A constrained maximum entropy method in polymer statistics

Probing protein stability: towards a computational atomistic, reliable, affordable, and improvable model

We present an improved application of a recently proposed computational method designed to evaluate the change of free energy as a function of the average value of a suitably chosen collective variable in proteins. The method is based on a full atomistic description of the protein and its environment. The goal is to understand how the protein melting temperature changes upon single-point mutations, because the sign of the temperature variation will allow us to discriminate stabilizing vs. destabilizing mutations in protein sequences. In this refined application the method is based on altruistic well-tempered metadynamics, a variant of multiple-walkers metadynamics. The resulting metastatistics is then modulated by the maximal constrained entropy principle. The latter turns out to be especially helpful in free-energy calculations as it is able to alleviate the severe limitations of metadynamics in properly sampling folded and unfolded configurations. In this work we apply the computational strategy outlined above in the case of the bovine pancreatic trypsin inhibitor, a well-studied small protein, which is a reference for computer simulations since decades. We compute the variation of the melting temperature characterizing the folding-unfolding process between the wild-type protein and two of its single-point mutations that are seen to have opposite effect on the free energy changes. The same approach is used for free energy difference calculations between a truncated form of frataxin and a set of five of its variants. Simulation data are compared to in vitro experiments. In all cases the sign of the change of melting temperature is reproduced, under the further approximation of using an empirical effective mean-field to average out protein-solvent interactions.

Modelling Protein Plasticity: The Example of Frataxin and Its Variants

Frataxin (FXN) is a protein involved in storage and delivery of iron in the mitochondria. Single-point mutations in the FXN gene lead to reduced production of functional frataxin, with the consequent dyshomeostasis of iron. FXN variants are at the basis of neurological impairment (the Friedreich's ataxia) and several types of cancer. By using altruistic metadynamics in conjunction with the maximal constrained entropy principle, we estimate the change of free energy in the protein unfolding of frataxin and of some of its pathological mutants. The sampled configurations highlight differences between the wild-type and mutated sequences in the stability of the folded state. In partial agreement with thermodynamic experiments, where most of the analyzed variants are characterized by lower thermal stability compared to wild type, the D104G variant is found with a stability comparable to the wild-type sequence and a lower water-accessible surface area. These observations, obtained with the new approach we propose in our work, point to a functional switch, affected by single-point mutations, of frataxin from iron storage to iron release. The method is suitable to investigate wide structural changes in proteins in general, after a proper tuning of the chosen collective variable used to perform the transition.

Structural Insights into the Osteopontin-Aptamer Complex by Molecular Dynamics Simulations

Osteopontin is an intrinsically disordered protein involved in tissue remodeling. As a biomarker for pathological hypertrophy and fibrosis, the protein is targeted by an RNA aptamer. In this work, we model the interactions between osteopontin and its aptamer, including mono- (Na⁺) and divalent (Mg²⁺) cations. The molecular dynamics simulations suggest that the presence of divalent cations forces the N-terminus of osteopontin to bind the shell of divalent cations adsorbed over the surface of its RNA aptamer, the latter exposing a high negative charge density. The osteopontin plasticity as a function of the local concentration of Mg is discussed in the frame of the proposed strategies for osteopontin targeting as biomarker and in theranostic.

Modeling the interplay of glycine protonation and multiple histidine binding of copper in the prion protein octarepeat subdomains

The octarepeat region of the prion protein can bind Cu(2+) ions up to full occupancy (one ion per octarepeat) at neutral pH. While crystallographic data show that the HGGG octarepeat subdomain is the basic binding unit, multiple histidine coordination at lower Cu occupancy has been reported by X-ray absorption spectroscopy, EPR, and potentiometric experiments. In this paper we investigate, with first principles Car-Parrinello simulations, the first step for the formation of the Cu low-level binding mode, where four histidine side chains are coordinated to the same Cu(2+) ion. This step involves the further binding of a second histidine to an already HGGG domain bonded Cu(2+) ion. The influence of the pH on the ability of Cu to bind two histidine side chains was taken into account by simulating different protonation states of the amide N atoms of the two glycines lying nearest to the first histidine. Multiple histidine coordination is also seen to occur when glycine deprotonation occurs and the presence of the extra histidine stabilizes the Cu-peptide complex. Though the stabilization effect slightly decreases with the number of deprotonated glycines (reaching a minimum when both N atoms of the two nearest glycines are available as Cu ligands), the system is still capable of binding the second histidine in a 4N tetrahedral (though slightly distorted) coordination, whose energy is very near to that of the crystallographic square-planar 3N1O coordination. This result suggests that at low metal concentration the reorganization energy associated with Cu(II)/Cu(I) reduction is small also at pH approximately 7, when glycines are deprotonated.

Modeling H3 histone N-terminal tail and linker DNA interactions

Molecular dynamics computer simulations were performed for the 25-residue N-terminal tail of the H3 histone protein in the proximity of a DNA segment of 10 base pairs (bp), representing a model for the linker DNA in chromatin. Several least biased configurations were used as initial configurations. The secondary structure content of the protein was increased by the presence of DNA close to it, but the locations of the secondary motifs were different for different initial orientations of the DNA grooves with respect to the protein. As a common feature to all simulations, the electrostatic attraction between negatively charged DNA and positively charged protein was screened by the water solvent and counterbalanced by the intrinsic compaction of the protein due to hydrophobic effects. The protein secondary structure limited the covering of DNA by the protein to 4-5 bp. The degree of compaction and charge density of the bound protein suggests a possible role of H3 tail in a nonspecific bending and plasticity of the linker DNA when the protein is located in the crowded dense chromatin.

Molecular statistics of cytochrome c: structural plasticity and molecular environment

Nuclear magnetic resonance experiments performed on yeast mitochondrial cytochrome c (Cytc), a paradigmatic electron transfer protein, reveal that the two oxidation states have similar structures, but different mobility: despite the few structural differences compared with the reduced form, the oxidized form displays a larger unfolding propensity. Molecular dynamics simulations performed on both NMR reduced and NMR oxidized forms show that the reduced form has a larger solvent-accessible surface area (SASA). Starting from this observation, a molecular statistical approach was then applied in order to correlate the molecular surface to molecular mobility. Simulations started from biased initial conditions corresponding to different molecular sizes were combined with the maximal constrained entropy method. The NMR structure of oxidized Cytc is more suited to expose a smaller SASA than the NMR structure of the reduced form, but the accessible conformational landscape at 300 K around the NMR oxidized structure is flatter than for the NMR reduced structure. Protein configurations of smaller SASA and size display larger plasticity when they resemble the NMR oxidized structure, whereas they are more rigid when they resemble the NMR reduced structure. Implications of the results for the protein properties during its functional process are discussed.

Hyaluronan chain conformation and dynamics

An overview of the present state of research in the field of hyaluronan chain conformational aspects is presented. The relationship between structure and dynamics are illustrated for a series of hyaluronan oligomers. Conformational characteristics of hyaluronan chains are discussed, together with the dynamic chain patterns, evaluated by using a theoretical approach to diffusive polymer dynamics. The dependence of correlation times and NMR relaxation parameters from the chain dimension are investigated. Topological features and dimensional properties are related to the structural determinants by using classical computational methods of molecular mechanics and Monte Carlo simulation.

Designing generalized statistical ensembles for numerical simulations of biopolymers

Conformational properties of polymers, such as average dihedral angles or molecular alpha-helicity, display a rather weak dependence on the detailed arrangement of the elementary constituents (atoms). We propose a computer simulation method to explore the polymer phase space using a variant of the standard multicanonical method, in which the density of states associated to suitably chosen configurational variables is considered in place of the standard energy density of states. This configurational density of states is used in the Metropolis acceptance/rejection test when configurations are generated with the help of a hybrid Monte Carlo algorithm. The resulting configurational probability distribution is then modulated by exponential factors derived from the general principle of the maximal constrained entropy by requiring that certain average configurational quantities take preassigned (possibly temperature dependent) values. Thermal averages of other configurational quantities can be computed by using the probability distributions obtained in this way. Moments of the energy distribution require an extra canonical sampling of the system phase space at the desired temperature, in order to locally thermalize the configurational degrees of freedom. As an application of these ideas we present the study of the structural properties of two simple models: a bead-and-spring model of polyethylene with independent hindered torsions and an all-atom model of alanine and glycine oligomers with 12 amino acids in vacuum.