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H Orland

Publications and source records attributed to H Orland.

14 recordsLinked to original sources
PubMed2006

Dominant pathways in protein folding.

We present a method to investigate the kinetics of protein folding and the dynamics underlying the formation of secondary and tertiary structures during the entire reaction. By writing the solution of the Fokker-Planck equation in terms of a path integral, we derive a Hamilton-Jacobi variational principle from which we are able to compute the most probable pathway of folding. The method is applied to the folding of the Villin headpiece subdomain simulated using a Go model. An initial collapsing phase driven by the initial configuration is followed by a rearrangement phase, in which secondary structures are formed and all computed paths display strong similarities. This completely general method does not require the prior knowledge of any reaction coordinate and is an efficient tool to perform simulations of the entire folding process with available computers.

Biophysics↗
PubMed2003

Variational charge renormalization in charged systems.

We apply general variational techniques to the problem of the counterion distribution around highly charged objects where strong condensation of counterions takes place. Within a field-theoretic formulation using a fluctuating electrostatic potential, the concept of surface-charge renormalization is recovered within a simple one-parameter variational procedure. As a test, we reproduce the Poisson-Boltzmann surface potential for a single-charged planar surface both in the weak-charge and strong-charge regime. We then apply our techniques to non-planar geometries where closed-form solutions of the non-linear Poisson-Boltzmann equation are not available. In the cylindrical case, the Manning charge renormalization result is obtained in the limit of vanishing salt concentration. However, for intermediate salt concentrations a slow crossover to the non-charged-renormalized regime (at high salt) is found with a quasi-power-law behavior which helps to understand conflicting experimental and theoretical results for the electrostatic persistence length of polyelectrolytes. In the spherical geometry charge renormalization is only found at intermediate salt concentrations, in agreement with previous numerical results.

Biophysical Phenomena↗
PubMed2000

General formalism for phase combination and phase refinement: a statistical thermodynamics approach in reciprocal space.

The mean-field optimization methodology has been used to recast in a single formalism the problem of phase optimization using an arbitrary energy function in the presence of an experimentally determined phase probability distribution function. It results naturally in the generalization of the notions of figure of merit and centroid phase where the weight of the energy refinement is controlled by an effective temperature in a self-consistent manner. In the limit of high temperature, the formalism reduces of course to the Blow & Crick [Acta Cryst. (1959), 12, 794-802] classical treatment. If a model is available, Sim's [Acta Cryst. (1960), 13, 511-512] weighting scheme for a combined map appears as the first step of a refinement to be conducted until self-consistency is achieved. Assuming that MIR phases exist and that they agree reasonably well with the phases of the model, a first-order expansion gives an estimate of the changes of weights and phases to be performed for the Fourier synthesis. This provides for a new way of doing phase combination that might prove useful in challenging cases of model refinement, e.g. in large macromolecular complexes. Thermodynamic considerations have been used to discuss the best determination of weights in phase refinement; they also suggest that a variational expression of maximum likelihood is best suited as a target for refinement because it is the free energy of the system. The formalism readily allows use of solvent flattening, density averaging and the atomicity criterion to refine phases, and automatically assigns a figure of merit to each reflection. Numerical tests of the method are presented in an attempt to resolve the phase-ambiguity problem of protein crystallography in the centrosymmetric P¿1¿ space group using an energy derived from the Sayre equation.

Biopolymers↗
PubMed1995

Partially folded states of proteins: characterization by X-ray scattering.

Partially folded states of proteins are found to occur with a wide variety of degrees of unfolding, ranging from the compact molten globule to the fully unfolded forms, depending on solvent conditions and the specific protein involved. Small to intermediate angle X-ray scattering from partially folded states of proteins yields low resolution scattering profiles that may be used to explore the degree of folding of a protein under given solution conditions. By Monte Carlo simulation of a highly simplified homopolymer model, we show that such partially folded states will yield a characteristic scattering profile that may be written as a linear superposition of scattering from a compact core and of scattering from random coil loops that emerge from this core. We also find a term resulting from interference of X-rays scattering from the core with those scattering from the loops. This interference term oscillates in sign and tends to enhance the core portion of the scattering profile. We compare the model calculations of the scattering profile with measurements of the scattering profile as a function of salt concentration for cytochrome c at pH 2. Because of our characterization of the scattering profiles, we suggest that these results may be re-interpreted in terms of the presence of a range of partially folded states as a function of pH and salt concentration, and that the observed scattering profiles are consistent with the characterization of the partially folded states in terms of random coil loops emerging from a compact core with the loop fraction increasing as the salt concentration is decreased. This characterization is consistent with data on amide protection against H-2H exchange of compact regions within partially folded states observed for a number of proteins, including cytochrome c.

Computer Simulation↗
PubMed1993

Biasing a Monte Carlo chain growth method with Ramachandran's plot: application to twenty-L-alanine.

In this paper, we explore the possibility of using experimental observations in the Monte Carlo chain growth method that we have previously developed. In this method, the macromolecule (peptide, protein, nuclei acid, etc.) is grown atom-by-atom (or residue-by-residue, etc.) and partial chains are replicated according to their Boltzmann weights. Once the molecule completed, we are left with a Boltzmann-distributed ensemble of configurations. For long molecules, an efficient sampling of the (extremely large) phase space is difficult for obvious reasons (existence of many local minima, limited computer memory, etc.). In the case in which one is mainly interested in the low energy conformations, we have incorporated in the growth scheme experimental observations taken from the Protein Data Banks. More precisely, we have considered the case of twenty-L-alanine and we have used the (experimental) Ramachandran's plot for this residue. The biased growth procedure goes as follows: (a) each time one adds along the main backbone chain, either a carbon atom belonging to a carbonyl group, or a nitrogen atom, its dihedral angle (theta) or (psi) is drawn with a probability law that reflects the experimental Ramachandran (theta, psi) plot; (b) the bias introduced in this way is canceled through an extra term in the energy (replication energy = true energy + bias energy); (c) the configurations, generated at T = 1000 K, are then energy minimized.(ABSTRACT TRUNCATED AT 250 WORDS)

Alanine↗