Akhila George
email: akhila.george@uq.edu.au

Gabriel Capson-Tojo
email: gabriel.capson-tojo@inrae.fr

Adrian Oehmen
email: a.oehmen@uq.edu.au

Metabolic network reconstruction providing insights into the metabolism relevant for resource recovery in Rhodobacter sphaeroides

Keywords: Hydrogen production, metabolic modelling, polyhydroxybutyrate, resource recovery, Rhodobacter sphaeroides

Rhodobacter sphaeroides is a versatile purple non-sulfur bacteria that can be used in resource recovery to produce hydrogen, polyhydroxyalkanoates, single-cell protein and other value-added products. We developed a genome-scale metabolic model representing the primary metabolism of a denitrifying strain R. sphaeroides ATCC 17025. This metabolic model predicted growth, production of hydrogen and polyhydroxybutyrate, and was in better agreement with literaturebased experimental values as compared to predictions from existing models for R. sphaeroides. We evaluated the growth, production rates and product distribution under different metabolisms and using different organic substrates. In addition, it allowed to assess the metabolic mechanisms governing the preferential generation of different products. This model can be a valuable tool to optimize the generation of value-added products.

INTRODUCTION

Purple phototrophic bacteria (PPB) can be used in the resource recovery of value-added products from waste streams. The versatility, high efficiency of removal of organics and the capability of PPB to utilize sunlight as its energy source for its growth and metabolism makes wastewater treatment using PPB economically feasible. Rhodobacter sphaeroides is one of the commonly observed PPB and was found dominant in mixed cultures cultivated outdoor [START_REF] Hülsen | Naturally illuminated photobioreactors for resource recovery from piggery and chicken-processing wastewaters utilising purple phototrophic bacteria[END_REF][START_REF] Hülsen | Outdoor demonstration-scale flat plate photobioreactor for resource recovery with purple phototrophic bacteria[END_REF]. A genome-scale metabolic model facilitates better understanding of the flexible metabolism of PPB and prediction of its varying physiological behaviour with different substrates and environmental conditions. Integration of this model with the bioprocess model would improve the reliability of the model and needs less recalibration with varying composition of wastewater feedstock or operational parameters.

To the best of our knowledge, there is no curated metabolic pathway database available for Rhodobacter sphaeroides, that would allow integration and visualization of the metabolic pathways, reactions, enzymes, proteins and genes and other evolving information related to transcript, protein and metabolite profiling. There are genome-scale metabolic models representing the photoheterotrophic growth of Rhodobacter sphaeroides strain 2.4.1 [START_REF] Imam | iRsp1095: a genome-scale reconstruction of the Rhodobacter sphaeroides metabolic network[END_REF][START_REF] Imam | Global insights into energetic and metabolic networks in Rhodobacter sphaeroides[END_REF], Rhodopseudomonas palustris [START_REF] Alsiyabi | Modeling the Interplay between Photosynthesis, CO2 Fixation, and the Quinone Pool in a Purple Non-Sulfur Bacterium[END_REF] that were applied to study the aspects of photosynthesis, hydrogen production, different substrate uptake and redox state. However, more study is needed to understand the substrate preferences of cells for growth and production of value-products and their distribution towards different products that are relevant to resource recovery. In the current study, a curated metabolic pathway database and a genome-scale metabolic model of Rhodobacter sphaeroides ATCC 17025 is developed, showing better predictions than that of existing models. The model was validated with experimental data under different trophic conditions like photoautotrophic, aerobic heterotrophic and anaerobic photoheterotrophic conditions. The metabolic model was employed to study the product distribution of hydrogen, polyhydroxybutyrate, CO2 fixation and growth under different light uptake rates.

MATERIALS AND METHODS

Development of pathway database & metabolic model

A genome-pathway database of R. sphaeroides ATCC 17025 was retrieved from the biochemical database, BioCyc. Pathways and reactions involved in the central carbon and nitrogen metabolism were curated by adding 111 modifications that were based on studies gathered from 42 scientific articles/reviews and genome-based evidence. The curation of the database was guided by analysis using the Metaflux module of Pathway Tools software [START_REF] Latendresse | Construction and completion of flux balance models from pathway databases[END_REF] and thus a draft metabolic model was developed from the database. Compartments of cytoplasm, membrane space, periplasmic space, and extracellular space were also included in the Rba_sphCyc database. The metabolic model was validated qualitatively and quantitatively by comparing the predictions of the model under various trophic conditions with the experimental observations or conclusions published in 17 articles.

RESULTS AND DISCUSSION

Curation and validation of the metabolic model

The details of the curated pathway-database, RbaSphCyc, which will be published in MetaCyc, are given in Table 2. A genome-scale metabolic model was generated from the curated pathway database. As a part of the qualitative assessment of the metabolic model, growth of R. sphaeroides was simulated under photoautotrophic, aerobic heterotrophic, anaerobic heterotrophic, anaerobic photoheterotrophic condition. The validation of the model was carried out by conducting quantitative assessment of flux under photoautotrophic, aerobic heterotrophic and anaerobic photoheterotrophic conditions. The predicted values along with experimental data (gathered from literature) used for validation of the model under these conditions are shown in Figure 1, Figure 2 and Figure 3, respectively.

The photoheterotrophic growth of R. sphaeroides on different substrates (succinate-glutamate, succinate-ammonia, glucose-glutamate and glutamate only) were simulated using the uptake rates reported by [START_REF] Imam | iRsp1095: a genome-scale reconstruction of the Rhodobacter sphaeroides metabolic network[END_REF]. In the first step, fluxes were optimized to produce maximum biomass and the specific growth rates predicted by RbaSphCyc model were in agreement with that observed in the reported experiments [START_REF] Imam | iRsp1095: a genome-scale reconstruction of the Rhodobacter sphaeroides metabolic network[END_REF] [START_REF] Imam | Global insights into energetic and metabolic networks in Rhodobacter sphaeroides[END_REF]. In the second step, a light constraint was applied and the production rates for polyhydroxybutyrate, hydrogen and CO2 were predicted, which were in good agreement with the experimental values obtained by [START_REF] Imam | iRsp1095: a genome-scale reconstruction of the Rhodobacter sphaeroides metabolic network[END_REF].

Under photoheterotrophic and NH3 limited conditions, when the light uptake rate is above the minimum rate that is needed for maximum growth, concomitant H2 and PHB production was predicted (shown in Figure 4). An increase in light uptake rate increases ATP production and thus increases the rate of H2 production, thereby affecting other electron sink pathways such as PHB production and CO2 fixation inversely. This pattern was found similar in all the four cases mentioned, but the range of light uptake rate differs based on substrate. When the activity of nitrogenase is not limited by ammonia, the main factors that affect H2 production were found to be light and redox condition of substrate.

CONCLUSION

We developed a genome-scale metabolic model representing primary metabolism of R. sphaeroides ATCC 17025, that can be used to simulate photoautotrophic, anaerobic heterotrophic, anaerobic photoheterotrophic growth and predict flux distribution towards production. Under photoheterotrophic and ammonia-limited condition, a light uptake rate higher than that needed for growth, is required to produce hydrogen. Under this condition, light uptake rate plays a major role in defining the flux distribution through electron sink pathways like production of hydrogen, PHB and CO2 fixation. Experimental data is taken from [START_REF] Spanoghe | Microbial food from light, carbon dioxide and hydrogen gas: Kinetic, stoichiometric and nutritional potential of three purple bacteria[END_REF].

Figure 2: Validation of metabolic model of R. sphaeroides for photoautotrophic growth. Experimental data is taken from [START_REF] Alloul | Cocultivating aerobic heterotrophs and purple bacteria for microbial protein in sequential photo-and chemotrophic reactors[END_REF].

Figure 3 :

 3 Figure 3:Validation of RbaSphCyc model for photoheterotrophic growth of R. sphaeroides growing on succinate as carbon source and glutamate as nitrogen source. iRsp1140 is a model developed for R. sphaeroides strain 2.4.1. by Imam et al. (2013).

Figure 4 :

 4 Figure 4: Growth of R. sphaeroides along with production of hydrogen, polyhydroxybutyrate (PHB) and CO2 with varying light uptake rate under photoheterotrophic condition. Succinate and glutamate were used as carbon source and nitrogen source.

Table 1 :

 1 Details of genome-pathway database, RbaSphCyc

	Model Field	Values
	Pathways	252
	Enzymatic reactions	1587
	Transport reactions	91
	Enzymes	1237
	Compounds	1220
	Genes	1020
	Compartments	4

Figure 1:Validation of metabolic model of R. sphaeroides for photoautotrophic growth.


Nelson Lossing

Walid Astaoui

Zhen Zhang

Denis Barthou

Recover Polyhedral Transformations From Polyhedral Scheduler

Keywords: Loop Transformations, Polyhedral Scheduling, Polyhedral Transformations

While Polyhedral optimization offers good performance results, it is often at the price of understandability. The Chlore project -using Clay transformations -is a first attempt at describing Polyhedral optimizations as sequences of highlevel transformations. However, Chlore's output may often be overly complex or contain redundant transformation passes.

In this paper, we extend on Chlore's ideas. We present techniques to reduce the number of generated transformation primitives and to optimize the recovery algorithm, showing some important speedups compared to the original Chlore algorithm.

Introduction

The polyhedral model is used in optimizing compilers to find and apply loop transformations automatically in order to maximize the input kernel performance. While much of the research focuses on developing better heuristics used by the polyhedral scheduler, a significant amount of effort has also been directed towards the explainability of the final transformation. A deeper understanding of this process can reveal the drawbacks of current heuristics and help identify areas for improvement, particularly when dealing with the heterogeneous characteristics of different architectures. Moreover, frameworks such as Halide [START_REF] Ragan-Kelley | Halide: a language and compiler for optimizing parallelism, locality, and recomputation in image processing pipelines[END_REF] or TVM [START_REF] Chen | {TVM}: An automated {End-to-End} optimizing compiler for deep learning[END_REF] provide users with high-level interfaces for manual scheduling and understanding good automatic optimization may help leveraging such frameworks, especially if the developper is not a polyhedral model expert.

Chlore [START_REF] Bagnères | Opening polyhedral compiler's black box[END_REF][START_REF] Zinenko | Interactive Program Restructuring[END_REF] attempted to translate the full polyhedral transformation, which is typically described as an algebraic transformation, into a series of transformation primitives. These transformation primitives include loop reordering, loop fusion, shifting, and more. This type of translation, or recovery, allows for a better understanding of the transformation applied by the polyhedral scheduler. However, Chlore's output may sometimes remain overly complex or contain redundant transformation passes.

In this paper, we propose extensions to address these issues. Experiments show that our approach significantly reduces the required number of transformations to retrieve an equivalent polyhedral optimization. Moreover, our recovery is much faster. Section 2 will present related work, mostly Chlore, and its drawbacks. We redefine a smaller set of transformation primitives presented in Section 3. Section 4 explains our recovery algorithm. Experimental results are presented in Section 5, and some future work is proposed in Section 6.

Related Work

Chlore [START_REF] Bagnères | Opening polyhedral compiler's black box[END_REF][START_REF] Zinenko | Interactive Program Restructuring[END_REF] uses Clay as the set of primitives to recover. Clay provides a series of scheduling primitives covering the full space of polyhedral scheduling transformation. It can be used to apply a list of transformations directly.

Chlore is a tool that translates polyhedral scheduling functions into a list of scheduling primitives. This list of primitives represents an equivalent transformation and is chosen from the set defined by Clay. The main advantage is that lists of scheduling primitives are oftentimes far easier to understand and customize for humans than mathematical formulas. Chlore expects as input two polyhedral schedules, in Openscop format [START_REF] Bastoul | Openscop: A specification and a library for data exchange in polyhedral compilation tools[END_REF]: a source and a target schedule. The recovery algorithm will try to generate a list of scheduling primitives that transforms the former into the latter.

The algorithm assumes that the source and target scheduling is represented using the 2d+1 format [START_REF] Verdoolaege | Schedule Trees[END_REF]. In this representation, even dimensions, named 𝛼-dimensions, represent loop iterator transformations while odd dimensions, named 𝛽-dimensions, represent statement orderings. If this representation is not respected, an initial preprocessing may be necessary.

The recovery algorithm implemented in Chlore can be decomposed into two components: 𝛼-recovery and 𝛽-recovery.

Transformation primitives

Table 1 shows the list of atomic transformations supported by our tool along with expected parameters and short summaries using the following notations:

• ì 𝐿 : A list of schedule IDs, an injection in [0 . . . 𝑁 -1]
where 𝑁 is the number of statements.

• ì

𝛽 : A beta-vector targeting an entity (loop or statement).

• ì

𝑝 : A permutation vector of size equal to the number of entities directly beneath the loop that is the target of ì 𝛽.

• ì

𝐶 : A list of parametric shift coefficients of size equal to the number of parametric bounds relevant to the schedules, which are the target of ì 𝐿.

• 𝑑, 𝑑 1 , 𝑑 2 : An output dimension • 𝑑 i𝑛𝑝𝑢𝑡 : An input dimension • 𝑐 : A scalar coefficient
All primitives are invertible. The 𝛼-primitives are versatile and not tied to a specific scheduling representation. Individual statements or groups of statements can be targeted, no matter their inner loop placement. In contrast, the 𝛽-primitives, Reorder, Fuse, and Split, are inherently loopcentric. In this context, the 2d+1 format is the most practical for loop transformations. Hence, it is the format of choice for the recovery algorithm.

We can note that our list of transformation primitives does not include Stripmine or Tile transformations. Our focus in this paper is to explain polyhedral scheduler transformations. We omit these transformations as current polyhedral scheduling algorithms would not propose such transformations.

Recovery Algorithm

The recovery algorithm requires a source and a target schedule. Both schedules are assumed to be defined over the same space (i.e. number of statements, identical domains, etc.). Figure 1 illustrates the main steps of the recovery algorithm.

Before the recovery algorithm, both input schedules are normalized. This normalization preprocessing is described in Section 4.1. The first step of the recovery algorithm is 𝛼-recovery and is explained in Section 4.2. The output of the 𝛼-recovery is then inversed for the target schedule. The second step, 𝛽-recovery is detailed in Section 4.3.

The output list of primitives is constructed as the concatenation of three lists: the 𝛼-recovery list for the source schedule, the 𝛽-recovery list, and the inverted 𝛼-recovery list for the target schedule.

Normalization step

The normalization step guarantees a normalized 2d+1 format [START_REF] Verdoolaege | Schedule Trees[END_REF] for the polyhedral representation. Indeed, polyhedral scheduling algorithms may not always output schedules in 2d+1 format.

This step is composed of three sub-steps:

𝛽-collapsing fuse consecutive 𝛽-dimensions into a single 𝛽-dimension 2d+1 format insert full-zero 𝛽-dimensions between consecutive 𝛼-dimensions 𝛽-normalization normalize the 𝛽-dimensions into minimal 𝛽 vector for each statement.

Figure 2 shows an example of the normalization. This step does not introduce, modify or drop primitives to recover since it simply modifies the representation while preserving the scheduling semantics.

𝛼-recovery step

The 𝛼-recovery strategy is to transform the source and target schedules into a common representation on the 𝛼-dimensions. This common representation is called minimal form [12, Section 5. To achieve this minimal form, the following 𝛼-primitives are considered: Unembed, Densify, Reverse, Shift, Skew, Interchange and Reshape. The 𝛼-recovery algorithm will iterate over these primitives and over statements. Primitives are applied to the schedule if their application helps progressing towards the minimal form until it is reached.

5 𝑖 0 𝑗 1 𝑘 0 5 𝑖 0 𝑗 2 𝑘 0 5 -𝑖 0 𝑗 2 𝑘 0 5 𝑖 0 𝑗 0 𝑘 0 5 𝑖 0 0 0 𝑘 0 (c) 2𝑑 + 1 format 0 𝑖 0 𝑗 1 𝑘 0 0 𝑖 0 𝑗 2 𝑘 0 0 -𝑖 0 𝑗 2 𝑘 1 0 𝑖 0 𝑗 0 𝑘 0 0 𝑖 0 0 0 𝑘 1 (d) 𝛽-normalization
The 𝛼-recovery algorithm may either first iterate over statements or over primitives. Option alpha-priority controls this behaviour:

schedule prioritize statement-by-statement recovery.

The process iterates focuses on a single statement and modifies only on scheduling function. primitive prioritize the recovery of a given primitive over all statements before another primitive is considered. It is applied if it useful for at least one statement. The schedule option is more intuitive and groups transformations by statements. This option is equivalent to Chlore's behaviour. The primitive option has the advantage of grouping similar transformations together.

𝛽-recovery step

The 𝛽-recovery focus on the 𝛽 dimensions of the source schedule to transform it to the target schedule. The 𝛽-recovery repeatedly considers the following 𝛽-primitives: Reorder, Split and Fuse.

Multiple strategies for 𝛽-recovery may be selected using option beta-strategy. The first two strategies, maxfuse and maxsplit attempt to find a common form, as in 𝛼-recovery, considering a maximum fused form or a maximum split form. Strategy isolate attempts to directly find a path from the source schedule to the target schedule since 𝛽-dimensions intuitively express an explicit order. None of the presented strategies is optimal for all the source and target schedules tried in our results section.

The 𝛽-recovery can be configured to attempt correcting a block of statements at once instead of one by one. Option beta-targeting can be set to statement, segment or group. For all variations, the first element of the said target, the anchor remains unchanged but the sizes of the blocks may vary.

The recovery iterates from outermost to innermost dimensions. Anchors are chosen by finding mismatches in 𝛽 values at the current depth between the source and target schedules. If multiple anchors candidates are found, the anchor is selected as follows: (1) it has not been correctly recovered in the source schedule and (2) its 𝛽-vector in the target schedule is the lexicographic minimum (among the anchors that satisfy the first condition). Thanks to this choice, correctly placed statements are never impacted by subsequently found 𝛽-primitives.

Option block-targeting influences how blocks expand. For segment targeting, they will expand as long as the next entity (loop or statement at the same depth as the anchor) is a statement and is also mismatched. For group targeting, blocks will expand as long as the next entity is also mismatched. The bigger the blocks corrected in one iteration, the better, which is why the default group option usually provides the simplest and fastest results.

Results

We implement our approach into PolyTOPS [START_REF] Consolaro | PolyTOPS: Reconfigurable and Flexible Polyhedral Scheduler[END_REF]. We experiment on the Polybench [START_REF] Pouchet | Polybench: The polyhedral benchmark suite[END_REF] and compare Polytops result with Chlore. Results show that, with our sub-set of transformation primitive defined in Section 3 and the new recovery algorithm defined in Section 4, we can (1) greatly reduce the recovery time and (2) reduce the number of transformation primitives to apply.

Figure 3 shows the speed up comparing our recovery algorithm to Chlore. Our algorithm is at least x18 and up to x300 faster than Chlore recovery time. These experiments were done on an AMD EPYC 7452, 32 cores (2 threads per core), 2 sockets, 256 MiB of L3 cache. The compiler is gcc-11.3.

Table 2 shows the number of transformations found for some Polybench cases by, respectively, Chlore and PolyTOPS. Test cases atax, deriche, nussinov, adi are not present in the

Future Work

We focused on understanding the output of a polyhedral scheduler and hence omitted stripmining and tiling. Future work may extend the scope to arbitrary polyhedral schedules. Future work may build upon this approach to make it possible to use polyhedral optimization in a wider variety of scenarios. In particular, translating automatic polyhedral schedules into sequences of transformations may ease the use of frameworks such as TVM [START_REF] Chen | {TVM}: An automated {End-to-End} optimizing compiler for deep learning[END_REF] or Halide [START_REF] Ragan-Kelley | Halide: a language and compiler for optimizing parallelism, locality, and recomputation in image processing pipelines[END_REF] where experts need to provide manual schedules. This could also increase inter-operability with existing work such as Clay [START_REF] Bagnères | Opening polyhedral compiler's black box[END_REF], CHiLL [START_REF] Chen | CHiLL : A Framework for Composing High-Level Loop Transformations[END_REF], URUK [START_REF] Girbal | Semi-automatic composition of loop transformations for deep parallelism and memory hierarchies[END_REF], Tiramisu [START_REF] Baghdadi | Tiramisu: A polyhedral compiler for expressing fast and portable code[END_REF], or even MLIR [START_REF] Lattner | MLIR: Scaling Compiler Infrastructure for Domain Specific Computation[END_REF].

Conclusion

In this paper, we present new techniques to recover transformation primitives from the output of a polyhedral scheduler. We show that an efficient recovery algorithm can be designed with a limited number of transformation primitives. There is no unique way to recover the transformation primitives that correspond to the output of a polyhedral scheduler and corresponding decisions can greatly influence the length of recovered sequences. Indeed, our experiments on PolyBench show that a good set of options can result in very short transformation primitive sequences for simple cases. Recovering transformation primitives can help non-experts understand and possibly tailor polyhedral scheduling. It may be useful in future work to leverage existing manual-scheduling tools such as TVM or Halide.

Figure 1 .

 1 Figure 1. Recovery Algorithm

  3.4]. It exhibits the following properties: (1) it contains exactly one polyhedral relation; (2) the scheduling relation union is defined exclusively by identity equalities between the input and the output dimensions in their respective orders; (3) 𝛽-dimensions are removed.

𝜙 𝑆0 : 5

 5 𝑖 𝑗 1 0 0 𝑘 𝜙 𝑆1 : 5 𝑖 𝑗 1 1 0 𝑘 𝜙 𝑆2 : 5 -𝑖 𝑗 1 1 0 𝑘 𝜙 𝑆3 : 5 𝑖 𝑗 0 0 0 𝑘 𝜙 𝑆4 : 5 𝑖 0 0 0 0 𝑘 (a) Initial 5 𝑖 𝑗 1 𝑘 5 𝑖 𝑗 2 𝑘 5 -𝑖 𝑗 2 𝑘 5 𝑖 𝑗 0 𝑘 5 𝑖 0 0 𝑘 (b) 𝛽-collapsing

Figure 2 .

 2 Figure 2. Normalization step example on a schedule for 5 statements 𝑆0...𝑆4

  h e a t -3 d j a c o b i -2 d s e i d e l -2 d j a c o b i -1 d f d t d -2 d fl o y d -w a r s h a l l t r m m c h o l e s k y l u s y m m 2 m m m v t g e m m g e m v e r s y r 2 k g e s u m m v s y r k b i c g d o i t g e n d u r b i

Figure 3 .

 3 Figure 3. Speedup to recover transformations in comparison with Chlore

Table 1 .

 1 List of supported primitives by the recovery tool

	Name	Type	Description
	Reorder( ì 𝛽, ì 𝑝)	𝛽-primitive Reorder inner-loops or statements di-
			rectly beneath the given outer-loop.
	Split( ì 𝛽)	𝛽-primitive Split outer-loop just before given inner-
			loop or statement.
	Fuse( ì 𝛽)	𝛽-primitive Fuse given loop with the next one on
			the same depth.
	Embed( ì 𝐿) Unembed( ì 𝐿)	𝛼-primitive Embed given statements beneath an in-nermost one-iteration extra loop. Un-
			embed removes the added innermost
			extra loop.
	Reverse( ì 𝐿, 𝑑)	𝛼-primitive Reverse given output dimension for
			given statements.
	Grain( ì 𝐿, 𝑑, 𝑐)
	Densify( ì 𝐿, 𝑑, 𝑐)

𝛼-primitive

Add some pad between consecutive iterations in given output dimension for given statements. Densify removes some/all of the pad. Shift( ì 𝐿, 𝑑, 𝑐, ì 𝐶) 𝛼-primitive Shift given output dimension by some (parametric) coefficient(s) for given statements. Interchange( ì 𝐿, 𝑑 1 , 𝑑 2 ) 𝛼-primitive Interchange two given output dimensions for given statements. Skew( ì 𝐿, 𝑑 1 , 𝑑 2 , 𝑐) 𝛼-primitive Skew first output dimension by a coefficient of the second output dimension. Reshape( ì 𝐿, 𝑑, 𝑑 i𝑛𝑝𝑢𝑡 , 𝑐) 𝛼-primitive Skew given output dimension by a coefficient of the given input dimension.

Table 2 .

 2 Number of primitives recovered with Chlore and our approach in PolyTOPS array because no new schedule is found. For correlation and covariance, Chlore recovery falls into an infinite loop. For gramschmidt*, Chlore and PolyTOPS do not use exactly the same target schedule, but an equivalent one. Over the 25 cases, 11 cases have more than 10 transformations for Chlore, when only 6 cases are over 10 transformations for PolyTOPS. Moreover, except doitgen and lu, our solution always find the same number of transformation or much more less than Chlore solution. We can highlight all the stencil cases, fdtd-2d, heat-3d, jacobi-1d, jacobi-2d and seidel-2d, where PolyTOPS find at least 3 times less transformations to apply than Chlore.

	Name	Chlore PolyTOPS
	correlation	NA	45
	covariance	NA	21
	2mm	16	7
	3mm	22	13
	bicg	14	10
	cholesky	13	9
	doitgen	1	5
	durbin	40	28
	gemm	3	3
	gemver	7	6
	gesummv	7	5
	gramschmidt*	29	13
	lu	2	4
	mvt	2	2
	symm	3	5
	syr2k	3	3
	syrk	3	3
	trisolv	9	5
	trmm	3	2
	floyd-warshall	0	0
	fdtd-2d	41	15
	heat-3d	38	12
	jacobi-1d	16	4
	jacobi-2d	26	8
	seidel-2d	12	3


A.* George

G Capson-Tojo

A Oehmen

Metabolic modelling of purple non sulfur bacteria for resource recovery

Keywords: R. sphaeroides, R. palustris, wastewater

Purple non sulfur bacteria (PNSB) have been used for resource recovery of hydrogen, polyhydroxyalkanoates, single-cell protein and other value-added products. Understanding their physiological behaviour and response to environmental conditions would benefit optimization of its growth and production of value-added products. In this work, we developed a pathway-based genomescale metabolic model for a PNSB, Rhodobacter sphaeroides ATCC 17025. The model was validated with literature based experimental values under conditions of various trophic conditions and the predictions of the model were in better agreement with the experimental values as compared to predictions from existing models for R. sphaeroides. The genome-scale metabolic models of two PNSB that are used in resource recovery, Rhodobacter sphaeroides and Rhodopseudomonas palustris, were analyzed in order to study the growth and their response to change in environmental conditions under anaerobic photoheterotrophic conditions. Under nitrogen-limited condition, R. palustris was predicted to show a higher hydrogen production at a rate double of that predicted in R. sphaeroides. In R. sphaeroides, a high C/N ratio favours poly(3-hydroxybutyrate) production whereas in R. palustris, a higher C/N ratio favours production of both hydrogen and poly(3-hydroxybutyrate) when the substrates were succinate and glutamate. Analysis of this models can reveal how operational conditions can influence the population dynamics, leading to strategies that favour the production of targeted resources of interest.

Background and relevance

Since 2000, various strains of purple non-sulfur bacteria (PNSB) and their enriched cultures have been studied and used for wastewater treatment and resource recovery [START_REF] Capson-Tojo | Purple phototrophic bacteria for resource recovery: Challenges and opportunities[END_REF]. If this technology is to be successfully implemented, value-added products (e.g., polyhydroxyalkanoates or single-cell proteins) must be generated. To do so efficiently, our understanding on how PNSB can generate different products depending on environmental conditions must be increased, as well as our knowledge on the interactions between different PNSB in mixed cultures [START_REF] Lu | Purple non-sulfur bacteria technology: a promising and potential approach for wastewater treatment and bioresources recovery[END_REF]. Metabolic modelling is a powerful tool that can allow us to do so.

Rhodobacter sphaeroides and Rhodopseudomonas palustris are two well-studied PNSB species for resource recovery from wastewater. These two species are commonly dominant in the microbial community of mixed PNSB cultures that have been studied for such applications [START_REF] Alloul | Cocultivating aerobic heterotrophs and purple bacteria for microbial protein in sequential photo-and chemotrophic reactors[END_REF]. There are genome-scale metabolic models representing the central carbon metabolism of Rhodobacter sphaeroides strain 2.4.1 [START_REF] Imam | iRsp1095: a genome-scale reconstruction of the Rhodobacter sphaeroides metabolic network[END_REF]Imam, Noguera, et al., 2013) and Rhodopseudomonas palustris [START_REF] Alsiyabi | Modeling the Interplay between Photosynthesis, CO2 Fixation, and the Quinone Pool in a Purple Non-Sulfur Bacterium[END_REF]. These have been applied to study different aspects of photosynthesis, hydrogen production, different substrate uptake and redox states. However, more research is needed to understand the physiological behaviour of the cells in terms of growth, production of different value-added products, and their flux distribution in changing environmental conditions. In this study, we present a novel pathway-based genome-scale metabolic model for Rhodobacter sphaeroides ATCC 17025 that provides many important extensions on previous models based on genome and experimental studies available from recent literature publications. Furthermore, we have conducted analyses of genome-scale metabolic models for two species, Rhodobacter sphaeroides and Rhodopseudomonas palustris, to study and compare the metabolic behaviour of these strains. We have analysed parameters related to growth and to the production of hydrogen, poly(3-hydroxybutyrate) (PHB) and glycogen for both strains when growing individually. As C/N ratio is one of the main factors that can impact the production rates of PHB and hydrogen in PNSB, the response of these organisms to the varying C/N ratio was also analysed. Understanding the response 10th IWA Microbial Ecology and Water Engineering Specialist Conference 10 -14 September, Brisbane, Australia of various strains to this and other operational conditions (to be covered in the conference) would help us to implement better process control of phototrophic processes for resource recovery.

Materials and Methods

A genome-pathway database of R. sphaeroides ATCC 17025 was retrieved from BioCyc. Pathways and reactions involved in the central carbon and nitrogen metabolism were curated by adding 111 modifications that were based on data gathered from 42 scientific articles/reviews and genome-based evidence. A metabolic model was thus curated and developed using the Pathway Tools software [START_REF] Karp | Pathway Tools version 13.0: integrated software for pathway/genome informatics and systems biology[END_REF]. The metabolic model of R. palustris CGA009 that was developed by [START_REF] Alsiyabi | Modeling the Interplay between Photosynthesis, CO2 Fixation, and the Quinone Pool in a Purple Non-Sulfur Bacterium[END_REF] was curated to simulate the growth of bacteria in photoautotrophic, aerobic heterotrophic and photoheterotrophic conditions. Using the COBRA toolbox (Schellenberger et al., 2011), flux balance analysis of individual models were conducted to study the growth of strains under anaerobic photoheterotrophic conditions. In addition to the inputs of light intensity, sulfate, phosphate and micronutrients, succinate (along with aspartate) and glutamate were used as carbon source and nitrogen source, respectively. The objective function for flux balance analysis (FBA) was maximizing growth rate in both cases. A C/N ratio of 12 was defined for comparison of growth and other parameters of two species as this C/N ratio has been previously applied experimentally by [START_REF] Imam | iRsp1095: a genome-scale reconstruction of the Rhodobacter sphaeroides metabolic network[END_REF] for the growth of R. sphaeroides. The C/N ratio was varied by adjusting the uptake rate of succinate (carbon source) when the glutamate uptake rate was kept constant at 1.08 mmol/dry weight/h.

Results

A well-curated, pathway-based, genome-scale metabolic model was developed for R. sphaeroides ATCC 17025 (see Table 1). The metabolic model was validated using experimental values available in the literature for photoautotrophic, aerobic heterotrophic and anaerobic photoheterotrophic growth of R. sphaeroides. The predicted values are shown in Figure 1 (photoautotrophic), Figure 2 (aerobic heterotrophic) and Figure 3 (photoheterotrophic). The growth of R. sphaeroides and R. palustris under anaerobic photoheterotrophic conditions was simulated using the developed model of R. sphaeroides and the refined model of R. palustris CGA009 [START_REF] Alsiyabi | Modeling the Interplay between Photosynthesis, CO2 Fixation, and the Quinone Pool in a Purple Non-Sulfur Bacterium[END_REF]. The predicted values for growth rates and for production rates of hydrogen, PHB and glycogen of R. sphaeroides and R. palustris were compared (see Table 2). The influence of varying C/N ratios on the values of these parameters for both strains are shown in Figure 4 and Figure 5.

Discussion

We developed a genome-scale metabolic model representing the primary metabolism of R. sphaeroides ATCC 17025 and the predictions were closer to the experimental values when compared with the predictions of other existing model (see Figure 3). When growth rates and production rates of R. sphaeroides and R. palustris were compared, the production rate of hydrogen of R. sphaeroides was predicted to be higher than that of R. palustris (Table 2). R. sphaeroides seems to divert the reducing equivalents from growth towards hydrogen production and growth was limited by glutamate availability (nitrogen source). Individual growth rates of R. sphaeroides and R. palustris were predicted to be constant with varying C/N ratio for both strains, as growth was limited by glutamate. As expected, the production rates of hydrogen and PHB for the two strains varied with the C/N ratio, however, the variation patterns were different (see Figure 4 and Figure 5). An inverse relationship was predicted between the production rates of hydrogen and PHB in R. sphaeroides, whereas the production of hydrogen and PHB increased simultaneously with the C/N ratio (at the lower range of C/N ratios) in R. palustris. A similar pattern of hydrogen production of R. sphaeroides was observed by [START_REF] Al-Mohammedawi | Synergistic effects and optimization of photo-fermentative hydrogen production of Rhodobacter sphaeroides DSM 158[END_REF]. A simultaneous production of hydrogen and PHB was also reported by [START_REF] Özsoy Demiriz | Hydrogen and poly-Β-hydroxybutyric acid production at various acetate concentrations using Rhodobacter capsulatus DSM 1710[END_REF] for R. capsulatus that was similar to the pattern predicted for hydrogen and PHB production rate in R. palustris. In R. sphaeroides, the flux distribution of hydrogen and PHB production was affected by glycogen production. This may be due to differences in the carbon flux distributions caused by pathways and reactions that were exclusive to one of these strains, such as the oxidative phase of the pentose phosphate pathway, phosphoenol pyruvate carboxylase, pyruvate carboxylase and the Entner-Doudoroff pathway. However, results reveal that, under glutamate limited conditions, R.

10th IWA Microbial Ecology and Water Engineering Specialist Conference 10 -14 September, Brisbane, Australia sphaeroides and R. palustris are better candidates for the production of PHB and hydrogen, respectively. The production rates for both products are favoured at high C/N ratios.

The flux distribution involved in both the models will be detailed in the presentation. Future work will involve the mixed metabolic modelling of R. sphaeroides and R. palustris to study the growth and the metabolic capabilities of mixed cultures, and to understand how other operational factors and the substrate composition impact the population dynamics.

  Chemical Engineering, The University of Queensland, St. Lucia, QLD 4072, Australia Is the presenting author an IWA Young Water Professional? N Bio: Akhila George is a Postdoctoral Research Fellow in the School of Chemical Engineering at the University of Queensland. Her research is on metabolic modelling focused on application of purple photosynthetic bacteria in resource recovery. She has a PhD in metabolic modelling of microalgae for biodiesel production.

Table 1 Details of the genome-scale metabolic model developed for R. sphaeroides ATCC 17025

 1

	Model Field	Values
	Pathways	252
	Enzymatic reactions	1,587
	Transport reactions	91
	Enzymes	1,237
	Compounds	1,220
	Genes	1,020
	Compartments	4

Table 2 Growth and production rates of key value-added compounds predicted by the metabolic models

 2

	R. sphaeroides	R. palustris

Validation of the metabolic model for R. sphaeroides for photoautotrophic growth. Experimental data was taken from Spanoghe et al. (2021). Figure 2. Validation of the metabolic model for R. sphaeroides for aerobic heterotrophic growth. Experimental data was taken from Alloul et al. (2021). Figure 3. Validation of the model for R. sphaeroides for photoheterotrophic growth. iRsp1140 is the model developed for R. sphaeroides strain 2.4.1. by Imam et al. (2013).

	8
	6
	4
	2
	0
				Growth rate (d-1)	Biomass yield (g Biomass/ g H2)	Protein yield (g protein/ g H2)
					Predicted	Experimental
	Yield (g	CODbiomass g-1	CODremoved)	0 0.2 0.4 0.6 0.8
					Predicted	Experimental
	8
	6
	4
	2
	0
			Growth rate (d-1)	H2 production	CO2 production	PHB production
					rate(mmol/gDW h)	(mmol/gDW h)	(mmol/gDW h)
				Predicted (RbaSphCyc)	Experimental	Predicted (iRsp1140)

10th IWA Microbial Ecology and Water Engineering Specialist Conference 10 -14 September, Brisbane, Australia Figure 4. Prediction of PHB, hydrogen and glycogen production rates for R. sphaeroides under photoheterotrophic conditions. Figure 5. Prediction of PHB, hydrogen and glycogen production rates for R. palustris under photoheterotrophic conditions.

				1.5									12
	PHB (mmol/DW/h),	Glycogen (mmol/DW/h)	0 0.5 1	8.5	12.1	15.6	19.2	22.7 C/N ratio	26.3	29.8 PHB	33.4 Glycogen 36.9	0 2 4 6 8 10 H2	H2 (mmol/DW/h)
					1.5									15
	PHB (mmol/DW/h),	Glycogen	(mmol/DW/h)	0 0.5 1	8.5	12.1	15.6	19.2	22.7 C/N ratio 26.3	29.8	33.4 PHB Glycogen H2 36.9 14.2	0 5 10	H2 (mmol/DW/h)

Schellenberger, J., Que, R., Fleming, R. M. T., Thiele, I., Orth, J. D., Feist, A. M., Zielinski, D. C., Bordbar, A., Lewis, N. E., Rahmanian, S., Kang, J., Hyduke, D. R., & Palsson, B. Ø. (2011). Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox v2.0. Nature Protocols, 6(9), 1290-1307. https://doi.org/10.1038/nprot.2011.308