Objective: To study the batch growth and production kinetics of A. suboxydans and establish key kinetic parameters by model simulation and experiment.
Theory: Basic concepts of Mathematical modeling
Basic definition and scope of Model –
Description of reality is basically termed as “Model”. For example maps of the city describing the locations of roads, parks colonies could also be described as model as they are the pictorial representation of the reality. Similarly graphs indicating population growth in a country in different years also gives an elegant presentation of facts about the population and therefore be called as model representation of population statistics. The extrapolation of the above definition(s) could also lead to the conclusion that mathematical model is nothing but the kinetic description of substrate disappearance primarily leading to appearance of growth and product by cellular (microorganism, plant or animal cell) activity in the bioreactor. Cell cultivations are done under aseptic conditions in bioreactor to produce strategic metabolites which have commercial values. However this is a labor intensive process thereby normal process optimization procedure for optimization of process parameters &/or culture mode(s) becomes a very tedious and frustrating exercise. On the contrary development of a mathematical model not only facilitates easy understanding of culture behavior under different cultivation conditions but also helps in the design of suitable reactor optimization strategy(ies) for maximum yield and productivity of a particular metabolites. This approach is particularly important for plant cell cultivation for the production of valuable secondary metabolites which exhibit slower growth with the result even a single batch cultivation takes months to complete.
Unstrutured Mathematical model and its limitation –
Accurate description of cell activity in model is very important for realistic description of culture behavior. Usually unstructured models are used as their experimental validation is simple and are easy to use for the prediction of reactor operation strategies. These models however assume cell to be described by a single number i.e., biomass which is easy measurable but it does not make any distinction between living and/or dead cells. This rather simplistic assumption of biomass as a representation of cell activity substitutes usage of thousands of highly complex reactions rate equations which are typically involved in the growth process, thereby it provides easy solution of the model equations but it invariably fails to describe the dynamic behavior of cells particular when the model is extrapolated to describe the cultivations other than what were used for identification of its model parameters. The typical situations where the unstructured model invariably fails are description of lag phase, fed batch cultivations & transients (shift up and shift down in dilution rates) in continuous cultivations where the culture metabolism shifts from nutrient limitation cultivation to excess nutrient availability (and vice versa) conditions. Structured models, which are based on usage of some “intracellular physiological state markers” are needed to describe the “cell activity” thereby making model more robust in order to describe lag phase and dynamic culture cultivation conditions. Physiological state markers (such as RNA, Typical enzyme activity etc) provide intelligent correlation between the model simulation and experimental reality thereby enabling it to describe situations not possible by unstructured models.
Basic features of Fermentation process –
Fermentation process features cell cultivation in a suitable medium and ideal environmental conditions under aseptic conditions to facilitate higher growth which may lead to increased turnover of substrate to produce important metabolites. It can be classified as anaerobic cultivation of cells in which cells grow strictly in the absence of air particularly using metabolic intermediates as their final electron acceptors in the culture metabolism. Aerobic cultivation of cells, however, features vigorous growth of microorganisms in the presence of oxygen which acts as final electron acceptor. Higher growth of cells is achieved in aerobic cultivation than in anaerobic cultivation. In some cultivation the product of interest is accumulated with-in the cell (intracellular) and eventually the cell wall is raptured to isolate and purify the product. Another variety of cultivation features extracellular product formation in which substrate diffuses in to the cell, reacts with different enzymes to produce metabolites which is then excreted out of the cell in the fermentation broth. In this case cells are removed from the fermentation broth after the cultivation process and thereafter product isolation protocols e.g., extraction, distillation, precipitation etc are employed for harvesting the product from the fermentation broth.
Batch Microbial Cultivation and modeling –
Batch cultivations are generally employed to grow cells for desired metabolite production as it is simple and involves least requirement of labor and equipments as opposed to other modes of cultivation (Fed-batch/ Continuous cultivations). However these cultivations work as closed system and thereby feature highly dynamic growth conditions and have less yield and productivity of desired product. This is particularly because of high non production time (Cleaning/Sterilization/Cooling etc) & due to significantly long Lag/Stationery phases in this mode of cultivation. Generally the higher activity featuring exponential growth (Balanced growth wherein all components of the cell grow by same proportion) of the culture is observed for only 25-40 % of total cultivation time of batch cultivation wherein the culture produces the metabolites of interest in growth associated fermentation processes. It is, therefore, desirable to study the culture growth and product formation characteristics (Kinetics) in detail and establish whether it is substrate or product inhibited system. If the kinetics turns out to be substrate inhibited (wherein, by increasing the initial substrate concentration in the bioreactor leads to significant decrease in growth) then it is desirable to design a fed-batch cultivation system such that higher initial substrate concentration in the bioreactor is replaced by gradual slow feeding of substrate such that at no point of time it reaches the inhibitory level. This will feature non limiting and non inhibitory nutrient availability cultivation conditions and result in increased product formation. If cultivation of growth in the presence of different product concentrations demonstrates slower growth at higher concentrations (product inhibition) then batch cultivation will not lead to higher rates of product formation as accumulated product will stay in the reactor and inhibit the growth. At significant higher product concentrations it may even stop the growth (and eventually product formation may cease) even under the conditions of high substrate (and associated nutrient) availability situations in the fermentation broth. To eliminate product inhibition growth conditions it is desirable to design either a plug flow or continuous reactor cultivations which features continuous feeding of nutrients and simultaneous withdrawal of fermentation broth along with the inhibitory product. Models are highly instrumental to design suitable reactors and their operation strategies to optimize any fermentation process.
Bioconversion of sorbitol to sorbose –
Bioconversion of sorbitol to sorbose is an intermediate step in the commercial production of L-ascorbic acid (Vitamin-C) (Kulhanek, 1970, Bourdant, 1990). It involves the microbial oxidation of D-sorbitol to L-sorbose by Acetobacter suboxydans. Chemical oxidation of D-sorbitol leads to formation of both the enantiomers of sorbose whereas microbial oxidation produces only L-sorbose and therefore it is necessary to focus on optimization of fermentation for economic production of sorbose.
Batch sorbose fermentation is severely inhibited by sorbitol. The rate of sorbitol oxidation decreases with increasing initial sorbitol concentration (Damodaran and Subramanian, 1951, Bonomi et al., Srivastava and Lasrado, 1998) It has been observed that complete oxidation of sorbitol with-in a reasonable period of time is possible only up-to an initial sorbitol concentration of 200 g/L there is a sharp decline in sorbose yields when the initial sorbitol concentrations are above limit (Rosenberg et al 1993) Usually the initial sorbose concentration has to be kept low in order to reduce the negative effect of high sorbitol concentration on culture growth. Sorbitol to Sorbose bioconversion is autocatalytic in nature i.e., an increase in sorbose concentration leads to an acceleration of the reaction (Mori et al., 1981; Beschkov and Tepavicharova, 1984).