Freezing Transition of Random Heteropolymers Consisting of an Arbitrary Set of Monomers

Mean field replica theory is employed to analyze the freezing transition of random heteropolymers comprised of an arbitrary number ($q$) of types of monomers. Our formalism assumes that interactions are short range and heterogeneity comes only from pairwise interactions, which are defined by an arbitrary $q \times q$ matrix. We show that, in general, there exists a freezing transition from a random globule, in which the thermodynamic equilibrium is comprised of an essentially infinite number polymer conformations, to a frozen globule, in which equilibrium ensemble is dominated by one or very few conformations. We also examine some special cases of interaction matrices to analyze the relationship between the freezing transition and the nature of interactions involved.Comment: 30 pages, 1 postscript figur

Free Energy Self-Averaging in Protein-Sized Random Heteropolymers

Current theories of heteropolymers are inherently macrpscopic, but are applied to folding proteins which are only mesoscopic. In these theories, one computes the averaged free energy over sequences, always assuming that it is self-averaging -- a property well-established only if a system with quenched disorder is macroscopic. By enumerating the states and energies of compact 18, 27, and 36mers on a simplified lattice model with an ensemble of random sequences, we test the validity of the self-averaging approximation. We find that fluctuations in the free energy between sequences are weak, and that self-averaging is a valid approximation at the length scale of real proteins. These results validate certain sequence design methods which can exponentially speed up computational design and greatly simplify experimental realizations.Comment: 4 pages, 3 figure

Random walks in the space of conformations of toy proteins

Monte Carlo dynamics of the lattice 48 monomers toy protein is interpreted as a random walk in an abstract (discrete) space of conformations. To test the geometry of this space, we examine the return probability $P(T)$, which is the probability to find the polymer in the native state after $T$ Monte Carlo steps, provided that it starts from the native state at the initial moment. Comparing computational data with the theoretical expressions for $P(T)$ for random walks in a variety of different spaces, we show that conformational spaces of polymer loops may have non-trivial dimensions and exhibit negative curvature characteristic of Lobachevskii (hyperbolic) geometry.Comment: 4 pages, 3 figure

A Multicanonical Molecular Dynamics Study on a Simple Bead-Spring Model for Protein Folding

We have performed a multicanonical molecular dynamics simulation on a simple model protein.We have studied a model protein composed of charged, hydrophobic, and neutral spherical bead monomers.Since the hydrophobic interaction is considered to significantly affect protein folding, we particularly focus on the competition between effects of the Coulomb interaction and the hydrophobic interaction. We found that the transition which occurs upon decreasing the temperature is markedly affected by the change in both parameters and forms of the hydrophobic potential function, and the transition changes from first order to second order, when the Coulomb interaction becomes weaker.Comment: 7 pages, 6 postscript figures, To appear in J.Phys.Soc.Jpn. Vol.70 No.

Geometrically Reduced Number of Protein Ground State Candidates

Geometrical properties of protein ground states are studied using an algebraic approach. It is shown that independent from inter-monomer interactions, the collection of ground state candidates for any folded protein is unexpectedly small: For the case of a two-parameter Hydrophobic-Polar lattice model for $L$-mers, the number of these candidates grows only as $L^2$. Moreover, the space of the interaction parameters of the model breaks up into well-defined domains, each corresponding to one ground state candidate, which are separated by sharp boundaries. In addition, by exact enumeration, we show there are some sequences which have one absolute unique native state. These absolute ground states have perfect stability against change of inter-monomer interaction potential.Comment: 9 page, 4 ps figures are include

Recognition of fold- and function-specific sites in the ligand-binding domain of the thyroid hormone receptor-like family

Background: The thyroid hormone receptor-like (THR-like) family is the largest transcription factors family belonging to the nuclear receptor superfamily, which directly binds to DNA and regulates the gene expression and thereby controls various metabolic processes in a ligand-dependent manner. The THR-like family contains receptors THRs, RARs, VDR, PPARs, RORs, Rev-erbs, CAR, PXR, LXRs, and others. THR-like receptors are involved in many aspects of human health, including development, metabolism and homeostasis. Therefore, it is considered an important therapeutic target for various diseases such as osteoporosis, rickets, diabetes, etc. Methods: In this study, we have performed an extensive sequence and structure analysis of the ligand-binding domain (LBD) of the THR-like family spanning multiple taxa. We have use different computational tools (information-theoretic measures; relative entropy) to predict the key residues responsible for fold and functional specificity in the LBD of the THR-like family. The MSA of THR-like LBDs was further used as input in conservation studies and phylogenetic clustering studies. Results: Phylogenetic analysis of the LBD domain of THR-like proteins resulted in the clustering of eight subfamilies based on their sequence homology. The conservation analysis by relative entropy (RE) revealed that structurally important residues are conserved throughout the LBDs in the THR-like family. The multi-harmony conservation analysis further predicted specificity in determining residues in LBDs of THR-like subfamilies. Finally, fold and functional specificity determining residues (residues critical for ligand, DBD and coregulators binding) were mapped on the three-dimensional structure of thyroid hormone receptor protein. We then compiled a list of natural mutations in THR-like LBDs and mapped them along with fold and function-specific mutations. Some of the mutations were found to have a link with severe diseases like hypothyroidism, rickets, obesity, lipodystrophy, epilepsy, etc. Conclusion: Our study identifies fold and function-specific residues in THR-like LBDs. We believe that this study will be useful in exploring the role of these residues in the binding of different drugs, ligands, and protein-protein interaction among partner proteins. So this study might be helpful in the rational design of either ligands or receptors

Protein folding using contact maps

We present the development of the idea to use dynamics in the space of contact maps as a computational approach to the protein folding problem. We first introduce two important technical ingredients, the reconstruction of a three dimensional conformation from a contact map and the Monte Carlo dynamics in contact map space. We then discuss two approximations to the free energy of the contact maps and a method to derive energy parameters based on perceptron learning. Finally we present results, first for predictions based on threading and then for energy minimization of crambin and of a set of 6 immunoglobulins. The main result is that we proved that the two simple approximations we studied for the free energy are not suitable for protein folding. Perspectives are discussed in the last section.Comment: 29 pages, 10 figure

On the exact gravitational lens equation in spherically symmetric and static spacetimes

Lensing in a spherically symmetric and static spacetime is considered, based on the lightlike geodesic equation without approximations. After fixing two radius values r_O and r_S, lensing for an observation event somewhere at r_O and static light sources distributed at r_S is coded in a lens equation that is explicitly given in terms of integrals over the metric coefficients. The lens equation relates two angle variables and can be easily plotted if the metric coefficients have been specified; this allows to visualize in a convenient way all relevant lensing properties, giving image positions, apparent brightnesses, image distortions, etc. Two examples are treated: Lensing by a Barriola-Vilenkin monopole and lensing by an Ellis wormhole.Comment: REVTEX, 11 pages, 12 eps-figures, figures partly improved, minor revision

Origin of Native Driving Force in Protein Folding

We derive an expression with four adjustable parameters that reproduces well the 20x20 Miyazawa-Jernigan potential matrix extracted from known protein structures. The numerical values of the parameters can be approximately computed from the surface tension of water, water-screened dipole interactions between residues and water and among residues, and average exposures of residues in folded proteins.Comment: LaTeX file, Postscript file; 4 pages, 1 figure (mij.eps), 2 table

Empowerment through enrichment on-farm IPM of chickpea in Nepal-2. Information bulletin no. 65

Empowerment Through Enrichment is the second information bulletin and is the part of the Project on ‘IPM of chickpea in Nepal’. It contains information about the mid-term evaluation of the project. This is in continuation of the first study, Chickpea Production Constraints and Promotion of Integrated Pest Management in Nepal. The mid-term evaluation revealed that the success of adoption of IPM technology was due to socio economic emancipation of peasants, freedom from the clutches of usurers and poorest among the poor being benefited. Market linkage strengthened farmer’s faith in technologies. Since the chickpea is highly remunerative as a crop of rice fallow lands in winter (rabi), the technology is fast spreading to other villages. Sustainable environment will make the intervention spread faster. Removal of poverty by IPM-chickpea in Nepal is quantified in the third bulletin, Wealth Generation through Chickpea Revolution