Grand Molecular Dynamics: A Method for Open Systems

We present a new molecular dynamics method for studying the dynamics of open systems. The method couples a classical system to a chemical potential reservior. In the formulation, following the extended system dynamics approach, we introduce a variable, v to represent the coupling to the chemical potential reservoir. The new variable governs the dynamics of the variation of number of particles in the system. The number of particles is determined by taking the integer part of v. The fractional part of the new variable is used to scale the potential energy and the kinetic energy of an additional particle: i.e., we introduce a fractional particle. We give the ansatz Lagrangians and equations of motion for both the isothermal and the adiabatic forms of grand molecular dynamics. The averages calculated over the trajectories generated by these equations of motion represent the classical grand canonical ensemble (μVT) and the constant chemical potential adiabatic ensemble (μVL) averages, respectively. The microcanonical phase space densities of the adiabatic and isothermal forms the molecular dynamics method are shown to be equivalent to adiabatic constant chemical potential ensemble, and grand canonical ensemble partition functions. We also discuss the extension to multi-component systems, molecular fluids, ionic solutions and the problems and solutions associated with the implementation of the method. The statistical expressions for thermodynamic functions such as specific heat; adiabatic bulk modulus, Grüneissen parameter and number fluctuations are derived. These expressions are used to analyse trajectories of constant chemical potential systems.     

Proton channel models: Filling the gap between experimental data and the structural rationale

Voltage-gated proton channels are integral membrane proteins with the capacity to permeate elementary particles in a voltage and pH dependent manner. These proteins have been found in several species and are involved in various physiological processes. Although their primary topology is known, lack of details regarding their structures in the open conformation has limited analyses toward a deeper understanding of the molecular determinants of their function and regulation. Consequently, the function-structure relationships have been inferred based on homology models. In the present work, we review the existing proton channel models, their assumptions, predictions and the experimental facts that support them. Modeling proton channels is not a trivial task due to the lack of a close homolog template. Hence, there are important differences between published models. This work attempts to critically review existing proton channel models toward the aim of contributing to a better understanding of the structural features of these proteins.     

Phenomenological and molecular-level Petri net modeling and simulation of long-term potentiation

Petri net-based modeling methods have been used in many research projects to represent biological systems. Among these, the hybrid functional Petri net (HFPN) was developed especially for biological modeling in order to provide biologists with a more intuitive Petri net-based method. In the literature, HFPNs are used to represent kinetic models at the molecular level. We present two models of long-term potentiation previously represented by differential equations which we have transformed into HFPN models: a phenomenological synapse model and a molecular-level model of the CaMKII regulation pathway. Through simulation, we obtained results similar to those of previous studies using these models. Our results open the way to a new type of modeling for systems biology where HFPNs are used to combine different levels of abstraction within one model. This approach can be useful in fully modeling a system at the molecular level when kinetic data is missing or when a full study of a system at the molecular level it is not within the scope of the research.     

Impact of ROS on ageing of two fungal model systems: Saccharomyces cerevisiae and Podospora anserina

To provide a foundation for the development of effective interventions to counteract various age-related diseases in humans, ageing processes have been extensively studied in various model organisms and systems. However, the mechanisms underlying ageing are still not unravelled in detail in any system including rather simple organisms. In this article, we review some of the molecular mechanisms that were found to affect ageing in two fungal models, the unicellular ascomycete Saccharomyces cerevisiae and the filamentous ascomycete Podospora anserina. A selection of issues like retrograde response, genomic instability, caloric restriction, mtDNA reorganisation and apoptosis is presented and discussed with special emphasis on the role reactive oxygen species (ROS) play in these diverse molecular pathways.     

Proton transport in carbonic anhydrase: Insights from molecular simulation

This article reviews the insights gained from molecular simulations of human carbonic anhydrase II (HCA II) utilizing non-reactive and reactive force fields. The simulations with a reactive force field explore protein transfer and transport via Grotthuss shuttling, while the non-reactive simulations probe the larger conformational dynamics that underpin the various contributions to the rate-limiting proton transfer event. Specific attention is given to the orientational stability of the His64 group and the characteristics of the active site water cluster, in an effort to determine both of their impact on the maximal catalytic rate. The explicit proton transfer and transport events are described by the multistate empirical valence bond (MS-EVB) method, as are alternative pathways for the excess proton charge defect to enter/leave the active site. The simulation results are interpreted in light of experimental results on the wild-type enzyme and various site-specific mutations of HCA II in order to better elucidate the key factors that contribute to its exceptional efficiency.     

Impact of ROS on ageing of two fungal model systems: Saccharomyces cerevisiae and Podospora anserina

To provide a foundation for the development of effective interventions to counteract various age-related diseases in humans, ageing processes have been extensively studied in various model organisms and systems. However, the mechanisms underlying ageing are still not unravelled in detail in any system including rather simple organisms. In this article, we review some of the molecular mechanisms that were found to affect ageing in two fungal models, the unicellular ascomycete Saccharomyces cerevisiae and the filamentous ascomycete Podospora anserina. A selection of issues like retrograde response, genomic instability, caloric restriction, mtDNA reorganisation and apoptosis is presented and discussed with special emphasis on the role reactive oxygen species (ROS) play in these diverse molecular pathways.     

Molecular alterations of canalicular transport systems in experimental models of cholestasis: possible functional correlations.

The discovery of unidirectional, ATP-dependent canalicular transport systems (also termed "export pumps") for bile salts, amphiphilic anionic conjugates, lipophilic cations, and phospholipids has opened new opportunities for understanding biliary physiology and the pathophysiology of cholestasis. In addition, ATP-independent canalicular transport systems for glutathione and bicarbonate contribute to (bile acid-independent) bile formation. Canalicular excretion of bile salts and several non-bile acid organic anions is impaired in various experimental models of cholestasis. Recent cloning of several canalicular transport systems now facilitates studies on their molecular regulation in cholestasis. Although the picture is far from complete, experimental evidence now exists that decreased or even absent expression of canalicular transport proteins may explain impaired transport function resulting in hyperbilirubinemia and cholestasis. With the increasing availability of molecular probes for these transport systems in humans, new information on the molecular regulation of canalicular transport proteins in human cholestatic liver diseases is beginning to emerge and should bring new insights into their pathophysiology and treatment. This article gives an overview on molecular alterations of canalicular transport systems in experimental models of cholestasis and discusses the potential implications of these changes for the pathophysiology of cholestasis.     

Studies of enzyme reactions in open systems

An experimental arrangement is described which allows studies of the temporal performance of enzyme reactions (also reactions of complexes of enzyme chains) under conditions of open systems. The various steady-state properties of such open systems can be recognized by measuring their input and output [1,2]. The various levels of flowing equilibria are perturbed by applying molecular modulators to the system, and the data obtained are compared to those found in closed systems. In order to prove the accuracy of the experimental configuration, the determination of K_m in a one-substrate reaction is carried out in the open system, using only one concentration of substrate at various flow rates.     

Conformational analysis and molecular dynamics simulations of maltose

Constrained conformational energy minimizations have been used to calculate an adiabatic (Φ, ψ) potential energy surface for the disaccharide β-maltose. The inclusion of molecular flexibility in the conformational energy analysis of the disaccharide was found to significantly lower the barriers to conformational transitions, as has been observed previously for other systems. Several low energy wells were identified on the adiabatic surface which differ in energy by small amounts and with low absolute barriers separating them, indicating the possibility of a non-negligible equilibrium population distribution in each well. If such a distribution of conformations existed in the physical system, the conformation observed by NMR NOE measurements would thus be a “virtual” conformation. Molecular dynamics simulations of the motions of this molecule in vacuum were also conducted and indicate that the rate of relaxation of the molecule to the adiabatic surface may be slower than the typical timescale of conformational fluctuations. This effect is apparently due to an unphysical persistence of hydrogen bond patterns in vacuum which does not occur in aqueous solution. Trajectories undergoing transitions between wells were calculated and the effects of such conformational transitions upon the ensemble mean structure, such as might be observed in an NMR experiment, were demonstrated.     

Pattern selection in a cooperative biochemical in vitro amplification system: the role of parasites

Previously, numerical simulations have shown that evolving systems can be stabilized against emerging parasites by pattern formation in spatially extended flow reactors. Hence, it can be argued that pattern formation is a prerequisite for any experimental investigation of the biochemical evolution of cooperative function. Here, we study a model of an experimental biochemical system for the cooperative in vitro amplification of DNA strands and show that emerging parasites can induce a complex pattern formation even when no pattern formation occurs without parasites. In an adiabatic approximation where the cooperative amplification reaction is assumed to adapt fast to slowly emerging parasites, the parasite concentration itself acts as a Steuer parameter for the selection of various complex patterns. Without such an adiabatic approximation only transient patterns emerge. As any species can grow for very low concentrations, the parasite is able to infect the entire reactor and the system is finally diluted out. In the experimental biochemical system, however, the species are individual molecules and the growth of spatially separated, non-infected regions becomes feasible. Hence a cutoff threshold for the minimal concentration is applied. In these simulations the otherwise lethal infection by parasites induces the formation of spatiotemporal spirals, and this spatial structure help the host and parasitoid species to survive together. These theoretical results describe an inherent property of cooperative reactions and have an important impact on experimental investigations on the molecular evolution and complex function in spatially extended reactors. Since the formation of the complex pattern is restricted either to a rather large cutoff value or a special choice of the kinetic parameters, we, however, conclude that the persistence of evolving cooperative amplification is not possible in a simple reaction-diffusion reactor. Experimental set-ups with patchy environments, e.g. biomolecular amplification in coupled microstructured flow chambers or in microemulsion, are eligible candidates for the observation of such a self-organized pattern selection.     

Predicting the profile of nutrients available for absorption: from nutrient requirement to animal response and environmental impact

Current feed evaluation systems for dairy cattle aim to match nutrient requirements with nutrient intake at pre-defined production levels. These systems were not developed to address, and are not suitable to predict, the responses to dietary changes in terms of production level and product composition, excretion of nutrients to the environment, and nutrition related disorders. The change from a requirement to a response system to meet the needs of various stakeholders requires prediction of the profile of absorbed nutrients and its subsequent utilisation for various purposes. This contribution examines the challenges to predicting the profile of nutrients available for absorption in dairy cattle and provides guidelines for further improved prediction with regard to animal production responses and environmental pollution.The profile of nutrients available for absorption comprises volatile fatty acids, long-chain fatty acids, amino acids and glucose. Thus the importance of processes in the reticulo-rumen is obvious. Much research into rumen fermentation is aimed at determination of substrate degradation rates. Quantitative knowledge on rates of passage of nutrients out of the rumen is rather limited compared with that on degradation rates, and thus should be an important theme in future research. Current systems largely ignore microbial metabolic variation, and extant mechanistic models of rumen fermentation give only limited attention to explicit representation of microbial metabolic activity. Recent molecular techniques indicate that knowledge on the presence and activity of various microbial species is far from complete. Such techniques may give a wealth of information, but to include such findings in systems predicting the nutrient profile requires close collaboration between molecular scientists and mathematical modellers on interpreting and evaluating quantitative data. Protozoal metabolism is of particular interest here given the paucity of quantitative data.Empirical models lack the biological basis necessary to evaluate mitigation strategies to reduce excretion of waste, including nitrogen, phosphorus and methane. Such models may have little predictive value when comparing various feeding strategies. Examples include the Intergovernmental Panel on Climate Change (IPCC) Tier II models to quantify methane emissions and current protein evaluation systems to evaluate low protein diets to reduce nitrogen losses to the environment. Nutrient based mechanistic models can address such issues. Since environmental issues generally attract more funding from governmental offices, further development of nutrient based models may well take place within an environmental framework.     

Advancing simulations of biological materials: applications of coarse-grained models on graphics processing unit hardware

The timescales of biological processes, primarily those inherent to the molecular mechanisms of disease, are long (>μs) and involve complex interactions of systems consisting of many atoms (>10⁶). Simulating these systems requires an advanced computational approach, and as such, coarse-grained (CG) models have been developed and highly optimised for accelerator hardware, primarily graphics processing units (GPUs). In this review, I discuss the implementation of CG models for biologically relevant systems, and show how such models can be optimised and perform well on GPU-accelerated hardware. Several examples of GPU implementations of CG models for both molecular dynamics and Monte Carlo simulations on purely GPU and hybrid CPU/GPU architectures are presented. Both the hardware and algorithmic limitations of various models, which depend greatly on the application of interest, are discussed.     

Molecular dynamics and structural models of the cyanobacterial NDH-1 complex

NDH-1 is a gigantic redox-driven proton pump linked with respiration and cyclic electron flow in cyanobacterial cells. Based on experimentally resolved X-ray and cryo-EM structures of the respiratory complex I, we derive here molecular models of two isoforms of the cyanobacterial NDH-1 complex involved in redox-driven proton pumping (NDH-1L) and CO₂-fixation (NDH-1MS). Our models show distinct structural and dynamic similarities to the core architecture of the bacterial and mammalian respiratory complex I. We identify putative plastoquinone-binding sites that are coupled by an electrostatic wire to the proton pumping elements in the membrane domain of the enzyme. Molecular simulations suggest that the NDH-1L isoform undergoes large-scale hydration changes that support proton-pumping within antiporter-like subunits, whereas the terminal subunit of the NDH-1MS isoform lacks such structural motifs. Our work provides a putative molecular blueprint for the complex I-analogue in the photosynthetic energy transduction machinery and demonstrates that general mechanistic features of the long-range proton-pumping machinery are evolutionary conserved in the complex I-superfamily.     

Membrane-mimetic systems for biophysical studies of the amyloid-β peptide

The interplay between the amyloid-β (Aβ) peptide and cellular membranes have been proposed as an important mechanism for toxicity in Alzheimer's disease (AD). Membrane environments appear to influence Aβ aggregation and may stabilize intermediate Aβ oligomeric states that are considered to be neurotoxic. One important role for molecular biophysics within the field of Aβ studies is to characterize the structure and dynamics of the Aβ peptide in various states, as well as the kinetics of transfer between these states. Because biological cell membranes are very complex, simplified membrane models are needed to facilitate studies of Aβ and other amyloid proteins in lipid environments. In this review, we examine different membrane-mimetic systems available for molecular studies of Aβ. An introduction to each system is given, and examples of important findings are presented for each system. The benefits and drawbacks of each system are discussed from methodical and biological perspectives.