The effect of disorder in the contact probability of elongated conformations of biopolymers

Biopolymers are characterized by heterogeneous interactions, and usually perform their biological tasks forming contacts within domains of limited size. Combining polymer theory with a replica approach, we study the scaling properties of the probability of contact formation in random heteropolymers as a function of their linear distance. It is found that close or above the theta--point, it is possible to define a contact probability which is typical (i.e. "self-averaging") for different realizations of the heterogeneous interactions, and which displays an exponential cut--off, dependent on temperature and on the interaction range. In many cases this cut--off is comparable with the typical sizes of domains in biopolymers. While it is well known that disorder causes interesting effects at low temperature, the behavior elucidated in the present study is an example of a non--trivial effect at high temperature

The network of stabilizing contacts in proteins studied by coevolutionary data

The primary structure of proteins, that is their sequence, represents one of the most abundant set of experimental data concerning biomolecules. The study of correlations in families of co--evolving proteins by means of an inverse Ising--model approach allows to obtain information on their native conformation. Following up on a recent development along this line, we optimize the algorithm to calculate effective energies between the residues, validating the approach both back-calculating interaction energies in a model system, and predicting the free energies associated to mutations in real systems. Making use of these effective energies, we study the networks of interactions which stabilizes the native conformation of some well--studied proteins, showing that it display different properties than the associated contact network

Ratcheted molecular-dynamics simulations identify efficiently the transition state of protein folding

The atomistic characterization of the transition state is a fundamental step to improve the understanding of the folding mechanism and the function of proteins. From a computational point of view, the identification of the conformations that build out the transition state is particularly cumbersome, mainly because of the large computational cost of generating a statistically-sound set of folding trajectories. Here we show that a biasing algorithm, based on the physics of the ratchet-and-pawl, can be used to identify efficiently the transition state. The basic idea is that the algorithmic ratchet exerts a force on the protein when it is climbing the free-energy barrier, while it is inactive when it is descending. The transition state can be identified as the point of the trajectory where the ratchet changes regime. Besides discussing this strategy in general terms, we test it within a protein model whose transition state can be studied independently by plain molecular dynamics simulations. Finally, we show its power in explicit-solvent simulations, obtaining and characterizing a set of transition--state conformations for ACBP and CI2

Statistical Analysis of Native Contact Formation in the Folding of Designed Model Proteins

The time evolution of the formation probability of native bonds has been studied for designed sequences which fold fast into the native conformation. From this analysis a clear hierarchy of bonds emerge a) local, fast forming highly stable native bonds built by some of the most strongly interacting amino acids of the protein, b) non-local bonds formed late in the folding process, in coincidence with the folding nucleus, and involving essentially the same strongly interacting amino acids already participating in the fast bonds, c) the rest of the native bonds whose behaviour is subordinated, to a large extent, to that of the local- and non-local native contacts

Inversion Formulas for the Dunkl Intertwining Operator and Its Dual on Spaces of Functions and Distributions

In this paper we prove inversion formulas for the Dunkl intertwining operator $V_k$ and for its dual ${}^tV_k$ and we deduce the expression of the representing distributions of the inverse operators $V_k^{-1}$ and ${}^tV_k^{-1}$, and we give some applications.Comment: This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Similar folds with different stabilization mechanisms: the cases of prion and doppel proteins

BACKGROUND: Protein misfolding is the main cause of a group of fatal neurodegenerative diseases in humans and animals. In particular, in Prion-related diseases the normal cellular form of the Prion Protein PrP (PrP(C)) is converted into the infectious PrP(Sc )through a conformational process during which it acquires a high β-sheet content. Doppel is a protein that shares a similar native fold, but lacks the scrapie isoform. Understanding the molecular determinants of these different behaviours is important both for biomedical and biophysical research. RESULTS: In this paper, the dynamical and energetic properties of the two proteins in solution is comparatively analyzed by means of long time scale explicit solvent, all-atom molecular dynamics in different temperature conditions. The trajectories are analyzed by means of a recently introduced energy decomposition approach (Tiana et al, Prot. Sci. 2004) aimed at identifying the key residues for the stabilization and folding of the protein. Our analysis shows that Prion and Doppel have two different cores stabilizing the native state and that the relative contribution of the nucleus to the global stability of the protein for Doppel is sensitively higher than for PrP. Moreover, under misfolding conditions the Doppel core is conserved, while the energy stabilization network of PrP is disrupted. CONCLUSION: These observations suggest that different sequences can share similar native topology with different stabilizing interactions and that the sequences of the Prion and Doppel proteins may have diverged under different evolutionary constraints resulting in different folding and stabilization mechanisms

Assessing the accuracy of direct-coupling analysis for RNA contact prediction

Many non-coding RNAs are known to play a role in the cell directly linked to their structure. Structure prediction based on the sole sequence is however a challenging task. On the other hand, thanks to the low cost of sequencing technologies, a very large number of homologous sequences are becoming available for many RNA families. In the protein community, it has emerged in the last decade the idea of exploiting the covariance of mutations within a family to predict the protein structure using the direct-coupling-analysis (DCA) method. The application of DCA to RNA systems has been limited so far. We here perform an assessment of the DCA method on 17 riboswitch families, comparing it with the commonly used mutual information analysis and with state-of-the-art R-scape covariance method. We also compare different flavors of DCA, including mean-field, pseudo-likelihood, and a proposed stochastic procedure (Boltzmann learning) for solving exactly the DCA inverse problem. Boltzmann learning outperforms the other methods in predicting contacts observed in high resolution crystal structures

An implementation of the maximum-caliber principle by replica-averaged time-resolved restrained simulations

Inferential methods can be used to integrate experimental informations and molecular simulations. The maximum entropy principle provides a framework for using equilibrium experimental data and it has been shown that replica-averaged simulations, restrained using a static potential, are a practical and powerful implementation of such principle. Here we show that replica-averaged simulations restrained using a time-dependent potential are equivalent to the principle of maximum caliber, the dynamic version of the principle of maximum entropy, and thus may allow to integrate time-resolved data in molecular dynamics simulations. We provide an analytical proof of the equivalence as well as a computational validation making use of simple models and synthetic data. Some limitations and possible solutions are also discussed

Design of HIV-1-PR inhibitors which do not create resistance: blocking the folding of single monomers

One of the main problems of drug design is that of optimizing the drug--target interaction. In the case in which the target is a viral protein displaying a high mutation rate, a second problem arises, namely the eventual development of resistance. We wish to suggest a scheme for the design of non--conventional drugs which do not face any of these problems and apply it to the case of HIV--1 protease. It is based on the knowledge that the folding of single--domain proteins, like e.g. each of the monomers forming the HIV--1--PR homodimer, is controlled by local elementary structures (LES), stabilized by local contacts among hydrophobic, strongly interacting and highly conserved amino acids which play a central role in the folding process. Because LES have evolved over myriads of generations to recognize and strongly interact with each other so as to make the protein fold fast as well as to avoid aggregation with other proteins, highly specific (and thus little toxic) as well as effective folding--inhibitor drugs suggest themselves: short peptides (or eventually their mimetic molecules), displaying the same amino acid sequence of that of LES (p--LES). Aside from being specific and efficient, these inhibitors are expected not to induce resistance: in fact, mutations which successfully avoid their action imply the destabilization of one or more LES and thus should lead to protein denaturation. Making use of Monte Carlo simulations within the framework of a simple although not oversimplified model, which is able to reproduce the main thermodynamic as well as dynamic properties of monoglobular proteins, we first identify the LES of the HIV--1--PR and then show that the corresponding p--LES peptides act as effective inhibitors of the folding of the protease which do not create resistance