Secondary Structures in Long Compact Polymers

Compact polymers are self-avoiding random walks which visit every site on a lattice. This polymer model is used widely for studying statistical problems inspired by protein folding. One difficulty with using compact polymers to perform numerical calculations is generating a sufficiently large number of randomly sampled configurations. We present a Monte-Carlo algorithm which uniformly samples compact polymer configurations in an efficient manner allowing investigations of chains much longer than previously studied. Chain configurations generated by the algorithm are used to compute statistics of secondary structures in compact polymers. We determine the fraction of monomers participating in secondary structures, and show that it is self averaging in the long chain limit and strictly less than one. Comparison with results for lattice models of open polymer chains shows that compact chains are significantly more likely to form secondary structure.Comment: 14 pages, 14 figure

Blind protein structure prediction using accelerated free-energy simulations.

We report a key proof of principle of a new acceleration method [Modeling Employing Limited Data (MELD)] for predicting protein structures by molecular dynamics simulation. It shows that such Boltzmann-satisfying techniques are now sufficiently fast and accurate to predict native protein structures in a limited test within the Critical Assessment of Structure Prediction (CASP) community-wide blind competition

Unbiased sampling of globular lattice proteins in three dimensions

We present a Monte Carlo method that allows efficient and unbiased sampling of Hamiltonian walks on a cubic lattice. Such walks are self-avoiding and visit each lattice site exactly once. They are often used as simple models of globular proteins, upon adding suitable local interactions. Our algorithm can easily be equipped with such interactions, but we study here mainly the flexible homopolymer case where each conformation is generated with uniform probability. We argue that the algorithm is ergodic and has dynamical exponent z=0. We then use it to study polymers of size up to 64^3 = 262144 monomers. Results are presented for the effective interaction between end points, and the interaction with the boundaries of the system

Binding of Small-Molecule Ligands to Proteins: “What You See” Is Not Always “What You Get”

We review insights from computational studies of affinities of ligands binding to proteins. The power of structural biology is in translating knowledge of protein structures into insights about their forces, binding, and mechanisms. However, the complementary power of computer modeling is in showing “the rest of the story” (i.e., how motions and ensembles and alternative conformers and the entropies and forces that cannot be seen in single molecular structures also contribute to binding affinities). Upon binding to a protein, a ligand can bind in multiple orientations; the protein or ligand can be deformed by the binding event; waters, ions, or cofactors can have unexpected involvement; and conformational or solvation entropies can sometimes play large and otherwise unpredictable roles. Computer modeling is helping to elucidate these factors

Analytical description of finite size effects for RNA secondary structures

The ensemble of RNA secondary structures of uniform sequences is studied analytically. We calculate the partition function for very long sequences and discuss how the cross-over length, beyond which asymptotic scaling laws apply, depends on thermodynamic parameters. For realistic choices of parameters this length can be much longer than natural RNA molecules. This has to be taken into account when applying asymptotic theory to interpret experiments or numerical results.Comment: 10 pages, 13 figures, published in Phys. Rev.

A possible mechanism for cold denaturation of proteins at high pressure

We study cold denaturation of proteins at high pressures. Using multicanonical Monte Carlo simulations of a model protein in a water bath, we investigate the effect of water density fluctuations on protein stability. We find that above the pressure where water freezes to the dense ice phase ($\approx2$ kbar), the mechanism for cold denaturation with decreasing temperature is the loss of local low-density water structure. We find our results in agreement with data of bovine pancreatic ribonuclease A.Comment: 4 pages for double column and single space. 3 figures Added references Changed conten

Exact enumeration of Hamiltonian circuits, walks, and chains in two and three dimensions

We present an algorithm for enumerating exactly the number of Hamiltonian chains on regular lattices in low dimensions. By definition, these are sets of k disjoint paths whose union visits each lattice vertex exactly once. The well-known Hamiltonian circuits and walks appear as the special cases k=0 and k=1 respectively. In two dimensions, we enumerate chains on L x L square lattices up to L=12, walks up to L=17, and circuits up to L=20. Some results for three dimensions are also given. Using our data we extract several quantities of physical interest

Timing Robustness in the Budding and Fission Yeast Cell Cycles

Robustness of biological models has emerged as an important principle in systems biology. Many past analyses of Boolean models update all pending changes in signals simultaneously (i.e., synchronously), making it impossible to consider robustness to variations in timing that result from noise and different environmental conditions. We checked previously published mathematical models of the cell cycles of budding and fission yeast for robustness to timing variations by constructing Boolean models and analyzing them using model-checking software for the property of speed independence. Surprisingly, the models are nearly, but not totally, speed-independent. In some cases, examination of timing problems discovered in the analysis exposes apparent inaccuracies in the model. Biologically justified revisions to the model eliminate the timing problems. Furthermore, in silico random mutations in the regulatory interactions of a speed-independent Boolean model are shown to be unlikely to preserve speed independence, even in models that are otherwise functional, providing evidence for selection pressure to maintain timing robustness. Multiple cell cycle models exhibit strong robustness to timing variation, apparently due to evolutionary pressure. Thus, timing robustness can be a basis for generating testable hypotheses and can focus attention on aspects of a model that may need refinement

Gene Expression Commons: an open platform for absolute gene expression profiling.

Gene expression profiling using microarrays has been limited to comparisons of gene expression between small numbers of samples within individual experiments. However, the unknown and variable sensitivities of each probeset have rendered the absolute expression of any given gene nearly impossible to estimate. We have overcome this limitation by using a very large number (>10,000) of varied microarray data as a common reference, so that statistical attributes of each probeset, such as the dynamic range and threshold between low and high expression, can be reliably discovered through meta-analysis. This strategy is implemented in a web-based platform named "Gene Expression Commons" (https://gexc.stanford.edu/) which contains data of 39 distinct highly purified mouse hematopoietic stem/progenitor/differentiated cell populations covering almost the entire hematopoietic system. Since the Gene Expression Commons is designed as an open platform, investigators can explore the expression level of any gene, search by expression patterns of interest, submit their own microarray data, and design their own working models representing biological relationship among samples

Heteropolymer Sequence Design and Preferential Solvation of Hydrophilic Monomers: One More Application of Random Energy Model

In this paper, we study the role of surface of the globule and the role of interactions with the solvent for designed sequence heteropolymers using random energy model (REM). We investigate the ground state energy and surface monomer composition distribution. By comparing the freezing transition in random and designed sequence heteropolymers, we discuss the effects of design. Based on our results, we are able to show under which conditions solvation effect improves the quality of sequence design. Finally, we study sequence space entropy and discuss the number of available sequences as a function of imposed requirements for the design quality