake function). The ⌸ factor of Coles wake function has a value of 0.11 (Table 2; see Fig. 2d) and is obtained using the velocity defect law with equal to 0.4. These values are typical for uniform open-channel flow with a rough bed [START_REF] Graf | Fluvial Hydraulics[END_REF].

In the following, we will apply the noise corrections to the fluctuating components of these measurements.

Results and discussion

a. Validation of the method Equation ( 16) gives the relations that are needed for the evaluation of the application of the proposed method to the sonar data. Figure 3 shows the variance profiles of the vertical fluctuating velocity component measured by the two independent multistatic subsystems. The relative error between the two measurements, which is also shown, never exceeds a value of 1%, except for the point nearest to the bed (z Ӎ 3 mm). That high error value is due to sound-scattering problems at the wallwater interface. The low error values at all other depths indicate that the first relation of Eq. ( 16) is valid and that the two subsystems can be taken as identical and close to ideal.

Figures 4a and4b show the magnitude of the crossspectrum ͗S xy,j ͘, the power spectral densities ͗S yy,j ͘, and ͗S xx,j ͘ measured simultaneously in the longitudinal and transverse planes at water depth z/h ϭ 0.4 and z/h ϭ 0.9, respectively. The last two relations of Eq. ( 16) can be considered as valid and it can be confirmed that the lower energy contained in ͗S xy,j ͘ is due to the attenuation of the uncorrelated signal parts between the two independent measurements of the vertical velocity fields. The difference between either of the power spectral densities and the magnitude of the cross-spectrum is identified as the noise spectrum of the vertical velocity component ͗ ͘, also drawn in Figs. 4a and4b. At each N* j depth, the calculated cross-spectrum has been taken to evaluate the noise spectrum common to all measured components.

In Fig. 5 the noise spectra ͗N j ͘ for different depths are given. In all cases we observe a flat noise spectrum over the investigated frequency domain confirming the assumption of white noise. The level of the noise signal changes with depth. This trend is confirmed by the noise profile in Fig. 6 where its standard deviation normalized with the friction velocity has been plotted. The noise contribution increases first slowly toward the bed but increases significantly for z/h Ͻ 0.15. Also shown in Fig. 6 is the relative difference of the standard noise deviations calculated with the cross-correlation method applied to two consecutive points [START_REF] Garbini | Measurement of fluid turbulence based on pulsed ultrasound techniques[END_REF] and the two independent vertical velocity field measurements, respectively. The relative difference is about 5% near the free surface and increases toward the wall where it reaches a value of 40%. The depth-averaged difference is about 20%. The disadvantage of the method used by [START_REF] Garbini | Measurement of fluid turbulence based on pulsed ultrasound techniques[END_REF] is evident because it The same effect is also seen in Fig. 7 where the spectrum calculated with the two point method, called ͗S j,jϩ1 ͘, is lower than the spectrum ͗S xy,j ͘ at depth z/h ϭ 0.4. Additionally, in the inertial subrange, the slope of ͗S j,jϩ1 ͘ is weakly increased compared to that of ͗S xy,j ͘. Furthermore, in the range from 10 to 20 Hz the spectrum ͗S j,jϩ1 ͘ becomes flat whereas the spectrum ͗S xy,j ͘ holds the same slope. That behaviour may originate from the overlapping of two consecutive sample volumes implying an incomplete decorrelation of the noise signals.

b. Results

1) POWER SPECTRAL DENSITIES

In Figs. 8a and 8b the uncorrected and corrected power spectral densities are shown for the longitudinal and transverse fluctuating velocity components at depth z/h ϭ 0.68. In the higher frequency domain, the characteristic flattening of the noise-affected spectra can be distinguished. As mentioned above, the contribution of the noise in the longitudinal and transverse velocity components is more pronounced than for the vertical component mainly because of the larger magnitude of the weighting factors due to the geometrical configuration. These factors are the same for the longitudinal and transverse components. Therefore the effect of noise attenuation on the power spectra is particularly significant for both components. The slope of Ϫ5/3 of the spectrum in the inertial subrange traced in Figs. 8a and 8b is followed by the two corrected spectra indicating an effective correction. FIG. 6. Profile of noise standard deviation relative to the friction velocity (squares). Profile of relative difference of the standard noise deviations calculated with the cross-correlation method applied to two consecutive points [START_REF] Garbini | Measurement of fluid turbulence based on pulsed ultrasound techniques[END_REF]) and the two independent vertical velocity field measurements.

2) TURBULENT INTENSITIES

Figure 9 shows the uncorrected and corrected turbulent intensities for each component normalized by the friction velocity. The turbulent intensity is defined as the magnitude of the turbulent velocity fluctuations. For each depth, the corrected quantities are obtained from the integration of the corresponding corrected spectra as those presented in Figs. 8a and8b. Also drawn in curves are in good agreement with the measurements in the flow region z/h Ͼ 0.2. In the range z/h Ͻ 0.2, the vertical and longitudinal intensities deviate significantly from the theoretical curves. If the comparison of the corrected data is limited to the curves expressed by Eq. ( 17) these deviations could be interpreted as inaccuracies of the instrument in the wall region of the flow. However, if we consider the effect of roughness on turbulence intensities, which is not taken into account in Eq. ( 17), these deviations may not necessarily be the result of measurement inaccuracies.

To investigate this point further, the corresponding curves from measurements of turbulent intensities over a rough bed with a normalized roughness value of ϩ k s ϭ 85, presented by [START_REF] Grass | Structural features of turbulent flow over smooth and rough boundaries[END_REF] using hydrogen-bubble technique, are also plotted in Fig. 9. It can be seen that the effect of roughness is to reduce the longitudinal turbulence intensity for z/h Ͻ 0.3. The vertical intensity is less affected. It is evident that our corrected measured data are in better agreement with these curves taking into account bed roughness. The deviation of the transverse intensity is less important. A similar behavior was also observed by [START_REF] Nezu | Turbulence in open channel flows[END_REF]. It confirms that the roughness strongly affects the longitudinal intensity for z/h Ͻ 0.3 and less so the transverse and vertical ones. FIG. 9. Profiles of turbulence intensities relative to the friction velocity: from the uncorrected data, from the corrected data, from the semitheoretical curves of [START_REF] Nezu | Turbulence in open channel flows[END_REF] and from hydrogen-bubble technique measurements of [START_REF] Grass | Structural features of turbulent flow over smooth and rough boundaries[END_REF]. FIG. 10. Profiles of turbulent kinetic energy relative to the friction velocity for uncorrected data, corrected data, and semitheoretical curve of [START_REF] Nezu | Turbulence in open channel flows[END_REF]. Profiles of shear stress relative to the friction velocity for uncorrected data and theoretical curve.

Again, the difference between the uncorrected and the corrected kinetic energy is important due to the sum of the geometrical weighting factors. The agreement of the corrected measurement with the semitheoretical prediction is good for z/h Ͼ 0.2. In the region z/h Ͻ 0.2, the deviation becomes more pronounced [the bottom roughness effect is not taken into account in Eqs. ( 18)].

The shear stress profile also shows a deviation of the measured profile from the theoretical prediction for z/h Ͻ 0.2. Since this quantity is inherently not affected by the noise signal present in the turbulent intensities [see section 2b(3)] the only remaining error source is related to the spatial averaging effect in the sample volume. However, the possible effect of bed roughness on the shear stress in this profile range is not well documented in the literature.

4) TERMS OF THE ENERGY BALANCE EQUATION

In Fig. 11 the profiles of the different terms of the energy balance equation, all normalized by the term h/ , over the whole water depth are presented. The un-3 u * corrected and corrected energy dissipation rates are evaluated from the inertial subrange of the longitudinal uncorrected and corrected spectra, respectively. The following formula is used: where C is the Kolmogorov constant (with a value of 0.5), and k u , S u (k u ), and uЈ 2 are the longitudinal wavenumber, the longitudinal wavenumber spectrum, and the longitudinal variance, respectively. It is obvious from Fig. 8 that the uncorrected dissipation rate is largely overestimated because the Ϫ5/3 power law is not observed in the uncorrected spectrum. In consequence, the dissipation rate calculated from the uncorrected spectrum is much higher than the one calculated from the corrected spectrum (Fig. 11). Good agreement is found between the corrected normalized h/ and the ex-3 u * pression given by [START_REF] Nezu | Turbulence in open channel flows[END_REF]:

Ϫ1 5/3 2 3/2 ϭ [C k uЈ S (k )] , (19)
h Ϫ1/2 ϭ E (z /h) exp(Ϫ3z /h), ( 20
) 1 3 u*
where the value E 1 is equal to 9.8 for a Reynolds number between 10 4 and 10 5 .

Also drawn in Fig. 11 are the normalized production and corrected transport terms, written as

Ph P h uЈwЈh ץu 11 ϭ ϭ Ϫ 3 3 3 u* 2u* u* ץz Th (T ϩ T ϩ T )h 11 22 33 ϭ 3 3 u* 2u* h ץ 2 2 2 ϭ Ϫ (uЈ ϩ Ј ϩ wЈ )wЈ. ( 21
) 3 2u* ץz
For z/h Ͻ 0.15, the profile of the production term decreases, which indicates an energy deficiency (the production is lower than the dissipation). This trend probably confirms the inaccuracies of the measurements in that region due to the spatial averaging process in the sheared velocity domain.

In the free-surface flow region the dissipation is slightly higher than the production term, which again is indicative for an energy deficiency. The normalized transport term is also drawn in Fig. 11 and is positive for z/h Յ 0.4 with a maximum value of 9. For z/h Ͼ 0.1, the corrected results are in agreement with the measurements found in [START_REF] Nezu | Turbulence in open channel flows[END_REF]. For z/h Ͻ 0.1, this term decreases toward the wall, which again indicates a deviation from the results found in the literature.

c. Error analysis

Here we present a quantitative value of the relative differences of the corrected mean turbulence measurements with the above-mentioned models. The profiles of relative differences are computed for the longitudinal, transverse, and vertical turbulent intensities, the turbulent kinetic energy and the shear stress, noted u , , w , K , uw , respectively. They are calculated as follows;

|q (z /h) Ϫ q (z /h)| c m (z /h) ϭ , ( 22
) i q (z /h) m
where q c is the corrected measured quantity and q m the quantity calculated from the model. Errors written with an overbar, i , are the depth-averaged relative differences.

For z/h Ͼ 0.2, the depth-averaged values do not exceed 10% (Fig. 12) (for the turbulent kinetic energy), which confirms the high accuracies of the corrected sonar measurements.

Except for the error of the transverse turbulent intensity, all other errors are significant for z/h Ͻ 0.2. As mentioned before it is difficult to attribute these high values clearly to measurement inaccuracies considering that some physical process, especially the bed roughness effects, are not taken into account in the semitheoretical models.

Conclusions

A combination of two techniques to improve the precision of turbulence measurements with a 3D ADVP is discussed.

The first concerns the use of a phase array emitter discussed in [START_REF] Hurther | A constant beamwidth transducer for 3D acoustic Doppler profile measurements in open channel flows[END_REF].

The following improvements have been made:

R the sample volume has a constant width (ϳ7 mm) over a maximal distance of 60 cm from the emitter R the effect of the beam divergence (or phase distortion of the front wave), appearing as an additional noise variance in the measurements, can no longer be distinguished on beam measurements R spatial averaging effect is considerably reduced and is only dependent on flow characteristics in the vertical flow direction since the emitter's normalized directivity function is no longer a function of the water depth.

The second technique used to increase the signal-tonoise ratio of the measurements is a direct correction method of the Doppler signal. It has been verified that the following noise signal characteristics apply to the method R the noise has a flat spectrum independent of the flow depth R the noise signal is uncorrelated from the velocity signal R the noise signal is uncorrelated between the different receivers R the receivers and the different analogic circuitries can be considered as identical.

Based on these results it is possible to apply the correction method. It consists in making a redundant measurement of the instantaneous vertical velocity field with two independent working tristatic subsystems in the longitudinal and transverse flow sections. By calculating the difference between the magnitudes of the auto-and cross-spectra we rebuild the noise spectra of each velocity component by considering the specific geometrical configuration. Thereby, the following mean turbulence quantities were corrected: R the three turbulence intensities (with a mean relative error of ϳ5% in the outer flow domain) R the turbulent kinetic energy (with a mean relative error of ϳ9% in the outer flow domain) R the turbulence spectra over the entire resolved frequency band R the turbulent energy dissipation rate, which is of particular importance if energy balances are investigated.

From comparisons of the corrected data with raw data and with results from literature, we have shown quantitatively that the corrected ADVP data are highly reliable and accurate in the flow region z/h Ͼ 0.2. This result is of major importance for our further investigations concerning free surface turbulence in openchannel flow based on 3D-ADVP velocity field measurements. Therefore the presented method has been programmed as a systematic correction method of the sonar measurements. Another advantage of the proposed technique is that it does not require assumptions about the flow characteristics. As a result the presented solution can be applied to any ADVP applications as long as the geometrical configuration permits a simultaneous redundant velocity component measurement. Voulgaris and Throwbridge (1998) have mentioned in their conclusion that the presence of high noise terms is an inescapable feature of the geometry of an ADV. This remark is valid for their case. We have shown here that with another geometrical configuration and an appro-priate signal treatment the noise contribution to the mean turbulence terms can be eliminated.

Supplementary studies are needed to quantitatively evaluate the ''true'' precision of sonar measurements in the wall region of an open-channel flow. From theoretical considerations (which are difficult to validate experimentally), we allocate the remaining deviations (in the wall region) of the corrected measurements to effects of the spatial averaging since no other noise process is identified after application of the presented correction method. However, effects of bottom roughness cannot be excluded either.

FIG. 1

 1 FIG. 1. (a) 3D acoustic Doppler velocity profiler configuration for open-channel flow application. TRA represents the phase array emitter, TRB, TRC, TRD, and TRE are the four large angle receivers arranged to compose two independently, simultaneously measuring tristatic subsystems in the longitudinal and transverse flow sections. (b) Schematic diagram showing the longitudinal subsystem and its velocity vector decomposition. (c) Velocity vector decomposition for the transverse subsystem.

FIG. 2 .

 2 FIG. 2. Mean velocity measurements in an open-channel flow (see Table 2 for the hydraulic flow characteristics). (a) Mean longitudinal velocity profile. (b) Universal logarithmic velocity profile. (c) Wall-law validation in the inner flow region and evaluation of the constant Br of the logarithmic profile. (d) Velocity-defect law validation and -factor evaluation of Cole's wake function.

FIG. 4 .

 4 FIG. 4. Power spectra of vertical fluctuating velocity and corresponding noise signals. (a) At depth z/h ϭ 0.4. (b) At depth z/h ϭ 0.9. In the two figures the solid line, dash-dotted line, and dashed line represent the power spectra from the longitudinal, transverse, and crosscorrelation measurements, respectively. The dotted lines show the extracted vertical noise signals.

  FIG.6. Profile of noise standard deviation relative to the friction velocity (squares). Profile of relative difference of the standard noise deviations calculated with the cross-correlation method applied to two consecutive points[START_REF] Garbini | Measurement of fluid turbulence based on pulsed ultrasound techniques[END_REF]) and the two independent vertical velocity field measurements. FIG. 5. Power spectra of noise signals at different water depths.

Fig. 9

 9 Fig. 9 are the semitheoretical curves of the turbulent intensities given by Nezu and Nakagawa (1993) as 2 ͙uЈ /u* ϭ 2.3 exp(Ϫz /h) 2 ͙Ј /u* ϭ 1.63 exp(Ϫz /h) 2 ͙wЈ /u* ϭ 1.27 exp(Ϫz /h).

  FIG. 11. Profiles of normalized terms of the turbulent energy balance equation: the turbulent energy dissipation term (from the corrected and uncorrected data), the production, and corrected transport terms.

  FIG.12. Profiles of relative errors: for the three turbulence intensities, the turbulent kinetic energy, and the shear stress. The variables written with overbars are the depth-averaged quantities (for z/h Ͼ 0.2).

  ͗R ͘() ϭ ͗wЈ ͘(t)͗w ˜Ј ͘(t ϩ )

				xy, j	j,l	j,t
				ϭ ͗w ˜Ј ͘(t)͗w ˜Ј ͘(t ϩ ) ϩ ͗w ˜Ј ͘(t)͗n*͘(t ϩ ) j,l j,t j,l j,t
				ϩ ͗w ˜Ј ͘(t ϩ )͗n*͘(t) ϩ ͗n*͘(t)͗n*͘(t ϩ ). j,t j,l j,l j,t
				(11)
				If the noise signals of the two velocity estimates are
				uncorrelated, we obtain
				͗R ͘() ϭ ͗w ˜Ј ͘(t)͗w ˜Ј ͘(t ϩ ), xy, j j,l j,t	(12)
				from which we can calculate the magnitude of the cross
				spectrum ͗S xy,j ͘,
				͗S ͘( f ) ϭ xy, j	ϩϱ ͵ xy, j ͗R ͘() exp(Ϫj2 f ) d , (13) Η Η Ϫϱ
				to finally express the noise spectrum,
	j,l	j,l	j,l
	͗wЈ ͘(t) ϭ ͗w ˜Ј ͘(t) ϩ ͗n*͘(t), j,t j,t j,t	(10)

where * denotes the geometrical weighted noise signal.

The cross correlation, ͗R xy,j ͘, of these two signals at location j is

TABLE 2 .

 2 Hydraulic parameters.

	Q	h	u* ,S	u* m	S	Re h
	(m 3 s Ϫ1 )	(cm)	(cm s Ϫ1 )	(cm s Ϫ1 )	(ϫ10 Ϫ4 )	(ϫ10 3 )	F r h	B/h	k ϩ S	⌸
	0.069	10	1.71	1.66	3	28	0.28	24.5	36	0.11
	transverse planes. Since these two spectra are identical,
	any difference can only originate from the uncorrelated
	noise signals between the two independent measure-
	ments of ͗wЈ͘(t). With the geometrical relations given
	in section 2b it is possible to extract the noise spectrum
	and the corresponding variances for each velocity com-
	ponent for all locations j.

Acknowledgments. Comments by two anonymous reviewers helped to improve the presentation. This work was funded by the Swiss National Science Foundation grant 20-39494.93. We are grateful for the support.