Generalized CNS arousal: An elementary force within the vertebrate nervous system.

Why do animals and humans do anything at all? Arousal is the most powerful and essential function of the brain, a continuous function that accounts for the ability of animals and humans to respond to stimuli in the environment by producing muscular responses. Following decades of psychological, neurophysiological and molecular investigations, generalized CNS arousal can now be analyzed using approaches usually applied to physical systems. The concept of "criticality" is a state that illustrates an advantage for arousal systems poised near a phase transition. This property provides speed and sensitivity and facilitates the transition of the system into different brain states, especially as the brain crosses a phase transition from less aroused to more aroused states. In summary, concepts derived from applied mathematics of physical systems will now find their application in this area of neuroscience, the neurobiology of CNS arousal.

Phenotypic differences in viral immune escape explained by linking within-host dynamics to host-population immunity.

Viruses that do not cause life-long immunity persist by evolving rapidly in response to prevailing host immunity. The immune-escape mutants emerge frequently, displacing or co-circulating with native strains even though mutations conferring immune evasion are often detrimental to viral replication. The epidemiological dynamics of immune-escape in acute-infection viruses with high transmissibility have been interpreted mainly through immunity dynamics at the host population level, despite the fact that immune-escape evolution involves dynamical processes that feedback across the within- and between-host scales. To address this gap, we use a nested model of within- and between-host infection dynamics to examine how the interaction of viral replication rate and cross-immunity imprint host population immunity, which in turn determines viral immune escape. Our explicit consideration of direct and immune-mediated competitive interactions between strains within-hosts revealed three insights pertaining to risk and control of viral immune-escape: (1) replication rate and immune-stimulation deficiencies (i.e., original antigenic sin) act synergistically to increase immune escape, (2) immune-escape mutants with replication deficiencies relative to their wildtype progenitor are most successful under moderate cross-immunity and frequent re-infections, and (3) the immunity profile along short host-transmission chains (local host-network structure) is a key determinant of immune escape.

Protein threading by learning.

By using techniques borrowed from statistical physics and neural networks, we determine the parameters, associated with a scoring function, that are chosen optimally to ensure complete success in threading tests in a training set of proteins. These parameters provide a quantitative measure of the propensities of amino acids to be buried or exposed and to be in a given secondary structure and are a good starting point for solving both the threading and design problems.

Conformations of proteins in equilibrium.

We introduce a simple theoretical approach for an equilibrium study of proteins with known native-state structures. We test our approach with results on well-studied globular proteins, chymotrypsin inhibitor (2ci2), barnase, and the alpha spectrin SH3 domain, and present evidence for a hierarchical onset of order on lowering the temperature with significant organization at the local level even at high temperatures. A further application to the folding process of HIV-1 protease shows that the model can be reliably used to identify key folding sites that are responsible for the development of drug resistance.

Boundary conditions at a fluid-solid interface.

We study the boundary conditions at a fluid-solid interface using molecular dynamics simulations covering a broad range of fluid-solid interactions and fluid densities and both simple and chain-molecule fluids. The slip length is shown to be independent of the type of flow, but rather is related to the fluid organization near the solid, as governed by the fluid-solid molecular interactions.

Dynamic modeling of gene expression data.

We describe the time evolution of gene expression levels by using a time translational matrix to predict future expression levels of genes based on their expression levels at some initial time. We deduce the time translational matrix for previously published DNA microarray gene expression data sets by modeling them within a linear framework by using the characteristic modes obtained by singular value decomposition. The resulting time translation matrix provides a measure of the relationships among the modes and governs their time evolution. We show that a truncated matrix linking just a few modes is a good approximation of the full time translation matrix. This finding suggests that the number of essential connections among the genes is small.

Learning effective amino acid interactions through iterative stochastic techniques.

The prediction of the three-dimensional structures of the native states of proteins from the sequences of their amino acids is one of the most important challenges in molecular biology. An essential task for solving this problem within coarse-grained models is the deduction of effective interaction potentials between the amino acids. Over the years, several techniques have been developed to extract potentials that are able to discriminate satisfactorily between the native and nonnative folds of a preassigned protein sequence. In general, when these potentials are used in actual dynamical folding simulations, they lead to a drift of the native structure outside the quasinative basin. In this article, we present and validate an approach to overcome this difficulty. By exploiting several numerical and analytical tools, we set up a rigorous iterative scheme to extract potentials satisfying a prerequisite of any viable potential: the stabilization of proteins within their native basin (less than 3-4 A RMSD). The scheme is flexible and is demonstrated to be applicable to a variety of parameterizations of the energy function, and it provides in each case the optimal potentials.

Deciphering the folding kinetics of transmembrane helical proteins.

Nearly a quarter of genomic sequences and almost half of all receptors that are likely to be targets for drug design are integral membrane proteins. Understanding the detailed mechanisms of the folding of membrane proteins is a largely unsolved, key problem in structural biology. Here, we introduce a general model and use computer simulations to study the equilibrium properties and the folding kinetics of a C(alpha)-based two-helix bundle fragment (comprised of 66 aa) of bacteriorhodopsin. Various intermediates are identified and their free energy are calculated together with the free energy barrier between them. In 40% of folding trajectories, the folding rate is considerably increased by the presence of nonobligatory intermediates acting as traps. In all cases, a substantial portion of the helices is rapidly formed. This initial stage is followed by a long period of consolidation of the helices accompanied by their correct packing within the membrane. Our results provide the framework for understanding the variety of folding pathways of helical transmembrane proteins.

Role of secondary motifs in fast folding polymers: a dynamical variational principle.

A fascinating and open question challenging biochemistry, physics, and even geometry is the presence of highly regular motifs such as alpha helices in the folded state of biopolymers and proteins. Stimulating explanations ranging from chemical propensity to simple geometrical reasoning have been invoked to rationalize the existence of such secondary structures. We formulate a dynamical variational principle for selection in conformation space based on the requirement that the backbone of the native state of biologically viable polymers be rapidly accessible from the denatured state. The variational principle is shown to result in the emergence of helical order in compact structures.

Topology of the fittest transportation network.

The presence or absence of loops in the emergent transportation networks, that are characterized by a minimum overall cost, is shown to depend on the convexity of the cost function for the local transportation of material. Our results are directly applicable to a variety of situations across disciplines.

Optimal shapes of compact strings.

Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest packing fraction; only recently has it been proved that the answer for infinite systems is a face-centred-cubic lattice. This simply stated problem has had a profound impact in many areas, ranging from the crystallization and melting of atomic systems, to optimal packing of objects and the sub-division of space. Here we study an analogous problem--that of determining the optimal shapes of closely packed compact strings. This problem is a mathematical idealization of situations commonly encountered in biology, chemistry and physics, involving the optimal structure of folded polymeric chains. We find that, in cases where boundary effects are not dominant, helices with a particular pitch-radius ratio are selected. Interestingly, the same geometry is observed in helices in naturally occurring proteins.

Fundamental patterns underlying gene expression profiles: simplicity from complexity.

Analysis of previously published sets of DNA microarray gene expression data by singular value decomposition has uncovered underlying patterns or "characteristic modes" in their temporal profiles. These patterns contribute unequally to the structure of the expression profiles. Moreover, the essential features of a given set of expression profiles are captured using just a small number of characteristic modes. This leads to the striking conclusion that the transcriptional response of a genome is orchestrated in a few fundamental patterns of gene expression change. These patterns are both simple and robust, dominating the alterations in expression of genes throughout the genome. Moreover, the characteristic modes of gene expression change in response to environmental perturbations are similar in such distant organisms as yeast and human cells. This analysis reveals simple regularities in the seemingly complex transcriptional transitions of diverse cells to new states, and these provide insights into the operation of the underlying genetic networks.

Scoring functions in protein folding and design.

We present an analysis of the assumptions behind some of the most commonly used methods for evaluating the goodness of the fit between a sequence and a structure. Our studies on a lattice model show that methods based on statistical considerations are easy to use and can capture some of the features of protein-like sequences and their corresponding native states, but unfortunately are incapable of recognizing, with certainty, the native-like conformation of a sequence among a set of decoys. Meanwhile, an optimization method, entailing the determination of the parameters of an effective free energy of interaction, is much more reliable in recognizing the native state of a sequence. However, the statistical method is shown to perform quite well in tests of protein design.

Size and form in efficient transportation networks.

Many biological processes, from cellular metabolism to population dynamics, are characterized by allometric scaling (power-law) relationships between size and rate. An outstanding question is whether typical allometric scaling relationships--the power-law dependence of a biological rate on body mass--can be understood by considering the general features of branching networks serving a particular volume. Distributed networks in nature stem from the need for effective connectivity, and occur both in biological systems such as cardiovascular and respiratory networks and plant vascular and root systems, and in inanimate systems such as the drainage network of river basins. Here we derive a general relationship between size and flow rates in arbitrary networks with local connectivity. Our theory accounts in a general way for the quarter-power allometric scaling of living organisms, recently derived under specific assumptions for particular network geometries. It also predicts scaling relations applicable to all efficient transportation networks, which we verify from observational data on the river drainage basins. Allometric scaling is therefore shown to originate from the general features of networks irrespective of dynamical or geometric assumptions.

Statistical mechanics of protein-like heteropolymers.

A strategy is outlined for obtaining the free energy of a typical designed heteropolymer. The design procedure considers the probability that the target conformation is occupied in comparison with all the other conformations that could house the given sequence. Numerical calculations on lattice heteropolymer models are presented to illustrate the key physical principles.

Design of proteins with hydrophobic and polar amino acids.

A two amino acid (hydrophobic and polar) scheme is used to perform the design on target conformations corresponding to the native states of 20 single chain proteins. Strikingly, the percentage of successful identification of the nature of the residues benchmarked against naturally occurring proteins and their homologues is around 75%, independent of the complexity of the design procedure. Typically, the lowest success rate occurs for residues such as alanine that have a high secondary structure functionality. Using a simple lattice model, we argue that one possible shortcoming of the model studied may involve the coarse-graining of the 20 kinds of amino acids into just two effective types.

Structure-based design of model proteins.

A structure-based, sequence-design procedure is proposed in which one considers a set of decoy structures that compete significantly with the target structure in being low energy conformations. The decoy structures are chosen to have strong overlaps in contacts with the putative native state. The procedure allows the design of sequences with large and small stability gaps in a random-bond heteropolymer model in both two and three dimensions by an appropriate assignment of the contact energies to both the native and nonnative contacts. The design procedure is also successfully applied to the two-dimensional HP model.

Interaction potentials for protein folding.

We outline a general strategy for determining the effective coarse-grained interactions between the amino acids of a protein from the experimentally derived native-state structures. The method is, in principle, free from any adjustable or empirically determined parameters, and it is tested on simple models and compared with other existing approaches.