Finding the optimum activation energy in DNA breathing dynamics: a simulated annealing approach
TL;DR: In this article, the authors demonstrate how the stochastic global optimization scheme of simulated annealing can be used to evaluate optimum parameters in the problem of DNA breathing dynamics and demonstrate that the method overcomes even large noise in the input surrogate data.
Abstract: We demonstrate how the stochastic global optimization scheme of simulated annealing can be used to evaluate optimum parameters in the problem of DNA breathing dynamics. The breathing dynamics is followed in accordance with the stochastic Gillespie scheme, the denaturation bubbles in double-stranded DNA being studied as a single molecule time series. Simulated annealing is used to find the optimum value of the activation energy for which the equilibrium bubble size distribution matches with a given value. It is demonstrated that the method overcomes even large noise in the input surrogate data.
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TL;DR: In this paper, the authors review how different physical mechanisms are either used by Nature or utilized in biotechnological processes to separate the two intertwined DNA strands, by insisting on quantitative results.
57 citations
TL;DR: In this paper, the authors discuss the dynamics at the base-pair scale and its pivotal coupling with the polymer one, with a polymerization index running from a few nucleotides to tens of kilo-bases.
Abstract: As a key molecule of Life, Deoxyribonucleic acid (DNA) is the focus of numbers of investigations with the help of biological, chemical and physical techniques. From a physical point of view, both experimental and theoretical works have brought quantitative insights into DNA base-pairing dynamics that we review in this Report, putting emphasis on theoretical developments. We discuss the dynamics at the base-pair scale and its pivotal coupling with the polymer one, with a polymerization index running from a few nucleotides to tens of kilo-bases. This includes opening and closure of short hairpins and oligomers as well as zipping and unwinding of long macromolecules. We review how different physical mechanisms are either used by Nature or utilized in biotechnological processes to separate the two intertwined DNA strands, by insisting on quantitative results. They go from thermally-assisted denaturation bubble nucleation to force- or torque- driven mechanisms. We show that the helical character of the molecule, possibly supercoiled, can play a key role in many denaturation and renaturation processes. We categorize the mechanisms according to the relative timescales associated with base-pairing and chain degrees of freedom such as bending and torsional elastic ones. In some specific situations, these chain degrees of freedom can be integrated out, and the quasi- static approximation is valid. The complex dynamics then reduces to the diffusion in a low-dimensional free-energy landscape. In contrast, some important cases of experimental interest necessarily appeal to far-from-equilibrium statistical mechanics and hydrodynamics.
37 citations
TL;DR: In this article, the thermodynamic stability parameters (nearest neighbor stacking and hydrogen bonding free energies) of double-stranded DNA molecules can be inferred reliably from time series of the size fluctuations (breathing) of local denaturation zones (bubbles).
Abstract: We suggest that the thermodynamic stability parameters (nearest neighbor stacking and hydrogen bonding free energies) of double-stranded DNA molecules can be inferred reliably from time series of the size fluctuations (breathing) of local denaturation zones (bubbles). On the basis of the reconstructed bubble size distribution, this is achieved through stochastic optimization of the free energies in terms of simulated annealing. In particular, it is shown that even noisy time series allow the identification of the stability parameters at remarkable accuracy. This method will be useful to obtain the DNA stacking and hydrogen bonding free energies from single bubble breathing assays rather than equilibrium data.
28 citations
TL;DR: It is shown that even noisy time series allow the identification of the stability parameters at remarkable accuracy, and this method will be useful to obtain the DNA stacking and hydrogen bonding free energies from single bubble breathing assays rather than equilibrium data.
Abstract: We suggest that the thermodynamic stability parameters (nearest neighbor stacking and hydrogen bonding free energies) of double-stranded DNA molecules can be inferred reliably from time series of the size fluctuations (breathing) of local denaturation zones (bubbles). On the basis of the reconstructed bubble size distribution, this is achieved through stochastic optimization of the free energies in terms of Simulated Annealing. In particular, it is shown that even noisy time series allow the identification of the stability parameters at remarkable accuracy. This method will be useful to obtain the DNA stacking and hydrogen bonding free energies from single bubble breathing assays rather than equilibrium data.
23 citations
TL;DR: In this paper, a polychromatic field with a very low field strength and low frequency ( ∼ 10 - 5 atomic unit) can bring about coherent destruction of tunneling (CDT) in a symmetric double well system.
16 citations
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TL;DR: There is a deep and useful connection between statistical mechanics and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters), and a detailed analogy with annealing in solids provides a framework for optimization of very large and complex systems.
Abstract: There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and provides an unfamiliar perspective on traditional optimization problems and methods.
41,772 citations
TL;DR: In this article, a modified Monte Carlo integration over configuration space is used to investigate the properties of a two-dimensional rigid-sphere system with a set of interacting individual molecules, and the results are compared to free volume equations of state and a four-term virial coefficient expansion.
Abstract: A general method, suitable for fast computing machines, for investigating such properties as equations of state for substances consisting of interacting individual molecules is described. The method consists of a modified Monte Carlo integration over configuration space. Results for the two‐dimensional rigid‐sphere system have been obtained on the Los Alamos MANIAC and are presented here. These results are compared to the free volume equation of state and to a four‐term virial coefficient expansion.
35,161 citations
TL;DR: In this article, a simulation algorithm for the stochastic formulation of chemical kinetics is proposed, which uses a rigorously derived Monte Carlo procedure to numerically simulate the time evolution of a given chemical system.
Abstract: There are two formalisms for mathematically describing the time behavior of a spatially homogeneous chemical system: The deterministic approach regards the time evolution as a continuous, wholly predictable process which is governed by a set of coupled, ordinary differential equations (the “reaction-rate equations”); the stochastic approach regards the time evolution as a kind of random-walk process which is governed by a single differential-difference equation (the “master equation”). Fairly simple kinetic theory arguments show that the stochastic formulation of chemical kinetics has a firmer physical basis than the deterministic formulation, but unfortunately the stochastic master equation is often mathematically intractable. There is, however, a way to make exact numerical calculations within the framework of the stochastic formulation without having to deal with the master equation directly. It is a relatively simple digital computer algorithm which uses a rigorously derived Monte Carlo procedure to numerically simulate the time evolution of the given chemical system. Like the master equation, this “stochastic simulation algorithm” correctly accounts for the inherent fluctuations and correlations that are necessarily ignored in the deterministic formulation. In addition, unlike most procedures for numerically solving the deterministic reaction-rate equations, this algorithm never approximates infinitesimal time increments df by finite time steps At. The feasibility and utility of the simulation algorithm are demonstrated by applying it to several well-known model chemical systems, including the Lotka model, the Brusselator, and the Oregonator.
10,275 citations
TL;DR: In this article, a unified scheme combining molecular dynamics and density-functional theory is presented, which makes possible the simulation of both covalently bonded and metallic systems and permits the application of density functional theory to much larger systems than previously feasible.
Abstract: We present a unified scheme that, by combining molecular dynamics and density-functional theory, profoundly extends the range of both concepts. Our approach extends molecular dynamics beyond the usual pair-potential approximation, thereby making possible the simulation of both covalently bonded and metallic systems. In addition it permits the application of density-functional theory to much larger systems than previously feasible. The new technique is demonstrated by the calculation of some static and dynamic properties of crystalline silicon within a self-consistent pseudopotential framework.
8,852 citations
TL;DR: In this paper, an exact method is presented for numerically calculating, within the framework of the stochastic formulation of chemical kinetics, the time evolution of any spatially homogeneous mixture of molecular species which interreact through a specified set of coupled chemical reaction channels.
5,875 citations