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

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

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

Farmers' empowerment, soil enrichment and wealth generation through chickpea-IPM in Nepal

IPM for chickpea is a sustainable development model developed andimplemented in Nepal by DFlD, NRI, l CRISAT and NARC. It haspositively affected soil fertility, human health and aided incomegeneration for the poor. The study was conducted with the help ofPRA, RRA techniques. The results suggest that IPM-chickpea hasbrought about a revolution in study villages. The empirical studies onchickpea-IPM cultivars show that the technology is an effective tool foreradicating hunger in Nepal's Terai region. The resulting starvation isprevented by systematically recreating a minimum level of incomes andentitlements. The project has proved that in the short run somethingeffective can be done to remedy these desperate situations.The production of chickpea will lead to higher yields of paddy;restoration of soil health and fertility; increase in human nutritionand reduce consumption of fertilizers; import substitution and exportspromotion; reduction in poverty, through wealth generation and socialupliftment, besides creating opportunities for development in Nepal.This project has provided food and nutritional security to farmers.The IPM-chickpea model can be replicated elsewhere in the worldwhere the same agroecological features exist

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

Atomistic structural ensemble refinement reveals non-native structure stabilizes a sub-millisecond folding intermediate of CheY

The dynamics of globular proteins can be described in terms of transitions between a folded native state and less-populated intermediates, or excited states, which can play critical roles in both protein folding and function. Excited states are by definition transient species, and therefore are difficult to characterize using current experimental techniques. Here, we report an atomistic model of the excited state ensemble of a stabilized mutant of an extensively studied flavodoxin fold protein CheY. We employed a hybrid simulation and experimental approach in which an aggregate 42 milliseconds of all-atom molecular dynamics were used as an informative prior for the structure of the excited state ensemble. This prior was then refined against small-angle X-ray scattering (SAXS) data employing an established method (EROS). The most striking feature of the resulting excited state ensemble was an unstructured N-terminus stabilized by non-native contacts in a conformation that is topologically simpler than the native state. Using these results, we then predict incisive single molecule FRET experiments as a means of model validation. This study demonstrates the paradigm of uniting simulation and experiment in a statistical model to study the structure of protein excited states and rationally design validating experiments

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

Dynamical chaos and power spectra in toy models of heteropolymers and proteins

The dynamical chaos in Lennard-Jones toy models of heteropolymers is studied by molecular dynamics simulations. It is shown that two nearby trajectories quickly diverge from each other if the heteropolymer corresponds to a random sequence. For good folders, on the other hand, two nearby trajectories may initially move apart but eventually they come together. Thus good folders are intrinsically non-chaotic. A choice of a distance of the initial conformation from the native state affects the way in which a separation between the twin trajectories behaves in time. This observation allows one to determine the size of a folding funnel in good folders. We study the energy landscapes of the toy models by determining the power spectra and fractal characteristics of the dependence of the potential energy on time. For good folders, folding and unfolding trajectories have distinctly different correlated behaviors at low frequencies.Comment: 8 pages, 9 EPS figures, Phys. Rev. E (in press

Molecular dynamics simulation of polymer helix formation using rigid-link methods

Molecular dynamics simulations are used to study structure formation in simple model polymer chains that are subject to excluded volume and torsional interactions. The changing conformations exhibited by chains of different lengths under gradual cooling are followed until each reaches a state from which no further change is possible. The interactions are chosen so that the true ground state is a helix, and a high proportion of simulation runs succeed in reaching this state; the fraction that manage to form defect-free helices is a function of both chain length and cooling rate. In order to demonstrate behavior analogous to the formation of protein tertiary structure, additional attractive interactions are introduced into the model, leading to the appearance of aligned, antiparallel helix pairs. The simulations employ a computational approach that deals directly with the internal coordinates in a recursive manner; this representation is able to maintain constant bond lengths and angles without the necessity of treating them as an algebraic constraint problem supplementary to the equations of motion.Comment: 15 pages, 14 figure