Dynamic bounds on stochastic chemical kinetic systems using semidefinite programming.

Applying the method of moments to the chemical master equation appearing in stochastic chemical kinetics often leads to the so-called closure problem. Recently, several authors showed that this problem can be partially overcome using moment-based semidefinite programs (SDPs). In particular, they showed that moment-based SDPs can be used to calculate rigorous bounds on various descriptions of the stochastic chemical kinetic system's stationary distribution(s)-for example, mean molecular counts, variances in these counts, and so on.

Bounds on stochastic chemical kinetic systems at steady state.

The method of moments has been proposed as a potential means to reduce the dimensionality of the chemical master equation (CME) appearing in stochastic chemical kinetics. However, attempts to apply the method of moments to the CME usually result in the so-called closure problem. Several authors have proposed moment closure schemes, which allow them to obtain approximations of quantities of interest, such as the mean molecular count for each species.

Dynamic Flux Balance Analysis Using DFBAlab.

Bioprocesses are of critical importance in several industries such as the food and pharmaceutical industries. Despite their importance and widespread application, bioprocess models remain rather simplistic and based on unstructured models. These simple models have limitations, making it very difficult to model complex bioprocesses.

Dynamic flux balance modeling to increase the production of high-value compounds in green microalgae.

Background: Photosynthetic organisms can be used for renewable and sustainable production of fuels and high-value compounds from natural resources. Costs for design and operation of large-scale algae cultivation systems can be reduced if data from laboratory scale cultivations are combined with detailed mathematical models to evaluate and optimize the process.

Results: In this work we present a flexible modeling formulation for accumulation of high-value storage molecules in microalgae that provides quantitative predictions under various light and nutrient conditions.

Spatiotemporal modeling of microbial metabolism.

Background: Microbial systems in which the extracellular environment varies both spatially and temporally are very common in nature and in engineering applications. While the use of genome-scale metabolic reconstructions for steady-state flux balance analysis (FBA) and extensions for dynamic FBA are common, the development of spatiotemporal metabolic models has received little attention.

Results: We present a general methodology for spatiotemporal metabolic modeling based on combining genome-scale reconstructions with fundamental transport equations that govern the relevant convective and/or diffusional processes in time and spatially varying environments.

Metabolic modeling of synthesis gas fermentation in bubble column reactors.

Background: A promising route to renewable liquid fuels and chemicals is the fermentation of synthesis gas (syngas) streams to synthesize desired products such as ethanol and 2,3-butanediol. While commercial development of syngas fermentation technology is underway, an unmet need is the development of integrated metabolic and transport models for industrially relevant syngas bubble column reactors.

Results: We developed and evaluated a spatiotemporal metabolic model for bubble column reactors with the syngas fermenting bacterium Clostridium ljungdahlii as the microbial catalyst.

DFBAlab: a fast and reliable MATLAB code for dynamic flux balance analysis.

Background: Dynamic Flux Balance Analysis (DFBA) is a dynamic simulation framework for biochemical processes. DFBA can be performed using different approaches such as static optimization (SOA), dynamic optimization (DOA), and direct approaches (DA). Few existing simulators address the theoretical and practical challenges of nonunique exchange fluxes or infeasible linear programs (LPs).

End-to-end continuous manufacturing of pharmaceuticals: integrated synthesis, purification, and final dosage formation.

A series of tubes: The continuous manufacture of a finished drug product starting from chemical intermediates is reported. The continuous pilot-scale plant used a novel route that incorporated many advantages of continuous-flow processes to produce active pharmaceutical ingredients and the drug product in one integrated system.

A master-equation approach to simulate kinetic traps during directed self-assembly.

Robust directed self-assembly of non-periodic nanoscale structures is a key process that would enable various technological breakthroughs. The dynamic evolution of directed self-assemblies towards structures with desired geometries is governed by the rugged potential energy surface of nanoscale systems, potentially leading the system to kinetic traps. To study such phenomena and to set the framework for the directed self-assembly of nanoparticles towards structures with desired geometries, the development of a dynamic model involving a master equation to simulate the directed self-assembly process is presented.

SENSITIVITY ANALYSIS FOR OSCILLATING DYNAMICAL SYSTEMS.

Boundary value formulations are presented for exact and efficient sensitivity analysis, with respect to model parameters and initial conditions, of different classes of oscillating systems. Methods for the computation of sensitivities of derived quantities of oscillations such as period, amplitude and different types of phases are first developed for limit-cycle oscillators. In particular, a novel decomposition of the state sensitivities into three parts is proposed to provide an intuitive classification of the influence of parameter changes on period, amplitude and relative phase.

The Per2 negative feedback loop sets the period in the mammalian circadian clock mechanism.

Processes that repeat in time, such as the cell cycle, the circadian rhythm, and seasonal variations, are prevalent in biology. Mathematical models can represent our knowledge of the underlying mechanisms, and numerical methods can then facilitate analysis, which forms the foundation for a more integrated understanding as well as for design and intervention. Here, the intracellular molecular network responsible for the mammalian circadian clock system was studied.

Biological network design strategies: discovery through dynamic optimization.

An important challenge in systems biology is the inherent complexity of biological network models, which complicates the task of relating network structure to function and of understanding the conceptual design principles by which a given network operates. Here we investigate an approach to analyze the relationship between a network structure and its function using the framework of optimization. A common feature found in a variety of biochemical networks involves the opposition of a pair of enzymatic chemical modification reactions such as phosphorylation-dephosphorylation or methylation-demethylation.

Global dynamic optimization for parameter estimation in chemical kinetics.

We present the first method guaranteed to find the best possible least-squares (chi2) fit of experimental data by a nonlinear kinetic model. Several important advantages of knowing with certainty the best possible fit rather than a locally optimum fit are discussed and demonstrated using data from the recent literature. This is particularly important when the model and the data appear to be inconsistent.