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Here we present a program aimed at free-energy calculations in molecular systems. It consists of a series of routines that can be interfaced with the most popular classical molecular dynamics (MD) codes through a simple patching procedure. This leaves the possibility for the user to exploit many different MD engines depending on the system simulated and on the computational resources available. Free-energy calculations can be performed as a function of many collective variables, with a particular focus on biological problems, and using state-of-the-art methods such as metadynamics, umbrella sampling and Jarzynski-equation based steered MD. The present software, written in ANSI-C language, can be easily interfaced with both fortran and C/C++ codes., Comment: to be submitted to Computer Physics Communications

Metadynamics is a powerful computational tool to obtain the free energy landscape of complex systems. The Monte Carlo algorithm has proven useful to calculate thermodynamic quantities associated with simplified models of proteins, and thus to gain an ever-increasing understanding on the general principles underlying the mechanism of protein folding. We show that it is possible to couple metadynamics and Monte Carlo algorithms to obtain the free energy of model proteins in a way which is computationally very economical., Comment: Submitted to Gene

The free-energy landscape of the alpha-helix of protein G is studied by means of metadynamics coupled with a solute tempering algorithm. Metadynamics allows to overcome large energy barriers, whereas solute tempering improves the sampling with an affordable computational effort. From the sampled free-energy surface we are able to reproduce a number of experimental observations, such as the fact that the lowest minimum corresponds to a globular conformation displaying some degree of beta-structure, that the helical state is metastable and involves only 65% of the chain. The calculations also show that the system populates consistently a pi-helix state and that the hydrophobic staple motif is present only in the free-energy minimum associated with the helices, and contributes to their stabilization. The use of metadynamics coupled with solute tempering results then particularly suitable to provide the thermodynamics of a short peptide, and its computational efficiency is promising to deal with larger proteins.

Being the HIV-1 Protease (HIV-1-PR) an essential enzyme in the viral life cycle, its inhibition can control AIDS. The folding of single domain proteins, like each of the monomers forming the HIV-1-PR homodimer, is controlled by local elementary structures (LES, folding units stabilized by strongly interacting, highly conserved, as a rule hydrophobic, amino acids). These LES have evolved over myriad of generations to recognize and strongly attract each other, so as to make the protein fold fast and be stable in its native conformation. Consequently, peptides displaying a sequence identical to those segments of the monomers associated with LES are expected to act as competitive inhibitors and thus destabilize the native structure of the enzyme. These inhibitors are unlikely to lead to escape mutants as they bind to the protease monomers through highly conserved amino acids which play an essential role in the folding process. The properties of one of the most promising inhibitors of the folding of the HIV-1-PR monomers found among these peptides is demonstrated with the help of spectrophotometric assays and CD spectroscopy.

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.

Being HIV-1-PR an essential enzyme in the viral life cycle, its inhibition can control AIDS. Because the folding of single domain proteins, like HIV-1-PR is controlled by local elementary structures (LES, folding units stabilized by strongly interacting, highly conserved amino acids) which have evolved over myriads of generations to recognize and strongly attract each other so as to make the protein fold fast, we suggest a novel type of HIV-1-PR inhibitors which interfere with the folding of the protein: short peptides displaying the same amino acid sequence of that of LES. Theoretical and experimental evidence for the specificity and efficiency of such inhibitors are presented.

The possibility of deriving the contact potentials between amino acids from their frequencies of occurence in proteins is discussed in evolutionary terms. This approach allows the use of traditional thermodynamics to describe such frequencies and, consequently, to develop a strategy to include in the calculations correlations due to the spatial proximity of the amino acids and to their overall tendency of being conserved in proteins. Making use of a lattice model to describe protein chains and defining a "true" potential, we test these strategies by selecting a database of folding model sequences, deriving the contact potentials from such sequences and comparing them with the "true" potential. Taking into account correlations allows for a markedly better prediction of the interaction potentials.

Some dimeric proteins first fold and then dimerize (three--state dimers) while others first dimerize and then fold (two--state dimers). Within the framework of a minimal lattice model, we can distinguish between sequences obeying to one or to the other mechanism on the basis of the partition of the ground state energy between bulk than for interface contacts. The topology of contacts is very different for the bulk than for the interface: while the bulk displays a rich network of interactions, the dimer interface is built up a set of essentially independent contacts. Consequently, the two sets of interactions play very different roles both in the the folding and in the evolutionary history of the protein. Three--state dimers, where a large fraction of the energy is concentrated in few contacts buried in the bulk, and where the relative contact energy of interface contacts is considerably smaller than that associated with bulk contacts, fold according to a hierarchycal pathway controlled by local elementary structures, as also happens in the folding of single--domain monomeric proteins. On the other hand, two--state dimers display a relative contact energy of interface contacts which is larger than the corresponding quantity associated with the bulk. In this case, the assembly of the interface stabilizes the system and lead the two chains to fold. The specific properties of three--state dimers acquired through evolution are expected to be more robust than those of two--state dimers, a fact which has consequences on proteins connected with viral diseases.

Protein folds are highly designable, in the sense that many sequences fold to the same conformation. In the present work we derive an expression for the designability in a 20 letter lattice model of proteins which, relying only on the Central Limit Theorem, has a generality which goes beyond the simple model used in its derivation. This expression displays an exponential dependence on the energy of the optimal sequence folding on the given conformation measured with respect to the lowest energy of the conformational dissimilar structures, energy difference which constitutes the only parameter controlling designability. Accordingly, the designability of a native conformation is intimately connected to the stability of the sequences folding to them., Comment: in press on Phys. Rev. E

The electron--phonon coupling in fullerene C28 has been calculated from first principles. The value of the associated coupling constant lambda/N(0) is found to be a factor three larger than that associated with C60. Assuming similar values of the density of levels at the Fermi surface N(0) and of the Coulomb pseudopotential for C28-based solids as those associated with alkali-doped fullerides A3C60, one obtains Tc(C28) \approx 8 Tc(C60)., Comment: 10 pages, 2 figures

The matrix elements of the deformation potential of C$_{70}$ are calculated by means of a simple, yet accurate solution of the electron-phonon coupling problem in fullerenes, based on a parametrization of the ground state electronic density of the system in terms of $sp^{2+x}$ hybridized orbitals. The value of the calculated dimensionless total electron-phonon coupling constant is $\lambda\approx0.1$, an order of magnitude smaller than in C$_{60}$, consistent with the lack of a superconducting phase transition in C$_{70}$A$_3$ fullerite, and in overall agreement with measurements of the broadening of Raman peaks in C$_{70}$K$_4$. We also calculate the photoemission cross section of C$_{70}^-$, which is found to display less structure than that associated with C$_{60}^-$, in overall agreement with the experimental findings., Comment: To be published in Phys. Rev. B