Niels T Eriksen

Martin Leegaard Riis

Kyndby Nikolaj

Niels Holm

Iversen

H 2 synthesis from pentoses and biomass in Thermotoga spp

Keywords: Arabinose, biohydrogen, Thermotoga maritima, Thermotoga neapolitana, xylose

We have investigated H 2 production on glucose, xylose, arabinose, and glycerol in Thermotoga maritima and T. neapolitana. Both species metabolised all sugars with hydrogen yields of 2.7 -3.8 mol mol -1 sugar. Both pentoses were at least comparable to glucose with respect to their qualities as substrates for hydrogen production, while glycerol was not metabolised by either species.

Glycerol was also not metabolised by T. elfii. We also demonstrated that T. neapolitana can use wet oxidised wheat straws, in which most sugars are stored in glycoside polymers, for growth and efficient hydrogen production, while glucose, xylose and arabinose are consumed in parallel.

Introduction

Biohydrogen can be produced from organic materials by a range of different bacteria. Hydrogen production processes have been characterised in complex as well as in defined growth media. When glucose is used as substrate, the yield of hydrogen has for many bacterial cultures been in the range of 1-2.5 mol H 2 mol -1 glucose [START_REF] Rachman | Hydrogen production with high yield and high evolution rate by self-flocculated cells of Enterobacter aerogenes in a packed-bed reactor[END_REF], Mizuno et al. 2000[START_REF] Fabiano | Thermodynamic study and optimization of hydrogen production by Enterobacter aerogenes[END_REF], Oh et al. 2003[START_REF] Lin | Fermentative hydrogen production at ambient temperature[END_REF], Morimoto et al. 2004[START_REF] Kotay | Microbial hydrogen production with Bacillus coagulans IIT-BT S1 isolated from anaerobic sewage sludge[END_REF]. In several hyperthermophilic bacteria belonging to the genus Thermotoga, yields of hydrogen on glucose is higher and may approach the theoretical maximum yield of 4 mol H 2 mol -1 glucose. [START_REF] Schröder | Glucose fermentation to acetate, CO 2 and H 2 in the anaerobic hyperthermophilic eubacterium Thermotoga maritima; involvement of the Embden-Meyerhof pathway[END_REF] reported that Thermotoga maritima converted 1 mol glucose into 2 mol acetic acid and 4 mol of H 2 . [START_REF] Takahata | Thermotoga petrophila sp. nov. and Thermotoga naphtophila sp. nov., two hyperthermophilic bacteria from the Kubiki oil reservoir in Niigata, Japan[END_REF] found yields of 3.7 and 4 mol H 2 mol -1 glucose in T. petrophila and T. naphtophila, respectively, while van Niel et al. (2002) found a yield of 3.8 mol H 2 mol -1 glucose in T. elfii. In T. neapolitana, which has been extensively characterised with respect to hydrogen production, van Ooteghem et al. (2002van Ooteghem et al. ( , 2004) ) reported H 2 yields at or even above 4 mol H 2 mol -1 glucose, [START_REF] Eriksen | Hydrogen production in anaerobic and microaerobic Thermotoga neapolitana[END_REF] found 3.5-3.8 mol H 2 mol -1 glucose when no lactic acid was formed, Munro et al. (2009) found 3.85 mol H 2 mol -1 glucose at the optimal temperature of 77 o C, and d [START_REF] Ippolito | Hydrogen metabolism in the extreme thermophile Thermotoga neapolitana[END_REF] found 4.05 mol H 2 mol -1 glucose, and that 12-15% of the hydrogen was produced from yeast extract added to the growth medium. Also in other hyperthermophilic bacteria, hydrogen yields on glucose may approach the theoretical maximum (Verhaart et al. 2010).

The high yields of hydrogen in Thermotoga seem related to a bifurcating hydrogenase that has recently been characterised in T. maritima [START_REF] Schut | The iron-hydrogenase of Thermotoga maritima utilizes ferredoxin and NADH synergistically: a new perspective on anaerobic hydrogen production[END_REF]. This hydrogenase needs NADH as well as reduced ferredoxin in a 1:2 stoichiometric ratio in order to function and is unable to use neither NADH nor reduced ferredoxin as the sole substrate. While the reduction potential of NADH is insufficient to effectively reduce protons to hydrogen, bacteria harbouring the bifurcating hydrogenase can use excess reducing power from reduced ferredoxin, which is a stronger reducing agent, to enhance the efficiency of proton reduction by NADH. When sugars are oxidised via glycolysis and the pentose phosphate pathway, NADH and reduced ferredoxin are produced exactly in a 1:2 stoichiometric ratio, and all reducing equivalents from sugar oxidation can therefore be used to produce hydrogen.

Most studies on hydrogen production in Thermotoga have used glucose as carbon source although hydrogen productions at a large scale will have to be based on cheaper substrates, such as plant biomass or waste streams like for example mash from the fermentation industry. These materials often have high contents of pentoses stored in carbohydrate polymers. Members of Thermotoga can grow on pentoses and encode and secrete amylases, cellulases, xylanases, pectinases and other glycoside hydrolases (Nelson et al. 1999[START_REF] Chhabra | Carbohydrateinduced differential gene expression patterns in the hyperthermophilic bacterium Thermotoga maritima[END_REF][START_REF] Conners | Microbial biochemistry, physiology, and biotechnology of hyperthermophilic Thermotoga species[END_REF]. The theoretical maximal yield of hydrogen on pentoses is 3.3 mol mol -1 , but whether this yield can be obtained in Thermotoga cultures is not known.

Considerable amounts of glycerol are also available as waste from the biodiesel industry and in mash from fermentation industries where it is produced by Saccharomyces cerevisiae. The genome of T. maritima contains coding sequences for a complete pathway for uptake and conversion of glycerol (Nelson et al. 1999), andvan Ooteghem et al. (2004) found a positive signal for oxidation of glycerol by T. neapolitana in a microplate assay. A single report also describes hydrogen production in T. neapolitana on waste glycerol, although the yield of hydrogen as well as the degree of glycerol conversion was low [START_REF] Ngo | Proceedings of the 3rd intertanional conference on fermentation technology for value added agricultural products[END_REF]. It is therefore not clear how well Thermotoga is able to utilise glycerol for growth and hydrogen synthesis.

In this study we have quantified yields of hydrogen in T. maritima and T. neapolitana growing on xylose or arabinose, the two dominating pentoses in angiosperms, as well as glucose and glycerol, and demonstrated that hydrogen production in Thermotoga can be carried out with high yields also on complex carbohydrates.

Materials and Methods

Strain and growth media

Thermotoga maritima DSM 3109, T. neapolitana DSM 4359, and T. elfii DSM 9442 were grown in a modified version of the ATCC 1977 medium (see van Ooteghem et al. 2002) containing 1 g cysteine.HCl l -1 as reducing agent, and glucose, xylose, arabinose or glycerol as carbon substrate.

The medium also contained 2 g yeast extract l -1 and 2 g peptone l -1 , which are needed by these bacteria. Potassium phosphate was increased from 0.6 to 6.3 g l -1 to increase the buffering capacity of the growth medium [START_REF] Eriksen | Hydrogen production in anaerobic and microaerobic Thermotoga neapolitana[END_REF], while the concentrations of MgCl.H 2 0 and CaCl 2 .H 2 0 were reduced to 0.2 and 0.01 g l -1 , respectively, to prevent formation of precipitates. MgCl, CaCl 2 and the carbon source (glucose, xylose, arabinose, or glycerol) were autoclaved in a separate solution before mixed with a solution containing the remaining medium constituents. A few crystals of resazurin were added as redox indicator.

T. neapolitana was also grown on media based on wheat straw, which had been pre-treated by wet-oxidation at 195 o C, under 12 bar O 2 pressure, and with 2 g Na 2 CO 3 l -1 added for 15 min (Varga et al. 2002). Remaining solids were removed by centrifugation, while 2 g peptone l -1 was added.

Culture conditions

Batch cultures of Thermotoga maritima, T. neapolitana, and T. elfii were grown in 120 ml serum bottles containing 60 ml medium with shaking at 200 rpm and 80 o C. Before the cultures were inoculated, the bottles were sealed by butyl rubber stoppers and flushed with N 2 . Cultures of T. neapolitana were also grown in a 3 l Applikon bioreactor containing 2.75 l medium. The reactor was equipped with a Pt100 temperature sensor and an autoclavable pH electrode (Mettler Toledo). Temperature and pH were automatically controlled by a heating blanket wrapped around the reactor wall, and by titration with 1 M NaOH. Cultures were stirred by a 4 bladed Rushton turbine and aerated by headspace or by sparger aeration with nitrogen gas. The exit gas was passed through a condenser at 4 o C to reduce evaporation before it was passed through online sensors for quantification of gas-flow rate (AWM3000, Honeywell), and hydrogen (EZT3HYE 'Easy Cal' CiTiceL) and CO 2 (IRcel, City Technology, Portsmouth, UK) in the off-gas.

Sampling and analyses

Gas and liquid samples from the head-spaces of the serum bottles were taken using syringes fitted with needles. Excess gas pressure in a serum bottle was released into a syringe and the amount of gas, which had been present in the headspace, was estimated at ambient air pressure as the total volume of gas in the flask and in the syringe. H 2 and CO 2 in the headspace gas were measured by GC.: 0.3 ml headspace gas equilibrated to ambient temperature was injected at 110 o C, and separated on a 2 m Hyacep Q column at 80 o C. The gasses were quantified by a thermal conductivity detector against known standards. N 2 was used as carrier at 10.3 ml min -1 .

Growth was determined from the OD 800 values, and correlated to the dry weight which was determined after filtration onto pre-dried 0.2 µm disc filters and drying at 105 o C, and by microscopic observation.

Glucose, xylose, arabinose, glycerol and organic acid concentrations as well as Maillard products formed in culture supernatants were quantified using HPLC: 50 µl of 0.22 µm filtered culture supernatant was separated on an Aminex HPX-87H column (Bio-rad), eluted with 0.5 mM H 2 SO 4 at 0.4 ml min -1 and 30 o C. Detection was performed with a refractive index detector. Total concentrations of glucose, xylose, arabinose in media based on wet oxidised wheat straw were measured after acid hydrolysis in 4% (w/v) H 2 SO 4 , for 10 min at 121 o C.

Results and Discussion

Hydrogen production on glucose, xylose and arabinose

All 3 Thermotoga species investigated: T. maritima, T. neapolitana and T. elfii grew and produced hydrogen on xylose, arabinose, as well as on glucose, which was included as substrate to allow comparisons of results to previous studies. Fig. 1a shows, as an example, the consumption of arabinose and the production of hydrogen, CO 2 , acetic acid and lactic acid in a 60 ml T. maritima batch culture grown in a closed serum bottle.

[POSITION FIGURE 1]

The stoichiometry of glucose, xylose, or arabinose conversion was quantified by plotting the produced amounts of the various metabolic products against the amount of sugar consumed (Fig. 1b). Table 1 summarises the observed molar yields of hydrogen on glucose, xylose and arabinose in T. maritima and in T. neapolitana. Two processes may have affected the yields shown in Table 1: metabolization of components from yeast extract and peptone by the cells, and by chemical processes transforming part of the sugars into Maillard products (Fig. 1a). d [START_REF] Ippolito | Hydrogen metabolism in the extreme thermophile Thermotoga neapolitana[END_REF] found that approx. 12-15% of the hydrogen produced in T. neapolitana came from conversion of such substrates, resulting in overestimation of the hydrogen yield on sugar. However, the amounts of sugar that went into Maillard reactions, predominantly in early stages of the cultures, were also in the order of 10-15%. Since the Maillard products, which were detectable by HPLC, were partly re-metabolised in late stages of batch cultures, the Maillard reactions have probably effected the estimated hydrogen yields to a lesser extend than the up-take of additional substrates, and the estimated hydrogen yields on sugars are therefore slightly higher than the true yields.

[POSITION TABLE 1]

The molar of yield of hydrogen on glucose was 3-4 in both species and similar to previously reported yields on glucose [START_REF] Schröder | Glucose fermentation to acetate, CO 2 and H 2 in the anaerobic hyperthermophilic eubacterium Thermotoga maritima; involvement of the Embden-Meyerhof pathway[END_REF], van Ooteghem et al. 2002[START_REF] Lin | Fermentative hydrogen production at ambient temperature[END_REF][START_REF] Eriksen | Hydrogen production in anaerobic and microaerobic Thermotoga neapolitana[END_REF], Munro et al. 2009, d'Ippolito et al. 2010). This indicates that our cultures have been grown at conditions that are comparable to conditions generally used for hydrogen production studies in Thermotoga.

The molar yields of hydrogen on xylose and arabinose were also close to or above 3.

In T. neapolitana, the measured hydrogen yields were even above the theoretical maximal value of 3.3 mol hydrogen per mol pentose (Table 1), most likely because yeast extract and peptone have played greater roles in as substrates in T. neapolitana cultures compared to T. maritima cultures.

Carbon balances, which included the sugar used as substrates, and the produced CO 2 , acetic acid, and lactic acid were positive in T. neapolitana cultures, while slightly negative in T. maritima cultures. Biomass was not included in the carbon balances since the biomass is predominantly produced from components in the yeast extract and peptone.

The rate by which hydrogen was produced was highest in T. neapolitana cultures (Table 1). During the growth phase, the average volumetric hydrogen production rates were 2-3 times higher in T. neapolitana than in T. maritima cultures, and similar in magnitude to the hydrogen production rates of 0.8 -0.9 mmol l -1 h -1 previously found in T. neapolitana under similar conditions (Munro et al. 2009). Also the specific hydrogen production rates, estimated as the yield of hydrogen on biomass (Fig. 1b, inset) during initial phases when growth was exponential multiplied by the specific growth rate, were highest in T. neapolitana. Individual cells were most productive in early stages of batch cultures but gradually their activity decreased. In some cultures, activity stopped before all sugar was taken up, a phenomenon that has been explained by decreasing pH [START_REF] Eriksen | Hydrogen production in anaerobic and microaerobic Thermotoga neapolitana[END_REF], Munro et al. 2009) but also metabolites, CO 2 and hydrogen accumulated and may have repressed the cultures. We found no systematic differences in hydrogen production rates on pentoses compared to glucose. The hydrogen yields and production rates shown in Table 1 therefore show that xylose and arabinose are at least comparable to glucose with respects to their qualities as substrates for hydrogen production in Thermotoga.

Glycerol as substrate for hydrogen production

Glycerol would also be an interesting substrate for hydrogen production in Thermotoga. However, we found no conversion of glycerol in cultures of T. maritima, T. neapolitana, nor T. elfii (data not shown). If glycerol was supplemented as sole carbon source, none of the 3 species grew and they did not produce more hydrogen than cultures supplemented only with yeast extract and peptone. If glycerol was supplemented simultaneously with one or more sugar species, all species took up the sugars but left the glycerol untouched.

Glycerol is apparently not a suitable substrate for hydrogen production in Thermotoga, possibly as a consequence of the bifurcating hydrogenase present in these bacteria. While hexoses or pentoses are metabolised with a concurrent production of NADH and reduced ferredoxin in the 1:2 stoichiometric ratio needed by the hydrogenase [START_REF] Schut | The iron-hydrogenase of Thermotoga maritima utilizes ferredoxin and NADH synergistically: a new perspective on anaerobic hydrogen production[END_REF], conversion of glycerol leads to formation of 2 mol NADH and 2 mol reduced ferredoxin per mol glycerol.

Reduction of acetic acid to ethanol would be a potential route for re-oxidation of excess NADH.

The T. maritima genome encodes a putative alcohol dehydrogenase (Nelson et al. 1999) and trace amounts of ethanol have been reported in cultures of T. hypogea [START_REF] Fardeau | Thermotoga hypogea sp. nov., a xylanolytic, thermophilic bacterium from an oil-producing well[END_REF]), but ethanol was not detected in our cultures. These bacteria may therefore need access to alternative electron acceptors, like elemental sulphur [START_REF] Huber | Thermotoga maritima sp. nov. represents a new genus of unique extremely thermophilic eubacteria growing up to 90 o C[END_REF]) that can be reduced directly by NADH in order to use glycerol as substrate, but this will decrease the yield of hydrogen.

Hydrogen production on biomass based substrates

T. neapolitana grew and produced hydrogen on the liquid fraction generated from wet oxidation of wheat straw. The culture, shown in Fig 2, was grown in a bioreactor where pH was controlled and hydrogen and CO 2 were continuously removed, in order to minimise inhibition of the process and allow maximal conversion of carbohydrates. The liquid fraction used as medium contained a mixture of free xylose, glucose and arabinose (7 mM) and the same sugars bound in glycoside polymers, probably mainly hemicellulose, corresponding to a monomer concentration of 24 mM. Also 15 mM acetic acid was present after the wet oxidation.

[ POSITION FIGURE 2] After a lag of 1 day, the culture started to produce H 2 and convert the sugars while biomass concentrations increased to reach a maximum of 0.5 g l -1 after 2.5 days (Fig. 2a). The apparent decrease in biomass concentration after 2.5 days was at least partly associated to biofilm formation, which developed at this point and brought a fraction of the cells out of suspension. Glucose, xylose, and arabinose were taken up in parallel, as also observed in cultures grown on two or more sugars in serum bottles. de Vrije et al. ( 2009) also observed parallel consumption of glucose and xylose in T. neapolitana and a second hyperthermophilic hydrogen producer, Caldicellulosiruptor saccharolyticus grown on Miscanthus hydrolysates. Most of the carbohydrates used by the culture in Fig. 2 were initially found in carbohydrate polymers, as hydrolysis was not included in the pretreatment of the wheat straws. Glucose has previously been shown to repress β-galactosidase activity and lactose metabolism in T. neapolitana resulting in diauxic growth (Vargas and Noll 1996), and glucose represses the synthesis of glycoside hydrolases at the transcription level in T. maritima [START_REF] Chhabra | Carbohydrateinduced differential gene expression patterns in the hyperthermophilic bacterium Thermotoga maritima[END_REF]. Still, the majority of the carbohydrate polymers were degraded in periods where the total sugar monomer concentration was in the order of 5 mM (Fig. 2b). Starch in untreated potato steam peels is also a suitable substrate for hydrogen synthesis in T. neapolitana (Mars et al. 2010). Catabolite repression by glucose or other sugars seems therefore not to play a decisive role in the ability of T. neapolitana to simultaneously degrade and utilise a variety of polymeric substrates, something that is quit advantageously in relation to the employment of these bacteria in hydrogen production processes.

The culture shown in Fig. 2 consumed a total of 27 mM sugars with a corresponding hydrogen production of 72.5 mmol l -1 , and a hydrogen yield on sugar of 2.6 mol mol -1 , or 74% of the theoretical maximal value based on the relative amounts of glucose and pentoses consumed. In 9 additional T. neapolitana batch or fed-batch cultures grown in the bioreactor on defined media with glucose as carbon source, the hydrogen yield on glucose was 3.8 ± 0.2 mol mol -1 (data not shown). This corresponds to 95% of the maximum theoretical yield, and is similar to what was found in cultures grown in serum bottles (Table 1). The slightly lower molar yield of hydrogen in the culture in Fig. 2 can have been affected by the presence of alternative electron acceptors or inhibitors in the wet oxidised materials but the yield was still above what is found in mesophilic bacteria [START_REF] Rachman | Hydrogen production with high yield and high evolution rate by self-flocculated cells of Enterobacter aerogenes in a packed-bed reactor[END_REF], Mizuno et al. 2000[START_REF] Fabiano | Thermodynamic study and optimization of hydrogen production by Enterobacter aerogenes[END_REF], Oh et al. 2003[START_REF] Lin | Fermentative hydrogen production at ambient temperature[END_REF], Morimoto et al. 2004[START_REF] Kotay | Microbial hydrogen production with Bacillus coagulans IIT-BT S1 isolated from anaerobic sewage sludge[END_REF], even though culture conditions and composition of biomass based media have not yet been optimised.

Hydrogen production potentials

Large amounts of organic feed-stocks will be needed if H 2 is to replace a considerable fraction of the hydrogen that is currently produced from fossil fuels and amounted more than 20 billion kg in the US in year 2008 [START_REF] Bromaghim | Hydrogen and fuel cells: The U.S. market report[END_REF]) and 3 times more world wide (van Ooteghem et al. 2002). In Table 2 we have, as an example, estimated how much of this current hydrogen production that in 2030 potentially can be replaced by bio-H 2 produced from leftover mash from the 2. generation industry. The US Department of Energy ( 2008) predicts a growth in bioethanol production from close to zero in 2010 to 6 •10 10 kg by 2030 in the US or 1.2 •10 11 kg world wide.

The mash therefore represents a resource not yet utilised by other applications. Depending on feedstock, and provided that pentose fermentation is not developed, this annual mash production will contain in the order of 2.8•10 11 or 5.6 •10 11 mol pentoses in the US or world wide, respectively.

From these pentoses, a maximum of 9•10 11 or 1.8•10 12 mol hydrogen can be produced to replace 9% of the current hydrogen production in the US or 6% world wide. If the hydrogen yield on pentoses is reduced to 75%, as was the case in the culture shown in Fig. 2, mash from bioethanol production will be able to provide enough feedstock to cover only 7% or 4.5% of the annual hydrogen production the US or world wide, respectively (Table 2). These numbers illustrate the massive scale by which large scale bio-H 2 needs to be produced, and the enormous challenge it will be to secure sufficient biomass resources for this purpose. This is why biological hydrogen producers should be able to utilise a broad spectrum of substrates and produce hydrogen with yields close to the theoretical maximum on hexoses as well as on pentoses. Several Thermotoga species fulfil both criteria, and are at the moment among the most promising candidates for employment in biohydrogen production processes.

Legends

Fig. 1 Thermotoga maritima grown with arabinose as carbon substrate at stirred at 500 rpm.

Initially, the headspace was flushed by 100 ml min -1 N 2 . After 1.8 days, the N 2 was sparged into the culture at same rate. a. Concentrations of arabinose (◊), acetic acid (▲), lactic acid (∆), and biomass (■), produced amounts of CO 2 (○) and hydrogen (•), and carbon balance (). b. Amounts of acetic acid (▲), lactic acid (∆),CO 2 (○), and hydrogen (•) produced compared to the amount of consumed arabinose. Inset shows amount of hydrogen produced compared to the amount of biomass produced during initial growth phase

Fig. 2

 2 Fig. 2 Thermotoga neapolitana grown on liquid fraction of wet oxidised wheat straw. a. Amounts

Table 1 .

 1 Observed yields of lactic acid (Y HLac/sugar ), acetic acid (Y HAc/sugar ), hydrogen (Y H2/sugar ) and CO 2 (Y CO2/sugar ), carbon balance, average volumetric rate of hydrogen production (r H2 ) during growth phase, specific rate of hydrogen production (q H2 ) during initial exponential growth phase of batch cultures of Thermotoga maritima and T. neapolitana grown with glucose, xylose or arabinose as carbon source. Number of replicate cultures indicated by n. Carbon balance is expressed as % change in total carbon content per day until stationary phase relative to initial carbon content.

	Species		Unit		Carbon substrate
				Glucose	Xylose	Arabinose
	T. maritima	Y HLac/sugar	mol mol -1	0.1 ± 0.0	0.1 ± 0.0	0.2±0.1
		Y HAc/sugar	mol mol -1	1.3 ± 0.0	1.2 ± 0.0	1.3±0.1
		Y H2/sugar	mol mol -1	3.2 ± 0.1	2.7 ± 0.0	3.2±0.3
		Y CO2/sugar	mol mol -1	1.4 ± 0.1	1.3 ± 0.1	1.6±0.2
		C-balance	% per day*	-1.6 ± 0.1	-2.6 ± 0.1	-0.6 ± 1.5

Table 2 .

 2 Potential biohydrogen production and replacement of fossil fuel based hydrogen production from conversion of leftover pentoses (C 5 ) in mash from 2. generation bioethanol production in the US and world wide in year 2030. Estimate is based on hydrogen production in 2008.van Ooteghem et al. (2002) estimated 3 times H 2 production world wide compared to the US c Calculated from data published by US Department ofEnergy (2008)

	Premises	Unit	Quantity
			USA	World
	Mass H 2 production in 2008	kg year -1	>2•10 10, a	6•10 10, b
	Molar H 2 production in 2008	mol year -1	>10 13	3•10 13
	Mass production of 2. generation bioethanol in 2030	kg year -1	6•10 10, c	1,2•10 11, c
	Molar production of 2. generation bioethanol in 2030	mol year -1	1.4•10 12	2.8•10 12
	Consumption of glucose for ethanol, glucose → 2 ethanol	mol year -1	7•10 11	1.4•10 12
	Generation of pentoses in mash, C 5 :C 6 = 0.4 in feedstock d	mol year -1	2.8•10 11	5.6•10 11
	Potential H 2 production from C 5 , Y H2/pentose = 3.3 mol mol -1	mol year -1	9•10 11	1.8•10 12
	Potential H 2 production from C 5 , Y H2/pentose = 2.6 mol mol -1	mol year -1	7•10 11	1.4•10 12
	Potential H 2 replacement in 2030, Y H2/pentose = 3.3 mol mol -1	%	9	6
	Potential H 2 replacement in 2030, Y H2/pentose = 2.6 mol mol -1	%	7	4.5

a Data from

Bromaghim et al. (2010) b d

Predicted from data in

[START_REF] Hamelinck | Ethanol from lignocellulosic biomass: technoeconomic performance in short-, middle-and long-term[END_REF]

Acknowledgements

We thank Anne Belinda Thomsen, Risø DTU for supplying wet oxidised wheat straw. Mars AE, Veuskens T, Budde MAW, van Doeveren PFNM, Lips SJ, Bakker RR, de Vrije T, Claassen PAM (2010) Biohydrogen production from untreated and hydrolyzed potato steam peels by the extreme thermophiles Caldicellulosiruptor saccharolyticus and Thermotoga neapolitana. Int J Hydrogen Energy 35: 7730-7737 Mizuno O, Dinsdale R, Hawkes FR, Hawkes DL, Noike T (2000) Enhancement of hydrogen production from glucose by nitrogen gas sparging. Biores Technol 73: 59-65 Morimoto M, Atsuko M, Atif AAY, Ngan MA, Fakhru'l-Razi A, Iyuke SE, Bakir AM (2004) Biological production of hydrogen from glucose by natural anaerobic microflora. Int J Hydrogen Energy 29: 709-713 Munro SA, Zinder SH, Walker LP (2009) The fermentation stoichiometry if Thermotoga neapolitana and influence of temperature, oxygen, and pH on hydrogen production. Biotechnol Prog 25: 1035-1042 Nelson KE, Clayton RA, Gill SR, Gwinn ML, Dodson RJ, Haft DH, Hickey EK, Peterson JD, Nelson WE, Ketchum, KA, McDonald L, Utterback TR, Malek JA, Linher KD, Garett MM, Stewart AM, Cotton MD, Pratt MS, Phillips CA, Richardson D, Heidelberg J, Sutton GG, Fleischmann RD, Eisen JA, White O, Salzberg SL, Smith HO, Venter JC, Fraser CM (1999) Evidence for lateral gene transfer between Archae and Bacteria from genome sequence of Thermotoga maritima. Nature 399: 323-329


Natasha K Martin
email: natasha.martin@bristol.ac.uk

Eamonn A Gaffney

Robert A Gatenby

Philip K Maini

Leaky vessels as a potential source of stromal acidification in tumours

Keywords: Cancer, pH, Acidity, Veins, Microenvironment

Malignant tumours are characterised by higher rates of acid production and a lower extracellular pH than normal tissues. Previous mathematical modelling has indicated that the tumour-derived production of acid leads to a gradient of low pH in the interior of the tumour extending to a normal pH in the peritumoural tissue. This paper uses mathematical modelling to examine the potential of leaky vessels as an additional source of stromal acidification in tumours. We explore whether and to what extent increasing vascular permeability in vessels can lead to a breakdown of the acid gradient from the core of the tumour to the normal tissue, and a progressive acidification of the peritumoural stroma. We compare our mathematical simulations to experimental results found in vivo with a tumour implanted in the mammary 1 fat pad of a mouse in a window chamber construct. We find that leaky vasculature can cause a net acidification of the normal tissue away from the tumour boundary, though not a progressive acidification over time as seen in the experiments. Only through progressively increasing the leakiness can the model qualitatively reproduce the experimental results. Furthermore, the extent of the acidification predicted by the mathematical model is less than seen in the window chamber, indicating not only that vessel leakiness might be acting as a source of acid, but also that it is not the only factor contributing to this phenomenon. Nevertheless, tumour destruction of vasculature could result in enhanced stromal acidification and invasion, hence current therapies aimed at buffering tumour pH should also examine the possibility of preventing vessel disruption.

Introduction

It is well established that malignant tumours exhibit increased glycolysis to produce lactic acid even in the presence of oxygen, a phenomenon called the Warburg effect and discovered by Otto Warburg in the 1930s [START_REF] Warburg | On the origin of cancer cells[END_REF][START_REF] Gatenby | Why do cancers have high aerobic glycolysis?[END_REF][START_REF] Gillies | Causes and consequences of increased glucose metabolism of cancers[END_REF]. The upregulated glucose consumption is used regularly in the diagnosis of malignancies through FDG-PET imaging, which images the high uptake of a glucose analogue [START_REF] Kroemer | Mitochondria in cancer[END_REF]. A consequence of the enhanced levels of aerobic glycolysis is the production of high amounts of acid. As a result, malignant tumours have a lower extracellular pH than normal tissues, at around 6.6-7.0, reduced from the normal pH of 7.2-7.4 [START_REF] Helmlinger | Interstitial pH and pO2 gradients in solid tumors in vivo: high-resolution measurements reveal a lack of correlation[END_REF][START_REF] Schornack | Contributions of cell metabolism and H+ diffusion to the acidic pH of tumors[END_REF][START_REF] Tannock | Acid pH in tumors and its potential for therapeutic exploitation[END_REF].

Despite the discovery of the Warburg effect nearly a century ago, the reason malignant tumours consistently utilise aerobic glycolysis has remained speculative. In a series of publications, Gatenby and co-workers have hypothesised that tumour acidification confers an advantage to the tumour cells, by producing a harsh environment which facilitates tumour proliferation and invasion by promoting normal cell death [START_REF] Gatenby | A reaction-diffusion model of cancer invasion[END_REF], 2003[START_REF] Gatenby | Why do cancers have high aerobic glycolysis?[END_REF][START_REF] Gatenby | Acid-mediated tumor invasion: a multidisciplinary study[END_REF], Gatenby and Gillies, 2007[START_REF] Smallbone | Metabolic changes during carcinogenesis: Potential impact on invasiveness[END_REF][START_REF] Gillies | Causes and consequences of increased glucose metabolism of cancers[END_REF].

Previous mathematical modelling has shown that the production of acid by the tumour leads to a gradient of acidity, characterised by low pH in the tumour interior, which extends into the normal tissue [START_REF] Gatenby | A reaction-diffusion model of cancer invasion[END_REF]. This qualitative prediction has been confirmed in vivo through the use of pH imaging of tumour bearing mice using a window chamber construct [START_REF] Gatenby | Acid-mediated tumor invasion: a multidisciplinary study[END_REF].

Window chamber experiments are excellent tools for examining small spatial changes in tumour pH in vivo. These window chambers allow the non-invasive observation of fine-scale pH gradients between the tumour and surrounding tissue over time. In the [START_REF] Gatenby | Acid-mediated tumor invasion: a multidisciplinary study[END_REF] experiments, a dorsal skinfold window chamber was surgically implanted in a mouse, and a slurry of tumour cells placed in the centre of the chamber. Tumour growth and extracellular pH were subsequently monitored.

As the tumour grew in the window chamber construct the normal peritumoural tissue in the chamber acidified, while the intratumoural tissue became less acidic, reducing the pH gradient from the interior to the exterior of the tumour [START_REF] Gatenby | Acid-mediated tumor invasion: a multidisciplinary study[END_REF]. It is unclear if this normal tissue acidification is an artifact of the window chamber itself, or a naturally occuring phenomenon of tumour growth. Experimental evidence of this disruption is shown in Figure 1, with the normal tissue acidifying and tumour tissue becoming less acidic as time progresses from day 2 to day 6.

Additionally, a local maximum in pH appears to develop near the tumour boundary (0.1-0.2 mm into the peritumoural stroma) by day 6.

One hypothesis for the acidification of the normal tissue in the chamber is that the vasculature transporting the excess acid out of the tumour is leaky. If so, the vessels might act as a source of acid in the surrounding normal tissue, thereby destroying the pH gradient between the tumour and normal tissue.

Additionally, the alkalinsation in the interior of the tumour could be explained by cellular death due to the high numbers of implanted cells which initially exceed the carrying capacity.

In order to examine this leaky vessel hypothesis, we have extended the Gatenby-Gawlinski acid-invasion model (1996) to explicitly incorporate the vascular evacuation of excess acid from the tumour. Their 'acid-mediated invasion model' proposes that tumour-derived acid facilitates invasion by promoting normal cell death. By using a mathematical model incorporating the production of acid, destruction of normal cells, and subsequent movement of tumour cells, they were able to examine intratumoural-peritumoural pH gradients and the subsequent effect on invasion.

Vascular evacuation of tumour-derived acid is achieved by venules and veins which have thin walls which are susceptible to disruption. As such, increased vascular permeability in venous outflow is a hallmark of acute inflammation [START_REF] Kumar | Pathologic Basis of Disease[END_REF]). Hence, it is possible that the acidic environment created by tumours may disrupt the vasculature, leading to leakiness. With the following model, we explore if increased vessel permeability can account for an acidification of the peritumoural tissue.

Mathematical Model

The mathematical model is based on the acid-mediated invasion model of [START_REF] Gatenby | A reaction-diffusion model of cancer invasion[END_REF], extended to include excess acid in the tumour vessels. In our model, N 1 represents the normal cell density (in cells/cm 3 ), N 2 is the tumour cell density (in cells/cm 3 ), L T is the excess H + ion concentration in the interstitial fluid of the tumour and adjacent tissue (in mol/cm 3 ), and L B is the excess H + ion concentration in the veins (in mol/cm 3 ), and the governing equations take the form

∂N 1 ∂t = growth r 1 N 1 1 - N 1 K 1 - death from acidity d 1 L T N 1 (1) ∂N 2 ∂t = growth r 2 N 2 1 - N 2 K 2 + diffusion into tissue ∇ x • D 2 1 - N 1 K 1 ∇ x N 2 (2) ∂L T ∂t = production r 3 N 2 - vascular evacuation d v (L T -L B ) - buffering in tissues κ 2 g 2 L T + diffusion D 3 ∇ 2 x L T (3) ∂L B ∂t = excess acid exchange d v (L T -L B ) - blood buffering g 2 L B - convection due to blood flow ∇ x • (UL B ) . (4)
As in the Gatenby-Gawlinski model (1996), Equation (1) describes the change in normal cell density. They proliferate with growth rate r 1 and carrying capacity K 1 . For simplicity and because it is not the focus of our investigation nor does it change the results found in this study, we do not alter the assumption made in [START_REF] Gatenby | A reaction-diffusion model of cancer invasion[END_REF] that the carrying capacities of the tumour and normal cells are uncoupled. The normal cells die in proportion to the excess acid produced by the tumour, at a rate of d 1 . As the normal tissue is assumed to be well regulated, it does not diffuse in space.

Equation (2) details the tumour cell dynamics. The tumour cells grow at a rate r 2 with a carrying capacity of K 2 . As tumour cells are more resilient to low pH than normal cells, and no decline in growth rate of tumour cells is observed at the pH in our simulations, we neglect tumour cell death from acidification [START_REF] Gatenby | A reaction-diffusion model of cancer invasion[END_REF]. As in the [START_REF] Gatenby | A reaction-diffusion model of cancer invasion[END_REF] and in proportion to the difference in concentration between the tumour and the blood acid. Interstitial pressures entail that there is no flux of fluid, but there can be a flux of ions across the vessel wall. We assume that the volume of the interstitial fluid is approximately the same volume as the blood vessels in the tumour. Although this volume fraction varies between tumour types, it is approximately the same order of magnitude [START_REF] Kim | Measurement of tumor interstitial volume fraction: Method and implication for drug delivery[END_REF]. The blood acid is buffered at a rate g 2 , and is convected with an effective velocity vector field U due to the flow of blood. As our length scale is focused on the microvasculature, we can assume that U is non-pulsatile [START_REF] Fung | Biomechanics: Motion, Flow, Stress and Growth[END_REF];

further, we take it that the velocity vector field is characterised by conservation of mass and incompressibility, so that ∇ x • U = 0. Finally, as a first approximation, we assume that the blood transports acid away from the interior of the tumour, neglecting the small amount which may be transported from the tumour rim into the core.

We solve the system assuming spherical symmetry, due to the relative dimensions of the tumour implant and the window chamber over the short timescale of the experiment. Using spherical polar coordinates, with

R 2 = |x| 2 , we have U = U R 2 e R ,
with U constant. Nondimensionalising the model by using the following substitutions:

η 1 = N 1 /K 1 , η 2 = N 2 /K 2 , Λ T = r1 r3K2 L T , Λ B = r1 r3K2 L B , τ = r 1 t, and ξ = r1 D3 R, we obtain ∂η 1 ∂τ = η 1 (1 -η 1 ) -ρ 1 Λ T η 1 (5) ∂η 2 ∂τ = δ 2 η 2 (1 -η 2 ) + 1 ξ 2 ∂ ∂ξ ξ 2 α 2 (1 -η 1 ) ∂η 2 ∂ξ (6) ∂Λ T ∂τ = η 2 -ν(Λ T -Λ B ) -κ 2 δ 6 Λ T + 1 ξ 2 ∂ ∂ξ ξ 2 ∂Λ T ∂ξ (7) ∂Λ B ∂τ = ν(Λ T -Λ B ) -δ 6 Λ B - σ ξ 2 ∂Λ B ∂ξ (8)
where

ρ 1 = d1r3K2 r 2 1 , δ 2 = r2 r1 , α 2 = D2 D3 , ν = dv r1 , δ 6 = g2 r1 , and σ = U r1 r1
D3 . The initial conditions are calculated from the experimental data in [START_REF] Gatenby | Acid-mediated tumor invasion: a multidisciplinary study[END_REF], where 2.5 × 10 6 tumour cells were placed in the window chamber. As the implanted slurry is has an initial radius of 0.7 mm (ξ ≈ 0.05), the initial cell density can be calculated as about 1 × 10 9 cells/cm 3 , approximately twice the carrying capacity of 5 × 10 8 cells/cm 3 . The normal cells were at their carrying capacity, and there was no initial excess acid.

Hence, the initial conditions are,

η 1 (0) = 1 (9) η 2 (0) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 2 if 0 ≤ ξ < 0.05 0 if 0.05 ≤ ξ (10) Λ T (0) = 0 (11) Λ B (0) = 0. ( 12
)
The boundary conditions will be selected from the appropriate equilibrium values of interest, and detailed in the numerical results section. There are four spatially uniform equilibrium points associated with the system, with (η 1 , η2 , ΛT , ΛB ) denoting the equilibrium values:

• FP1= (0, 0, 0, 0), the trivial state with no tumour, tissue, or excess H + ions, which is linearly unstable to perturbations of normal or malignant tumour cells.

• FP2= (1, 0, 0, 0), the normal cell state with no tumour or excess H + ions which is linearly unstable to perturbations of malignant tumour cells.

• FP3= (1 -ρ 1 ΛT , 1, ν+δ6 ν+νδ6+κ2νδ6+κ2δ6+κ2δ 2 6 , ν ν+νδ6+κ2νδ6+κ2δ6+κ2δ 2 6
), the coexistent state of tumour and tissue, which is linearly stable if

1 > ρ 1 ΛT and unstable if 1 < ρ 1 ΛT . • FP4= (0, 1, ν+δ6 ν+νδ6+κ2νδ6+κ2δ6+κ2δ 2 6 , ν ν+νδ6+κ2νδ6+κ2δ6+κ2δ 2 6
), the tumour state, which is linearly stable if 1 < ρ 1 ΛT and unstable if 1 > ρ 1 ΛT .

With these equilibrium points, we can see that altering the vessel permeability, ν, will alter the pH in the cases of FP3 and FP4. However, it does not affect the tumour free normal steady state of FP2. Hence, if we look for waves advancing with a tumour state behind the wave, and tumour-free state ahead, there will be no alteration in the acidity far in front of the wave.

Nevertheless, the local profiles at the tumour boundary might be altered by the change in vessel permeability, ν, which we will explore through numerical simulations.

Numerical results

Equations ( 5)-( 8) were solved on a spatial grid from 0 ≤ ξ ≤ 1, using the Method of Lines with centered finite difference discretisation of the diffusion terms, and an upwind discretisation of the convection term. Parameter values used were obtained from [START_REF] Gatenby | A reaction-diffusion model of cancer invasion[END_REF], [START_REF] Gatenby | Acid-mediated tumor invasion: a multidisciplinary study[END_REF], [START_REF] Torchilin | Nanoparticulates as Drug Carriers[END_REF], [START_REF] Jain | Delivery of molecular medicine to solid tumors: lessons from in vivo imaging of gene expression and function[END_REF], and are detailed in Table 1. Initial conditions used were as in Equations ( 10). Boundary conditions are no flux at ξ = 0 representing the core of the tumour, and (η 1 , η2 , ΛT , ΛB ) = (1, 0, 0, 0) representing the tumour-free state at ξ = 1.

As the window chamber experiments only measure tumours with a radius up to approximately 1.5mm (ξ ≈ 0.1), it is important to examine the dynamics at the tumour front on this length scale. Hence, although we simulate the equations on a domain of 0 ≤ ξ ≤ 1, for some of the figures we display the solution on a domain of 0 ≤ ξ ≤ 0.1. As we are interested in the pH at 6 days (the final measurement in [START_REF] Gatenby | Acid-mediated tumor invasion: a multidisciplinary study[END_REF]), we simulate 0 ≤ τ ≤ τ max where τ max = 1.05.

Normal vasculature

In this section we simulate Equations ( 5)-( 8) where the vessels have normal permeability, so we choose ν = ν 1 . The simulations are shown in Figure 2, where the tumour and tumour-derived H + ion profiles advance, killing the normal tissue. In addition, acid is removed from the tumour into the blood, and convected out of the tumour and through the normal tissue in the blood vessels.

The tumour/tissue pH is shown in Figure 3 where there is a clear acid gradient from the interior of the tumour to the peritumoural tissue. The interior of the tumour has a low pH, rising at the tumour/normal tissue interface until it is normal in the peritumoural tissue. Figure 3 also shows a rise in tumour pH over the time course of the simulation, consistent with the rise in tumour pH found in the window chamber. This is due to the concentration of tumour cells implanted in the chamber initially exceeding the carrying capacity, which produce a large amount of excess acid and then die.

Leaky vasculature

In Figure 4, we simulate Equations ( 5)-( 8) with the leaky vessels, so we choose ν = ν 2 , hence increasing vessel permeability by two orders of magnitude.

The tumour pH is shown in Figure 5. On the full domain, there is no reduction in the normal tissue pH far from the tumour as predicted by the equilibrium state analysis. However, on the scale of the window chamber, there is an marked absolute reduction of peritumoural pH as compared to the perfect vasculature case (7.20 in the leaky case, 7.40 perfect case at 6 days).

Therefore, it is reasonable to conclude that leaky venules (if present) in the direct vicinity of the tumours in the window chamber can act to reduce the acidic gradient from tumour to tissue. However, this effect is not as pronounced as seen experimentally in Figure 1, which shows an acidification of the peritumoural tissue to about pH 7.15. Furthermore, although there is a net acidification of the chamber in the leaky versus perfect vasculature simulation, it is important to note that in the leaky simulation there is an increase in peritumoural pH from days 2-6, from 7.16 to 7.20 at ξ = 0.1 (Figure 5b). Hence, although with the leakiness there is a net acidification of the tissue, this acidification is predicted to lessen over time. The increase in peritumoural pH over time is as a result of the initial tumour cell death and reduction of acidity (causing the alkalinisation of the intratumoural pH). This simulated alkalinisation of peritumoural pH is not consistent with the window chamber results, which show a total and progressive acidification of the normal tissue.

With the leaky vasculature, the intratumoural pH is higher than the perfect vasculature case (7.07 at 6 days in Figure 5 versus 6.74 in Figure 3) and still exhibits an increased alkalinisation over the course of the simulation (from 7.01 to 7.07).

Progressively leaky vasculature

In this section we simulate the situation where the vasculature becomes increasingly leaky over time, hence we use the following function for vessel permeability, ν = ν 1 + τ τmax (ν 2ν 1 ). This might occur due to acid damage to the endothelial cells, or another type of tumour disruption of the vessels.

In this case, the tumour and normal cell profiles look similar to the constant vasculature case (not shown), but the pH profiles are slightly altered.

Figure 6 shows the pH on the window chamber length scale. This simulation matches the qualitative behaviour seen in the experimental results (Figure 1).

Notably, the progressive acidification of the peritumoural tissue over time, in conjunction with the alkalinisation of the intratumoural tissue. Overall, the gradient between tumour and normal tissue is reduced at the tumour boundary.

Although this scenario fits the qualitative experimental results, the magnitude of acidification of the normal tissue is much less pronounced in the simulations, where the simulated pH lowers from 7.26 to 7.22 from days 2 to 6.

By constrast, the experimental pH lowers from approximately 7.25 to 7.15 in Figure 1. Furthermore, the increase in the vascular permeability parameter, ν needed to produce such a response is extreme (two orders of magnitude).

Additionally, none of the simulations predict the development of a local maximum in pH adjacent to the tumour boundary as seen in Figure 1 by day 6. To conclude, this extreme acidification in the window chambers could not be solely due to vessel leakiness, and the alterations in pH seen in this study would require extremely large increases in vessel permeability.

Discussion

The efficacy of the tumour vasculature is a critical component for tumour perfusion, acid burden, and drug delivery. A wide body of literature exists on how leaky capillaries affect therapy delivery to the tumour, and mathematical models have increasingly tried to account for this phenomenon [START_REF] Chapman | Multiscale modeling of fluid transport in tumors[END_REF]. However, to our knowledge, no one has mathematically examined how leaky veneous outflow from the tumour can act as a source of acid in the peritumoural tissue.

Our analysis indicates that although the tumour free steady state (far ahead of the tumour) will not acidify with increasing leakiness, numerical simulations show that increasing vascular permeability will have a large effect on the spatial intratumoural-peritumoural pH gradients on the millimeter/centimeter scale. In particular, at the tumour boundary, leaky veins will cause a local acidification of the normal tissue. This will have an especially pronounced effect on the length scale of the window chamber experiments, consistent with experimental evidence. Importantly, simulations with leaky vasculature result in a lower peritumoural tissue pH than in normal vasculature, but not a progressive acidification from 2 to 6 days (as seen in the window chamber). However, simulations with increasingly leaky vasculature (such as could be the case with increasing vasculature disruption due to tumour growth) cause both a progressive acidification over time, and also a total decrease in normal tissue pH. All simulations show a slight alkalinisation of the intratumoural tissue due to the initially high concentrations of cells injected in the window chamber, which produce a large amount of acid and then experience cell death towards the tumour carrying capacity. Hence, the initial reduction in tumour cell number serves to reduce the amount of intratumoural acid produced during the timescale of the experiment.

Previous experimental results which showed an acidification of the peritumoural tissue in the window chamber over time, an alkalanisation of the intratumoural tissue, and a breakdown of the intratumoural-peritumoural pH gradient, were hypothesised to be a result of the experimental construct.

However, this model indicates the acidification could be as a result of increasing vessel disruption due to the tumour growth. This could be due to a particularly aggressive tumour cell line which actively causes vessel destruction and enhances permeability. Nevertheless it is important to note that in our simulations the permeability had to be substantially increased (by two orders of magnitude) to produce an acidification that was still less than seen in the window chamber. Therefore, it is likely that even if leaky vessels are contributing to acidification, there are additional factors acidifying the window chamber experiments. Futhermore, the window chamber experiments appear to show the development of a local maximum in the pH near the tumour boundary towards the peritumoural stroma which is not predicted by the modelling. As window chambers are one of the primary methods to measure fine spatial tumour pH gradients, it is worthwhile to assess the importance of this effect with different blood vessel co-cultures and also cell lines.

Overall, tumour disruption of local vasculature may aid in stromal acidification and acid-mediated tumour invasion. Hence, in addition to local acidification at the tumour boundary, leaky vessels may cause a longer-range acidification into the peritumoural tissue, which could potentially aid in the invasion of individual cells who alone could not acidify the local environment.

Recent experiments have shown that oral administration of the buffer sodium bicarbonate raises tumour pH and prevent metastasis formation [START_REF] Robey | Bicarbonate increases tumor pH and inhibits spontaneous metastases[END_REF]. In addition to raising the tumour pH, buffer therapies which increase the buffering capacity of the blood in the tumour vasculature could prevent the vessel disruption and stromal acidification modelled in this study.

Therefore, further exploration of the benefits of buffer therapy to prevent vessel disruption is warranted.

Captions

Figure 1: In colour online. Experimentally derived pH gradients at the tumour-host interface in a window chamber of a mouse. The tumour front is located at 0 on the horizontal axis (which accounts for tumour cell movement), and hence the implanted tumour has an initial radius of 0.7mm, which does not increase over the short timescale of the experiment. Note the slightly different horizontal axis scale between the two figures. A) Radial pH values (shown in varying colours) from the centre of the tumour into the surrounding tissue at 2 days post injection. Here, the tumour pH varies from a low of 6.9 in the core to around 7.0-7.15 at the tumour boundary, and then rises to between 7.1 and 7.3 in the peritumoural tissue. B) Radial pH values at 6 days post injection. Compared to day 2, the tumour pH has risen slightly to between 7 and 7.05 in the tumour core, is relatively steady (6.97-7.12) at the tumour boundary, and greatly acidified in the peritumoural tissue, ranging from 7.07 to 7.17. Overall, the intratumoural pH has become slightly less acidic, and the peritumoural pH more acidic over time. Additionally, there appears to be a local maximum in the pH just past the tumour boundary into the peritumoural stroma (0.1-0.3 mm in the figure). Reprinted with permission from Cancer Research (Figure 3 in [START_REF] Gatenby | Acid-mediated tumor invasion: a multidisciplinary study[END_REF]). 4 days (green dash/dot), and 6 days (black line). Note the initially high level of tumour cells implanted in the window chamber, which die due to the carrying capacity, creating an initially high level of tumour acid which gradually lowers. Simulations are of Equations ( 5)-( 8) with parameters as in Table 1, ν = ν 1 . Each unit of ξ corresponds to ≈15mm, the radius of the window chamber imaging. days (red dash), 4 days (green dash/dot), and 6 days (black line). Figure (a) shows the whole domain (≈15 mm) and (b) zoomed-in version of (a) on the length scale of the window chamber imaging (≈1.5 mm). Note the expected gradient of acidity from the interior of the tumour (low pH at around 6.7) to normal levels in the peritumoural tissue (normal pH at 7.4). Also note the slight increase in pH inside the tumour over the course of the simulation, which corresponds to the results seen in Figure 1. Simulations are of Equations ( 5)-( 8) with parameters as in Table 1, ν = ν 1 . The pH is calculated from the excess interstitial tumour/tissue H + ions, Λ T and with a baseline pH of 7.4. Each unit of ξ corresponds to ≈15mm. 5)-( 8) with parameters as in Table 1, ν = ν 2 . Each unit of ξ corresponds to ≈15mm. of (a) on the length scale of the window chamber imaging (≈1.5 mm). In constrast to the perfect vasculature case (Figure 3), there is an absolute reduction in pH in the peritumoural region at the edge of the window chamber (ξ = 0.1) from 7.4 to 7.2 at 6 days, but no progressive acidification over the course of the simulation. The intratumoural pH is higher than the perfect vasculature case (7.07 at 6 days in this figure versus 6.74 in Figure 3), and exhibits an increased alkalinisation over the course of the simulation (from 7.02 to 7.07). Simulations are of Equations ( 5)-( 8) with parameters as in Table 1, ν = ν 2 . The pH is calculated from the excess interstitial tumour/tissue H + ions,, Λ T and with a baseline pH of 7.4. Each unit of ξ corresponds to ≈15mm. there is an alkalinisation of the intratumoural region from 6.88 to 7.05. As compared to the leaky vasculature case (Figure 5), there is progressive acidification through time of the peritumoural tissue. As in all the simulations, there is a progressive alkalinisation of the intratumoural tissue. This simulation matches the qualitative behaviour seen in the window chamber (Figure 1), though the magnitude of the acidification is lower.

Simulations are of Equations ( 5)-( 8). The parameters used are in Table 1,

ν = ν 1 + τ τmax (ν 2 -ν 1
). The pH is calculated from the excess interstitial tumour/tissue H + ions, Λ T and with a baseline pH of 7.4.

Table 1: Parameters used to solve Equations ( 5)-( 8). The carrying capacities of normal and tumour cells (K 1,2 respectively), growth rates (r 1,2 ), tumour diffusion (D 2 ), and vascular evacuation (d v ) parameters were taken from a previous acid-invasion modelling and experimental study by [START_REF] Gatenby | Acid-mediated tumor invasion: a multidisciplinary study[END_REF]. The diffusion of protons occurs in association with mobile buffer species to ensure charge balance, and the effective diffusion coefficient value used was estimated in [START_REF] Gatenby | Acid-mediated tumor invasion: a multidisciplinary study[END_REF]. From these values, [START_REF] Gatenby | Acid-mediated tumor invasion: a multidisciplinary study[END_REF] calculate the tumour acid production rate (r 3 ), and a range of values for the normal cell death rate from acid (d 1 ) from which we select. The blood convection rate (U ) is determined from the experimental values found in venules [START_REF] Jain | Delivery of molecular medicine to solid tumors: lessons from in vivo imaging of gene expression and function[END_REF][START_REF] Torchilin | Nanoparticulates as Drug Carriers[END_REF]. The blood buffering and proportional delivery of buffer from the bloodstream to the tissue is estimated from extensive systemic buffering simulations (Martin et al., A Mathematical Model of Tumour and Blood pH, Submitted). For the increased vascular permeability simulations, we use ν 2 which is increased two-fold from the baseline value of vessel permeability, ν 1 .

Figure 2 :

 2 Figure 2: In colour online. (a) Full domain (≈15 mm) and (b) zoomed-in (≈1.5 mm, the scale of the window chamber) simulations of normal vasculature showing tumour cell (top left), normal cell (top right), tumour excess H + ion (bottom left) and blood excess H + ion (bottom right) profiles over the course of the simulation. The profiles are shown at 2 days (red dash),

Figure 3 :

 3 Figure 3: In colour online. Tumour/tissue pH gradient from interior of the tumour into the peritumoural tissue with no vessel leakiness, shown at 2

Figure 4 :

 4 Figure 4: In colour online. (a) Full domain (≈15 mm) and (b) zoomed-in (≈1.5 mm, the scale of the window chamber) simulations of the effect of leaky vasculature on tumour cell (top left), normal cell (top right), tumour excess H + ion (bottom left) and blood excess H + ion (bottom right) profiles over the course of the simulation. The profiles are shown at 2 days (red dash), 4 days (green dash/dot), and 6 days (black line). The vessel leakiness increases the blood acid levels, and decreases the tumour acid. Simulations are of Equations (5)-(8) with parameters as in Table1, ν = ν 2 . Each unit of ξ corresponds to

Figure 5 :

 5 Figure 5: In colour online. Tumour/tissue pH gradient from interior of the tumour into the peritumoural tissue with vessel leakiness, shown at 2 days (red dash), 4 days (green dash/dot), and 6 days (black line). (a) Simulations of the whole domain (≈15 mm). Despite the leakiness, the tissue pH returns to a normal 7.4 far away from the tumour (at ξ = 1). (b) A zoomed-in version

Figure 6 :

 6 Figure 6: In colour online. Tumour/tissue pH with increasing leakiness over time. The figure shows the pH profile at 2 days (red dash), 4 days (green dash/dot), and 6 days (black line). The length scale is (a) ≈ 15 mm and (b) ≈ 1.5 mm, that of the window chamber. Consistent with the experimental data,

Figure 1

 1 Figure 1

  Figure 1

  Figure 2

  Figure 3

  Figure 4

  model, the tumour cells are assumed to diffuse into free space with a rate of D 2 , but are confined by the presence of normal cells. Hence, if the normal tissue is at its carrying capacity, the tumour cells are confined and unable to spread. Equation (3) describes excess tumour H + ions, L T , which are produced by the tumour at a rate r 3 . The excess acid is exchanged with the vasculature, which is proportional to the difference in concentration of the tumour excess H + ion concentration L T , and the blood excess H + ion concentration, L B .

	The vascular exchange is represented by d v , which incorporates the effects of
	vessel permability and surface area for exchange. By varying the vascular
	exchange parameter, d v , we will be able to examine if increased permeability
	can contribute to peritumoural acidification. The tumour acid is neutralised
	by buffers (such as bicarbonate) brought in by the vasculature at a rate κ 2 g 2
	where g 2 represents the buffering rate in the blood, and κ 2 represents the
	fraction of buffers present in the tissue from that in the blood. In this case,
	κ 2 < 1 as only a proportion of blood buffers reach the tissue. The acid diffuses
	in the tissue with diffusion rate of D 3 .
	Equation (4) describes excess blood acid, L B , which is exchanged between
	the tumour and vessels at rate d v (which includes vessel permeability effects),

6 Acknowledgements 6.1 Grant Support NKM: This publication was funded by the National Cancer Institute, NIH grant U56CA113004. EAG: This publication is based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). PKM: This work was partially supported by a Royal Society-Wolfson Research Merit Award. RAG and PKM: This work was partially supported by NIH grant 1U54CA143970-01.