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Bistability versus bimodal distributions in gene regulatory processes from population balance.

ABSTRACT: In recent times, stochastic treatments of gene regulatory processes have appeared in the literature in which a cell exposed to a signaling molecule in its environment triggers the synthesis of a specific protein through a network of intracellular reactions. The stochastic nature of this process leads to a distribution of protein levels in a population of cells as determined by a Fokker-Planck equation. Often instability occurs as a consequence of two (stable) steady state protein levels, one at the low end representing the "off" state, and the other at the high end representing the "on" state for a given concentration of the signaling molecule within a suitable range. A consequence of such bistability has been the appearance of bimodal distributions indicating two different populations, one in the "off" state and the other in the "on" state. The bimodal distribution can come about from stochastic analysis of a single cell. However, the concerted action of the population altering the extracellular concentration in the environment of individual cells and hence their behavior can only be accomplished by an appropriate population balance model which accounts for the reciprocal effects of interaction between the population and its environment. In this study, we show how to formulate a population balance model in which stochastic gene expression in individual cells is incorporated. Interestingly, the simulation of the model shows that bistability is neither sufficient nor necessary for bimodal distributions in a population. The original notion of linking bistability with bimodal distribution from single cell stochastic model is therefore only a special consequence of a population balance model.

SUBMITTER: Shu CC

PROVIDER: S-EPMC3161895 | biostudies-literature | 2011 Aug

REPOSITORIES: biostudies-literature

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Bistability versus bimodal distributions in gene regulatory processes from population balance.

Shu Che-Chi CC Chatterjee Anushree A Dunny Gary G Hu Wei-Shou WS Ramkrishna Doraiswami D

PLoS computational biology 20110825 8

In recent times, stochastic treatments of gene regulatory processes have appeared in the literature in which a cell exposed to a signaling molecule in its environment triggers the synthesis of a specific protein through a network of intracellular reactions. The stochastic nature of this process leads to a distribution of protein levels in a population of cells as determined by a Fokker-Planck equation. Often instability occurs as a consequence of two (stable) steady state protein levels, one at ...[more]

PMID: 21901083

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Project description:BACKGROUND:Extensive experimentation has been conducted to increment 1,3-propanediol (PDO) production using Clostridium butyricum cultures in glycerol, but computational predictions are limited. Previously, we reconstructed the genome-scale metabolic (GSM) model iCbu641, the first such model of a PDO-producing Clostridium strain, which was validated at steady state using flux balance analysis (FBA). However, the prediction ability of FBA is limited for batch and fed-batch cultures, which are the most often employed industrial processes. RESULTS:We used the iCbu641 GSM model to develop a dynamic flux balance analysis (DFBA) approach to predict the PDO production of the Colombian strain Clostridium sp IBUN 158B. First, we compared the predictions of the dynamic optimization approach (DOA), static optimization approach (SOA), and direct approach (DA). We found no differences between approaches, but the DOA simulation duration was nearly 5000 times that of the SOA and DA simulations. Experimental results at glycerol limitation and glycerol excess allowed for validating dynamic predictions of growth, glycerol consumption, and PDO formation. These results indicated a 4.4% error in PDO prediction and therefore validated the previously proposed objective functions. We performed two global sensitivity analyses, finding that the kinetic input parameters of glycerol uptake flux had the most significant effect on PDO predictions. The other input parameters evaluated during global sensitivity analysis were biomass composition (precursors and macromolecules), death constants, and the kinetic parameters of acetic acid secretion flux. These last input parameters, all obtained from other Clostridium butyricum cultures, were used to develop a population balance model (PBM). Finally, we simulated fed-batch cultures, predicting a final PDO production near to 66 g/L, almost three times the PDO predicted in the best batch culture. CONCLUSIONS:We developed and validated a dynamic approach to predict PDO production using the iCbu641 GSM model and the previously proposed objective functions. This validated approach was used to propose a population model and then an increment in predictions of PDO production through fed-batch cultures. Therefore, this dynamic model could predict different scenarios, including its integration into downstream processes to predict technical-economic feasibilities and reducing the time and costs associated with experimentation.

Dataset Information

Bistability versus bimodal distributions in gene regulatory processes from population balance.

Publications

Bistability versus bimodal distributions in gene regulatory processes from population balance.

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