Nonlinear optical spectroscopy of chiral molecules

We review nonlinear optical processes that are specific to chiral molecules in solution and on surfaces. In contrast to conventional natural optical activity phenomena, which depend linearly on the electric field strength of the optical field, we discuss how optical processes that are nonlinear (quadratic, cubic, and quartic) functions of the electromagnetic field strength may probe optically active centers and chiral vibrations. We show that nonlinear techniques open entirely new ways of exploring chirality in chemical and biological systems: The cubic processes give rise to nonlinear circular dichroism and nonlinear optical rotation and make it possible to observe dynamic chiral processes at ultrafast time scales. The quadratic second-harmonic and sum-frequency-generation phenomena and the quartic processes may arise entirely in the electric-dipole approximation and do not require the use of circularly polarized light to detect chirality. They provide surface selectivity and their observables can be relatively much larger than in linear optical activity. These processes also give rise to the generation of light at a new color, and in liquids this frequency conversion only occurs if the solution is optically active. We survey recent chiral nonlinear optical experiments and give examples of their application to problems of biophysical interest.     

Games network and application to PAs system

In this article, we present a game theory based framework, named games network, for modeling biological interactions. After introducing the theory, we more precisely describe the methodology to model biological interactions. Then we apply it to the plasminogen activator system (PAs) which is a signal transduction pathway involved in cancer cell migration. The games network theory extends game theory by including the locality of interactions. Each game in a games network represents local interactions between biological agents. The PAs system is implicated in cytoskeleton modifications via regulation of actin and microtubules, which in turn favors cell migration. The games network model has enabled us a better understanding of the regulation involved in the PAs system.     

Reciprocal sign epistasis is a necessary condition for multi-peaked fitness landscapes

Having multiple peaks within fitness landscapes critically affects the course of evolution, but whether their presence imposes specific requirements at the level of genetic interactions remains unestablished. Here we show that to exhibit multiple fitness peaks, a biological system must contain reciprocal sign epistatic interactions, which are defined as genetic changes that are separately unfavorable but jointly advantageous. Using Morse theory, we argue that it is impossible to formulate a sufficient condition for multiple peaks in terms of local genetic interactions. These findings indicate that systems incapable of reciprocal sign epistasis will always possess a single fitness peak. However, reciprocal sign epistasis should be pervasive in nature as it is a logical consequence of specificity in molecular interactions. The results thus predict that specific molecular interactions may yield multiple fitness peaks, which can be tested experimentally.     

An exact expression to calculate the derivatives of position-dependent observables in molecular simulations with flexible constraints

In this work, we introduce an algorithm to compute the derivatives of physical observables along the constrained subspace when flexible constraints are imposed on the system (i.e., constraints in which the constrained coordinates are fixed to configuration-dependent values). The presented scheme is exact, it does not contain any tunable parameter, and it only requires the calculation and inversion of a sub-block of the Hessian matrix of second derivatives of the function through which the constraints are defined. We also present a practical application to the case in which the sought observables are the Euclidean coordinates of complex molecular systems, and the function whose minimization defines the flexible constraints is the potential energy. Finally, and in order to validate the method, which, as far as we are aware, is the first of its kind in the literature, we compare it to the natural and straightforward finite-differences approach in a toy system and in three molecules of biological relevance: methanol, N-methyl-acetamide and a tri-glycine peptide.     

A network of net-workers: report of the Euresco conference on 'Bacterial Neural Networks' held at San Feliu (Spain) from 8 to 14 May 2004

In May 2004, over 100 bacteriologists from 19 different countries discussed recent progress in identification and understanding of individual signal transfer mechanisms in bacteria and in the mutual interactions between these systems to form a functional living cell. The meeting was held in San Feliu and supported by ESF and EMBO. In part through the extensive sequencing efforts of the past few years, the bulk of the bacterial signal transfer systems have been resolved and their detailed characterization is revealing such characteristics as signal specificity, signalling rate constants, molecular interaction affinities, subcellular localization, etc., which should provide a solid basis to a computational extension of this field of studies. In parallel, the new genomics techniques are providing tools to characterize the way a collection of such systems interact in an individual cell, to give rise to 'life'. Systems theory provides rational and convenient ways to bring order to the wide range of observables thus obtained. Ultimately, the performance of engineered design will have to prove whether or not we know enough about the processes involved.     

An analysis of the analysis of herbivore population dynamics

Time series analysis of herbivore data with weather included as covariate is commonly used as a mean to shed light on the state and ecology of the studied population. Conclusions about the herbivore population are drawn from statistical parameter values and presence/absence in the most parsimonious model. However, this procedure is only reliable if the statistical parameters have general interpretations regardless of system characteristics. Here we investigated the extent to which this is true by deriving six different vegetation–herbivore-systems and analyzing their respective statistical parameters. The analysis was done in both continuous and discrete time. It turned out that both density parameters (a₁ and a₂) and rainfall coefficients change with biological interactions and amount of average rainfall, and they do so in different ways in different systems. This means that there is no valid general interpretation of them and, most important, the probability of detecting density dependence and effects of rainfall vary between systems. Hence, you can not make inference about the biological processes from statistical analysis without knowing the system that you study and what model best describes the interactions within it.     

On the number of experiments required to find the causal structure of complex systems

The need to capture the complexity of biological systems in a simpler formalism is the underlying impetus of biological sciences. Understanding the function of many biological complex systems, such as genetic networks or molecular signalling pathways, requires precise identification of the interactions between their individual components. A number of questions in the study of complex systems are then important-in particular, what can be inferred about the interactions in a complex system from an arbitrary set of experiments, and, what is the minimum number of experiments required to characterize the system? This paper shows that the problem of finding the minimal causal structure of a system based on a set of observations is computationally intractable for even moderately sized systems (it is NP-hard), but a reasonable approximation can be found in a relatively short (polynomial) time. Next, it is shown that the number of experiments required to characterize a complex system grows exponentially with the upper bound on the number of immediate upstream influences of each element, but only logarithmically with the number of elements in the system. This makes it possible to study biological systems with extremely large number of interacting elements and relatively sparse interconnections, such as gene regulatory and cell signalling networks. Finally, the construction of a randomized experimental sequence which achieves this bound is discussed.     

Multiscale analysis of reaction networks

In most natural sciences there is currently the insight that it is necessary to bridge gaps between different processes which can be observed on different scales. This is especially true in the field of chemical reactions where the different abilities to form bonds between different types of atoms and molecules create much of the properties we experience in our everyday life, especially in all biological activity. There are essentially two types of processes related to biochemical reaction networks, the interactions among molecules and interactions involving their conformational changes, so in a sense, their internal state. The first type of processes can be conveniently approximated by the so-called mass-action kinetics, but this is not necessarily so for the second kind: here molecular states do not define any kind of density or concentration. In this paper, we demonstrate the necessity to study reaction networks in a stochastic formulation for which we can construct a coherent approximation in terms of specific space–time scales and the number of particles. The continuum limit procedure naturally creates equations of Fokker–Planck type where the evolution of the concentration occurs on a slower time scale when compared to the evolution of the conformational changes, for example triggered by binding or unbinding events with other (typically smaller) molecules. We apply the asymptotic theory to derive the effective, i.e. macroscopic dynamics of a general biochemical reaction system. The theory can also be applied to other processes where entities can be described by finitely many internal states, with changes of states occurring by arrival of other entities described by a birth–death process.     

Structural systems biology: modelling protein interactions

Much of systems biology aims to predict the behaviour of biological systems on the basis of the set of molecules involved. Understanding the interactions between these molecules is therefore crucial to such efforts. Although many thousands of interactions are known, precise molecular details are available for only a tiny fraction of them. The difficulties that are involved in experimentally determining atomic structures for interacting proteins make predictive methods essential for progress. Structural details can ultimately turn abstract system representations into models that more accurately reflect biological reality.