Water polygons in high‐resolution protein crystal structures

We have analyzed the interstitial water (ISW) structures in 1500 protein crystal structures deposited in the Protein Data Bank that have greater than 1.5 Å resolution with less than 90% sequence similarity with each other. We observed varieties of polygonal water structures composed of three to eight water molecules. These polygons may represent the time‐ and space‐averaged structures of “stable” water oligomers present in liquid water, and their presence as well as relative population may be relevant in understanding physical properties of liquid water at a given temperature. On an average, 13% of ISWs are localized enough to be visible by X‐ray diffraction. Of those, averages of 78% are water molecules in the first water layer on the protein surface. Of the localized ISWs beyond the first layer, almost half of them form water polygons such as trigons, tetragons, as well as expected pentagons, hexagons, higher polygons, partial dodecahedrons, and disordered networks. Most of the octagons and nanogons are formed by fusion of smaller polygons. The trigons are most commonly observed. We suggest that our observation provides an experimental basis for including these water polygon structures in correlating and predicting various water properties in liquid state.     

Molecular insights into the ecology of a psychrotolerant Pseudomonas syringae

Low temperatures constrain cellular life due to reductions in nutrient uptake, enzyme kinetics, membrane permeability, and function of other biomacromolecules. This has implications for the biophysical limits of life on Earth, and the plausibility of life in extraterrestrial locations. Although most pseudomonads are mesophilic in nature, isolates such as the Antarctic Pseudomonas syringae Lz4W exhibit considerable psychrotolerance, with an ability to grow even between 4 and 0°C. In this review, we explore the molecular traits and characteristic phenotypes of P. syringae Lz4W that enable life at low temperatures. We describe adaptations that enhance membrane fluidity; examine genes involved in cellular function and survival in the cold; assess capability for energy generation at low temperature; and detail the mechanics of DNA repair and RNA processing at low temperature, and speculate that P. syringae Lz4W can also synthesize glycerol to maintain flexibility of macromolecular systems. In the range 4 to 0ºC, there are considerable changes in the properties and behaviour of water. Specifically, density can have adverse impacts on plasma-membrane functions, cytoplasmic viscosity, protein behaviour, and other essential properties of cellular system. We identified a combination of adaptations that may be peculiar to cold-tolerant P. syringae, including increase of unsaturated fatty acids in the plasma membrane; a RNA polymerase able to function at 0°C; RecBCD- and RuvAB-dependent reestablishment of replication fork; and efficiencies of degradosome machinery and RNA processing by RNaseR at low temperature. Several unresolved questions are discussed in the context of astrobiology, and further work needed on the psychrotolerance of P. syringae.     

Robustness from flexibility in the fungal circadian clock

Background  

Robustness is a central property of living systems, enabling function to be maintained against environmental perturbations. A key challenge is to identify the structures in biological circuits that confer system-level properties such as robustness. Circadian clocks allow organisms to adapt to the predictable changes of the 24-hour day/night cycle by generating endogenous rhythms that can be entrained to the external cycle. In all organisms, the clock circuits typically comprise multiple interlocked feedback loops controlling the rhythmic expression of key genes. Previously, we showed that such architectures increase the flexibility of the clock's rhythmic behaviour. We now test the relationship between flexibility and robustness, using a mathematical model of the circuit controlling conidiation in the fungus Neurospora crassa.     

Oscillations and chaos behind predator-prey invasion: mathematical artifact or ecological reality?

A constant dilemma in theoretical ecology is knowing whether model predictions corrspond to real phenomena or whether they are artifacts of the modelling framework. The frequent absence of detailed ecological data against which models can be tested gives this issue particular importance. We address this question in the specific case of invasion in a predator-prey system with oscillatory population kinetics, in which both species exhibit local random movement. Given only these two basic qualitative features, we consider whether we can deduce any properties of the behaviour following invasion. To do this we study four different types of mathematical model, which have no formal relationship, but which all reflect our two qualitative ingredients. The models are: reaction-diffusion equations, coupled map lattices, deterministic cellular automata, and integrodifference equations. We present results of numerical simulations of the invasion of prey by predators for each model, and show that although there are certain differences, the main qualitative features of the behaviour behind invasion are the same for all the models. Specifically, there are either irregular spatiotemporal oscillations behind the invasion, or regular spatiotemporal oscillations with the form of a periodic travelling ''wake'', depending on parameter values. The observation of this behaviour in all types of model strongly suggests that it is a direct consequence of our basic qualitative assumptions, and as such is an ecological reality which will always occur behind invasion in actual oscillatory predator-prey systems.     

Discrete Element Framework for Modelling Extracellular Matrix,Deformable Cells and Subcellular Components

This paper presents a framework for modelling biological tissues based on discrete particles. Cell components (e.g. cell membranes, cell cytoskeleton, cell nucleus) and extracellular matrix (e.g. collagen) are represented using collections of particles. Simple particle to particle interaction laws are used to simulate and control complex physical interaction types (e.g. cell-cell adhesion via cadherins, integrin basement membrane attachment, cytoskeletal mechanical properties). Particles may be given the capacity to change their properties and behaviours in response to changes in the cellular microenvironment (e.g., in response to cell-cell signalling or mechanical loadings). Each particle is in effect an ‘agent’, meaning that the agent can sense local environmental information and respond according to pre-determined or stochastic events. The behaviour of the proposed framework is exemplified through several biological problems of ongoing interest. These examples illustrate how the modelling framework allows enormous flexibility for representing the mechanical behaviour of different tissues, and we argue this is a more intuitive approach than perhaps offered by traditional continuum methods. Because of this flexibility, we believe the discrete modelling framework provides an avenue for biologists and bioengineers to explore the behaviour of tissue systems in a computational laboratory.     

Theory of one-dimension rotational isomerization: A study of thecis-trans isomerization of HS-NS compared to that of HO-NO

A theoretical approach, in which the potential functions representing rotational isomerization processes are expressed in terms of linear combinations of local potentials, is presented. Partitioning the torsional potential allows identification of specific contributions that are at the origin of the shape of potential curves at different regions along the torsional variable. Key properties, such as barrier heights, may then be expressed parametrically in terms of properties associated to the stable conformations. Simple analytical expressions intended to explore, quantitatively and qualitatively, the main characteristics of the transition states connecting stable isomers are formulated. As a first step towards the study of complex systems, we use this procedure to analyseab initio results concerning thecis-trans isomerization reaction of two simple prototype molecules: HSNS and HONO. We determine the relative stabilities of the different isomers and molecular structures and evaluate the associated potential barriers. It is shown that the mathematical procedure used to get potential functions is quite convenient and may be applied to the study of more complex isomerization reactions. Numerical results concerning molecular structures, potential barriers, ionization potentials and dipole moments are discussed. Comparing the values for barrier heights suggests that S(O)-S(O) bonding through the mechanism of hyperconjugation may be present, to some extent, especially in HSNS.     

Can molecular dynamics simulations help in discriminating correct from erroneous protein 3D models?

Background  

Recent approaches for predicting the three-dimensional (3D) structure of proteins such asde novoor fold recognition methods mostly rely on simplified energy potential functions and a reduced representation of the polypeptide chain. These simplifications facilitate the exploration of the protein conformational space but do not permit to capture entirely the subtle relationship that exists between the amino acid sequence and its native structure. It has been proposed that physics-based energy functions together with techniques for sampling the conformational space, e.g., Monte Carlo or molecular dynamics (MD) simulations, are better suited to the task of modelling proteins at higher resolutions than those of models obtained with the former type of methods. In this study we monitor different protein structural properties along MD trajectories to discriminate correct from erroneous models. These models are based on the sequence-structure alignments provided by our fold recognition method, FROST. We define correct models as being built from alignments of sequences with structures similar to their native structures and erroneous models from alignments of sequences with structures unrelated to their native structures.     

Empirical modelling using dummy atoms (EMUDA): an alternative approach for studying “auxetic” structures

Auxetics (materials or structures) are systems with a negative Poisson's ratio, a property that arises from the way various geometric features in the structure (or internal structure in the case of materials) deform when subjected to uniaxial loads. Such systems are normally studied by examining the behaviour of idealised representations of structures, which deform in a controlled fashion (e.g. deforming solely through hinging or stretching). Methods used for the analysis typically involve construction of real physical macro-models and/or derivation of analytical expressions for the mechanical properties. This paper proposes an alternative method for analysing such structures whereby idealised “hinging” or “stretching” structures are constructed within a molecular modelling environment using dummy atoms and examined using standard molecular mechanics techniques. We will show that this methodology of “empirical modelling using dummy atoms” (EMUDA) successfully reproduces the known properties of 2D conventional and auxetic hexagonal honeycombs hence confirming the suitability of this technique for studying auxetic structures.     

Dynamics of vibrational frequency fluctuations in deuterated liquid ammonia: roles of fluctuating hydrogen bonds and free ND modes

We present an ab initio molecular dynamics study of the roles of fluctuating hydrogen bonds and free ND modes in the dynamics of ND stretch frequency fluctuations in deuterated liquid ammonia. We have also looked at some of the other dynamical quantities such as diffusion and orientational relaxation and also structural quantities such as pair correlations and hydrogen bonding properties which are relevant in the current context. The time correlation function of ND stretch frequencies is found to decay with primarily two time scales: A short-time decay with a time scale of less than 100 fs arising from intermolecular motion of intact hydrogen bonds and also from fast hydrogen bond breaking and a longer time scale of about 500 fs which can be assigned to the lifetime of free ND modes. Unlike water, in liquid ammonia an ND mode is found to remain free for a longer period than it stays hydrogen bonded and this longer lifetime of free ND modes determines the long-time behaviour of frequency fluctuations. Our hole dynamics calculations produced results of vibrational spectral diffusion that are similar to the decay of frequency time correlation. Inclusion of dispersion corrections is found to make the dynamics slightly faster.     

Proliferation and competition in discrete biological systems

We study the emergence of collective spatio-temporal objects in biological systems by representing individually the elementary interactions between their microscopic components. We use the immune system as a prototype for such interactions. The results of this detailed explicit analysis are compared with the traditional procedure of representing the collective dynamics in terms of densities that obey partial differential equations. The simulations show even for very simple elementary reactions the spontaneous emergence of localized complex structures, from microscopic noise. In turn the effective dynamics of these structures affects the average behaviour of the system in a very decisive way: systems which would according to the differential equations approximation die, display in reality a very lively behaviour. As the optimal modelling method we propose a mixture of microscopic simulation systems describing each reaction separately, and continuous methods describing the average behaviour of the agents.     

Behavioural syndromes in Merriam's kangaroo rats (Dipodomys merriami): a test of competing hypotheses

Behavioural syndromes, correlations of behaviours conceptually analogous to personalities, have been a topic of recent attention due to their potential to explain trade-offs in behavioural responses, apparently maladaptive behaviour and limits to plasticity. Using Merriam's kangaroo rats (Dipodomys merriami), we assessed the explanatory power and generality of hypothesized syndrome structures derived from the literature and the natural history of the species. Several aspects of functionally distinct behavioural responses of D. merriami were quantified. Syndrome structures were compared using structural equation modelling and model selection procedures. A domain-general behavioural syndrome incorporating cross-functional relationships between measures of boldness, agonistic behaviour, flexibility and food hoarding best explained the data. This pattern suggests that D. merriami behaviours should not be viewed as discrete elements but as components of a multivariate landscape. Our results support arguments that a lack of independence between behaviours may be a general aspect of behavioural phenotypes and suggest that the ability of D. merriami's behaviour to respond to selection may be constrained by underlying connections.     

Understanding on the residue contact network using the log‐normal cluster model and the multilevel wheel diagram

Residue clusters play essential role in stabilizing protein structures in the form of complex networks. We show that the cluster sizes in a native protein follow the log‐normal distribution for a dataset consisting of 424 proteins. To our knowledge, this is the first time of such fitting for the native structures. Based on log‐normal model, the asymptotically increasing mean cluster sizes produce a critical protein chain length of about 200 amino acids, beyond which length most globular proteins have nearly the same mean cluster sizes. This suggests that the larger proteins use a different packing mechanism than the smaller proteins. We confirmed the scale‐free property of the residue contact network for most of the protein structures in the dataset, although the violations were observed for the tightly packed proteins. Residue cluster network wheel (RCNW) is proposed to visualize the relationship between the multiple properties of the residue network such as the cluster size, the residue types and contacts, and the flexibility of the residue. We noticed that the residues with large cluster size have smaller Cα displacement measured using the normal mode analysis. © 2010 Wiley Periodicals, Inc. Biopolymers 93: 904–916, 2010.     

Income distribution trends and future food demand

This paper surveys the theoretical literature on the relationship between income distribution and food demand, and identifies main gaps of current food modelling techniques that affect the accuracy of food demand projections. At the heart of the relationship between income distribution and food demand is Engel''s law. Engel''s law establishes that as income increases, households'' demand for food increases less than proportionally. A consequence of this law is that the particular shape of the distribution of income across individuals and countries affects the rate of growth of food demand. Our review of the literature suggests that existing models of food demand fail to incorporate the required Engel flexibility when (i) aggregating different food budget shares among households; and (ii) changing budget shares as income grows. We perform simple simulations to predict growth in food demand under alternative income distribution scenarios taking into account nonlinearity of food demand. Results suggest that (i) distributional effects are to be expected from changes in between-countries inequality, rather than within-country inequality; and (ii) simulations of an optimistic and a pessimistic scenario of income inequality suggest that world food demand in 2050 would be 2.7 per cent higher and 5.4 per cent lower than distributional-neutral growth, respectively.     

Flexibility is a mechanical determinant of antimicrobial activity for amphipathic cationic α-helical antimicrobial peptides

Antimicrobial peptides (AMPs) are recognized as the potential substitutions for common antibiotics. Flexibility has been demonstrated to be a dominant on antimicrobial activity of an AMP, similar to the structural parameters such as hydrophobicity and hydrophobic moment as well as positive charge. To better understand the effect of flexibility on antimicrobial activity, we herein examined seventy-eight peptides derived from nine different species. Defined as a weighted average of amino acid flexibility indices over whole residue chain of AMP, flexibility index was used to scale the peptide flexibility and indicated to be a reflection of mechanical properties such as tensile and flexural rigidities. The results demonstrated that flexibility index is relevant to but different from other structural properties, may enhance activity against Escherichia coli for stiff clustered peptides or reduce activity against E. coli for flexible clustered peptides, and its optimum occurs at about − 0.5. This effect of flexibility on antimicrobial activity may be involved to the antimicrobial actions, such as stable peptide-bound leaflet formation and sequent stress concentration in target cell membrane, mechanically. The present results provide a new insight in understanding antimicrobial actions and may be useful in seeking for a new structure–activity relationship for cationic and amphipathic α-helical peptides.     

Molecular dynamics simulation of hydrated Nafion with a reactive force field for water

We apply a newly parameterized central force field to highlight the problem of proton transport in fuel cell membranes and show that central force fields are potential candidates to describe chemical reactions on a classical level. After a short sketch of the parameterization of the force field, we validate the obtained force field for several properties of water. The experimental and simulated radial distribution functions are reproduced very accurately as a consequence of the applied parameterization procedure. Further properties, geometry, coordination, diffusion coefficient and density, are simulated adequately for our purposes. Afterwards we use the new force field for the molecular dynamics simulation of a swollen polyelectrolyte membrane similar to the widespread Nafion 117. We investigate the equilibrated structures, proton transfer, lifetimes of hydronium ions, the diffusion coefficients, and the conductivity in dependence of water content. In a short movie we demonstrate the ability of the obtained force field to describe the bond breaking/formation, and conclude that this force field can be considered as a kind of a reactive force field. The investigations of the lifetimes of hydronium ions give us the information about the kinetics of the proton transfer in a membrane with low water content. We found the evidence for the second order reaction. Finally, we demonstrate that the model is simple enough to handle the large systems sufficient to calculate the conductivity from molecular dynamics simulations. The detailed analysis of the conductivity reveals the importance of the collective moving of hydronium ions in membrane, which might give an interesting encouragement for further development of membranes. Figure: The structure of water in one pore of the highly hydrated Nafion membranes. Figure The structure of water in one of pore of the highly hydrated Nafion membrane Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Predicting Evolutionary Site Variability from Structure in Viral Proteins: Buriedness,Packing, Flexibility,and Design

Several recent works have shown that protein structure can predict site-specific evolutionary sequence variation. In particular, sites that are buried and/or have many contacts with other sites in a structure have been shown to evolve more slowly, on average, than surface sites with few contacts. Here, we present a comprehensive study of the extent to which numerous structural properties can predict sequence variation. The quantities we considered include buriedness (as measured by relative solvent accessibility), packing density (as measured by contact number), structural flexibility (as measured by B factors, root-mean-square fluctuations, and variation in dihedral angles), and variability in designed structures. We obtained structural flexibility measures both from molecular dynamics simulations performed on nine non-homologous viral protein structures and from variation in homologous variants of those proteins, where they were available. We obtained measures of variability in designed structures from flexible-backbone design in the Rosetta software. We found that most of the structural properties correlate with site variation in the majority of structures, though the correlations are generally weak (correlation coefficients of 0.1–0.4). Moreover, we found that buriedness and packing density were better predictors of evolutionary variation than structural flexibility. Finally, variability in designed structures was a weaker predictor of evolutionary variability than buriedness or packing density, but it was comparable in its predictive power to the best structural flexibility measures. We conclude that simple measures of buriedness and packing density are better predictors of evolutionary variation than the more complicated predictors obtained from dynamic simulations, ensembles of homologous structures, or computational protein design.     

Reverse Monte Carlo Simulation: A New Technique for the Determination of Disordered Structures

Abstract

We have developed a new technique, based on the standard Monte Carlo simulation method with Markov chain sampling, in which a set of three dimensional particle configurations are generated that are consistent with the experimentally measured structure factor. A(Q), and radial distribution function, g(r), of a liquid or other disordered system. Consistency is determined by a standard χ² test using the experimental errors. No input potential is required, we present initial results for liquid argon. Since the technique can work directly from the structure factor it promises to be useful for modelling the structures of glasses or amorphous materials. It also has other advantages in multicomponent systems and as a tool for experimental data analysis.