Protein Folding Dynamics via Quantification of Kinematic Energy Landscape

Kachalo, Sëma; Lu, Hsiao Mei; Liang, Jie

doi:10.1103/physrevlett.96.058106

Cited by 25 publications

(29 citation statements)

References 15 publications

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“…Models such as lattice self-avoiding walks with only hydrophobic and polar interactions allow the complete enumeration of all feasible conformations and the calculation of exact thermodynamics as well as folding dynamics from the master equation for model molecules. Such studies have played important roles in elucidating the principles of protein folding (31)(32)(33)(34).…”

Section: Discussionmentioning

confidence: 99%

Probability landscape of heritable and robust epigenetic state of lysogeny in phage lambda

Cao

Liang

2010

Proc. Natl. Acad. Sci. U.S.A.

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Computational studies of biological networks can help to identify components and wirings responsible for observed phenotypes. However, studying stochastic networks controlling many biological processes is challenging. Similar to Schrödinger's equation in quantum mechanics, the chemical master equation (CME) provides a basic framework for understanding stochastic networks. However, except for simple problems, the CME cannot be solved analytically. Here we use a method called discrete chemical master equation (dCME) to compute directly the full steady-state probability landscape of the lysogeny maintenance network in phage lambda from its CME. Results show that wild-type phage lambda can maintain a constant level of repressor over a wide range of repressor degradation rate and is stable against UV irradiation, ensuring heritability of the lysogenic state. Furthermore, it can switch efficiently to the lytic state once repressor degradation increases past a high threshold by a small amount. We find that beyond bistability and nonlinear dimerization, cooperativity between repressors bound to O R 1 and O R 2 is required for stable and heritable epigenetic state of lysogeny that can switch efficiently. Mutants of phage lambda lack stability and do not possess a high threshold. Instead, they are leaky and respond to gradual changes in degradation rate. Our computation faithfully reproduces the hair triggers for UVinduced lysis observed in mutants and the limitation in robustness against mutations. The landscape approach computed from dCME is general and can be applied to study broad issues in systems biology.B acteriophage lambda is a virus that infects Escherichia coli cells. It has served as a model system for studying regulatory networks and for engineering gene circuits (1-5). Of central importance is the molecular circuitry that controls phage lambda to choose between two productive modes of development, namely, the lysogenic state and the lytic state (Fig 1A). In the lysogenic state, phage lambda represses its developmental function, integrates its DNA into the chromosome of the host E. coli bacterium, and is replicated in cell cycles for potentially many generations. When threatening DNA damage occurs, phage lambda switches from the epigenetic state of lysogeny to the lytic state and undergoes massive replications in a single cell cycle, releases 50-100 progeny phages upon lysis of the E. coli cell. This switching process is called prophage induction (5).The molecular network that controls the choice between these two different physiological states has been studied extensively during the past 40 y (5-9). All of the major molecular components of the network have been identified, binding constants and reaction rates characterized, and there is a good experimental understanding of the general mechanism of the molecular switch (5). Theoretical studies have also contributed to the illumination of the central role of stochasticity (3) and the stability of lysogen against spontaneous switching (4, 10). With the advent o...

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Section: Discussionmentioning

confidence: 99%

Probability landscape of heritable and robust epigenetic state of lysogeny in phage lambda

Cao

Liang

2010

Proc. Natl. Acad. Sci. U.S.A.

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“…(15) and (16) is that the propensity matrix is typically a very sparse matrix. This sparsity should be exploited to produce computational codes of significantly lower complexity than the implementations which employ dense representations of the (n α × n α ) propensity matrices.…”

Section: B Numerical Implementationmentioning

confidence: 99%

“…Models based on a master equation have been successfully applied to simulate kinetic traps in related fields such as the folding kinetics of macromolecules. [12][13][14][15][16] Monte Carlo based methods are often used to solve instances of models involving master equations, 17,18 which rely on the computation of a large number of solution trajectories to approximate certain statistical properties of the system. Typical advantages of Monte Carlo based methods are: (a) identification of all possible connections between all states is not necessary as connected states can be determined on the fly during the simulation of a solution trajectory, and (b) there is no need to solve simultaneously a large number of stiff ordinary differential equations (ODEs).…”

Section: Introductionmentioning

confidence: 99%

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

Lakerveld

Stephanopoulos

Barton

2012

The Journal of Chemical Physics

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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. The model describes the probability of each possible configuration of a fixed number of nanoparticles on a domain, including parametric sensitivities that can be used for optimization, as a function of time during self-assembly. An algorithm is presented that solves large-scale instances of the model with linear computational complexity. Case studies illustrate the influence of several degrees of freedom on directed self-assembly. A design approach that systematically decomposes the ergodicity of the system to direct self-assembly of a targeted configuration with high probability is illustrated. The prospects for extending such an approach to larger systems using coarse graining techniques are also discussed.

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“…Instead, coarse grained models such as the Gaussian network model and elastic network model treat the molecules as connected graphs with nodes representing amino acid residues and edges representing contacts between residues [1][2][3][4]. By analyzing the dominant eigen modes of jliang@uic.edu molecular motion and the key residue sites, much insight has been gained [1][2][3][4]6].…”

Section: Introductionmentioning

confidence: 99%

Perturbation-based Markovian Transmission Model for Macromolecular Machinery in Cell

Liang

2007

2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society

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The study of the dynamics of a complex system is an important problem that includes large macromolecular complexes, molecular interaction networks, and cell functional modules. Large macromolecular complexes in cellular machinery can be modeled as a connected network, as in the elastic or Gaussian network models as demonstrated by Bahar and colleagues. Here we propose the Perturbation-based Markovian Transmission Model for studying the dynamics of signal transmission in macromolecular machinery. The initial perturbation is transmitted by a Markovian processes, and the dynamics of the probability flow is analytically solved using the master equation. Due to the large size of macromolecular complexes, it is very difficult to obtain analytical time-dependent Markovian dynamics of all atoms from the first perturbation until stationary state. To overcome it, we decrease the level of complexity of the transition matrix using a Krylov subspace method. This method is equivalent to integrating all eigen modes, and we show it can provide a globally accurate solution to the dynamics problem of signal transmission for very large macromolecular complexes with reasonable computational time. We give results of the dynamics of the GroEL-GroES chaperone system by applying uniform perturbation to all residues. We are able to identify experimentally found important residues and provide a set of predicted pivot, messenger, and effector residues, each with distinct dynamic behavior. Further results of selective perturbation on the surface of ATP binding pocket identifies the path of maximal probability flow of signal.

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Protein Folding Dynamics via Quantification of Kinematic Energy Landscape

Cited by 25 publications

References 15 publications

Probability landscape of heritable and robust epigenetic state of lysogeny in phage lambda

Probability landscape of heritable and robust epigenetic state of lysogeny in phage lambda

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

Perturbation-based Markovian Transmission Model for Macromolecular Machinery in Cell

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