Residual entropy and waterlike anomalies in the repulsive one dimensional lattice gas.

The thermodynamics and kinetics of the one dimensional lattice gas with repulsive interaction are investigated using transfer matrix technique and Monte Carlo simulations. This simple model is shown to exhibit waterlike anomalies in density, thermal expansion coefficient, and self-diffusion. An unified description for the thermodynamic anomalies in this model is achieved based on the ground state residual entropy which appears in the model due to mixing entropy in a ground state phase transition.

Thermodynamic and dynamic anomalies in a one-dimensional lattice model of liquid water.

We investigate the occurrence of waterlike thermodynamic and dynamic anomalous behavior in a one dimensional lattice gas model. The system thermodynamics is obtained using the transfer matrix technique and anomalies on density and thermodynamic response functions are found. When the hydrogen bond (molecules separated by holes) is more attractive than the van der Waals interaction (molecules in contact) a transition between two fluid structures is found at null temperature and high pressure. This transition is analogous to a 'critical point' and intimately connects the anomalies in density and in thermodynamic response functions. Monte Carlo simulations were performed in the neighborhood of this transition and used to calculate the self diffusion constant, which increases with density as in liquid water.

Solution of an associating lattice-gas model with density anomaly on a Husimi lattice.

We study a model of a lattice gas with orientational degrees of freedom which resemble the formation of hydrogen bonds between the molecules. In this model, which is the simplified version of the Henriques-Barbosa model, no distinction is made between donors and acceptors in the bonding arms. We solve the model in the grand-canonical ensemble on a Husimi lattice built with hexagonal plaquettes with a central site. The ground state of the model, which was originally defined on the triangular lattice, is exactly reproduced by the solution on this Husimi lattice. In the phase diagram, one gas and two liquid [high density liquid (HDL) and low density liquid (LDL)] phases are present. All phase transitions (GAS-LDL, GAS-HDL, and LDL-HDL) are discontinuous, and the three phases coexist at a triple point. A line of temperatures of maximum density in the isobars is found in the metastable GAS phase, as well as another line of temperatures of minimum density appears in the LDL phase, part of it in the stable region and another in the metastable region of this phase. These findings are at variance with simulational results for the same model on the triangular lattice, which suggested a phase diagram with two critical points. However, our results show very good quantitative agreement with the simulations, both for the coexistence loci and the densities of particles and of hydrogen bonds. We discuss the comparison of the simulations with our results.

Entropy reduction effect imposed by hydrogen bond formation on protein folding cooperativity: evidence from a hydrophobic minimalist model.

Conformational restrictions imposed by hydrogen bond formation during protein folding are investigated by Monte Carlo simulations of a non-native-centric, two-dimensional, hydrophobic model in which the formation of favorable contacts is coupled to an effective reduction in lattice coordination. This scheme is intended to mimic the requirement that polar backbone groups of real proteins must form hydrogen bonds concomitantly to their burial inside the apolar protein core. In addition to the square lattice, with z=3 conformations per monomer, we use extensions in which diagonal step vectors are allowed, resulting in z=5 and z=7. Thermodynamics are governed by the hydrophobic energy function, according to which hydrophobic monomers tend to make contacts unspecifically while the reverse is true for hydrophilic monomers, with the additional restriction that only contacts between monomers adopting one of zh

Relevance of structural segregation and chain compaction for the thermodynamics of folding of a hydrophobic protein model.

The relevance of inside-outside segregation and chain compaction for the thermodynamics of folding of a hydrophobic protein model is probed by complete enumeration of two-dimensional chains of up to 18 monomers in the square lattice. The exact computation of Z scores for uniquely designed sequences confirms that Z tends to decrease linearly with sigma square root of N, as previously suggested by theoretical analysis and Monte Carlo simulations, where sigma, the standard deviation of the number of contacts made by different monomers in the target structure, is a measure of structural segregation and N is the chain length. The probability that the target conformation is indeed the unique global energy minimum of the designed sequence is found to increase dramatically with sigma, approaching unity at maximal segregation. However, due to the huge number of conformations with sub-maximal values of sigma, which correspond to intermediate, only mildly discriminative, values of Z, in addition to significant oscillations of Z around its estimated value, the probability that a correctly designed sequence corresponds to a maximally segregated conformation is small. This behavior of Z also explains the observed relation between sigma and different measures of folding cooperativity of correctly designed sequences.

Non-native interactions, effective contact order, and protein folding: a mutational investigation with the energetically frustrated hydrophobic model.

By Monte Carlo simulations, we explored the effect of single mutations on the thermodynamics and kinetics of the folding of a two-dimensional, energetically frustrated, hydrophobic protein model. Phi-Value analysis, corroborated by simulations beginning from given sets of judiciously chosen initial contacts, suggests that the transition state of the model consists of a limited region of the native structure, that is, a folding nucleus. It seems that the most important contacts in the transition state (large and positive Phi) are not the ones with the highest contact order, because in this case the entropic cost of their formation would be too high, but exactly the ones that decrease the entropic cost of difficult contacts, reducing their effective contact order. Mutations of internal monomers involved in high-order contacts were actually the ones resulting in the fastest kinetics (and Phi < 0), indicating they tend to make low order, non-native contacts of low entropic cost that stabilize the unfolded state with respect to the transition state. Folding acceleration by other non-native interactions was also observed and a simple general mechanism is proposed according to which non-native contacts can act indirectly over the folding nucleus, "chelating" out potentially harmful contacts. The polymer graph of our model, which facilitates the visualization of effective contact orders, successfully suggests the relative kinetic importance of different contacts and is reasonably consistent with analogous graphs for the well characterized family of SH3 domains.