The complexity of the catabolic pathway of B. methylotrophicum makes it difficult to extract patterns of metabolic regulation from the experimental data. Metabolic models that calculate the fluxes of carbon, electron, and ATP fluxes through the various branches from the experimental data can aid in this process. However, development of such models requires that the stoichiometry of the individual reactions of the pathway be known. Sufficient information about the CO metabolism by B. methylotrophicum is available (77,74,27) for development of a metabolic model.

Model Development Following the approach developed by Papoutsakis (22), an equation was written for cell mass production that is balanced for carbon, electrons and ATP. In acetogenic anaerobes, such as B. methylotrophicum, acetyl-CoA is a precursor for cell mass production and links catabolism with anabolism (7). Consequently, cell mass was assumed to be produced from acetyl-CoA, as shown in Equation 1:

Acetyl-CoA + yi NADH2 + y2 ATP -> 2 Cell Mass (1)

Applying an electron balance to Equation 1, the coefficient yi can be estimated to be 0.2 mol NADH^mol Acetyl-CoA. In an alternative approach (17), the value of yi was estimated to be 1.5 mol NADH2/mol Acetyl-CoA from the following stoichiometric equation that was determined from batch growth of B. methylotrophicum on CO (20):

4 CO -» 2.17 C02 + 0.74 CH3COOH + 0.45 Cell mass (2)

This equation balances to within 3% for both carbon and electrons. The elemental composition measured for B. methylotrophicum cells closely matched the average cell formula (CHi. gOo. sNo. s) suggested by Roels (25).

Estimation of y2 required the assumption of a second mechanism of ATP production. When only substrate-level phosphorylation (SLP) is considered, conversion of CO to acetate is an ATP-neutral process (one ATP is consumed by formyl-THF synthase for each ATP produced by acetate kinase), and production of

butyrate, ethanol, and butanol result in net consumption of ATP by SLP. Zeikus et al. proposed that an electron-transport phosphorylation (ETP) mechanism contributes the remaining ATP needed for cell maintenance and growth (7). In this mechanism, electrons generated by CO dehydrogenase are shuttled through two membrane-bound electron carriers. One of these carries both a proton and an electron, and the other carries only electrons. The net result is the ejection of protons from the cell, generating a transmembrane proton gradient. The protons reenter the cell via a proton-translocating ATP synthase that generates ATP. Six moles of electrons are produced by CO dehydrogenase per mole acetyl-CoA produced, so a theoretical maximum of 6 protons could be ejected per acetyl-CoA produced. A conservative value of 2 moles of protons ejected per mole of acetyl — CoA produced was used, along with a standard ratio of 1 mole ATP produced per 3 moles of protons translocated (24), to calculate ATP yields by both SLP and ETP for the growth data given in Equation 2. The net ATP yield for production of 0.74 mol of acetate and the acetyl-CoA used to produce the cell mass was calculated to be 2 mol ATP/mol acetyl-CoA used for cell mass. This value equals the amount of ATP available to convert one mole of acetyl-CoA into cell mass (i. e., y2). This y2 value translates into a Yx/atp value of 26 g cells/mole ATP. By comparison, the accepted value for cell growth on glucose is 10.5 g cells/mole ATP (25).

Reaction equations were written that capture the stoichiometry and structure of the branched pathway. Consecutive reactions that did not involve branch points reactions were lumped together.

CO -> CO2 + nadh2	(3)
CO2 + 3 NADH2 + ATP -> [CH3OH]	(4)
CO + [CH3OH] Acetyl-CoA	(5)
Acetyl-CoA -> CH3COOH + ATP	(6)
Acetyl-CoA + 2 NADH2 -> C2H5OH	(7)
Acetyl-CoA -> 0.5 Acetoacetyl-CoA	(8)
Acetoacetyl-CoA + 2 NADH2 Butyryl-CoA	(9)
Butyryl-CoA -> C3H7COOH + ATP	(10)
Butyryl-CoA + 2 NADH2 -» C4H, OH	(11)

Equations 1 and 3-11 were each assigned an unknown rate (or flux) coefficient. An expression for the rate of production of each species (n) was then written from these equations in terms of the unknown flux coefficients and the reaction stoichiometries. The reaction rates for non-secreted intermediates NADH2, [CH3OH], acetyl-CoA, butyryl-CoA, and acetoacetyl-CoA were set equal to zero, based the pseudo-steady-state assumption (22). The r* terms for other compounds (acetate, butyrate, ethanol, butanol) were calculated from experimental measurements of their liquid-phase concentrations (Q) , using the following, unsteady-state conservation equation:

r{ = — j — — DC( (12)

at

where D is the dilution rate. The CO2 production rate was determined from the flow rate and CO2 concentration of the effluent gas stream. For the steady-state experiments, the time derivative was set equal to zero. The resulting set of 10 equations with 10 unknowns was solved using Gaussian Elimination to calculate the flux coefficients.

Application of the Metabolic Model to Experimental Data. Calculation of the pathway fluxes allowed the relative ATP contributions from ETP and SLP to be calculated (77). Even though ATP is a non-secreted intermediate, the pseudo­steady-state assumption does not apply, because ATP can be consumed in a variety of unknown reactions in the сей, including miscellaneous maintenance-energy requirements. The model predicted that, for the steady-state fermentations, there was significant net consumption of ATP due to SLP (-0.12 mol ATP/mol CO). However, this was offset by sufficient production of ATP via ETP (+0.14 mol ATP/mol CO) to result in a small net gain of ATP.

An unsteady-state approach had to be used for the oscillatory fermentations. The time

derivative in Equation 12 was evaluated by graphically differentiating the C* vs. time data. The net ATP yield predicted by the model was slightly negative throughout the experiment. Since the culture could not be sustained under a long­term ATP deficit, this result suggests that there is more ATP produced than is accounted for by the model. The assumed ratio of 2 protons ejected per acetyl — CoA may have been too conservative. Assuming 4 moles of protons ejected per mole of acetyl-CoA produced instead of 2 would give a Yx/atp value of 10 g cells/mol ATP, which closely matches the accepted value for glucose (25). Alternatively, there is evidence (G. J. Shen and J. G. Zeikus, unpublished results) that the electron carrier for the reduction crotonyl-CoA to butyryl-CoA is membrane-bound and may thus participate in ETP.

The mechanism driving the oscillations is believed to be related to metabolic regulation, rather than the CO mass-transfer rate or the liquid flow rate. Both the rate of CO addition and the liquid flow rate were constant throughout the experiments. The mean residence time of the liquid (66 h) was much shorter than the period of the oscillations (about 250 h). Although there were oscillations in both the acetate and butyrate concentrations, these oscillations were out of phase, indicating that the carbon flux was being alternately regulated through the two — carbon and four-carbon pathway branches. The cells obtain twice as much ATP via SLP per carbon equivalent by producing acetate from acetyl-CoA than butyrate. However, acetate production eliminates fewer electrons per carbon equivalent. Thus, the oscillations may have arisen from the cells alternately responding to needs to eliminate electrons and generate ATP. Consistent with this hypothesis, the oscillations in the CO uptake rate are in phase with butyrate production and out of phase with acetate production. More CO has to be consumed when butyrate is produced to maintain an equivalent rate of ATP production via SLP.

Gas Mass-Transfer Issues in Synthesis-Gas Fermentations

Oxygen mass transfer from the gas to the liquid phase is commonly rate-limiting in commercial-scale, aerobic fermentations (26). For this reason, design of fermenters for aerobic applications centers around providing an adequate volumetric mass — transfer coefficient (Кід). In a commercial-scale synthesis-gas bioprocess, providing sufficient mass transfer would be expected to be even more challenging, for two reasons. First, about twice as many moles of gas must be transferred per electron equivalent in the substrate for fermentations based on synthesis gas than those based on glucose. Second, under mass-transfer limiting conditions, the volumetric mass-transfer rate is directly proportional to the gas solubility (18), and the molar solubilities of CO and H2 are only 77% and 65% of that of oxygen, respectively (27).

Mass-transfer-limiting conditions are readily identified in synthesis-gas fermentations by applying an unsteady-state mass balance to the gas uptake rate data. This approach has been used to demonstrate mass-transfer limitations in a variety of bioreactor configurations, including batch (28), stirred tanks (18), airlift fermenters, and trickle-bed reactors (16). Under such conditions, the gas uptake rate is constant. Thus, increases in the concentration or intrinsic reaction rate of the cells will not translate into improved productivity unless comparable increases are made in the gas mass-transfer rate.

Traditionally, gas mass transfer has been enhanced by increasing the power input to the bioreactor, which reduces the average bubble size and hence increases the interfacial area. In the previously described continuous CO fermentations using cell recycle (17), efforts were made to increase interfacial area by rapidly recycling the gas from the headspace, through a frit, and back into the fermentation broth. A high impeller rate was also used to maintain small bubble size. Even then, the highest specific CO gas consumption rate observed was 0.0044 mol/h*g cell. Calculations based on batch data with this organism at lower cell densities (20) have yielded CO consumption rates as high as 0.02 mol/h®g cell for much lower cell densities. These results suggest that, even with a high agitation rate and gas recycle, CO mass transfer was still rate-limiting. Moreover, this approach would not be economically feasible at the commercial scale, because power consumption increases with the impeller diameter to the fifth power and the impeller rate to the third power (29).

Formation and Stability of Microbubble Dispersions. Microbubble aeration has recently been proposed as an energy-efficient approach to enhancing synthesis-gas mass transfer (30). Aficrobubbles are surfactant-stabilized gas bubbles having radii on the order of 25 pm. The surfactant layer provides a surface charge that prevents bubble coalescence by electrical repulsion (57). Microbubble dispersions have colloidal properties and can be pumped, unlike conventional foams that collapse upon pumping. The formation and coalescence properties of microbubbles have been studied (30). The microbubble generator consisted of a 5-cm diameter, stainless-steel disk spinning at 7000 rpm in the vicinity of stationary baffles. The number-averaged diameter was 107 pm for room-temperature microbubbles generated using Triton X-100 at a concentration of twice the critical micelle concentration (30). Modifications of the microbubble generator later reduced the number-averaged bubble diameter to 56 pm.

The rate of drainage of the microbubble dispersion was measured as a function of surfactant concentration and type. This technique gives information on stability and initial gas void fraction. As the concentration of surfactant increased beyond the critical micelle concentration, the stability of the dispersion increased to an asymptotic value that varied with the surfactant used. The initial gas void fraction of the dispersion was virtually unaffected by surfactant concentration, surfactant type, or the addition of sodium chloride. The constant value of the initial gas void fraction approximated the theoretical packing limit for monosized spheres. These results indicated that salts commonly used in growth media should not interfere with microbubble formation and stability.

The power required to generate microbubbles was measured using a Lightnin Labmaster unit capable of simultaneously measuring the impeller rate and power input (Bredwell and Worden, manuscript in preparation). The Power Number of the microbubble generator was measured to be 0.036, and the projected power requirement for microbubble generation for commercial-scale B. methylotrophicum fermentations was calculated to be 0.0081 kW per m3 of fermentation capacity. Compared to a nominal power input for commercial-scale fermentations of 1 kW/m3 (26), these data indicate that power requirements for microbubble production should be low at the commercial scale. Moreover, minimal power input would be required for the bioreactor, because the mass-transfer rate from microbubbles is virtually independent of agitation rate (33). Some power input would be required for liquid-mixing requirements, but this input could be minimized by the use of advanced, axial-flow impellers or a pneumatically mixed bioreactor configuration (e. g., airlift) reactor.

Non-toxic Surfactants for Microbubble Formation. The surfactant used to form the microbubbles must be non-toxic to the biocatalysts. The effects of several anionic, cationic and nonionic surfactants on the growth and product formation by B. methylotrophicum were determined in batch culture on CO (Bredwell, et al, submitted). A phosphate-buffered-basal (PBB) medium was used with the addition of 1, 2, or 3 times the critical micelle concentration of the surfactant in the media. The ionic surfactants, cetyl pyridium chloride and sodium dodecyl sulfate, inhibited growth at concentrations lower than the critical micelle concentration. The non­ionic surfactants tested were polyoxyethylene alcohols (Brij surfactants) and polyoxyethylene sorbitan esters (Tween surfactants). These surfactants had little or no effect on the growth rate of the bacteria. Concentrations of Tween 20, Tween 40, and Tween 80 between 0 and 3 times the critical micelle concentration had a negligible effect on the growth rate. The longer chain length surfactants (Brij 56 and Brij 58) appeared to inhibit growth at higher concentrations. Product concentration was measured using gas chromatography to evaluate the effects of the surfactant on the fermentation products. Carbon and electron balances were used to compute the stoichiometric equations. These equations, listed in Table V, show little effect of the Tween surfactants on the stoichiometry. Combined with the growth data, these results suggest that non-ionic Tween surfactants are well suited for making microbubbles for synthesis-gas fermentations.

Table V. Effect of Surfactants on Fermentation Stoichiometries

pH__________________ Fermentation Stoichiometry___________________

Control 4CO —> 2.17C02 + O.4OCH3COOH + O. O65C3H7COOH + O. O76C2H5OH

+ 0.61 CELLS

Tween 20 4CO —> 2.17C02 + O.45CH3COOH + O. O26C3H7COOH + 0.1 ЮС2Н5ОН

+ 0.60 CELLS

Tween 40 4CO —> 2.18C02 + О. З7СН3СООН + O. O82C3H7COOH + O. O68C2H5OH

+ 0.62 CELLS

Tween 80 4CO —> 2.20CO2 + О. З7СН3СООН + O. O78C3H7COOH + O. O96C2H5OH

+ 0.55 CELLS

Mass-Transfer Properties of Microbubbles. The mass-transfer properties of microbubble dispersions were measured using oxygen as the transferred gas (Bredwell and Worden, manuscript in preparation). The experimental system consisted of a 60-cm long column that had four ports along its length. A stream of oxygen microbubbles was combined with a stream of degassed water in a small mixing zone at the bottom of the column. The resulting steady-state oxygen profile across the column was measured using an oxygen minielectrode. An aqueous solution of Tween 20 at twice the critical micelle concentration was used to prepare the oxygen microbubbles. The concentration of surfactant in the degassed water stream varied from 0 to 5 times the critical micelle concentration.

The overall average mass-transfer coefficients based on the liquid phase (KL, av) calculated from the experimental data varied between 0.00002 and 0.0002 m/s. The largest values, which were obtained when the bulk liquid contained no surfactant, are about a factor of 2 greater than the value predicted by the well — known theoretical result that the Sherwood Number (Sh) = 2.0. The lowest values were obtained when the surfactant concentration in the bulk liquid was 5 times the critical micelle concentration. The high Kl>8v values, coupled with the extremely high interfacial areas provided by microbubbles, resulted in Kl2l values up to 1800 h’1, even without mechanical agitation. By comparison, reported Кьа values for synthesis-gas fermentations are 2.1 h’1 for a packed bubble column, 56 h"1 for a trickle-bed bioreactor, and a range of 28 — 101 h’1 for a stirred-tank bioreactor operated with a high impeller rate (76).

Analysis of the microbubble mass-transfer data indicated that a significant fraction of the transferred gas was lost from the microbubbles within seconds. Consequently, to mathematically model the mass-transfer process, an unsteady-
state approach was needed that accounts for phenomena that can often be neglected when using conventional bubbles, including changes in the microbubble size, gas composition, and intrabubble pressure.

Mathematical Model of Microbubble Mass Transfer. An unsteady-state mathematical model has been developed to explore the dynamics of microbubble mass transfer (Worden et al, submitted). The unsteady-state mass balance on the transferred gas component dissolved in the liquid phase is

This equation was derived in terms of a substantial derivative (DQ/Dt) that follows the movement of the gas-liquid interface as the bubble shrinks at a velocity vR. Two different sets of initial conditions for Q were used for the simulations: a pseudo-steady-state profile (PSS) and a gas-free profile (GF). The PSS initial condition assumes the initial concentration profile surrounding the bubble is that given by the steady-state solution to Equation 13 for the initial bubble radius and gas composition. The GF initial condition assumes the the liquid surrounding the microbubble is initially devoid of the transferring gas. The GF profile resulted in much steeper initial concentration gradients and hence more rapid initial gas mass transfer. The unsteady-state mass balances on the transferred gas and total gas in the microbubble, along with the initial conditions, are given below

(15)

t = 0 X=X0 RB=Ro

where X is the mole fraction of the transferred gas in the gas phase, and Di is the mass diffusivity in the liquid phase. The gas and liquid concentrations are related using Henry’s Law. In some cases, an additional film resistance is added at the interface to account for the surfactant shell.

The model was used to calculate the instantaneous mass transfer coefficient (k) at each time, as well as an average value (kav), defined below, for comparison with experimental Kl,.v values:
(17)

where C* is the liquid-phase concentration of the dissolved gas in equilibrium with the gas phase, and C“ is the concentration in the bulk liquid.

The model, which contained no adjustable parameters, was used to predict the mass-transfer rate from a microbubble into an infinite pool of degassed water. The rate of bubble shrinkage, and the corresponding changes in the к and kaV values are shown in Figure 1 for the GF initial condition. The predicted lifetime of an pure-gas microbubble is on the order of seconds in degassed liquid. During bubble shrinkage, к changes significantly, but kaV is approximately constant except for very early in the transfer process. This result validates the use of average mass-transfer coefficients to characterize microbubble mass transfer in experimental systems. The range of kav predicted by the model compares favorably to the steady-state к values predicted by the theoretical model of Waslo and Gal-Or (32). The experimental KL, av values measured in pure water were similar in magnitude to the predicted kav values. However, KL, av values measured in liquid containing high surfactant concentrations were an order of magnitude less. These results suggest that the mass-transfer resistance of the surfactant shell may be controlled by manipulating the properties of the fermentation medium.

Figure 1: Predicted Rate of Change of Microbubble Radius and Mass

Transfer Coefficient

As shown in Figure 2, the rate of microbubble mass transfer is predicted to decrease considerably as the initial concentration of transferred gas in the microbubble decreases. The average mass-transfer rate for a microbubble containing 100% transferable gas was predicted to be 14 times that for a microbubble containing only 20% transferable gas (e. g., air). Because synthesis gas consists of about 90% CO and H2 (2), it is well suited for microbubble mass — transfer on this account.

Figure 2. Effect of Concentration of Transferred Gas on Microbubble Shrinkage Rate