A systems-biology approach to molecular machines: Exploration of alternative transporter mechanisms

Motivated by growing evidence for pathway heterogeneity and alternative functions of molecular machines, we demonstrate a computational approach for investigating two questions: (1) Are there multiple mechanisms (state-space pathways) by which a machine can perform a given function, such as cotransport across a membrane? (2) How can additional functionality, such as proofreading/error-correction, be built into machine function using standard biochemical processes? Answers to these questions will aid both the understanding of molecular-scale cell biology and the design of synthetic machines. Focusing on transport in this initial study, we sample a variety of mechanisms by employing Metropolis Markov chain Monte Carlo. Trial moves adjust transition rates among an automatically generated set of conformational and binding states while maintaining fidelity to thermodynamic principles and a user-supplied fitness/functionality goal. Each accepted move generates a new model. The simulations yield both single and mixed reaction pathways for cotransport in a simple environment with a single substrate along with a driving ion. In a “competitive” environment including an additional decoy substrate, several qualitatively distinct reaction pathways are found which are capable of extremely high discrimination coupled to a leak of the driving ion, akin to proofreading. The array of functional models would be difficult to find by intuition alone in the complex state-spaces of interest. SIGNIFICANCE Molecular machines, which operate on the nanoscale, are proteins/complexes that perform remarkable tasks such as the selective absorption of nutrients into the cell by transporters. These complex machines are often described using a fairly simple set of states and transitions that may not account for the stochasticity and heterogeneity generally expected at the nanoscale at body temperature. New tools are needed to study the full array of possibilities. This study presents a novel in silico method to systematically generate testable molecular-machine kinetic models and explore alternative mechanisms, applied first to transporters. Our approach should aid the experimental study of physiological processes such as renal glucose re-absorption, and potentially the development of synthetic machines.

[1]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[2]  D. Loo,et al.  Stochastic steps in secondary active sugar transport , 2016, Proceedings of the National Academy of Sciences.

[3]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[4]  Elijah Roberts,et al.  Approximation and inference methods for stochastic biochemical kinetics—a tutorial review , 2017 .

[5]  Anatoly B Kolomeisky,et al.  Trade-Offs between Error, Speed, Noise, and Energy Dissipation in Biological Processes with Proofreading. , 2019, The journal of physical chemistry. B.

[6]  Wandi Zhu,et al.  Mechanisms and models of cardiac sodium channel inactivation , 2017, Channels.

[7]  J. Lolkema,et al.  The 2-Hydroxycarboxylate Transporter Family: Physiology, Structure, and Mechanism , 2005, Microbiology and Molecular Biology Reviews.

[8]  James R. Faeder,et al.  Energy-based modeling in BioNetGen , 2016, 2016 IEEE International Conference on Bioinformatics and Biomedicine (BIBM).

[9]  D. Loo,et al.  Novel and Unexpected Functions of SGLTs. , 2017, Physiology.

[10]  Jonathan R. Silva,et al.  A computationally efficient algorithm for fitting ion channel parameters , 2016, MethodsX.

[11]  Anatoly B Kolomeisky,et al.  Elucidating interplay of speed and accuracy in biological error correction , 2017, Proceedings of the National Academy of Sciences.

[12]  Vahid Shahrezaei,et al.  Scalable Rule-Based Modelling of Allosteric Proteins and Biochemical Networks , 2010, PLoS Comput. Biol..

[13]  Bert Poolman,et al.  Coupling efficiency of secondary active transporters. , 2019, Current opinion in biotechnology.

[14]  M. G. Madej,et al.  A Loose Relationship: Incomplete H+/Sugar Coupling in the MFS Sugar Transporter GlcP , 2017, Biophysical journal.

[15]  J. Ninio Kinetic amplification of enzyme discrimination. , 1975, Biochimie.

[16]  M. Jacobson,et al.  Inhibitor binding mode and allosteric regulation of Na+-glucose symporters , 2018, Nature Communications.

[17]  J. Davies,et al.  Molecular Biology of the Cell , 1983, Bristol Medico-Chirurgical Journal.

[18]  Rob Phillips,et al.  Combinatorial Control through Allostery , 2018, bioRxiv.

[19]  H. Sauro,et al.  Preliminary Studies on the In Silico Evolution of Biochemical Networks , 2004, Chembiochem : a European journal of chemical biology.

[20]  Oleg Demin,et al.  Analysis of the efficacy of SGLT2 inhibitors using semi-mechanistic model , 2014, Front. Pharmacol..

[21]  PETER MITCHELL,et al.  A General Theory of Membrane Transport From Studies of Bacteria , 1957, Nature.

[22]  W. Austin Elam,et al.  Physical Biology of the Cell , 2014, The Yale Journal of Biology and Medicine.

[23]  R. Fenton,et al.  Sodium-glucose cotransport , 2015, Current opinion in nephrology and hypertension.

[24]  T. L. Hill,et al.  Free Energy Transduction and Biochemical Cycle Kinetics , 1988, Springer New York.

[25]  T. L. Hill,et al.  Free Energy Transduction in Biology: The Steady-State Kinetic and Thermodynamic Formalism , 1977 .

[26]  K. Henzler-Wildman,et al.  New free-exchange model of EmrE transport , 2017, Proceedings of the National Academy of Sciences.

[27]  J. Hopfield Kinetic proofreading: a new mechanism for reducing errors in biosynthetic processes requiring high specificity. , 1974, Proceedings of the National Academy of Sciences of the United States of America.

[28]  Carsten Kettner,et al.  Electrophysiological analysis of the yeast V-type proton pump: variable coupling ratio and proton shunt. , 2003, Biophysical journal.

[29]  Harel Weinstein,et al.  The mechanism of a neurotransmitter:sodium symporter--inward release of Na+ and substrate is triggered by substrate in a second binding site. , 2008, Molecular cell.

[30]  Lior Rokach,et al.  Clustering Methods , 2005, The Data Mining and Knowledge Discovery Handbook.

[31]  Hanspeter Herzel,et al.  Elucidating the adaptation and temporal coordination of metabolic pathways using in-silico evolution , 2014, Biosyst..

[32]  Alon Korngreen,et al.  A Numerical Approach to Ion Channel Modelling Using Whole-Cell Voltage-Clamp Recordings and a Genetic Algorithm , 2007, PLoS Comput. Biol..

[33]  Nieng Yan,et al.  GLUT, SGLT, and SWEET: Structural and mechanistic investigations of the glucose transporters , 2016, Protein science : a publication of the Protein Society.

[34]  John C Mason,et al.  An energetic reformulation of kinetic rate laws enables scalable parameter estimation for biochemical networks. , 2019, Journal of theoretical biology.

[35]  Paola Bisignano,et al.  Structural Insights into Sodium-Dependent Sugar Transporters and their Inhibition Mechanism , 2017 .

[36]  Wendell A Lim,et al.  Design principles of regulatory networks: searching for the molecular algorithms of the cell. , 2013, Molecular cell.

[37]  J. Goutsias,et al.  Markovian dynamics on complex reaction networks , 2012, 1205.5524.

[38]  S. Whitelam,et al.  Avoiding unphysical kinetic traps in Monte Carlo simulations of strongly attractive particles. , 2005, The Journal of chemical physics.

[39]  Stanislas Leibler,et al.  Discriminatory proofreading regimes in non-equilibrium systems , 2013, 1312.2286.

[40]  O. Jardetzky,et al.  Simple Allosteric Model for Membrane Pumps , 1966, Nature.

[41]  Nelson Spruston,et al.  A state-mutating genetic algorithm to design ion-channel models , 2009, Proceedings of the National Academy of Sciences.

[42]  A. Fersht,et al.  Editing mechanisms in protein synthesis. Rejection of valine by the isoleucyl-tRNA synthetase. , 1977, Biochemistry.