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A Simple SelfMaintaining Metabolic System:
, 2010
"... A living organism must not only organize itself from within; it must also maintain its organization in the face of changes in its environment and degradation of its components. We show here that a simple (M,R)system consisting of three interlocking catalytic cycles, with every catalyst produced by ..."
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A living organism must not only organize itself from within; it must also maintain its organization in the face of changes in its environment and degradation of its components. We show here that a simple (M,R)system consisting of three interlocking catalytic cycles, with every catalyst produced by the system itself, can both establish a nontrivial steady state and maintain this despite continuous loss of the catalysts by irreversible degradation. As long as at least one catalyst is present at a sufficient concentration in the initial state, the others can be produced and maintained. The system shows bistability, because if the amount of catalyst in the initial state is insufficient to reach the nontrivial steady state the system collapses to a trivial steady state in which all fluxes are zero. It is also robust, because if one catalyst is catastrophically lost when the system is in steady state it can recreate the same state. There are three elementary flux modes, but none of them
cuTauLeaping: A GPUpowered tauleaping stochastic simulator for massive parallel analyses of biological systems. PLoS One 2014
"... Tauleaping is a stochastic simulation algorithm that efficiently reconstructs the temporal evolution of biological systems, modeled according to the stochastic formulation of chemical kinetics. The analysis of dynamical properties of these systems in physiological and perturbed conditions usually r ..."
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Tauleaping is a stochastic simulation algorithm that efficiently reconstructs the temporal evolution of biological systems, modeled according to the stochastic formulation of chemical kinetics. The analysis of dynamical properties of these systems in physiological and perturbed conditions usually requires the execution of a large number of simulations, leading to high computational costs. Since each simulation can be executed independently from the others, a massive parallelization of tauleaping can bring to relevant reductions of the overall running time. The emerging field of General Purpose Graphic Processing Units (GPGPU) provides powerefficient highperformance computing at a relatively low cost. In this work we introduce cuTauLeaping, a stochastic simulator of biological systems that makes use of GPGPU computing to execute multiple parallel tauleaping simulations, by fully exploiting the Nvidia’s Fermi GPU architecture. We show how a considerable computational speedup is achieved on GPU by partitioning the execution of tauleaping into multiple separated phases, and we describe how to avoid some implementation pitfalls related to the scarcity of memory resources on the GPU streaming multiprocessors. Our results show that cuTauLeaping largely outperforms the CPUbased tauleaping implementation when the number of parallel simulations increases, with a breakeven directly depending on the size of the biological system and on the complexity of its emergent dynamics. In particular, cuTauLeaping is exploited to investigate the probability distribution of bistable states in the Schlögl model, and to carry out a bidimensional parameter sweep
Stochasticity, Bistability and the Wisdom of Crowds: A Model for Associative Learning in Genetic Regulatory Networks
"... It is generally believed that associative memory in the brain depends on multistable synaptic dynamics, which enable the synapses to maintain their value for extended periods of time. However, multistable dynamics are not restricted to synapses. In particular, the dynamics of some genetic regulatory ..."
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It is generally believed that associative memory in the brain depends on multistable synaptic dynamics, which enable the synapses to maintain their value for extended periods of time. However, multistable dynamics are not restricted to synapses. In particular, the dynamics of some genetic regulatory networks are multistable, raising the possibility that even single cells, in the absence of a nervous system, are capable of learning associations. Here we study a standard genetic regulatory network model with bistable elements and stochastic dynamics. We demonstrate that such a genetic regulatory network model is capable of learning multiple, general, overlapping associations. The capacity of the network, defined as the number of associations that can be simultaneously stored and retrieved, is proportional to the square root of the number of bistable elements in the genetic regulatory network. Moreover, we compute the capacity of a clonal population of cells, such as in a colony of bacteria or a tissue, to store associations. We show that even if the cells do not interact, the capacity of the population to store associations substantially exceeds that of a single cell and is proportional to the number of bistable elements. Thus, we show that even single cells are endowed with the computational power to learn associations,
Systems Biology and the Integration of Mechanistic Explanation and Mathematical Explanation
"... The paper discusses how systems biology is working toward complex accounts that integrate explanation in terms of mechanisms and explanation by mathematical models—which some philosophers have viewed as rival models of explanation. Systems biology is an integrative approach, and it strongly relies o ..."
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The paper discusses how systems biology is working toward complex accounts that integrate explanation in terms of mechanisms and explanation by mathematical models—which some philosophers have viewed as rival models of explanation. Systems biology is an integrative approach, and it strongly relies on mathematical modeling. Philosophical accounts of mechanisms capture integrative in the sense of multilevel and multifield explanations, yet accounts of mechanistic explanation (as the analysis of a whole in terms of its structural parts and their qualitative interactions) have failed to address how a mathematical model could contribute to such explanations. I discuss how mathematical equations can be explanatorily relevant. Several cases from systems biology are discussed to illustrate the interplay between mechanistic research and mathematical modeling, and I point to questions about qualitative phenomena (rather than the explanation of quantitative details), where quantitative models are still indispensable to the explanation. Systems biology shows that a broader philosophical conception of mechanisms is needed, which takes into account functionaldynamical aspects, interaction in complex networks with feedback loops, systemwide functional properties such as distributed functionality and robustness, and a mechanism’s ability to respond to perturbations (beyond its actual operation). I offer general conclusions for philosophical accounts of explanation.
Presented by B. Gaveau
, 2003
"... We give a new and direct proof of the nonexistence of limit cycle in a bimolecular system and the characterization of the unique bimolecular oscillator. The proof is an application of classification theorems on vector fields with homogeneous second degree polynomial perturbations. © 2003 Éditions sc ..."
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We give a new and direct proof of the nonexistence of limit cycle in a bimolecular system and the characterization of the unique bimolecular oscillator. The proof is an application of classification theorems on vector fields with homogeneous second degree polynomial perturbations. © 2003 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Résumé On donne une nouvelle démonstration de la non existence de cycle limite dans un système bimoleculaire et la caractérisation de l’unique oscillateur bimoléculaire. La preuve est une application directe des théorèmes de classification des champs de vecteurs polynomiaux avec une perturbation homogène quadratique. © 2003 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. MSC: 34C07; 37G15; 80A30
Chemical Reaction Systems with a Homoclinic Bifurcation: an Inverse Problem
"... Abstract: An inverse problem framework for constructing reaction systems with prescribed properties is presented. Kinetic transformations are defined and analysed as a part of the framework, allowing an arbitrary polynomial ordinary differential equation to be mapped to the one that can be represen ..."
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Abstract: An inverse problem framework for constructing reaction systems with prescribed properties is presented. Kinetic transformations are defined and analysed as a part of the framework, allowing an arbitrary polynomial ordinary differential equation to be mapped to the one that can be represented as a reaction network. The framework is used for construction of specific two and threedimensional bistable reaction systems undergoing a supercritical homoclinic bifurcation, and the topology of their phase spaces is discussed. 1
1Shaping Pulses to Control Bistable Biological Systems.
"... Abstract—In this paper we study how to shape temporal pulses to switch a bistable system between its stable steady states. Our motivation for pulsebased control comes from applications in synthetic biology, where it is generally difficult to implement realtime feedback control systems due to techn ..."
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Abstract—In this paper we study how to shape temporal pulses to switch a bistable system between its stable steady states. Our motivation for pulsebased control comes from applications in synthetic biology, where it is generally difficult to implement realtime feedback control systems due to technical limitations in sensors and actuators. We show that for monotone bistable systems, the estimation of the set of all pulses that switch the system reduces to the computation of one nonincreasing curve. We provide an efficient algorithm to compute this curve and illustrate the results with a genetic bistable system commonly used in synthetic biology. We also extend these results to models with parametric uncertainty and provide a number of examples and counterexamples that demonstrate the power and limitations of the current theory. In order to show the full potential of the framework, we consider the problem of inducing oscillations in a monotone biochemical system using a combination of temporal pulses and eventbased control. Our results provide an insight into the dynamics of bistable systems under external inputs and open up numerous directions for future investigation. I.
DOI 10.1007/s1091001199469 Global dynamics of the smallest chemical reaction system with Hopf bifurcation
"... Your article is protected by copyright and all rights are held exclusively by Springer Science+Business Media, LLC. This eoffprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to selfarchive your work, please use the accepted author’s version for ..."
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Your article is protected by copyright and all rights are held exclusively by Springer Science+Business Media, LLC. This eoffprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to selfarchive your work, please use the accepted author’s version for posting to your own website or your institution’s repository. You may further deposit the accepted author’s version on a funder’s repository at a funder’s request, provided it is not made publicly available until 12 months after publication.