42 research outputs found
Scale Free Cluster Distributions from Conserving Merging-Fragmentation Processes
We propose a dynamical scheme for the combined processes of fragmentation and
merging as a model system for cluster dynamics in nature and society displaying
scale invariant properties. The clusters merge and fragment with rates
proportional to their sizes, conserving the total mass. The total number of
clusters grows continuously but the full time-dependent distribution can be
rescaled over at least 15 decades onto a universal curve which we derive
analytically. This curve includes a scale free solution with a scaling exponent
of -3/2 for the cluster sizes.Comment: 4 pages, 3 figure
Compact phases of polymers with hydrogen bonding
We propose an off-lattice model for a self-avoiding homopolymer chain with
two different competing attractive interactions, mimicking the hydrophobic
effect and the hydrogen bond formation respectively. By means of Monte Carlo
simulations, we are able to trace out the complete phase diagram for different
values of the relative strength of the two competing interactions. For strong
enough hydrogen bonding, the ground state is a helical conformation, whereas
with decreasing hydrogen bonding strength, helices get eventually destabilized
at low temperature in favor of more compact conformations resembling
-sheets appearing in native structures of proteins. For weaker hydrogen
bonding helices are not thermodynamically relevant anymore.Comment: 5 pages, 3 figures; revised version published in PR
Mean first passage time analysis reveals rate-limiting steps, parallel pathways and dead ends in a simple model of protein folding
We have analyzed dynamics on the complex free energy landscape of protein
folding in the FOLD-X model, by calculating for each state of the system the
mean first passage time to the folded state. The resulting kinetic map of the
folding process shows that it proceeds in jumps between well-defined, local
free energy minima. Closer analysis of the different local minima allows us to
reveal secondary, parallel pathways as well as dead ends.Comment: 7 page
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Bayesian generalised ensemble Markov chain Monte Carlo
Bayesian generalised ensemble (BayesGE) is a new method that addresses two major drawbacks of standard Markov chain Monte Carlo algorithms for inference in high-dimensional probability models: inapplicability to estimate the partition function, and poor mixing properties. BayesGE uses a Bayesian approach to iteratively update the belief about the density of states (distribution of the log likelihood under the prior) for the model, with the dual purpose of enhancing the sampling efficiency and make the estimation of the partition function tractable. We benchmark BayesGE on Ising and Potts systems and show that it compares favourably to existing state-of-the-art methods.JF acknowledge funding from the Danish Council for Independent Research | Natural Sciences. ZG acknowledge funding from EPSRC EP/I036575/1 and Google.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by Microtome Publishing
What thermodynamic features characterize good and bad folders? Results from a simplified off-lattice protein model
The thermodynamics of the small SH3 protein domain is studied by means of a
simplified model where each bead-like amino acid interacts with the others
through a contact potential controlled by a 20x20 random matrix. Good folding
sequences, characterized by a low native energy, display three main
thermodynamical phases, namely a coil-like phase, an unfolded globule and a
folded phase (plus other two phases, namely frozen and random coil, populated
only at extremes temperatures). Interestingly, the unfolded globule has some
regions already structured. Poorly designed sequences, on the other hand,
display a wide transition from the random coil to a frozen state. The
comparison with the analytic theory of heteropolymers is discussed
Design of amino acid sequences to fold into C_alpha-model proteins
In order to extend the results obtained with minimal lattice models to more
realistic systems, we study a model where proteins are described as a chain of
20 kinds of structureless amino acids moving in a continuum space and
interacting through a contact potential controlled by a 20x20 quenched random
matrix. The goal of the present work is to design and characterize amino acid
sequences folding to the SH3 conformation, a 60-residues recognition domain
common to many regulatory proteins. We show that a number of sequences can
fold, starting from a random conformation, to within a distance root mean
square deviation (dRMSD) of 2.6A from the native state. Good folders are those
sequences displaying in the native conformation an energy lower than a
sequence--independent threshold energy
Competition between Diffusion and Fragmentation: An Important Evolutionary Process of Nature
We investigate systems of nature where the common physical processes
diffusion and fragmentation compete. We derive a rate equation for the size
distribution of fragments. The equation leads to a third order differential
equation which we solve exactly in terms of Bessel functions. The stationary
state is a universal Bessel distribution described by one parameter, which fits
perfectly experimental data from two very different system of nature, namely,
the distribution of ice crystal sizes from the Greenland ice sheet and the
length distribution of alpha-helices in proteins.Comment: 4 pages, 3 figures, (minor changes
General Protocol for Constructing Molecular Models of Nanodiscs
Nanodisc technology is increasingly being applied for structural and biophysical studies of membrane proteins. In this work, we present a general protocol for constructing molecular models of nanodiscs for molecular dynamics simulations. The protocol is written in python and based on geometric equations, making it fast and easy to modify, enabling automation and customization of nanodiscs in silico. The novelty being the ability to construct any membrane scaffold protein (MSP) variant fast and easy given only an input sequence. We validated and tested the protocol by simulating seven different nanodiscs of various sizes and with different membrane scaffold proteins, both circularized and noncircularized. The structural and biophysical properties were analyzed and shown to be in good agreement with previously reported experimental data and simulation studies
Potentials of Mean Force for Protein Structure Prediction Vindicated, Formalized and Generalized
Understanding protein structure is of crucial importance in science, medicine
and biotechnology. For about two decades, knowledge based potentials based on
pairwise distances -- so-called "potentials of mean force" (PMFs) -- have been
center stage in the prediction and design of protein structure and the
simulation of protein folding. However, the validity, scope and limitations of
these potentials are still vigorously debated and disputed, and the optimal
choice of the reference state -- a necessary component of these potentials --
is an unsolved problem. PMFs are loosely justified by analogy to the reversible
work theorem in statistical physics, or by a statistical argument based on a
likelihood function. Both justifications are insightful but leave many
questions unanswered. Here, we show for the first time that PMFs can be seen as
approximations to quantities that do have a rigorous probabilistic
justification: they naturally arise when probability distributions over
different features of proteins need to be combined. We call these quantities
reference ratio distributions deriving from the application of the reference
ratio method. This new view is not only of theoretical relevance, but leads to
many insights that are of direct practical use: the reference state is uniquely
defined and does not require external physical insights; the approach can be
generalized beyond pairwise distances to arbitrary features of protein
structure; and it becomes clear for which purposes the use of these quantities
is justified. We illustrate these insights with two applications, involving the
radius of gyration and hydrogen bonding. In the latter case, we also show how
the reference ratio method can be iteratively applied to sculpt an energy
funnel. Our results considerably increase the understanding and scope of energy
functions derived from known biomolecular structures