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. Our solution procedure involves spatial discretization of the partial differential equation model followed by numerical integration of the resulting system of ordinary differential equations with embedded linear programs using DFBAlab, a MATLAB code that performs reliable and efficient dynamic FBA simulations. We demonstrate our methodology by solving spatiotemporal metabolic models for two systems of considerable practical interest: (1) a bubble column reactor with the syngas fermenting bacterium Clostridium ljungdahlii; and (2) a chronic wound biofilm with the human pathogen Pseudomonas aeruginosa. Despite the complexity of the discretized models which consist of 900 ODEs/600 LPs and 250 ODEs/250 LPs, respectively, we show that the proposed computational framework allows efficient and robust model solution. Conclusions Our study establishes a new paradigm for formulating and solving genome-scale metabolic models with both time and spatial variations and has wide applicability to natural and engineered microbial systems

Efficient solution of ordinary differential equations with a parametric lexicographic linear program embedded

This work analyzes the initial value problem in ordinary differential equations with a parametric lexicographic linear program (LP) embedded. The LP is said to be embedded since the dynamics depend on the solution of the LP, which is in turn parameterized by the dynamic states. This problem formulation finds application in dynamic flux balance analysis, which serves as a modeling framework for industrial fermentation reactions. It is shown that the problem formulation can be intractable numerically, which arises from the fact that the LP induces an effective domain that may not be open. A numerical method is developed which reformulates the system so that it is defined on an open set. The result is a system of semi-explicit index-one differential algebraic equations, which can be solved with efficient and accurate methods. It is shown that this method addresses many of the issues stemming from the original problem’s intractability. The application of the method to examples of industrial fermentation processes demonstrates its effectiveness and efficiency

From sugars to biodiesel using microalgae and yeast

The economic production of algal biofuels requires novel strategies, such as microbial consortia and synthetic ecologies, to boost the productivity of open pond systems. These strategies have not been fully explored partly due to the lack of reliable and predictive process models. This study uses genome-based metabolic networks to build a process model of a raceway pond. This process model is used as a discovery tool for novel process strategies. First, an algal monoculture with flue gas sparging is modeled. Then, an oleaginous yeast monoculture is modeled. The yeast monoculture is O[subscript 2] limited and the presence of algae in the culture would result in better resource utilization. Next, an algal/fungal raceway pond with a feed of cellulosic glucose is explored. Finally, an oleaginous yeast that can consume a glucose/xylose mix, resulting from the hydrolysis of lignocellulosic waste, is modeled. This model predicts biomass and lipids productivities comparable to those reported in the literature. Assuming 50% yield loss due to contamination and invasion, a simple economic analysis shows that an algae/yeast coculture can produce biodiesel at competitive prices, $2.01 per liter for pure glucose and$1.44 per liter for the sugar mix, whereas the algae monoculture can do so only at very short distances from a flue gas source. This modeling framework will enable the use of optimization algorithms in the design of open pond systems in the near future and will allow the exploration of novel strategies in bioprocesses employing microbial communities

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). Both are common sources of failure and inefficiencies for these simulators. Results: DFBAlab, a MATLAB-based simulator that uses the LP feasibility problem to obtain an extended system and lexicographic optimization to yield unique exchange fluxes, is presented. DFBAlab is able to simulate complex dynamic cultures with multiple species rapidly and reliably, including differential-algebraic equation (DAE) systems. In addition, DFBAlab's running time scales linearly with the number of species models. Three examples are presented where the performance of COBRA, DyMMM and DFBAlab are compared. Conclusions: Lexicographic optimization is used to determine unique exchange fluxes which are necessary for a well-defined dynamic system. DFBAlab does not fail during numerical integration due to infeasible LPs. The extended system obtained through the LP feasibility problem in DFBAlab provides a penalty function that can be used in optimization algorithms