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.

Hidden scaling patterns and universality in written communication.

The temporal statistics exhibited by written correspondence appear to be media dependent, with features which have so far proven difficult to characterize. We explain the origin of these difficulties by disentangling the role of spontaneous activity from decision-based prioritizing processes in human dynamics, clocking all waiting times through each agent's "proper time" measured by activity. This unveils the same fundamental patterns in written communication across all media (letters, email, sms), with response times displaying truncated power-law behavior and average exponents near -3/2. When standard time is used, the response time probabilities are theoretically predicted to exhibit a bimodal character, which is empirically borne out by our newly collected years-long data on email. These perspectives on the temporal dynamics of human correspondence should aid in the analysis of interaction phenomena in general, including resource management, optimal pricing and routing, information sharing, and emergency handling.

Spontaneously broken neutral symmetry in an ecological system.

Spontaneous symmetry breaking plays a fundamental role in many areas of condensed matter and particle physics. A fundamental problem in ecology is the elucidation of the mechanisms responsible for biodiversity and stability. Neutral theory, which makes the simplifying assumption that all individuals (such as trees in a tropical forest)--regardless of the species they belong to--have the same prospect of reproduction, death, etc., yields gross patterns that are in accord with empirical data. We explore the possibility of birth and death rates that depend on the population density of species, treating the dynamics in a species-symmetric manner. We demonstrate that dynamical evolution can lead to a stationary state characterized simultaneously by both biodiversity and spontaneously broken neutral symmetry.

On species persistence-time distributions.

We present new theoretical and empirical results on the probability distributions of species persistence times in natural ecosystems. Persistence times, defined as the timespans occurring between species' colonization and local extinction in a given geographic region, are empirically estimated from local observations of species' presence/absence. A connected sampling problem is presented, generalized and solved analytically. Species persistence is shown to provide a direct connection with key spatial macroecological patterns like species-area and endemics-area relationships. Our empirical analysis pertains to two different ecosystems and taxa: a herbaceous plant community and a estuarine fish database. Despite the substantial differences in ecological interactions and spatial scales, we confirm earlier evidence on the general properties of the scaling of persistence times, including the predicted effects of the structure of the spatial interaction network. The framework tested here allows to investigate directly nature and extent of spatial effects in the context of ecosystem dynamics. The notable coherence between spatial and temporal macroecological patterns, theoretically derived and empirically verified, is suggested to underlie general features of the dynamic evolution of ecosystems.

Simplified exactly solvable model for ß-amyloid aggregation.

We propose an exactly solvable simplified statistical mechanical model for the thermodynamics of ß-amyloid aggregation, generalizing a well-studied model for protein folding. The monomer concentration is explicitly taken into account as well as a nontrivial dependence on the microscopic degrees of freedom of the single peptide chain, both in the α-helix folded isolated state and in the fibrillar one. The phase diagram of the model is studied and compared to the outcome of fibril formation experiments which is qualitatively reproduced.

Form of growing strings.

Patterns and forms adopted by nature are often the results of simple dynamical paradigms. Here we show that a growing self-interacting string attached to a tracking origin, modeled to resemble nascent polypeptides in vivo, develops helical structures which are more pronounced at the growing end. We also show that the dynamic growth ensemble shares several features of an equilibrium ensemble in which the growing end of the polymer is under an effective stretching force. A statistical analysis of native states of proteins shows that the signature of this nonequilibrium phenomenon has been fixed by evolution at the C terminus, the growing end of a nascent protein. These findings suggest how evolution may have built on the properties of a generic nonequilibrium growth process in favoring helical structures in nascent chains.

Pretransitional behavior of a water in liquid crystal microemulsion close to the demixing transition: evidence for intermicellar attraction mediated by paranematic fluctuations.

We present a study of a water-in-oil microemulsion in which surfactant coated water nanodroplets are dispersed in the isotropic phase of the thermotropic liquid-crystal penthyl-cyanobiphenyl (5CB). As the temperature is lowered below the isotropic to nematic phase transition of pure 5CB, the system displays a demixing transition leading to a coexistence of a droplet-rich isotropic phase with a droplet-poor nematic. The transition is anticipated, in the high T side, by increasing pretransitional fluctuations in 5CB molecular orientation and in the nanodroplet concentration. The observed phase behavior supports the notion that the nanosized droplets, while large enough for their statistical behavior to be probed via light scattering, are also small enough to act as impurities, disturbing the local orientational ordering of the liquid crystal and thus experiencing pretransitional attractive interaction mediated by paranematic fluctuations. The pretransitional behavior, together with the topology of the phase diagram, can be understood on the basis of a diluted Lebwohl-Lasher model which describes the nanodroplets simply as holes in the liquid crystal.

A new interpolation formula for semiflexible polymers.

A new formula for the force vs. extension relation is derived from the discrete version of the so-called Worm-like chain model. This formula correctly fits some recent experimental data on polymer stretching. Moreover, we have compared our formula with a Monte Carlo simulation of a semiflexible polymer.

Stepwise unfolding of collapsed polymers.

Motivated by recent experimental data on DNA stretching in presence of polyvalent counterions, we study the force-induced unfolding of a homopolymer on and off lattice. In the fixed force ensemble the globule unravels via a series of steps due to surface effects which play an important role for finite-size chains. This holds both for flexible and stiff polymers. We discuss in a qualitative way how this result may impact on the interpretation of DNA stretching experiments showing peaks in the characteristic curves, by extracting from the raw data the corresponding elongation- versus-force characteristic curves. Furthermore, approximate analytical and numerical calculations, valid in a quasi-equilibrium fixed stretch ensemble, and if the initial low-temperature state is ordered in a spool, show that the average force versus elongation displays peaks related to the geometry of the initial configuration. We finally argue how the proposed mechanisms identified for the arising of peaks may couple in the experiments, and comment on the role of dynamic effects.

Fluctuation mediated interaction and phase separation of nanoparticles in a liquid crystal solvent.

Water-in-oil microemulsions of nanodroplets in the isotropic phase of a thermotropic liquid crystal exhibit, with decreasing temperature and in anticipation of a demixing transition, enhanced correlation in fluctuations of both molecular orientation and droplet concentration. Mean field modeling of this pretransition behavior, on the basis of a lattice in which the nanodroplets are introduced as holes, shows that the observed interdroplet attractive interaction is produced by the disordering effect of the droplets on the liquid crystal and mediated solely by paranematic fluctuations.

Elucidation of the disulfide-folding pathway of hirudin by a topology-based approach.

A theoretical model for the folding of proteins containing disulfide bonds is introduced. The model exploits the knowledge of the native state to favor the progressive establishment of native interactions. At variance with traditional approaches based on native topology, not all native bonds are treated in the same way; in particular, a suitable energy term is introduced to account for the special strength of disulfide bonds, as well as their ability to undergo intramolecular reshuffling. The model thus possesses the minimal ingredients necessary to investigate the much debated issue of whether the refolding process occurs through partially structured intermediates with native or non-native disulfide bonds. This strategy is applied to a context of particular interest, the refolding process of hirudin, a thrombin-specific protease inhibitor, for which conflicting folding pathways have been proposed. We show that the only two parameters in the model (temperature and disulfide strength) can be tuned to reproduce well a set of experimental transitions between species with different number of formed disulfides. This model is then used to provide a characterization of the folding process and a detailed description of the species involved in the rate-limiting step of hirudin refolding.

Mechanical unfolding of directed polymers in a poor solvent: critical exponents.

We study the thermodynamics of an exactly solvable model of a self-interacting, partially directed self-avoiding walk in two dimensions when a force is applied on one end of the chain. The critical force for the unfolding is determined exactly, as a function of the temperature, below the Theta transition. The transition is of second order and is characterized by new critical exponents that are determined by a careful numerical analysis. The usual polymer critical index nu on the critical line, and another one which we call zeta, takes a nontrivial value that is numerically close to 2/3.

Stretching of a polymer below the theta point.

The unfolding of a polymer below the theta point when pulled by an external force is studied both in d=2 on the lattice and in d=3 off the lattice. At T=0 and for finite length chains, it is found that the globule unfolds via multiple steps, corresponding to transitions between different minima, in both cases. In d=3 one of these intermediates is a regular helix. In the infinite length limit, these steps have a qualitative effect only in d=2. The phase diagram in d=2 is determined via the transfer matrix. To rationalize these results, energy-entropy and renormalization group arguments are given.

Dynamical scaling of the DNA unzipping transition.

We report studies of the dynamics of a set of exactly solvable lattice models for the force-induced DNA unzipping transition. Besides yielding the whole equilibrium phase diagram, which reveals a reentrance, these models enable us to characterize the dynamics of the process starting from a nonequilibrium initial condition. The thermal melting of DNA displays a model dependent time evolution. On the contrary, the dynamical mechanism for the unzipping by force is very robust and the scaling behavior is independent of the details of the description and, hence, superuniversal.

Master equation approach to molecular motors.

A master equation approach to molecular motors allows us to describe a mechanochemical cyclic system where chemical and translational degrees of freedom are treated on an equal footing. A generalized detailed balance condition in the out-of-equilibrium regime is shown to be compatible with the Fokker-Planck equation in the continuum limit. The Onsager reciprocity relations hold for stationary states close to equilibrium, provided the generalized detailed balance condition is satisfied. Semiphenomenological considerations in the case of motor proteins lead to a discrete kinetics model, for which interesting observable quantities may be directly calculated and compared with experimental data.

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.

Phase diagram of force-induced DNA unzipping in exactly solvable models.

The mechanical separation of a double helical DNA structure induced by forces pulling apart the two DNA strands ("unzipping") has been the subject of recent experiments. Analytical results are obtained within various models of interacting pairs of directed walks in the (1,1,ellipsis,1) direction on the hypercubic lattice, and the phase diagram in the force-temperature plane is studied for a variety of cases. The scaling behavior is determined at both the unzipping and melting transitions. We confirm the existence of a cold denaturation transition recently observed in numerical simulations: for a finite range of forces, the system is unzipped by decreasing the temperature. The existence of this transition is rigorously established for generic lattice and continuum space models.

Role of native-state topology in the stabilization of intracellular antibodies.

The role played by the geometric position of each amino acid in the folding process of the immunoglobulin (Ig) variable domain is identified and measured through molecular dynamics simulations of models based on the topology of its native state. This measure allows identifying the parts of the protein that, for geometrical reasons, when mutated, would result in relevant protein stability changes. Simulations were performed without considering the covalent disulfide bond present in most of the Ig domains. The results are in good agreement with site-directed mutagenesis experiments on the folding of intracellular antibodies in which the disulfide bond does not form. We also found agreement with data on amino acid conservation in the Ig variable domain sequences. This indicates a new way for a rational approach to the design of intracellular antibodies more resistant to the suppression of the disulfide bond that occurs in the cytoplasm.

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.