Clifford W Fong
email: cwfong@internode.on.net

Keywords: Anti-tuberculosis drugs: targeting outer membrane channel proteins, ion channel blockers and the use of cucurbit[7] Mycobacterium tuberculosis, drug resistance, outer membrane, CpnT protein ion channel, ion channel inhibitors, cell membrane lipophilicity, isoniazid, ethambutol, pyrazinamide, cucurbit[7]uril, binding energy inclusion complexes, macrophages, quantum mechanics, TD DFT, excitation energy, HOMO-LUMO energy gap

Anti-tuberculosis drugs: targeting outer membrane channel proteins, ion channel blockers and the use of cucurbit[7]uril as an excipient to improve oral drug delivery and efficacy against resistant Mycobacterium Tuberculosis

Clifford W Fong

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Introduction

Multi (MDR), extensively (XDR), extremely (XXDR) and total (TDR) drug-resistant Mycobacterium tuberculosis (M.tuberculosis) strains are now considered a potential global pandemic threat requiring the need to develop new tuberculosis (TB) prevention and treatment strategies. The potency of M.tuberculosis in infection and evading the host immune system is in part due to its unique and dynamic cell envelope, composed mainly of lipids and carbohydrates. The dynamic cell envelope changes to adapt to the different lung microenvironments in response to local environmental factors, and also protects the pathogen against harsh environments and many antimicrobial drugs due to its low permeability. So most combined treatments for anti-TB agents target the mycobacterial cell envelope. Standard clinical treatment for drug-susceptible TB consists of administering four first-line drugs for 6 months (2 months of isoniazid, rifampicin, ethambutol and pyrazinamide, followed by 4 months of isoniazid and rifampicin), with a success rate of 85% (WHO, 2019). However, the worldwide emergence of drug-resistant strains in recent years, especially in TB endemic areas, poses a global threat. [START_REF] Allué-Guardia | Evolution of Drug-Resistant Mycobacterium tuberculosis Strains and Their Adaptation to the Human Lung Environment[END_REF] Isoniazid is delivered as a prodrug that inhibits the formation of the mycobacterial cell wall. Isoniazid is activated by KatG, a bacterial catalase-peroxidase enzyme in M. tuberculosis. KatG catalyzes the formation of the isonicotinic acyl radical, which spontaneously couples with NADH to form the nicotinoyl-NAD adduct. This adduct binds to the enoyl-acyl carrier protein reductase InhA, thereby blocking the natural enoyl-AcpM substrate and the action of fatty acid synthase. [START_REF] Suarez | An oxyferrous heme/protein-based radical intermediate is catalytically competent in the catalase reaction of Mycobacterium tuberculosis catalase-peroxidase (KatG)[END_REF] Pyrazinamide is a prodrug that diffuses into the granuloma of M. tuberculosis, where the tuberculosis enzyme pyrazinamidase converts pyrazinamide to the active form pyrazinoic acid. At acidic conditions of pH 5 to 6, the pyrazinoic acid that slowly leaks out is thought to diffuse back into the bacilli and accumulate, and indirectly acts to stop the growth of the bacterium. [START_REF] Zhang | The curious characteristics of pyrazinamide: a review[END_REF] Ethambutol is bacteriostatic against actively growing TB bacilli. It inhibits the formation of the cell wall, and eventually leads to increased permeability of the bacterial cell wall. It was developed to be active against isoniazid resistant strains of M. tuberculosis.

Chen et al [START_REF] Chen | The Mycobacterial Membrane: A Novel Target Space for Anti-tubercular Drugs[END_REF] have discussed two classes of membrane targeting agents: drugs that interact directly with the bacterial membrane bilayer to disrupt its structure and functionality. These cationic amphiphiles are characterized by their lipophilicity and a positively charged state that is usually associated with a basic nitrogen moiety. Lipophilicity is required for interaction with the lipid rich membrane. The positively charged state will enhance interaction with the bacterial membranes, which unlike mammalian membranes, are rich in negatively charged phospholipids and polyanionic surface groups. The second class of membrane active agents can disrupt the function of membrane bound proteins such as enzymes involved in energy production or cell wall biosynthesis. These drugs may or may not be cationic amphiphiles.

While the double membrane cell envelope is a defining feature of mycobacteria, it appears that the outer membrane is a lipid bilayer whose lipophilicity is very important to mycobacterial viability. Antimicrobial peptides can interact with the outer and inner membrane of microbacteria, forming pores. Pore formation compromises the integrity of the membrane by increasing its permeability, thereby increase leakage of ions and metabolites from the cytosol, and the collapse of the transmembrane potential resulting in membrane disruption. [START_REF] Chen | The Mycobacterial Membrane: A Novel Target Space for Anti-tubercular Drugs[END_REF] Danilchanka [START_REF] Danilchanka | An outer membrane channel protein of Mycobacterium tuberculosis with exotoxin activity[END_REF] showed that the outer membrane channel protein CpnT of M. tuberculosis is essential for persistence and toxicity of the pathogen in macrophages. CpnT promotes replication of M. tuberculosis in macrophages. CpnT contains a secreted toxic C-terminal domain (CTD) and an N-terminal channel domain (NTD). CpnT was demonstrated to have a dual activity in the promotion of host cell death as well as uptake the nutrients by M. tuberculosis. CpnT can act as a major drug susceptibility determinant for M. tuberculosis, where mutations in CpnT appear to be associated with increased drug resistance in M. tuberculosis clinical isolates. [START_REF] Danilchanka | The Mycobacterium tuberculosis outer membrane channel protein CpnT confers susceptibility to toxic molecules[END_REF] Machado [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] has investigated the role of ion channel blockers in drug resistant M. tuberculosis, particularly how these drugs act as antimicrobial agents, efflux inhibitors and their role in macrophage killing activity. It is expected that results of Machado and Danilchanka should be complementary to some degree.

We have recently described a predictive quantum mechanical TD DFT method which can describe the time dependent behaviour of inhibitors of voltage gated ion channels. The key determinants are the excitation energy of the first excited state of the inhibitor and the ground state HOMO-LUMO gap of the inhibitor that govern the dynamic binding between the inhibitor and the protein target. The method applies to the inhibition of the E protein ion channel of SARS-CoV-2. It is possible that the outer membrane channel protein CpnT of M. tuberculosis could be a major drug target similar to that found in SARS-CoV-2 [START_REF] Fong | Inhibition of SARS-CoV-2 envelope ion channel and the relationship with the membrane dipole potential[END_REF] particularly since mutations in CpnT appear to be associated with increased drug resistance in M. tuberculosis clinical isolates, as well as promoting the replication of M. tuberculosis in macrophages.

The cucurbit [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF]uril (CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF]) molecular container is efficiently internalized by mouse leukaemic monocyte macrophage cells indicating their potential for the intracellular delivery of drugs. Ethambutol was found to be as efficient in treating M. smegmatis infected macrophages when loaded into CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] as opposed to when it was delivered in the unbound form, suggesting that CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF]-bound drug molecules can be released from the container to find their intracellular target. [START_REF] Hettiarachchi | Toxicology and Drug Delivery by Cucurbit[n]uril Type Molecular Containers[END_REF] The unique feature of M. tuberculosis depends upon its ability to convert antimicrobial macrophage cells into a permissive cellular state. [START_REF] Upadhyay | Tuberculosis and the art of macrophage manipulation[END_REF] There is potential to use molecular container oral drug delivery excipient systems [START_REF] Gu | Macrocycles as drug-enhancing excipients in pharmaceutical formulations[END_REF] such as CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] to enhance the efficacy of commonly used anti-tuberculosis drugs such as isoniazid, ethambutol and pyrazinamide. At pH 1.5, isoniazid binds CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] with a binding constant of 5.6 × 10 5 M -1 , whilst pyrazinamide binds CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] at pH 7 with a much smaller binding constant (4.8 × 10 3 M -1 ). [START_REF] Nj Wheate | Host-guest complexes of the antituberculosis drugs pyrazinamide and isoniazid with cucurbit[END_REF] Study objectives: (a) Examine whether the outer membrane channel protein and other membrane characteristics of M. tuberculosis could be target of various anti-tuberculosis drugs, (b) Examine whether CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] can function as an excipient drug delivery container to enhance and target the anti-tuberculosis efficacy of isoniazid, ethambutol and pyrazinamide.

Results

(a) Analysis of outer membrane channels and antibiotic resistance of the CpnT mutants of M. bovis BCG Danilchanka [START_REF] Danilchanka | An outer membrane channel protein of Mycobacterium tuberculosis with exotoxin activity[END_REF] examined the outer membrane channel protein CpnT of M. tuberculosis and its role as a major drug susceptibility determinant for M. tuberculosis. Mutations in CpnT appear to be associated with increased drug resistance in M. tuberculosis clinical isolates. Table 1 shows the MICs for the antibiotic resistance of the cpnT mutants of M. bovis BCG from Danilchanka along with the excitation energies from TD DFT, the HOMO-LUMO gaps, the lipophilicity (ΔG lipo,CDS ) from n-octanol, and molecular volumes of the antibiotics calculated as per our previous study [71 of the inhibition of the E protein ion channel of SARS-CoV-2. The MICs for the 17 drugs were tested against the excitation energy of the first excited state, the HOMO-LUMO energy gap, and the molecular volume in n-octanol, since have previously found linear relationships for the antiviral inhibition of the E protein ion channel of SARS-CoV-2 and the excitation energy and the ground state HOMO-LUMO gap. [START_REF] Fong | Inhibition of SARS-CoV-2 envelope ion channel and the relationship with the membrane dipole potential[END_REF] Octanol was chosen as it is known to be a good surrogate for lipophilic behaviour of cell membranes, with mainly hydrophobic properties balanced with some hydrophilic behaviour. We have previously shown that octanol better represents a cell membrane environment where some water interaction can occur, whereas octane is a better representative of a more hydrophobic environment found in deep pockets where drug-protein environments exists with very little water interaction. [START_REF] Fong | Permeability of the blood-brain barrier: molecular mechanism of transport of drugs and physiologically important compounds[END_REF] The octanol/buffer partition coefficient is widely used method to predict the probability that molecules with molecular weights below 400-600 Da can be passively transported across a lipophilic membrane.

Extensive statistical testing using stepwise regression identified the following LFER relationships shown in eq 1-3 for 14 antibiotics. It was very clear that ampicillin, tetracycline and erythromycin A were consistent large outliers in all equations. It is not clear why these drugs are such outliers from the other 14 analyzed drugs used in eqs 1-3.

Eq 1 Antibiotic resistance of wild type M. bovis BCG MIC WT = 0.65ΔG It is clear from eqs 1-3 that the antibiotic resistance is primarily dependent upon the lipophilicity of the drugs. No dependence on the excitation energy or the HOMO-LUMO gap was found. The mutants cpnT::Tn/mspA and cpnT::Tn/cpnT show an increased sensitivity (ca 25%) to the lipophilicity of the drugs compared to the wild type. This is an important observation since mutations in CpnT appear to be associated with increased drug resistance in M. tuberculosis.

(b) Analysis of ion channel blockers acting as antimicrobial agents, efflux inhibitors, and enhancers of macrophage killing activity against drug resistant M. tuberculosis Macado's data [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] for nine drugs (isoniazid, rifampicin, amikacin, ofloxacin, verapamil, thioridazine, chlorpromazine, flupenthixol, haloperidol) tested against nine resistant M. tuberculosis strains was analyzed using the same LFER methodology as described above in section (a). (see Table 2) Verapamil was a consistent statistical outlier and was omitted from all derived LFERs shown in Table 2. Verapamil has been shown to be a strong depolarizer of the mycobacterium membrane, resulting in a loss of membrane potential and bacterial death. [START_REF] Chen | The Mycobacterial Membrane: A Novel Target Space for Anti-tubercular Drugs[END_REF] In most cases strong statistical relationships were found with the exception of strains H37Rv and 69/11 in particular which are less significant. It is clear overall that the dominant molecular specifiers for the drugs that govern the MICs are the excitation energy of the first excited state, the HOMO-LUMO energy gap in the ground state, and the lipophilicity ΔG lipo,CDS in n-octanol as the surrogate for the cell membrane. For the LFERs that showed a strong statistical relationship (ie excluding the LFERs for H37Rv and 69/11) it can be concluded that MICs are negatively related to the excitation energy, positively related to the HOMO-LUMO gap, and negatively related to the lipophilicity as defined, (or positively related to the hydrophobicity). In some instances there strong dependencies on the molecular volume of the drugs, but the magnitude is small compared to the excitation energy, HOMO-LUMO or the lipophilicity.

There is generally a negative dependency between MICs and the excitation energy of the drugs, a positive dependency between MICs and innate reactivity of the drugs the HOMO-LUMO gap, and a negative dependency between the MICs and lipophilicity of the drugs.

Strains 269/03 and 294 of M. tuberculosis are similar to wild type and mutant M. bovis BCG (as per eqs 1-3) in being dependent on drug lipophilicity as the governing determinant.

(c) Analysis of CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] as an excipient drug delivery container to enhance and target the antituberculosis efficacy of isoniazid, ethambutol and pyrazinamide

The results from (a) above for the mutants cpnT::Tn/mspA and cpnT::Tn/cpnT of M. bovis BCG clearly indicate that it is the lipophilicity of the antibiotics that govern their efficacy. So measures that can enhance the lipophilicity of isoniazid, ethambutol and pyrazinamide should increase their efficacy at the outer membrane of M. tuberculosis. An excipient molecular container like CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] should increase the effective lipophilicity of isoniazid, ethambutol and pyrazinamide within the CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] because of the shielding by the more lipophilic CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] container compared to the naked drugs. A second advantage related to the shielding by the container compared to the naked drugs within the biological environment is the reduced metabolism wastage thereby delivering a higher payload at the target. In addition, inclusion complexes can increase the solubility of the guest drug. Not all molecular containers provide such an outer lipophilic shield and hydrophobic inner cavity as CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] and related cucurbiturils, as other containers such as cyclodextrins have increased outer hydrophilicity by comparison.

Figure 1 and 2 shows the side and top views of the isoniazid@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF],pyrazinamide@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF], ethambutol@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF], and electrostatic potential maps for ethambutol@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] in n-octanol. Table 3 shows Molecular specifiers for anti-tuberculosis drugs isoniazid, pyrazinamide and ethambutol in the free form or as complexes with CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF]. Also shown are the values for the reactive intermediate radical species of isoniazid, pyrazinoic acid the active species of the prodrug pyrazinamide. Three major outcomes are obvious.

Firstly, it is immediately clear that the antibiotics complexed with CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] are much more lipophilic than the naked antibiotics as judged by ΔG lipo,CDS in n-octanol, as the surrogate for a lipophilic cell membrane. These values quantitatively rank the gains in lipophilicity.

Secondly, the reactivity or potency of the antibiotics when enclosed within CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] is higher than the naked drugs, as judged by the HOMO-LUMO gap or the excitation energy in n-octanol, as the surrogate for a lipophilic cell membrane.

Thirdly, the binding energies of the inclusion complexes: isoniazid@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF], pyrazinamide@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF], and ethambutol@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] are higher in n-octanol than in water, which means that the dynamic equilibria that exists between the inclusion complexes and their components favours release of the antibiotic in a lipophilic environment (such as a cell membrane) rather than in an aqueous environment.

The binding energies of isoniazid@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] and the free radical intermediate isoniazid acyl radical@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] are the same in n-octanol, indicating that the formation of this intermediate if it occurred from the free isoniziad (from the dynamic equilibrium) or from the complexed isoniazid@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] species would equally likely to have similar antibiotic potencies as the parent isoniziad complex in the outer bacterial membrane. Figure 3 shows the reported reaction sequence for the antibiotic potency of isoniazid. [START_REF] Suarez | An oxyferrous heme/protein-based radical intermediate is catalytically competent in the catalase reaction of Mycobacterium tuberculosis catalase-peroxidase (KatG)[END_REF] Figure 3. Reaction mechanism for the antibiotic behaviour of isoniazid Pyrazinoic acid@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] may be slightly more stable than pyrazinamide@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] in n-octanol, suggesting that it may be possible to use the pyrazinoic acid@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] directly as a antibiotic agent, rather than pyazinamide. Figure 4 shows enzymatic formation of the active pyrazinoic acid from the prodrug pyazinamide.

Discussion

This study and other literature studies strongly support the notion that the outer membrane of M. tuberculosis is the target for the many antibiotics, including isoniazid, pyrazinamide and ethambutol. Eqs 1-3 show that the antibiotic resistance of 14 drugs is primarily dependent upon the lipophilicity of the drugs for wt M. bovis BCG and the mutants cpnT::Tn/mspA and cpnT::Tn/cpnT. The outer membrane channel protein cpnT of M. tuberculosis is essential for persistence and toxicity of the pathogen in macrophages and promotes replication of M. tuberculosis in macrophages. Mutations in CpnT appear to be associated with increased drug resistance in M. tuberculosis.

Results for M. bovis BCG and the resistant strains of M. tuberculosis indicate that the three dominant factors governing drug efficacy are the excitation energy of the first excited state, the HOMO-LUMO gap, and the lipophilicity of the drugs, which was common to both bacterium studied. For the LFERs that showed a strong statistical relationship, it can be concluded that MICs are negatively related to the excitation energy, positively related to the HOMO-LUMO gap, and negatively related to the lipophilicity. The ion channel of resistant forms of these bacteria can be targeted by an appropriate selection of drugs using these three factors to design appropriate inhibitors or antibiotics.

Machado [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] has shown that the ion channel blockers verapamil, thioridazine, chlorpromazine, flupenthixol and haloperidol exhibit synergistic activity when combined with the antibiotics izoniazid, rifampin, amikacin, capreomycin and ofloxacin. These inhibitors also act as efflux inhibitors, and efflux mechanisms are known to contribute to overall antibiotic resistance in M tuberculosis. The bactericidal action of the ion channel blockers is considered to be associated with their interference with the energy metabolism of the bacterium. Ion channel blockers can play a role as adjuvants in tuberculosis chemotherapy.

Examination of the use of the molecular container CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] to form inclusion complexes of the type antibiotic@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] show that these formulations may be contenders to enhance the potencies of the commonly used M. tuberculosis antibiotics isoniazid, pyrazinamide and ethambutol. This is portrayed in Figure 5.

Figure 5. Schematic representation of inclusion complexes that can enhance the deliverability and potencies of current anti-tuberculosis antibiotics.

Conclusions

This study shows that the antibiotic resistance of 14 drugs is primarily dependent upon the lipophilicity of the drugs for wt M. bovis BCG and the mutants cpnT::Tn/mspA and cpnT::Tn/cpnT. The outer membrane channel protein CpnT of M. tuberculosis is essential for persistence and toxicity of the pathogen in macrophages, and promotes replication of M. tuberculosis in macrophages. Also it is known that mutations in CpnT appear to be associated with increased drug resistance in M. tuberculosis.

The results for M. bovis BCG and the resistant strains of M. tuberculosis indicate that the three dominant factors governing drug efficacy are the excitation energy of the first excited state, the HOMO-LUMO gap, and the lipophilicity of the drugs. It can be concluded that MICs are negatively related to the excitation energy, positively related to the HOMO-LUMO gap, and negatively related to the lipophilicity. The ion channels of resistant forms of these bacteria can be targeted by an appropriate selection of drugs using these three factors to design appropriate inhibitors or antibiotics. Ion channel inhibitors can act as synergistic adjuvants to tuberculosis antibiotics.

Based on the notion that the commonly used anti-tuberculosis drugs isoniazid, pyrazinamide and ethambutol target the outer membrane of M. tuberculosis, a study of the cucurbit [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF]uril inclusion complexes isoniazid@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF], pyrazinamide@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF], and ethambutol@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] shows that these complexes have enhanced lipophilicity over that for the naked antibiotics, as well as enhanced potency. Such properties may offer increased anti-tuberculosis potency compared to the naked antibiotics, as well as offer reduced metabolic degradation, oral administration and increased solubility of such drugs as routinely associated with inclusion complexes.

Ethambutol@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] is known to be as efficient in treating M. smegmatis infected macrophages as opposed to when it was delivered in the unbound form, suggesting that CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF]-bound drug molecules can be released from the container to find their intracellular target and to be effective in macrophages.

Studies of (a) isoniazid@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] and its free radical intermediate isoniazid acyl radical@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF], (b) the prodrug pyrazinamide@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] and its active species pyrazinoic acid@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF], indicate that these reactive intermediates may offer enhanced anti-tuberculosis activity over that for the normal inclusion complexes.

Materials and methods

All calculations were carried out using the Gaussian 09 package. Energy optimizations were at the DFT/B3LYP/6-31G(d) (6d, 7f) level of theory for all atoms in water, with the empirical dispersion correction GD3BJ. Selected optimizations at the DFT/B3LYP/6-31++G(d,p) (6d, 7f) with the empirical dispersion correction GD3BJ level of theory gave very similar results to those at the lower level. Calculations were conducted using the IEFPCM/SMD solvent model in water and n-octanol. With the 6-31G* basis set, the SMD model achieves mean unsigned errors of 0.6 -1.0 kcal/mol in the solvation free energies of tested neutrals and mean unsigned errors of 4 kcal/mol on average for ions. [START_REF] Av Marenich | Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions[END_REF] The 6-31G** basis set has been used to calculate absolute free energies of solvation and compare these data with experimental results for more than 500 neutral and charged compounds. The calculated values were in good agreement with experimental results across a wide range of compounds. [START_REF] Rayne | Accuracy of computational solvation free energies for neutral and ionic compounds: Dependence on level of theory and solvent model[END_REF][START_REF] Rizzo | Estimation of Absolute Free Energies of Hydration Using Continuum Methods: Accuracy of Partial Charge Models and Optimization of Nonpolar Contributions[END_REF]] Adding diffuse functions to the 6-31G* basis set (ie 6-31+G**) had no significant effect on the solvation energies with a difference of less than 1% observed in solvents, which is within the literature error range for the IEFPCM/SMD solvent model.

Binding energies for the cucurbit [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF]uril inclusion complexes: isoniazid@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF], pyrazinamide@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF], ethambutol@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF], isoniazid radical@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF], and pyrazinoic acid@CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] were calculated using the DFT/B3LYP/6-311G(d,p) (6d, 7f) with the empirical dispersion correction GD3BJ and the CP BSSE correction in n-octanol and water. It is noted that the particular configurations shown in Figures 1 and2 are not unique as other configurations are possible with respect to how the ligands are orientated within the CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF] cavity, and how deeply the ligands are inserted into the cavity. The solvent also impacts the particular configurations of the complexes as occurs with the dynamic equilibia amongst the CB [START_REF] Machado | Ion Channel Blockers as Antimicrobial Agents, Efflux Inhibitors, and Enhancers of Macrophage Killing Activity against Drug Resistant Mycobacterium tuberculosis[END_REF], ligand and solvent species. [START_REF] Das | Applications of Cucurbiturils in Medicinal Chemistry and Chemical Biology[END_REF] It is noted that high computational accuracy for each species in different environments is not the focus of this study, but comparative differences between various species is the aim of the study. Experimental errors in inhibitory studies are substantially higher than those for calculated molecular specifiers. The LFER methodology has been previously described. [START_REF] Fong | The extravascular penetration of tirapazamine into tumours: a predictive model of the transport and efficacy of hypoxia cytotoxic analogues and the potential use of cucurbiturils to facilitate delivery[END_REF] Table 1. MICs (µg/ml) for the antibiotic resistance of the cpnT mutants of M. bovis BCG and calculated molecular specifiers of antibiotics in n-octanol.

Figure 1 .Figure 2 .

 12 Figure 1. Left & Centre Left: isoniazid@CB[7], Right & Centre Right: pyrazinamide@CB[7]

  [START_REF] Zhang | The curious characteristics of pyrazinamide: a review[END_REF]

Figure 4 .

 4 Figure 4. Formation of active species pyrazinoic acid from pyrazinamide.

lipo,CDS -0.0045Mol Vol + 1.21

	Where R 2 = 0.596, SEE = 1.19, SE(ΔG lipoCDS ) = 0.16, SE(Mol Vol) = 0.003, F=8.13, Significance= 0.007. P-values for ΔG lipo,CDS
	= 0.002 and Mol Vol = 0.067
	Eq 2 Antibiotic resistance of cpnT::Tn/mspA mutation of M. bovis BCG
	MIC = 0.81ΔG lipo,CDS -0.056
	Where R 2 = 0.677, SEE = 1.63, SE(ΔG lipoCDS ) = 0.16, F=23.08, Significance= 0.0005.
	Eq 3 Antibiotic resistance of cpnT::Tn/cpnT mutation of M. bovis BCG
	MIC = 0.82ΔG lipo,CDS + 0.055
	Where R 2 = 0.703, SEE = 1.63, SE(ΔG lipoCDS ) = 0.16, F=23.72, Significance= 0.0006.

Table 2 . LFER analysis of MIC for nine drugs (isoniazid, rifampicin, amikacin, capreomycin, ofloxacin, thioridazine, chlorpromazine, flupenthixol, haloperidol) tested against nine resistant M. tuberculosis strains. [7]

 2 Verapamil was found to be a consistent large statistical outlier in all derived LFERs.

		Wild	cpnT::Tn/mspA	cpnT::Tn/cpnT	Excitation	HOMO-	ΔG lipo,CDS	Molec
		Type MIC	mutation MIC	mutation MIC	Energy octanol eV	LUMO octanol eV	octanol kcal/mol	Volume octanol cm 3 /mol
	Ampicillin	30	60	60	4.58	5.35	2.13	243
	Tetracycline	31.25	62.5	62.5	3.20	4.20	4.83	272
	Erythromycin A	16	32	16	3.91	5.14	-0.17	529
	Chloramphenicol	4	8	8	3.39	3.97	2.41	176
	4-Aminosalicylic Acid	2	2	2	4.51	4.90	3.06	106
	Ethambutol	0.125	0.125	0.125	7.03	8.04	-1.21	165
	Cycloserine	4	4	4	5.31	6.45	3.07	92
	Streptomycin	0.16	0.32	0.32	3.51	3.91	2.72	358
	Clarithromycin	0.125	0.5	0.25	4.00	4.66	2.31	571
	Rifampin	0.008	0.032	0.032	2.10	2.54	3.45	494
	Ciprofloxacin	1	2	2	3.49	4.00	0.15	233
	Ofloxacin	0.25	0.25	0.25	3.33	7.87	0.59	264
	Levofloxacin	0.125	0.125	0.125	3.34	3.87	0.59	199
	Moxifloxacin	0.5	0.5	0.5	3.40	3.91	-0.08	284
	Norfloxacin	1	2	2	3.53	4.04	0.81	222
	Vancomycin	5	10	10	3.87	4.05	10.11	783
	Isoniazid	0.25	0.25 Not determined	4.42	5.58	2.64	118

M.

tb strains Best fit LFER from general eqn: MIC=EE+HL+MV+ ΔG lipo,CDS +constant

  ΔG lipo,CDS =Lipophilicity (kcal/mol). See ref 18 for LFER methodology.

			Significance
			F
	H37Rv	78.3EE -64.7HL + 6.2	0.277
	H37Rv katG -142.8EE + 112.2 HL-0.3MV + 151.0	0.021
	82/09	-58.8EE + 265.0	0.147
	149/09	158.2HL + 1.5MV -1013.3	0.013
	286/09	-54.2EE + 31.0HL + 93.0	0.107
	69/11	-287.0HL + 192.0MV + 284.3	0.262
	29/12	157.9HL + 1.6MV -1019.1	0.009
	269/03	-4.2 ΔG lipo,CDS + 19.2	0.033
	294 -4.4 ΔG lipo,CDS + 18.2	0.029
	Footnotes: EE= First Excitation Energy (eV), HL=HOMO-LUMO gap (eV),
	MV=Molecular Volume (cm 3 /mol),

Table 3 . Molecular specifiers for anti-tuberculosis drugs isoniazid, pyrazinamide and ethambutol as CB[7] complexes and naked species.

 3

		Binding	Binding	Excitation	HOMO-	ΔG lipo,CDS	Molec
		Energy kcal/mol	Energy kcal/mol	Energy eV	LUMO eV	octanol kcal/mol	Volume cm 3 /mol
		water	octanol	octanol	octanol		octanol
	Isoniazid@CB7	-15.1	-11.34	4.282	4.98	-4.96	735
	Pyrazinamde@CB7	-21.72	-16.86	3.551	5.04	-3.82	821
	Ethambutol@CB7	-2.14	-2.29	4.906	5.43	-9.2	841
	Ethambutol Ion@CB7		-55.22	5.552	6.36	-8.79	803
	Isoniazid Radical@CB7		-11.34	2.283	4.37	-4.21	814
	Pyrazinoic Acid@CB7		-19.94	3.813	4.94	-3.79	851
	Pyrazinoic Acid@CB7*			3.809*	4.53*	9.12**	758*
	Water
	Izoniazid			4.417	5.58	2.66	107
	Pyrazinamide			3.858	5.15	2.62	87
	Ethambutol			7.031	5.98	-1.21	185
	Izoniazid Radical			2.014	3.83	2.58	90
	Pyrazinoic Acid			3.758	4.99	2.82	88

Footnote: * values are in water, ** values are ΔG water,CDS


Yves Rabinowitz

Martinez-Maure
email: yves.martinez-maure@imj-prg.fr

Non-circular algebraic curves of constant width: an answer to

published or not. The documents may come

Introduction

A disk has the property that it can be rotated between two …xed parallel lines without losing contact with either line. It has been known for a long time that there are many other plane convex bodies with the same property. Such plane convex bodies are called plane convex bodies 'of constant width' or 'orbiforms'. Their boundaries are of course called 'plane convex curves of constant width'. A classical non-circular example is the Reuleaux triangle [START_REF]Reuleaux triangle: en.wikipedia.org/wiki/Reuleaux_triangle Y. Martinez-Maure[END_REF] which is made of three circular arcs. But a non-circular plane convex curve of constant width can be smooth, and not having any circular arc in its boundary. The notion of a convex body of constant width can of course be extended to higher dimensions. For a recent survey on the topic, we refer the reader to [START_REF] Martini | Bodies of constant width. An introduction to convex geometry with applications[END_REF] In this paper, we are essentially interested in non-circular algebraic curves of constant width. Rabinowitz [START_REF] Rabinowitz | A polynomial curve of constant width[END_REF] found that the zero set of the following polynomial P 2 R [X; Y ] forms a non-circular algebraic curve of constant width in R 2 :

P (x; y) := (x 2 + y 2 ) 4 45 (x 2 + y 2 ) 3 41283 (x 2 + y 2 ) 2 +7950960 (x 2 + y 2 ) + 16 (x 2 3y 2 ) 3 + 48 (x 2 + y 2 ) (x 2 3y 2 ) 2 +x (x 2 3y 2 ) 16 (x 2 + y 2 ) 2 5544 (x 2 + y 2 ) + 266382 720 3 .
Then, he raised the following open questions: "The polynomial curve found is pretty complicated. Can it be put in simpler form? Our polynomial is of degree 8. Is there one with lower degree? What is the lowest degree polynomial whose graph is a noncircular curve of constant width? ". Recently, it has been proved by Bardet and Bayen [1, Cor. 2.1] that the degree of P , that is 8, is the minimum possible degree for a non-circular plane convex curve of constant width. Here, we emphasize the convexity assumption because it is implicit in the statement of Corollary 2.1 in [START_REF] Bardet | On the degree of the polynomial de…ning a planar algebraic curves of constant width[END_REF]. In this short note, we provide additional answers to Rabinowitz's open questions. First, we recall the notion of a plane hedgehog curve of constant width, and we notice that in this setting, we can …nd algebraic curves of constant width much simpler. Second, we give an example of a non-circular smooth algebraic curve of constant width whose equation is simpler than the one of Rabinowitz. Finally, we notice that we can deduce from it (relatively) simple examples in higher dimensions.

Plane algebraic hedgehogs of constant width

Here, we will follow more or less [START_REF] Martinez-Maure | A Note on the Tennis Ball Theorem[END_REF].

De…nition For any smooth function h :

S 1 = R n 2 Z ! R; 7 ! h ( ),
we let H h denote the envelope of the family of lines given by

x cos + y sin = h( ) (1)
where (x; y) are the coordinates in the canonical basis of the Euclidean vector space R 2 . We say that H h is the plane hedgehog with support function h, and that H h is projective if h( + ) = h( ) for all 2 S 1 .

Partial di¤erentiation of (1) yields

x sin + y cos = h 0 ( ):

From ( 1) and ( 2), the parametric equations for H h are

x = h( ) cos h 0 ( ) sin y = h( ) sin + h 0 ( ) cos .
The family of lines (D ( )) 2S 1 of which H h is the envelope is the family of 'support lines' of H h . Suppose that H h has a well de…ned tangent line at the point (x; y), say T . Then T is the support line with equation (1): the unit vector u( ) = (cos ; sin ) is normal to T and h( ) may be interpreted as the signed distance from the origin to T .

A plane hedgehog is thus simply a plane envelope that has exactly one oriented support line in each direction. A singularity-free plane hedgehog is simply a convex curve. A plane hedgehog is projective if it has exactly one nonoriented support line in each direction Now, we can de…ne the width, say w h ( ), of such a plane hedgehog H h in the direction u ( ) to be the signed distance between the two support lines of H h that are orthogonal to u ( ), that is by

w h ( ) = h ( ) + h ( + ) .
Thus plane projective hedgehogs are hedgehogs of constant width 0, and the condition that a plane hedgehog H h is of constant width 2r is simply that its support function h has the form f + r, where f is the support function of a projective hedgehog. Here are three examples of plane hedgehogs: (a) a convex hedgehog of constant width; (b) a hedgehog with four cusps; (c) a plane projective hedgehog which is a hypocycloid with three cusps. 3) is a non-circular algebraic curve of constant width 0 with equation

(a) (b) (c) h ( ) = 10 + cos (3 ) h ( ) = cos (2 ) h ( ) = sin 3 Figure 1 Theorem. The projective hedgehog H h R 2 with support function h : S 1 ! R, 7 ! sin (
x 2 + y 2 2 + 18 x 2 + y 2
8y y 2 3x 2 = 27:

Proof. We already know that H h is a non-circular curve of constant width 0. From the parametric equations for H h , we deduce that 3) is the restriction of the polynomial y (y 2 3x 2 ) to the unit circle S 1 , and the linearization of y (y 2 3x 2 ) as a trigonometric function of gives We then eliminate s by computing the resultant of the polynomials A (s) = 64 (1 s 2 ) (s 3 1) 2

x 2 + y 2 = h ( ) 2 + h 0 ( ) 2 = sin 2 (3 ) + 9 cos 2 (3 ) = 5 + 4 cos (6 ) . Now, h : S 1 ! R, 7 ! sin (
x 2 and B (s) = 3 + 4s (2 + 3s 2s 3 ) y with Mathematica, and …nd after simpli…cation that:

(x 2 + y 2 )
2 + 8y (y 2 3x 2 ) 2 + 432y (y 2 3x 2 ) (351 10 (x 2 + y 2 ))

= 567 3 + 28 (x 2 + y 2 ) 3 + 486 (x 2 + y 2 ) (67 (x 2 + y 2 ) 567 18) :

Higher dimension

The notion of a hedgehog of constant width can of course be extended to higher dimensions (see, e.g. [START_REF] Martinez-Maure | A stability estimate for the Aleksandrov-Fenchel inequality under regularity assumptions[END_REF]). Each of the above two examples of algebraic curves of constant width admits an axis of symmetry in R 2 . By rotating it around such an axis, we deduce immediately an example of algebraic surface of revolution that is of constant width in R 3 . More precisely, the algebraic surface with equation :

x 2 + y 2 + z 2 2 + 18 x 2 + y 2 + z 2 8z z 2 3 x 2 + y 2 = 27 is a 'projective hedgehog'of revolution and a surface of constant width 0 in R 3 (see Figure 3, left), and the algebraic surface with equation

Figure 2 .

 2 Figure 2. The non-circular convex curve of constant width 16 with equation (3)

(x 2 + 3 +486 (x 2 +

 232 y 2 + z 2 ) 2 + 8z (z 2 3 (x 2 + y 2 )) 2 +432z (z 2 3 (x 2 + y 2 )) (351 10 (x 2 + y 2 + z 2 ))= 567 3 + 28 (x 2 + y 2 + z 2 ) y 2 + z 2 ) (67 (x 2 + y 2 + z 2 ) 567 18) is a convex surface of constant width 16 in R 3 (see Figure3, right).

Figure 3 :

 3 Figure 3: Our two algebraic surfaces of constant width

y y 2 3x 2 = 12 14 cos (6 ) cos (12 ) = 11 14 cos (6 ) 2 cos 2 (6 ) .

From the above two equations, we deduce easily that

8y y 2 3x 2 = 27;

Proof. The parametric equations for H h are equivalent to:

x = 8 sin 3 ( ) 1 cos ( ) y = 2 cos (2 ) cos (4 ) + 8 sin ( ) .

Expanding x and y in terms of c = cos and s = sin , we obtain after simpli…cation:

x = 8 (s 3 1) c y = 3 + 4s (2 + 3s 2s 3 ) .

Squaring the …rst equation and substituting in c 2 = 1 s 2 gives us the following system of equations in the three unknowns x, y, and s: 64 (1 s 2 ) (s 3 1)

x 2 = 0 3 + 4s (2 + 3s 2s 3 ) y = 0.


Hiroki Kurita
email: kurita@material.tohoku.ac.jp

Chrystelle Bernard

Agathe Lavrovsky

Fumio Narita

Tensile Properties of Mechanically-Defibrated Cellulose Nanofiber-Reinforced Polylactic Acid Matrix Composites Fabricated by Fused Deposition Modeling

Keywords: cellulose nanofiber, polylactic acid, tensile property, fused deposition modeling

Biodegradable polymers are highly attractive as potential alternatives to petroleum-based polymers in an attempt to achieve carbon neutrality whilst maintaining the mechanical properties of the structures. Among these polymers, polylactic acid (PLA) is particularly promising due to its good mechanical properties, biocompatibility and thermoplasticity. In this work, we aim to enhance the mechanical properties of PLA using mechanically-defibrated cellulose nanofibers (CNFs), which exhibit remarkable mechanical properties and biodegradability. Moreover, we employ fused deposition modeling (FDM), one of the three-dimensional printing methods for thermoplastic polymers, for the low-cost fabrication of the products. In this study, mechanicallydefibrated CNF-reinforced PLA matrix composites are fabricated by FDM. Their tensile properties are investigated in two printing directions (0°/90° and 45°/-45°) and discussed with regards to their microstructure and fracture surface observed from scanning electron microscopy.

Introduction

Polymers are widely used due to their flexibility, low fabrication cost, workability and so on. However, nowadays, polymers have been pointed out for the enormous plastic pollution they generate in oceans and landfill. In addition, their recycling and incineration appears often complex and expensive. Therefore, interest in biodegradable polymers, such as polylactic acid (PLA), polybutylene adipate terephthalate and polybutylene succinate [START_REF] Zhang | Fully Biodegradable and Biorenewable Ternary Blends from Polylactide, Poly(3-hydroxybutyrate-cohydroxyvalerate) and Poly(butylene succinate) with Balanced Properties[END_REF] , has surged on the basis that they may be used as replacements for petroleum-based polymers, thereby assisting in achieving carbon neutrality. In particular, PLA attracts attention due to its strength, stiffness and biocompatibility, although it also possesses low toughness and biodegradability, and is expensive [2- 3] .

Cellulose nanofibers (CNFs) are regarded as promising next-generation fibers owing to their sustainability, outstanding mechanical properties, biodegradability and so on [START_REF] Henriksson | Structure and properties of cellulose nanocomposite films containing melamine formaldehyde[END_REF][START_REF] Mörseburg | Assessing the combined benefits of clay and nanofibrillated cellulose in layered TMP-based sheets[END_REF] . CNFs are generally obtained by either chemical treatment or mechanical defibration.

2,2,6,6-Tetramethylpiperidinyloxy (TEMPO) oxidation is one of the most well-known chemical treatments to obtain CNFs [START_REF] Saito | Cellulose nanofibers prepared by TEMPOmediated oxidation of native cellulose[END_REF][START_REF] Shinoda | Relationship between length and degree of polymerization of TEMPO-oxidized cellulose nanofibrils[END_REF] . However, it has been reported that TEMPO is toxic and pollutes the environment [START_REF] Sehaqui | Highly carboxylated cellulose nanofibers via succinic anhydride esterification of wheat fibers and facile mechanical disintegration[END_REF] . In contrast, aqueous counter collision (ACC) methods based on mechanical defibration can obtain CNFs using only water, although CNF bundles (as opposed to single nanofibers) are often produced [START_REF] Kondo | Aqueous counter collision using paired water jets as a novel means of preparing bio-nanofibers[END_REF] .

Three-dimensional (3D) printing is a promising approach for the fabrication of complex products at low cost. Various methods, such as fused deposition modeling (FDM) and stereolithography for thermoplastic polymers, additive manufacturing for metals and direct ink writing for ceramics, have been studied [START_REF] Vaezi | review on 3d micro-additive manufacturing technologies[END_REF] . In particular, FDM is a widely distributed 3D printing method for thermoplastic polymers, due to its low fabrication costs, capability of printing large-sized products, easy maintenance, and variation of raw filaments. The fabrication and mechanical properties of carbon fiber-reinforced thermoplastics by FDM have been recently

reported by Li et al. [START_REF] Li | Rapid prototyping of continuous carbon fiber reinforced polylactic acid composites by 3D printing[END_REF] .

Xie et al. [START_REF] Xie | Assessing the Flexural Properties of Epoxy Composites with Extremely Low Addition of Cellulose Nanofiber Content[END_REF] reported that epoxy resin can be enhanced by the molecular chain cross-linkage of epoxy with extremely low CNF addition. This strengthening mechanism shifts to a rule of mixture (i.e. mechanical enhancement) with higher CNF addition. Moreover, Narita et al. [START_REF] Narita | Multi-Scale Analysis and Testing of Tensile Behavior in Polymers with Randomly Oriented and Agglomerated Cellulose Nanofibers[END_REF]

Materials and Methods

As starting materials, we prepared PLA pellets (Terramac® TE-2000, Unitika Ltd., Japan) and mechanically-defibrated dry CNFs (BiNFi-s® WFo-UNDP, Sugino Mashine Ltd., Japan). The PLA pellets and CNF were mixed at 12000 rpm using a mixer (TM-8100, TESCOM Denki Co., Ltd., Japan) and the CNF volume fraction was controlled between 0 and 0.5 vol.%. After mixing, PLA-CNF filaments were prepared from the mixed powder at 168°C by an extruder (Filabot Ex2, Filabot, USA).

Tensile testing was performed in compliance with JIS K 7161 1BA. Tensile specimens (see Fig. Tensile testing was carried out using a universal testing machine (Autograph TM AG-Xplus, Shimadzu Corporation, Japan) with a crosshead speed of 1 mm/min. We assumed that the crosssectional area proportionally decreases by applying the load and that the true strain (𝜀 T ) and true stress (𝜎 T ) were estimated as follows:

𝜀 T = ln(1 + 𝜀 N ) (1)
𝜎 T = 𝜎 N (1 + 𝜀 N ) (2)
where 𝜀 N and 𝜎 N are nominal strain and stress, respectively.

Results and Discussion

The CNFs were not burned during extrusion and white PLA-CNF filaments were obtained. The apparent CNF agglomeration was not visually observed. Fig. 3 shows the relationship between specimen shape and stage temperature. The specimens were deformed because of thermal shrinkage when the stage temperature was high.

Therefore, we determined 40°C as the stage temperature in this study. Fig. 4 shows the printed PLA-CNF 0.5 vol.% tensile specimen in the 0°/90° direction. It is well known that voids are formed along the printing direction inside the fabricated products by FDM and the printing direction inside the tensile specimens was also visible [START_REF] Lu | Improving the impact strength of poly(lactic acid) (PLA) in fused layer modeling (FLM)[END_REF] . Fig. 5 shows the SEM images of CNFs inside the PLA-CNF specimen. The CNFs were agglomerated in PLA at any CNF volume fraction and the number of agglomerated CNF clusters was proportionally increased with the CNF volume fraction. The PLA/CNF interface was not intimate, possibly because PLA is hydrophobic while CNF has hydrophilic groups on its surface [START_REF] Halonen | Environmental protection of inkjetprinted Ag conductors[END_REF][START_REF] Nitani | Organic temperature sensors based on conductive polymers patterned by a selectivewetting method[END_REF] . This result implies that the load transfer efficiency at the PLA/CNF interface is low. Furthermore, the CNF orientation along the printing direction was not observed.

Fig. 3. Relationship between specimen shape and stage temperature.

1 )

 1 were printed by a 3D printer (L-DEVO M2030TP, Fusion technology Co., Ltd., Japan) with a printing speed of 30 mm/sec, a filling density of 100%, a lamination pitch of 0.2 mm, a nozzle temperature of 200°C and a nozzle hole diameter of 0.4 mm in two printing directions of 0°/90° and 45°/-45° (see Fig.1). Fig.2shows the dimension of the tensile specimens. The stage temperature was controlled between 40 and 70°C.

Fig. 1 .

 1 Fig. 1. The specimens have been 3D-printed using the fused deposition modeling in the a) 0°/90° and b) +45°/-45° direction.

Fig. 2 .

 2 Fig. 2. Dimension of tensile specimens (JIS K 7161 1BA). All dimension are in mm.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Printed PLA-CNF 0.5 vol.% tensile specimen in the 0°/90° direction.

Fig. 6

 6 Fig. 6 shows typical stress-strain curves of the PLA-CNF composites printed in the 0°/90° and 45°/-45° directions. The PLA-CNF composites printed in 45°/-45° showed an apparent plastic deformation, while the PLA-CNF composites printed in 0°/90° showed a proportional relationship between tensile stress and strain and therefore, seems to exhibit a brittle behavior. Fig. 7 shows the CNF volume fraction versus ultimate tensile strength (UTS) and fracture elongation of the PLA-CNF composites. The UTS and fracture

Fig. 6 .Fig. 7 .

 67 Fig. 6. Typical stress-strain curves of PLA-CNF composites printed at (a) 0°/90° and (b) 45°/-45°.

Fig. 8 .

 8 Fig. 8. Mechanical behavior of PLA-CNF composites printed a 0°/90° and 45°/-45° under tensile load.

Fig. 9 .Fig. 10 .

 910 Fig. 9. SEM fractographs of PLA-CNF 0.1 vol.% composite printed in the 0°/90° direction.

Acknowledgements This work was supported by Program for Creation of Interdisciplinary Research and Ensemble Program of Frontier Research Institute for Interdisciplinary Sciences, Tohoku University.

Author Assist. Prof. KURITA Hiroki received Ph.D. degree in materials science from Tohoku University in 2012. From 2018 to present, he is assistant professor in Tohoku University, Japan.

He studies on natural fiber reinforced biodegradable polymer matrix composites (green composites). He is interested in the relationships between mechanical properties and decomposition level of natural fiber reinforced biodegradable polymer matrix composites.