A stochastic automaton shows how enzyme assemblies may contribute to metabolic efficiency

<p>Abstract</p> <p>Background</p> <p>The advantages of grouping enzymes into metabolons and into higher order structures have long been debated. To quantify these advantages, we have developed a stochastic automaton that allows experiments to be performed in a virtual bacterium with both a membrane and a cytoplasm. We have investigated the general case of transport and metabolism as inspired by the phosphoenolpyruvate:sugar phosphotransferase system (PTS) for glucose importation and by glycolysis.</p> <p>Results</p> <p>We show that PTS and glycolytic metabolons can increase production of pyruvate eightfold at low concentrations of phosphoenolpyruvate. A fourfold increase in the numbers of enzyme EI led to a 40% increase in pyruvate production, similar to that observed <it>in vivo </it>in the presence of glucose. Although little improvement resulted from the assembly of metabolons into a hyperstructure, such assembly can generate gradients of metabolites and signaling molecules.</p> <p>Conclusion</p> <p><it>in silico </it>experiments may be performed successfully using stochastic automata such as HSIM (Hyperstructure Simulator) to help answer fundamental questions in metabolism about the properties of molecular assemblies and to devise strategies to modify such assemblies for biotechnological ends.</p

Modeling reaction-diffusion of molecules on surface and in volume spaces with the E-Cell System

The-Cell System is an advanced open-source simulation platform to model and analyze biochemical reaction networks. The present algorithm modules of the system assume that the reacting molecules are all homogeneously distributed in the reaction compartments, which is not the case in some cellular processes. The MinCDE system in Escherichia coli, for example, relies on intricately controlled reaction, diffusion and localization of Min proteins on the membrane and in the cytoplasm compartments to inhibit cell division at the poles of the rod-shaped cell. To model such processes, we have extended the E-Cell System to support reaction-diffusion and dynamic localization of molecules in volume and surface compartments. We evaluated our method by modeling the in vivo dynamics of MinD and MinE and comparing their simulated localization patterns to the observations in experiments and previous computational work. In both cases, our simulation results are in good agreement

Detailed simulations of cell biology with Smoldyn 2.1.

Most cellular processes depend on intracellular locations and random collisions of individual protein molecules. To model these processes, we developed algorithms to simulate the diffusion, membrane interactions, and reactions of individual molecules, and implemented these in the Smoldyn program. Compared to the popular MCell and ChemCell simulators, we found that Smoldyn was in many cases more accurate, more computationally efficient, and easier to use. Using Smoldyn, we modeled pheromone response system signaling among yeast cells of opposite mating type. This model showed that secreted Bar1 protease might help a cell identify the fittest mating partner by sharpening the pheromone concentration gradient. This model involved about 200,000 protein molecules, about 7000 cubic microns of volume, and about 75 minutes of simulated time; it took about 10 hours to run. Over the next several years, as faster computers become available, Smoldyn will allow researchers to model and explore systems the size of entire bacterial and smaller eukaryotic cells

METABOLIC ENGINEERING OF THE DEOXYXYLULOSE PHOSPHATE PATHWAY FOR ISOPRENOID PRODUCTION IN E.COLI

Ph.DDOCTOR OF PHILOSOPH

Dynamic Model for Production of Polyhydroxyalkanoates by Thermophilic Bacterium S. thermodepolymerans

Tato diplomová práce se zabývá rekonstrukcí dynamického modelu produkce polyhydroxyalkanoátů (PHA) termofilní bakterií Schlegelella thermodepolymerans. První kapitola poskytuje čtenářům krátký úvod do systémové biologie a matematické teorie grafů. Na ni navazuje druhá kapitola zabývající se různými přístupy v dynamickém modelování, včetně běžně používaných nástrojů pro dynamickou analýzu komplexních systémů. Třetí kapitola pak sleduje další pojmy a možnosti týkající se analýzy modelu. Následující kapitola se zaměřuje na metabolomiku a často používané laboratorní techniky a pátá kapitola je pak věnována polyhydroxyalkanoátům, zejména jejich chemické struktuře a vlastnostem. V kapitole šesté je navržen obecný booleovský model pro produkci PHA termofilními bakteriemi. Kapitola sedmá se poté zaměřuje na zdokonalení modelu se zaměřením na S. thermodepolymerans. Výsledný dynamický model je podroben analýze a výsledky jsou diskutovány.This master's thesis deals with the reconstruction of a dynamic model for production of polyhydroxyalkanoates (PHA) by thermophilic bacterium Schlegelella thermodepolymerans. The first chapter provides readers with a brief introduction into the systems biology and mathematical graph theory. It is followed by Chapter Two dealing with different approaches in dynamic modelling, including the commonly used tools for dynamic analysis of complex systems. The third chapter then pursues further terms and possibilities regarding the model analysis. The following chapter focuses on metabolomics and the frequently used laboratory techniques and the fifth chapter is then occupied with polyhydroxyalkanoates, especially their chemical structure and properties. In Chapter Six, a general Boolean model for PHA production by thermophilic bacteria is proposed. Chapter Seven then aims at model refinement with focus on S. thermodepolymerans. The final dynamic model is analysed and the results are discussed.

Structural modelling and robustness analysis of complex metabolic networks and signal transduction cascades

The dissertation covers the topic of structural robustness of metabolic networks on the basis of the concept of elementary flux modes (EFMs). It is shown that the number of EFMs does not reflect the topology of a network sufficiently. Thus, new methods are developed to determine the structural robustness of metabolic networks. These methods are based on systematic in-silico knockouts and the subsequent calculation of dropped out EFMs. Thereby, together with single knockouts also double and multiple knockouts can be used. After evaluation of these methods they are applied to metabolic networks of human erythrocyte and hepatocyte as well as to a metabolic network of Escherichia coli (E. coli). It is found that the erythrocyte has the lowest structural robustness, followed by the hepatocyte and E. coli. These results coincide very well with the circumstance that human erythrocyte and hepatocyte and E. coli are able to adapt to conditions with increasing diversity. In a further part of the dissertation the concept of EFMs is expanded to signal transduction pathways consisting of kinase cascades. The concept of EFMs is based on the steady-state condition for metabolic pathways. It is shown that under certain circumstances this steady-state condition also holds for signalling cascades. Furthermore, it is shown that it is possible to deduce minimal conditions for signal transduction without knowledge about the kinetics involved. On the basis of these assumptions it is possible to calculate EFMs for signalling cascades. But due to the fact that these EFMs do no longer just have mass flux but also information flux, they are now called elementary signalling modes (ESMs).Die Dissertation behandelt die strukturelle Robustheit von metabolischen Netzwerken auf der Basis des Konzepts der elementaren Flussmoden (EFMen). Es wird gezeigt, dass die Anzahl der EFMen die Topologie eines metabolischen Netzes nicht ausreichend widerspiegelt. Darauf aufbauend werden neue Methoden entwickelt, um die strukturelle Robustheit metabolischer Netze zu bestimmen. Diese Methoden beruhen auf systematischen in-silico-Knockouts und der anschließenden Bestimmung des Anteils an weggefallenen EFMen. Dabei können neben Einfach-Knockouts auch Doppel- oder Mehrfach-Knockouts verwendet werden. Nach der Evaluierung werden diese Methoden auf metabolische Netzwerke des menschlichen Erythrozyten und Hepatozyten, sowie des Bakteriums Escherichia coli (E. coli) angewendet. Es zeigt sich, dass der Erythrozyt die im Vergleich geringste strukturelle Robustheit besitzt, gefolgt vom Hepatozyten und E. coli. Diese Ergebnisse stimmen sehr gut mit der Beobachtung überein, dass sich die menschlichen Erythrozyten und Hepatozyten, sowie E. coli an zunehmend verschiedene Bedingungen anpassen können. In einem weiteren Teil der Dissertation wird das Konzept der EFMen auf Signaltransduktionswege bestehend aus Kinase-Kaskaden erweitert. Das Konzept der EFMen beruht auf der Annahme eines quasi-stationären Zustands für metabolische Netzwerke. Es wird gezeigt, dass dieser quasi-stationäre Zustand unter bestimmten Bedingungen auch in Signal-Kaskaden angenommen werden kann. Weiterhin wird gezeigt, dass man ohne Kenntnis der beteiligten Kinetiken Minimalbedingungen für die Signalweiterleitung ableiten kann. Auf Basis dieser Annahmen lassen sich für Signal-Kaskaden EFMen berechnen. Aber aufgrund der Tatsache, dass sie nicht mehr nur Masse-, sondern auch Informationsfluss beschreiben, werden sie nun als elementare Signalmoden (ESMen) bezeichnet

A new multicompartmental reaction-diffusion modeling method links transient membrane attachment of E. coli MinE to E-ring formation

Many important cellular processes are regulated by reaction-diffusion (RD) of molecules that takes place both in the cytoplasm and on the membrane. To model and analyze such multicompartmental processes, we developed a lattice-based Monte Carlo method, Spatiocyte that supports RD in volume and surface compartments at single molecule resolution. Stochasticity in RD and the excluded volume effect brought by intracellular molecular crowding, both of which can significantly affect RD and thus, cellular processes, are also supported. We verified the method by comparing simulation results of diffusion, irreversible and reversible reactions with the predicted analytical and best available numerical solutions. Moreover, to directly compare the localization patterns of molecules in fluorescence microscopy images with simulation, we devised a visualization method that mimics the microphotography process by showing the trajectory of simulated molecules averaged according to the camera exposure time. In the rod-shaped bacterium _Escherichia coli_, the division site is suppressed at the cell poles by periodic pole-to-pole oscillations of the Min proteins (MinC, MinD and MinE) arising from carefully orchestrated RD in both cytoplasm and membrane compartments. Using Spatiocyte we could model and reproduce the _in vivo_ MinDE localization dynamics by accounting for the established properties of MinE. Our results suggest that the MinE ring, which is essential in preventing polar septation, is largely composed of MinE that is transiently attached to the membrane independently after recruited by MinD. Overall, Spatiocyte allows simulation and visualization of complex spatial and reaction-diffusion mediated cellular processes in volumes and surfaces. As we showed, it can potentially provide mechanistic insights otherwise difficult to obtain experimentally

Accurate implementation of leaping in space: The spatial partitioned-leaping algorithm

There is a great need for accurate and efficient computational approaches that can account for both the discrete and stochastic nature of chemical interactions as well as spatial inhomogeneities and diffusion. This is particularly true in biology and nanoscale materials science, where the common assumptions of deterministic dynamics and well-mixed reaction volumes often break down. In this article, we present a spatial version of the partitioned-leaping algorithm (PLA), a multiscale accelerated-stochastic simulation approach built upon the tau-leaping framework of Gillespie. We pay special attention to the details of the implementation, particularly as it pertains to the time step calculation procedure. We point out conceptual errors that have been made in this regard in prior implementations of spatial tau-leaping and illustrate the manifestation of these errors through practical examples. Finally, we discuss the fundamental difficulties associated with incorporating efficient exact-stochastic techniques, such as the next-subvolume method, into a spatial-leaping framework and suggest possible solutions.Comment: 15 pages, 9 figures, 2 table

Simulation of reaction diffusion processes over biologically relevant size and time scales using multi-GPU workstations

AbstractSimulation of in vivo cellular processes with the reaction–diffusion master equation (RDME) is a computationally expensive task. Our previous software enabled simulation of inhomogeneous biochemical systems for small bacteria over long time scales using the MPD-RDME method on a single GPU. Simulations of larger eukaryotic systems exceed the on-board memory capacity of individual GPUs, and long time simulations of modest-sized cells such as yeast are impractical on a single GPU. We present a new multi-GPU parallel implementation of the MPD-RDME method based on a spatial decomposition approach that supports dynamic load balancing for workstations containing GPUs of varying performance and memory capacity. We take advantage of high-performance features of CUDA for peer-to-peer GPU memory transfers and evaluate the performance of our algorithms on state-of-the-art GPU devices. We present parallel efficiency and performance results for simulations using multiple GPUs as system size, particle counts, and number of reactions grow. We also demonstrate multi-GPU performance in simulations of the Min protein system in E. coli. Moreover, our multi-GPU decomposition and load balancing approach can be generalized to other lattice-based problems