Computational Soft Nanotechnology with Mesodyn

The simulation of microstructures on a scale 1–1000?nm is a typical problem in colloid and polymer science, and this is also the realm of modern computational “soft nanotechnology”. Accordingly, computational methods rely heavily on time-honoured approaches for calculating the thermodynamical stability of complex mixtures. We describe such approaches in the framework of MesoDyn, a general purpose software package for field-based simulations methods, such as the polymer mean-field model for microphase formation and the Poisson–Boltzmann model for electrostatic interactions. The paper concludes with a small review of examples of application: the formation of microscopic structures in block copolymer bulk solutions, block copolymer melt structures on surfaces (thin films) and structure formation in tiny polymer surfactant droplets (polymersomes). The method works quite well in all cases where a mean-field model is appropriate, but it is a challenge to extend the simulations to systems in which specific correlations are important.     

Universal sequence replication, reversible polymerization and early functional biopolymers: a model for the initiation of prebiotic sequence evolution

Many models for the origin of life have focused on understanding how evolution can drive the refinement of a preexisting enzyme, such as the evolution of efficient replicase activity. Here we present a model for what was, arguably, an even earlier stage of chemical evolution, when polymer sequence diversity was generated and sustained before, and during, the onset of functional selection. The model includes regular environmental cycles (e.g. hydration-dehydration cycles) that drive polymers between times of replication and functional activity, which coincide with times of different monomer and polymer diffusivity. Template-directed replication of informational polymers, which takes place during the dehydration stage of each cycle, is considered to be sequence-independent. New sequences are generated by spontaneous polymer formation, and all sequences compete for a finite monomer resource that is recycled via reversible polymerization. Kinetic Monte Carlo simulations demonstrate that this proposed prebiotic scenario provides a robust mechanism for the exploration of sequence space. Introduction of a polymer sequence with monomer synthetase activity illustrates that functional sequences can become established in a preexisting pool of otherwise non-functional sequences. Functional selection does not dominate system dynamics and sequence diversity remains high, permitting the emergence and spread of more than one functional sequence. It is also observed that polymers spontaneously form clusters in simulations where polymers diffuse more slowly than monomers, a feature that is reminiscent of a previous proposal that the earliest stages of life could have been defined by the collective evolution of a system-wide cooperation of polymer aggregates. Overall, the results presented demonstrate the merits of considering plausible prebiotic polymer chemistries and environments that would have allowed for the rapid turnover of monomer resources and for regularly varying monomer/polymer diffusivities.     

Studying the Cu binding sites in the PrP N-terminal region: a test case for ab initio simulations

First principle ab initio molecular dynamics simulations of the Car-Parrinello type have proved to be of invaluable help in understanding the microscopic mechanisms of chemical bonding both in solid state physics and in structural biophysics. In this work we present as a test case a study of the Cu coordination mode at the Prion Protein binding sites localized in the N-terminal octarepeat region. Using medium size PC-clusters, we are able to deal with systems with up to about 350 atoms and 10(3) electrons for as long as approximately 2 ps. With a foreseeable forthcoming scaling up of the available CPU times by a factor 10(3), one can hope to be soon able to simulate systems of biological interest of realistic size and for physical times of the order of the nanosecond.     

The relationship of intercompartmental excitation transfer rate constants to those of an underlying physical model

In studies on photosynthetic systems it is common practice to interpret the results of time-resolved fluorescence experiments on the basis of compartmental, or target, models. Each compartment represents a group of molecules with similar fluorescence characteristics. In cases of practical interest, the members of each compartment are spatially contiguous and make up part of an overall energy-transferring system. Since a rate constant describing the overall transfer between compartments is not that of any pair of molecules in the system, this question naturally rises: what do we learn about the microscopic structure from these data? In this note we introduce ‘compartment melting’, a smooth mathematical connection between the compartmental and microscopic levels. We then show, on the basis of model calculations on finite lattices in one, two, and three dimensions, that average microscopic rates at the interfaces between compartments may be estimated from observed intercompartmental rates. The estimate involves a modest number of structural assumptions about the system. As examples of the method, which is applicable mainly to systems containing homogeneous pigment pools, some recent chlorophyll-protein antenna studies are analyzed.     

Testing demographic models of effective population size

Due to practical difficulties in obtaining direct genetic estimates of effective sizes, conservation biologists have to rely on so-called 'demographic models' which combine life-history and mating-system parameters with F-statistics in order to produce indirect estimates of effective sizes. However, for the same practical reasons that prevent direct genetic estimates, the accuracy of demographic models is difficult to evaluate. Here we use individual-based, genetically explicit computer simulations in order to investigate the accuracy of two such demographic models aimed at investigating the hierarchical structure of populations. We show that, by and large, these models provide good estimates under a wide range of mating systems and dispersal patterns. However, one of the models should be avoided whenever the focal species' breeding system approaches monogamy with no sex bias in dispersal or when a substructure within social groups is suspected because effective sizes may then be strongly overestimated. The timing during the life cycle at which F-statistics are evaluated is also of crucial importance and attention should be paid to it when designing field sampling since different demographic models assume different timings. Our study shows that individual-based, genetically explicit models provide a promising way of evaluating the accuracy of demographic models of effective size and delineate their field of applicability.     

Exploring the origin of the ion selectivity of the KcsA potassium channel

The availability of structural information about biological ion channels provides an opportunity to gain a detailed understanding of the control of ion selectivity by biological systems. However, accomplishing this task by computer simulation approaches is very challenging. First, although the activation barriers for ion transport can be evaluated by microscopic simulations, it is hard to obtain accurate results by such approaches. Second, the selectivity is related to the actual ion current and not directly to the individual activation barriers. Thus, it is essential to simulate the ion currents and this cannot be accomplished at present by microscopic MD approaches. In order to address this challenge, we developed and refined an approach capable of evaluating ion current while still reflecting the realistic features of the given channel. Our method involves generation of semimacroscopic free energy surfaces for the channel/ions system and Brownian dynamics (BD) simulations of the corresponding ion current. In contrast to most alternative macroscopic models, our approach is able to reproduce the difference between the free energy surfaces of different ions and thus to address the selectivity problem. Our method is used in a study of the selectivity of the KcsA channel toward the K+ and Na+ ions. The BD simulations with the calculated free energy profiles produce an appreciable selectivity. To the best of our knowledge, this is the first time that the trend in the selectivity in the ion current is produced by a computer simulation approach. Nevertheless, the calculated selectivity is still smaller than its experimental estimate. Recognizing that the calculated profiles are not perfect, we examine how changes in these profiles can account for the observed selectivity. It is found that the origin of the selectivity is more complex than generally assumed. The observed selectivity can be reproduced by increasing the barrier at the exit and the entrance of the selectivity filter, but the necessary changes in the barrier approach the limit of the error in the PDLD/S-LRA calculations. Other options that can increase the selectivity are also considered, including the difference between the Na+...Na+ and K+...K+ interaction. However, this interesting effect does not appear to lead to a major difference in selectivity since the Na+ ions at the limit of strong interaction tend to move in a less concerted way than the K+ ions. Changes in the relative binding energies at the different binding sites are also not so effective in changing the selectivity. Finally, it is pointed out that using the calculated profiles as a starting point and forcing the model to satisfy different experimentally based constraints, should eventually provide more detailed understanding of the different complex factors involved in ion selectivity of biological channels.     

Size-Independent Differences between the Mean of Discrete Stochastic Systems and the Corresponding Continuous Deterministic Systems

In this paper, it is shown that for a class of reaction networks, the discrete stochastic nature of the reacting species and reactions results in qualitative and quantitative differences between the mean of exact stochastic simulations and the prediction of the corresponding deterministic system. The differences are independent of the number of molecules of each species in the system under consideration. These reaction networks are open systems of chemical reactions with no zero-order reaction rates. They are characterized by at least two stationary points, one of which is a nonzero stable point, and one unstable trivial solution (stability based on a linear stability analysis of the deterministic system). Starting from a nonzero initial condition, the deterministic system never reaches the zero stationary point due to its unstable nature. In contrast, the result presented here proves that this zero-state is a stable stationary state for the discrete stochastic system, and other finite states have zero probability of existence at large times. This result generalizes previous theoretical studies and simulations of specific systems and provides a theoretical basis for analyzing a class of systems that exhibit such inconsistent behavior. This result has implications in the simulation of infection, apoptosis, and population kinetics, as it can be shown that for certain models the stochastic simulations will always yield different predictions for the mean behavior than the deterministic simulations.     

The first living systems: a bioenergetic perspective.

The first systems of molecules having the properties of the living state presumably self-assembled from a mixture of organic compounds available on the prebiotic Earth. To carry out the polymer synthesis characteristic of all forms of life, such systems would require one or more sources of energy to activate monomers to be incorporated into polymers. Possible sources of energy for this process include heat, light energy, chemical energy, and ionic potentials across membranes. These energy sources are explored here, with a particular focus on mechanisms by which self-assembled molecular aggregates could capture the energy and use it to form chemical bonds in polymers. Based on available evidence, a reasonable conjecture is that membranous vesicles were present on the prebiotic Earth and that systems of replicating and catalytic macromolecules could become encapsulated in the vesicles. In the laboratory, this can be modeled by encapsulated polymerases prepared as liposomes. By an appropriate choice of lipids, the permeability properties of the liposomes can be adjusted so that ionic substrates permeate at a sufficient rate to provide a source of monomers for the enzymes, with the result that nucleic acids accumulate in the vesicles. Despite this progress, there is still no clear mechanism by which the free energy of light, ion gradients, or redox potential can be coupled to polymer bond formation in a protocellular structure.     

Growing biological networks: beyond the gene-duplication model

In this paper we propose a generalized growth model for biological interaction networks, including a set of biological features which have been inspired by a long tradition of simulations of immune system and chemical reaction networks. In our models we include characteristics such as the heterogeneity of biological nodes, the existence of natural hubs, the nodes binding by mutual affinity and the significance of type-based networks as compared with instance-based networks. Under these assumptions, we analyse the importance of the nodes concentration with respect to the selection of incoming nodes. We show that networks with fat-tailed degree distribution and highly clustered structure naturally emerge in systems possessing certain properties: new instances need to be produced through an endogenous source and this source needs to provide a positive feedback favouring nodes with high concentration to receive new connections. Furthermore, we show that understanding the concentration dynamics of each node and the consequent correlation between connectivity and concentration is a more adequate way to capture the global properties of type-based biological networks.     

Mapping the importance of four factors in creating monovalent ion selectivity in biological molecules

The ability of macrocycles, enzymes, ion channels, transporters, and DNA to differentiate among ion types is often crucial to their function. Using molecular dynamics simulations on both detailed systems and simple models, we quantify the importance of several factors which affect the ion selectivity of such molecules, including the number of coordinating ligands, their dipole moment, and their vibrational motion. The information resulting from our model systems is distilled into a series of selectivity maps that can be used to read off the relative free energy associated with binding of different ions, and to provide an estimate of the importance of the various factors. Although our maps cannot capture all elements of real systems, it is remarkable that they produce differential site-binding energies that are in line with experiment and more-detailed simulations for a variety of systems—making them useful for understanding the origins of selective binding and transport. The chemical nature of the coordinating ligands is essential for creating thermodynamic ion selectivity in flexible molecules (such as 18c6), but as the binding site becomes more rigid, the number of ligands (as in ion channels) and the reduction of thermal fluctuations (as in amino-acid transporters) can become important. In the future, our maps could aid in the determination of the local structure from binding energies and assist in the design of novel ion selective molecules.     

Dynamics of molecular motors and polymer translocation with sequence heterogeneity

The effect of sequence heterogeneity on polynucleotide translocation across a pore and on simple models of molecular motors such as helicases, DNA polymerase/exonuclease, and RNA polymerase is studied in detail. Pore translocation of RNA or DNA is biased due to the different chemical environments on the two sides of the membrane, whereas the molecular motor motion is biased through a coupling to chemical energy. An externally applied force can oppose these biases. For both systems we solve lattice models exactly both with and without disorder. The models incorporate explicitly the coupling to the different chemical environments for polymer translocation and the coupling to the chemical energy (as well as nucleotide pairing energies) for molecular motors. Using the exact solutions and general arguments, we show that the heterogeneity leads to anomalous dynamics. Most notably, over a range of forces around the stall force (or stall tension for DNA polymerase/exonuclease systems) the displacement grows sublinearly as t(micro), with micro < 1. The range over which this behavior can be observed experimentally is estimated for several systems and argued to be detectable for appropriate forces and buffers. Similar sequence heterogeneity effects may arise in the packing of viral DNA.     

Effect of natural modifications on the functional properties of extracellular bacterial polysaccharides

Extracellular bacterial polysacharides comprise the capsules and slimes secreted by many bacteria. Little is known about the features of the chemical structure which are of importance in determining the helical conformation and inter- or intramolecular associations of these polysaccharides. An understanding of such structure-function relationships is hampered by the often complex chemical repeat units of these bacterial polysaccharides. One approach is to investigate and compare the properties of families of polysaccharides in which individual members of the group show small naturally arising modifications to the chemical structure. This approach is illustrated by studies which show the effects of changes in the polymer backbone, polymer side chains and non-carbohydrate substituents on polymer functionality. It is shown how such studies form a basis for explaining and optimizing the industrial applications of bacterial polysaccharides and for understanding the natural roles of extracellular polysaccharides.     

Determination of Lennard-Jones interaction parameters using a new procedure

For theoretical and chemical engineering applications, accurate and, if possible, simple models of molecular interactions are needed. We have recently proposed a new procedure for determining Lennard-Jones interaction parameters for fluids, forcing agreement between the values of the pressure obtained from empirical equations of state and those obtained from computer simulations. In this work we obtain new intermolecular Lennard-Jones parameters for non-polar molecules, taking into account their deviation from the spherical shape by means of an acentric factor. Our procedure could help to connect the microscopic and macroscopic worlds and it will be progressively implemented in order to obtain a better representation of other substances and mixtures of chemical interest.     

Study of PE and iPP orientations on the surface of carbon nanotubes by using molecular dynamic simulations

In this study, the early stage of interfacial crystallisation behaviour of low molecular weight polyethylene (PE) and isotactic polypropylene (iPP) oligomer on the surface of carbon nanotubes (CNTs) with different diameters, chiralities and topography structures was studied using MD simulations. We started to simulate the effect of CNTs chirality and diameter on PE molecular chain orientation, and then the effect of CNTs topography structure on PE and iPP molecular chain orientation was investigated. Finally, some experiments were carried out to prove the simulated results. Our study shows that for CNTs with a diameter comparable with the radius of gyration (R_g) of a polymer chain, an easy orientation of PE chains along CNTs axis is observed for all the systems of the CNTs with different chiralities due to a geometric confinement effect. For CNTs with a much larger diameter, multiple orientation of PE chains is induced on its surface due to the lattice matching between graphite lattice and PE molecular chains. In this case, the chirality of CNTs dominates the orientation of graphite lattice, which determines the orientation of PE chains arrangement on CNTs surface. More importantly, it was found that the groove structure formed by CNT bundles is very useful for the stabilisation of polymer chain, and thus facilitates the orientation of molecular chain along the long axis of CNTs. As a result, a novel nanohybrid shish–kebab (NHSK) structure with CNTs acting as central shish while polymer lamellae as kebab can be successfully obtained for both PE with zigzag conformation and iPP with helical conformation. This simulation result was well supported by the experimental observation. Our study could provide not only a deep understanding of the origin of the polymer chain orientation on CNTs surface but also the guidance for the preparation of polymer/CNTs nanocomposites with novel NHSK structure.     

Spatial self-organization in a cyclic resource-species model

Biological communities are remarkable in their ability to form cooperative ensembles that lead to coexistence through various types of niche partitioning, usually intimately tied to spatial structure. This is especially true in microbial settings where differential expression and regulation of genes allows members of a given species to alter their lifestyle so as to fill a functional role within the community. The resulting species interactions can involve feedback, as in the case of some bacterial consortia that participate in the cooperative degradation of a given resource in a succession of steps and in such a way that certain "later" species provide catalytic support for the primary degrader. We seek to capture the essential features of such spatially extended biological systems by introducing a lattice-based stochastic spatial model (interacting particle system) with cyclic local dynamics. Here, a given site progresses through a sequence of resource and species states in a prescribed order. Furthermore, this succession of states (at a site) is assumed to form a cyclic pattern due to a natural feedback mechanism. We explore conditions under which all the species are able to coexist and consider the extent to which this coexistence requires the development of spatio-temporal patterns, including spiral waves. This self-organization, if it occurs, results when synchronization of the dynamics at the microscopic level leads to macroscopic patterns. These patterns result in consumer-driven resource fluctuations that generate a form of spatio-temporal niche partitioning. As with most models of this complexity, we employ a mixture of mathematical analysis and simulations to develop an understanding of the resulting dynamics.     

Coarse-grained molecular dynamics simulations of phase transitions in mixed lipid systems containing LPA, DOPA, and DOPE lipids

The mechanisms that mediate biomembrane shape transformations are of considerable interest in cell biology. Recent in vitro experiments show that the chemical transformation of minor membrane lipids can induce dramatic shape changes in biomembranes. Specifically, it was observed that the addition of DOPA to DOPE has no effect on the stability of the bilayer structure of the membrane. In contrast, the addition of LPA to DOPE stabilizes the bilayer phase of DOPE, increasing the temperature of a phase transition from the bilayer to the inverted hexagonal phase. This result suggests that the chemical conversion of DOPA to LPA is sufficient for triggering a dramatic change in the shape of biomembranes. The LPA/DOPA/DOPE mixture of lipids provides a simple model system for understanding the molecular events driving the shape change. In this work, we used coarse-grained molecular dynamics simulations to study the phase transitions of this lipid mixture. We show that despite the simplicity of the coarse-grained model, it reproduces the experimentally observed phase changes of: 1), pure LPA and DOPA with respect to changes in the concentration of cations; and 2), LPA/DOPE and DOPA/DOPE mixtures with respect to temperature. The good agreement between the model and experiments suggests that the computationally inexpensive coarse-grained approach can be used to infer macroscopic membrane properties. Furthermore, analysis of the shape of the lipid molecules demonstrates that the phase behavior of single-lipid systems is consistent with molecular packing theory. However, the phase stability of mixed lipid systems exhibits significant deviations from this theory, which suggests that the elastic energy of the lipids, neglected in the packing theory, plays an important role.