Cristian Micheletti

Accurate and efficient description of protein vibrational dynamics: Comparing molecular dynamics and Gaussian models

Current all‐atom potential based molecular dynamics (MD) allows the identification of a proteins functional motions on a wide‐range of timescales, up to few tens of nanoseconds. However, functional, large‐scale motions of proteins may occur on a timescale currently not accessible by all‐atom potential based MD. To avoid the massive computational effort required by this approach, several simplified schemes have been introduced. One of the most satisfactory is the Gaussian network approach based on the energy expansion in terms of the deviation of the protein backbone from its native configuration. Here, we consider an extension of this model that captures in a more realistic way the distribution of native interactions due to the introduction of effective side‐chain centroids. Since their location is entirely determined by the protein backbone, the model is amenable to the same exact and computationally efficient treatment as previous simpler models. The ability of the model to describe the correlated motion of protein residues in thermodynamic equilibrium is established through a series of successful comparisons with an extensive (14 ns) MD simulation based on the AMBER potential of HIV‐1 protease in complex with a peptide substrate. Thus, the model presented here emerges as a powerful tool to provide preliminary, fast yet accurate characterizations of protein near‐native motion. Proteins 2004.

Protein Structures and Optimal Folding from a Geometrical Variational Principle

A novel approach, validated by an analysis of barnase and chymotrypsin inhibitor, is introduced to elucidate the paramount role played by the geometry of the protein backbone in steering the folding to the native state. It is found that native states of proteins, compared with compact artificial backbones, have an exceedingly large number of conformations with a given amount of structural overlap with them; moreover, the density of overlapping conformations, at a given overlap, of unrelated proteins of the same length are nearly equal. These results suggest an extremality principle underlying protein evolution, which, in turn, is shown to be possibly associated with the emergence of secondary structures.

Polymers with spatial or topological constraints: Theoretical and computational results

In this review, we provide an organized summary of the theoretical and computational results that are available for polymers subject to spatial or topological constraints. Because of the interdisciplinary character of the topic, we provide an accessible, non-specialist introduction to the main topological concepts, polymer models, and theoretical/computational methods used to investigate dense and entangled polymer systems. The main body of our review deals with (i) the effect that spatial confinement has on the equilibrium topological entanglement of one or more polymer chains and (ii) the metric and entropic properties of polymer chains with fixed topological states. These problems have important technological applications and implications for life sciences. Both aspects, especially the latter, are amply covered. A number of selected open problems are finally highlighted.

DNA–DNA interactions in bacteriophage capsids are responsible for the observed DNA knotting

Recent experiments showed that the linear double-stranded DNA in bacteriophage capsids is both highly knotted and neatly structured. What is the physical basis of this organization? Here we show evidence from stochastic simulation techniques that suggests that a key element is the tendency of contacting DNA strands to order, as in cholesteric liquid crystals. This interaction favors their preferential juxtaposition at a small twist angle, thus promoting an approximately nematic (and apolar) local order. The ordering effect dramatically impacts the geometry and topology of DNA inside phages. Accounting for this local potential allows us to reproduce the main experimental data on DNA organization in phages, including the cryo-EM observations and detailed features of the spectrum of DNA knots formed inside viral capsids. The DNA knots we observe are strongly delocalized and, intriguingly, this is shown not to interfere with genome ejection out of the phage.

Reconstructing the density of states by history-dependent metadynamics.

We present a novel method for the calculation of the energy density of states D(E) for systems described by classical statistical mechanics. The method builds on an extension of a recently proposed strategy that allows the free-energy profile of a canonical system to be recovered within a preassigned accuracy [Proc. Natl. Acad. Sci. U.S.A. 99, 12562 (2002)]]. The method allows a good control over the error on the recovered system entropy. This fact is exploited to obtain D(E) more efficiently by combining measurements at different temperatures. The accuracy and efficiency of the method are tested for the two-dimensional Ising model (up to size 50 x 50) by comparison with both exact results and previous studies. This method is a general one and should be applicable to more realistic model systems.

Recurrent oligomers in proteins: An optimal scheme reconciling accurate and concise backbone representations in automated folding and design studies

A novel scheme is introduced to capture the spatial correlations of consecutive amino acids in naturally occurring proteins. This knowledge‐based strategy is able to carry out optimally automated subdivisions of protein fragments into classes of similarity. The goal is to provide the minimal set of protein oligomers (termed “oligons” for brevity) that is able to represent any other fragment. At variance with previous studies in which recurrent local motifs were classified, our concern is to provide simplified protein representations that have been optimised for use in automated folding and/or design attempts. In such contexts, it is paramount to limit the number of degrees of freedom per amino acid without incurring loss of accuracy of structural representations. The suggested method finds, by construction, the optimal compromise between these needs. Several possible oligon lengths are considered. It is shown that meaningful classifications cannot be done for lengths greater than six or smaller than four. Different contexts are considered for which oligons of length five or six are recommendable. With only a few dozen oligons of such length, virtually any protein can be reproduced within typical experimental uncertainties. Structural data for the oligons are made publicly available. Proteins 2000;40:662–674.

Biopolymer organization upon confinement

Biopolymers in vivo are typically subject to spatial restraints, either as a result of molecular crowding in the cellular medium or of direct spatial confinement. DNA in living organisms provides a prototypical example of a confined biopolymer. Confinement prompts a number of biophysics questions. For instance, how can the high level of packing be compatible with the necessity to access and process the genomic material? What mechanisms can be adopted in vivo to avoid the excessive geometrical and topological entanglement of dense phases of biopolymers? These and other fundamental questions have been addressed in recent years by both experimental and theoretical means. A review of the results, particularly of those obtained by numerical studies, is presented here. The review is mostly devoted to DNA packaging inside bacteriophages, which is the best studied example both experimentally and theoretically. Recent selected biophysical studies of the bacterial genome organization and of chromosome segregation in eukaryotes are also covered.

Geometry and physics of proteins

A conceptual framework for understanding the protein folding problem has remained elusive in spite of many significant advances. We show that geometrical constraints imposed by chain connectivity, compactness, and the avoidance of steric clashes can be encompassed in a natural way using a three‐body potential and lead to a selection in structure space, independent of chemical details. Strikingly, secondary motifs such as hairpins, sheets, and helices, which are the building blocks of protein folds, emerge as the chosen structures for segments of the protein backbone based just on elementary geometrical considerations. Proteins 2002;47:315–322.

Probing the Entanglement and Locating Knots in Ring Polymers: A Comparative Study of Different Arc Closure Schemes

The interplay between the topological and geometrical properties of a polymer ring can be clarified by establishing the entanglement trapped in any portion (arc) of the ring. The task requires closing the open arcs into a ring, and the resulting topological state may depend on the specific closure scheme that is followed. To understand the impact of this ambiguity in contexts of practical interest, such as knot localization in a ring with non trivial topology, we apply various closure schemes to model ring polymers. The rings have the same length and topological state (a trefoil knot) but have different degree of compactness. The comparison suggests that a novel method, called the minimally-interfering closure, can be profitably used to characterize the arc entanglement in a robust and computationally-efficient way. This closure method is applied to the knot localization problem which is tackled using two different localization schemes based on top-down or bottom-up searches.

Evolutionarily Conserved Functional Mechanics across Pepsin-like and Retroviral Aspartic Proteases

The biological function of the aspartic protease from HIV-1 has recently been related to the conformational flexibility of its structural scaffold. Here, we use a multistep strategy to investigate whether the same mechanism affects the functionality in the pepsin-like fold. (i) We identify the set of conserved residues by using sequence-alignment techniques. These residues cluster in three distinct regions: near the cleavage-site cavity, in the four beta-sheets cross-linking the two lobes, and in a solvent-exposed region below the long beta-hairpin in the N-terminal lobe. (ii) We elucidate the role played by the conserved residues for the enzymatic functionality of one representative member of the fold family, the human beta-secretase, by means of classical molecular dynamics (MD). The conserved regions exhibit little overall mobility and yet are involved into the most important modes of structural fluctuations. These modes influence the substrate-catalytic aspartates distance through a relative rotation of the N- and C-terminal lobes. (iii) We investigate the effects of this modulation by estimating the reaction free energy at different representative substrate/enzyme conformations. The activation free energy is strongly affected by large-scale protein motions, similarly to what has been observed in the HIV-1 enzyme. (iv) We extend our findings to all other members of the two eukaryotic and retroviral fold families by recurring to a simple, topology-based, energy functional. This analysis reveals a sophisticated mechanism of enzymatic activity modulation common to all aspartic proteases. We suggest that aspartic proteases have been evolutionarily selected to possess similar functional motions despite the observed fold variations.