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Register a new userStochastic dynamics of model proteins on a directed graph
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A method for reconstructing the energy landscape of simple polypeptidic chains is described. We show that we can construct an equivalent representation of the energy landscape by a suitable directed graph. Its topological and dynamical features are shown to yield an effective estimate of the time scales associated with the folding and with the equilibration processes. This conclusion is drawn by comparing molecular dynamics simulations at constant temperature with the dynamics on the graph, defined by a temperature dependent Markov process. The main advantage of the graph representation is that its dynamics can be naturally renormalized by collecting nodes into hubs, while redefining their connectivity. We show that both topological and dynamical properties are preserved by the renormalization procedure. Moreover, we obtain clear indications that the heteropolymers exhibit common topological properties, at variance with the homopolymer, whose peculiar graph structure stems from its spatial homogeneity. In order to obtain a clear distinction between a fast folder and a slow folder in the heteropolymers one has to look at kinetic features of the directed graph. We find that the average time needed to the fast folder for reaching its native configuration is two orders of magnitude smaller than its equilibration time, while for the bad folder these time scales are comparable. Accordingly, we can conclude that the strategy described in this paper can be successfully applied also to more realistic models, by studying their renormalized dynamics on the directed graph, rather than performing lengthy molecular dynamics simulations.
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Assemblies of allosteric proteins, nano-scale Brownian computers, are the principle information processing devices in biology. The troponin C-troponin I (TnC-TnI) complex, the Ca$^{2+}$-sensitive regulatory switch of the heart, is a paradigm for Brownian computation. TnC and TnI specialize in sensing (reading) and reporting (writing) tasks of computation. We have examined this complex using a newly developed phenomenological model of allostery. Nearest-neighbor-limited interactions among members of the assembly place previously unrecognized constrains the topology of the systems free energy landscape and generate degenerate transition probabilities. As a result, signaling fidelity and deactivation kinetics can not be simultaneously optimized. This trade-off places an upper limit on the rate of information processing by assemblies of allosteric proteins that couple to a single ligand chemical bath.
Directed paths have been used extensively in the scientific literature as a model of a linear polymer. Such paths models in particular the conformational entropy of a linear polymer and the effects it has on the free energy. These directed models are simplifi
We study the problem of identifying macroscopic structures in networks, characterizing the impact of introducing link directions on the detectability phase transition. To this end, building on the stochastic block model, we construct a class of hardly detectable directed networks. We find closed form solutions by using belief propagation method showing how the transition line depends on the assortativity and the asymmetry of the network. Finally, we numerically identify the existence of a hard phase for detection close to the transition point.
We present a model for semiflexible polymers in Hamiltonian formulation which interpolates between a Rouse chain and worm-like chain. Both models are realized as limits for the parameters. The model parameters can also be chosen to match the experimental force-extension curve for double-stranded DNA. Near the ground state of the Hamiltonian, the eigenvalues for the longitudinal (stretching) and the transversal (bending) modes of a chain with N springs, indexed by p, scale as lambda_lp ~ (p/N)^2 and lambda_tp ~ p^2(p-1)^2/N^4 respectively for small p. We also show that the associated decay times tau_p ~ (N/p)^4 will not be observed if they exceed the orientational time scale tau_r ~ N^3 for an equally-long rigid rod, as the driven decay is then washed out by diffusive motion.
We study the dynamical properties of semiflexible polymers with a recently introduced bead-spring model. We focus on double-stranded DNA. The two parameters of the model, $T^*$ and $ u$, are chosen to match its experimental force-extension curve. The bead-spring Hamiltonian is approximated in the first order by the Hessian that is quadratic in the bead positions. The eigenmodels of the Hessian provide the longitudinal (stretching) and transverse (bending) eigenmodes of the polymer, and the corresponding eigenvalues match well with the established phenomenology of semiflexible polymers. Using the longitudinal and transverse eigenmodes, we obtain analytical expressions of (i) the autocorrelation function of the end-to-end vector, (ii) the autocorrelation function of a bond (i.e., a spring, or a tangent) vector at the middle of the chain, and (iii) the mean-square displacement of a tagged bead in the middle of the chain, as sum over the contributions from the modes. We also perform simulations with the full dynamics of the model. The simulations yield numerical values of the correlation functions (i-iii) that agree very well with the analytical expressions for the linearized dynamics. We also study the mean-square displacement of the longitudinal component of the end-to-end vector that showcases strong nonlinear effects in the polymer dynamics, and we identify at least an effective $t^{7/8}$ power-law regime in its time-dependence. Nevertheless, in comparison to the full mean-square displacement of the end-to-end vector the nonlinear effects remain small at all times --- it is in this sense we state that our results demonstrate that the linearized dynamics suffices for dsDNA fragments that are shorter than or comparable to the persistence length. Our results are consistent with those of the wormlike chain (WLC) model, the commonly used descriptive tool of semiflexible polymers.
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