J-factors of short DNA molecules

The propensity of short DNA sequences to convert to the circular form is studied by a mesoscopic Hamiltonian method which incorporates both the bending of the molecule axis and the intrinsic twist of the DNA strands. The base pair fluctuations with respect to the helix diameter are treated as path trajectories in the imaginary time path integral formalism. The partition function for the sub-ensemble of closed molecules is computed by imposing chain ends boundary conditions both on the radial fluctuations and on the angular degrees of freedom. The cyclization probability, the J-factor, proves to be highly sensitive to the stacking potential, mostly to its nonlinear parameters. We find that the J-factor generally decreases by reducing the sequence length ( N ) and, more significantly, below N = 100 base pairs. However, even for very small molecules, the J-factors remain sizeable in line with recent experimental indications. Large bending angles between adjacent base pairs and anharmonic stacking appear as the causes of the helix flexibility at short length scales.Comment: The Journal of Chemical Physics - May 2016 ; 9 page

Differential hydrophobicity drives self-assembly in Huntington's disease

Identifying the driving forces and the mechanism of association of huntingtin-exon1, a close marker for the progress of Huntington's disease, is an important prerequisite towards finding potential drug targets, and ultimately a cure. We introduce here a modelling framework based on a key analogy of the physico-chemical properties of the exon1 fragment to block copolymers. We use a systematic mesoscale methodology, based on Dissipative Particle Dynamics, which is capable of overcoming kinetic barriers, thus capturing the dynamics of significantly larger systems over longer times than considered before. Our results reveal that the relative hydrophobicity of the poly-glutamine block as compared to the rest of the (proline-based) exon1 fragment, ignored to date, constitutes a major factor in the initiation of the self-assembly process. We find that the assembly is governed by both the concentration of exon1 and the length of the poly-glutamine stretch, with a low length threshold for association even at the lowest volume fractions we considered. Moreover, this self-association occurs irrespective of whether the glutamine stretch is in random coil or hairpin configuration, leading to spherical or cylindrical assemblies, respectively. We discuss the implications of these results for reinterpretation of existing research within this context, including that the routes towards aggregation of exon1 may be distinct to those of the widely studied homopolymeric poly-glutamine peptides

DNA cyclization and looping in the wormlike limit: normal modes and the validity of the harmonic approximation

For much of the last three decades Monte Carlo-simulation methods have been the standard approach for accurately calculating the cyclization probability, $J$, or J factor, for DNA models having sequence-dependent bends or inhomogeneous bending flexibility. Within the last ten years, however, approaches based on harmonic analysis of semi-flexible polymer models have been introduced, which offer much greater computational efficiency than Monte Carlo techniques. These methods consider the ensemble of molecular conformations in terms of harmonic fluctuations about a well-defined elastic-energy minimum. However, the harmonic approximation is only applicable for small systems, because the accessible conformation space of larger systems is increasingly dominated by anharmonic contributions. In the case of computed values of the J factor, deviations of the harmonic approximation from the exact value of $J$ as a function of DNA length have not been characterized. Using a recent, numerically exact method that accounts for both anharmonic and harmonic contributions to $J$ for wormlike chains of arbitrary size, we report here the apparent error that results from neglecting anharmonic behavior. For wormlike chains having contour lengths less than four times the persistence length the error in $J$ arising from the harmonic approximation is generally small, amounting to free energies less than the thermal energy, $k_B T$. For larger systems, however, the deviations between harmonic and exact $J$ values increase approximately linearly with size.Comment: 23 pages, 6 figures. Typos corrected. Manuscript improve

Knowledge-based energy functions for computational studies of proteins

This chapter discusses theoretical framework and methods for developing knowledge-based potential functions essential for protein structure prediction, protein-protein interaction, and protein sequence design. We discuss in some details about the Miyazawa-Jernigan contact statistical potential, distance-dependent statistical potentials, as well as geometric statistical potentials. We also describe a geometric model for developing both linear and non-linear potential functions by optimization. Applications of knowledge-based potential functions in protein-decoy discrimination, in protein-protein interactions, and in protein design are then described. Several issues of knowledge-based potential functions are finally discussed.Comment: 57 pages, 6 figures. To be published in a book by Springe

Equation of state and critical behavior of polymer models: A quantitative comparison between Wertheim's thermodynamic perturbation theory and computer simulations

We present an application of Wertheim's Thermodynamic Perturbation Theory (TPT1) to a simple coarse grained model made of flexibly bonded Lennard-Jones monomers. We use both the Reference Hyper-Netted-Chain (RHNC) and Mean Spherical approximation (MSA) integral equation theories to describe the properties of the reference fluid. The equation of state, the density dependence of the excess chemical potential, and the critical points of the liquid--vapor transition are compared with simulation results and good agreement is found. The RHNC version is somewhat more accurate, while the MSA version has the advantage of being almost analytic. We analyze the scaling behavior of the critical point of chain fluids according to TPT1 and find it to reproduce the mean field exponents: The critical monomer density is predicted to vanish as $n^{-1/2}$ upon increasing the chain length $n$ while the critical temperature is predicted to reach an asymptotic finite temperature that is attained as $n^{-1/2}$. The predicted asymptotic finite critical temperature obtained from the RHNC and MSA versions of TPT1 is found to be in good agreement with the $\Theta$ point of our polymer model as obtained from the temperature dependence of the single chain conformations.Comment: to appear in J.Chem.Phy

Single-molecule pulling: phenomenology and interpretation

Single-molecule pulling techniques have emerged as versatile tools for probing the noncovalent forces holding together the secondary and tertiary structure of macromolecules. They also constitute a way to study at the single-molecule level processes that are familiar from our macroscopic thermodynamic experience. In this Chapter, we summarize the essential phenomenology that is typically observed during single-molecule pulling, provide a general statistical mechanical framework for the interpretation of the equilibrium force spectroscopy and illustrate how to simulate single-molecule pulling experiments using molecular dynamics.Comment: arXiv admin note: text overlap with arXiv:0908.220