Monte Carlo Simulations of the Chemical Potential and Free Energy for Trimer and Hexamer Rings

Abstract

The chemical potential of a trimer and hexamer model ring system was determined by computer simulation over a range of temperatures and densities. Such ring molecules are important as model aromatic and naphthenic hydrocarbons. Thermodynamic integration of the pressure along a reversible path, Widom's ghost particle insertion method and Kirkwood's charging parameter method were used over a molecular density range of 0.05 to 0.30. Data were obtained by Monte Carlo simulation of a 96 molecule system that was modelled with a Lennard-Jones 6-12 truncated potential. The original insertion method, which does not take into account the orientation of the molecule when it is inserted, gives results for the chemical potential which deviate from that obtained using the thermodynamic pressure integration. At high density or temperature the deviation is significant. We have modified the Widom insertion technique to account for this short range orientation and find good agreement between this technique and the thermodynamic integration method for the chemical potential. We also calculated the free energy difference between our model ring molecules and ring molecules made up of hard spheres.     

A dynamical system model of neurofilament transport in axons

We develop a dynamical system model for the transport of neurofilaments in axons, inspired by Brown's "stop-and-go" model for slow axonal transport. We use fast/slow time-scale arguments to lower the number of relevant parameters in our model. Then, we use experimental data of Wang and Brown to estimate all but one parameter. We show that we can choose this last remaining parameter such that the results of our model agree with pulse-labeling experiments from three different nerve cell types, and also agree with stochastic simulation results.     

An Intermittent Model for Intracellular Motions of Gold Nanostars by k-Space Scattering Image Correlation

Anisotropic metallic nanoparticles have been devised as powerful potential tools for in vivo imaging, photothermal therapy, and drug delivery thanks to plasmon-enhanced absorption and scattering cross sections, ease in synthesis and functionalization, and controlled cytotoxicity. The rational design of all these applications requires the characterization of the nanoparticles intracellular trafficking pathways. In this work, we exploit live-cell time-lapse confocal reflectance microscopy and image correlation in both direct and reciprocal space to investigate the intracellular transport of branched gold nanostars (GNSs). Different transport mechanisms, spanning from pure Brownian diffusion to (sub-)ballistic superdiffusion, are revealed by temporal and spatio-temporal image correlation spectroscopy on the tens-of-seconds timescale. According to these findings, combined with numerical simulations and with a Bayesian (hidden Markov model-based) analysis of single particle tracking data, we ascribe the superdiffusive, subballistic behavior characterizing the GNSs dynamics to a two-state switching between Brownian diffusion in the cytoplasm and molecular motor-mediated active transport. For the investigation of intermittent-type transport phenomena, we derive an analytical theoretical framework for Fourier-space image correlation spectroscopy (kICS). At first, we evaluate the influence of all the dynamic and kinetic parameters (the diffusion coefficient, the drift velocity, and the transition rates between the diffusive and the active transport regimes) on simulated kICS correlation functions. Then we outline a protocol for data analysis and employ it to derive whole-cell maps for each parameter underlying the GNSs intracellular dynamics. Capable of identifying even simpler transport phenomena, whether purely diffusive or ballistic, our intermittent kICS approach allows an exhaustive investigation of the dynamics of GNSs and biological macromolecules.     

An Isogeometric Analysis Computational Platform for Material Transport Simulation in Complex Neurite Networks

Neurons exhibit remarkably complex geometry in their neurite networks. So far, how materials are transported in the complex geometry for survival and function of neurons remains an unanswered question. Answering this question is fundamental to understanding the physiology and disease of neurons. Here, we have developed an isogeometric analysis (IGA) based platform for material transport simulation in neurite networks. We modeled the transport process by reaction-diffusion-transport equations and represented geometry of the networks using truncated hierarchical tricubic B-splines (THB-spline3D). We solved the Navier-Stokes equations to obtain the velocity field of material transport in the networks. We then solved the transport equations using the streamline upwind/Petrov-Galerkin (SU/PG) method. Using our IGA solver, we simulated material transport in three basic models of the network geometry: a single neurite, a neurite bifurcation, and a neurite tree with three bifurcations. In addition, the robustness of our solver is illustrated by simulating material transport in three representative and complex neurite networks. From the simulation we discovered several spatial patterns of the transport process. Together, our simulation provides key insights into how material transport in neurite networks is mediated by their complex geometry.     

Phase response characteristics of model neurons determine which patterns are expressed in a ring circuit model of gait generation

In order to assess the relative contributions to pattern-generation of the intrinsic properties of individual neurons and of their connectivity, we examined a ring circuit composed of four complex physiologically based oscillators. This circuit produced patterns that correspond to several quadrupedal gaits, including the walk, the bound, and the gallop. An analysis using the phase response curve (PRC) of an uncoupled oscillator accurately predicted all modes exhibited by this circuit and their phasic relationships – with the caveat that in certain parameter ranges, bistability in the individual oscillators added nongait patterns that were not amenable to PRC analysis, but further enriched the pattern-generating repertoire of the circuit. The key insights in the PRC analysis were that in a gait pattern, since all oscillators are entrained at the same frequency, the phase advance or delay caused by the action of each oscillator on its postsynaptic oscillator must be the same, and the sum of the normalized phase differences around the ring must equal to an integer. As suggested by several previous studies, our analysis showed that the capacity to exhibit a large number of patterns is inherent in the ring circuit configuration. In addition, our analysis revealed that the shape of the PRC for the individual oscillators determines which of the theoretically possible modes can be generated using these oscillators as circuit elements. PRCs that have a complex shape enable a circuit to produce a wider variety of patterns, and since complex neurons tend to have complex PRCs, enriching the repertoire of patterns exhibited by a circuit may be the function of some intrinsic neuronal complexity. Our analysis showed that gait transitions, or more generally, pattern transitions, in a ring circuit do not require rewiring the circuit or any changes in the strength of the connections. Instead, transitions can be achieved by using a control parameter, such as stimulus intensity, to sculpt the PRC so that it has the appropriate shape for the desired pattern(s). A transition can then be achieved simply by changing the value of the control parameter so that the first pattern either ceases to exist or loses stability, while a second pattern either comes into existence or gains stability. Our analysis illustrates the predictive value of PRCs in circuit analysis and can be extended to provide a design method for pattern-generating circuits. Received: 20 November 1996 / Accepted: 29 July 1997     

Duplication and extension of the Thorneley and Lowe kinetic model for Klebsiella pneumoniae nitrogenase catalysis using a MATHEMATICA software platform

The Thorneley and Lowe kinetic model for nitrogenase catalysis was developed in the early to mid 1980s, and has been of value in accounting for many aspects of nitrogenase catalysis. It has also been of value by providing a model for predicting new catalytic behavior. Since its original publication, new results have been obtained and have been successfully incorporated into the model. However, the computer program used for nitrogenase simulations has not been generally available. Using kinetic schemes and assumptions previously outlined by Thorneley and Lowe, we report attempts to duplicate the original T&L kinetic simulation for Klebsiella pneumoniae nitrogenase catalysis using an updated simulation based on the MATHEMATICA programming format, which makes it more user-friendly and more readily available. Comparisons of our simulations with the original T&L simulations are generally in agreement, but in some cases serious discrepancy is observed. Possible reasons for the differences are discussed. In addition to duplicating the original T&L model, we report effects of updating it by including information that has come to light subsequent to its original publication.     

Closing the ring: historical biogeography of the salamander ring species Ensatina eschscholtzii

Aim The salamander Ensatina eschscholtzii Gray is a classic example of a ring species, or a species that has expanded around a central barrier to form a secondary contact characterized by species‐level divergence. In the original formulation of the ring species scenario, an explicit biogeographical model was proposed to account for the occurrence of intraspecific sympatry between two subspecies in southern California (the ‘southern closure’ model). Here we develop an alternative ring species model that is informed by the geomorphological development of the California Coast Ranges, and which situates the point of ring closure in the Monterey Bay region of central coastal California (the ‘Monterey closure’ model). Our study has two aims. The first is to use phylogenetic methods to evaluate the two competing biogeographical models. The second is to describe patterns of phylogeographical diversity throughout the range of the Ensatina complex, and to compare these patterns with previously published molecular systematic data. Location Western North America, with a focus on the state of California, USA. Methods We obtained mitochondrial DNA sequence data from 385 individuals from 224 populations. A phylogeny was inferred using Bayesian techniques, and the geographical distributions of haplotypes and clades were mapped. The two biogeographical ring species models were tested against our Bayesian topology, including the associated Bayesian 95% credible set of trees. Results High levels of phylogeographical diversity were revealed, especially in central coastal and northern California. Our Bayesian topology contradicts the Monterey closure model; however, 0.08% of the trees in our Bayesian 95% credible set are consistent with this model. In contrast, the classic ring species biogeographical model (the southern closure model) is consistent with our Bayesian topology, as were 99.92% of the trees in our 95% credible set. Main conclusions Our Bayesian phylogenetic analysis most strongly supports the classic ring species model, modified to accommodate an improved understanding of the complex geomorphological evolution of the California Coast Ranges. In addition, high levels of phylogeographical diversity in central and northern California were identified, which is consistent with the striking levels of allozymic differentiation reported previously from those regions.     

Improving noise resistance of intrinsic rhythms in a square-wave burster model

The square-wave burster (Wang and Rinzel, 2003) is a class of autonomous bursting cells that share a bifurcation structure. It is known that this class of cells is involved in the generation of various life-supporting rhythms. In our research to realize an electronic circuit that mimics the rhythm generating mechanism in the square-wave burster, our circuit experimentally exhibited severe fluctuations in its rhythmic activity. We have found a noise-sensitive region in the phase portrait of the ideal model and have proposed modifications of the model that can reduce this fluctuation. A possible modification to ionic-conductance neuron models (Kohno and Aihara, 2011) was inspired by them. This modification, however, cannot be applied to a group of square-wave bursters, including the Butera–Rinzel–Smith model (0010 and 0050), which is a model of the pre-Bötzinger complex bursting neuron that plays a crucial role in the generation of respiration rhythms, because this modification premises that the slow dynamics originates from an activation gate variable of a hyperpolarizing ionic current. However, in some square-wave bursters, they are controlled by an inactivation gate variable of a depolarizing ionic current. In this study, we proposed a similar modification with a completely different mechanism that can be applied to this group of square-wave bursters. In the presence of noises, the modified Butera–Rinzel–Smith model can generate rhythmic activity that is more stable and similar to biological observations than the original model. The mechanisms underlying this modification are explained with noisy bifurcation diagrams.     

ATP-dependent rotation of mutant ATP synthases defective in proton transport

During ATP hydrolysis, the gammaepsilon c10 complex (gamma and epsilon subunits and a c subunit ring formed from 10 monomers) of F0F1 ATPase (ATP synthase) rotates relative to the alpha3beta3delta ab2 complex, leading to proton transport through the interface between the a subunit and the c subunit ring. In this study, we replaced the two pertinent residues for proton transport, cAsp-61 and aArg-210 of the c and a subunits, respectively. The mutant enzymes exhibited lower ATPase activities than that of the wild type but exhibited ATP-dependent rotation in planar membranes, in which their original assemblies are maintained. The mutant enzymes were defective in proton transport, as shown previously. These results suggest that proton transport can be separated from rotation in ATP hydrolysis, although rotation ensures continuous proton transport by bringing the cAsp-61 and aArg-210 residues into the correct interacting positions.     

Real time image processing with an analog vision chip system

A linear analog network model is proposed to characterize the function of the outer retinal circuit in terms of the standard regularization theory. Inspired by the function and the architecture of the model, a vision chip has been designed using analog CMOS Very Large Scale Integrated circuit technology. In the chip, sample/hold amplifier circuits are incorporated to compensate for statistic transistor mismatches. Accordingly, extremely low noise outputs were obtained from the chip. Using the chip and a zero-crossing detector, edges of given images were effectively extracted in indoor illumination.     

Conformation of ring single-stranded DNA measured by DNA origami structures

Measuring the mechanical properties of single-stranded DNA (ssDNA) is a complex challenge that has been addressed lately by different methods. We measured the persistence length of ring ssDNA using a combination of a special DNA origami structure, a self-avoiding ring polymer simulation model, and nonparametric estimation statistics. The method overcomes the complexities set forth by previously used methods. We designed the DNA origami nano structures and measured the ring ssDNA polymer conformations using atomic force microscopy. We then calculated their radius of gyration, which was used as a fitting parameter for finding the persistence length. As there is no simple formulation for the radius of gyration distribution, we developed a simulation program consisting of a self-avoiding ring polymer to fit the persistence length to the experimental data. ssDNA naturally forms stem-loops, which should be taken into account in fitting a model to the experimental measurement. To overcome that hurdle, we found the possible loops using minimal energy considerations and used them in our fitting procedure of the persistence length. Due to the statistical nature of the loops formation, we calculated the persistence length for different percentages of loops that are formed. In the range of 25–75% loop formation, we found the persistence length to be 1.9–4.4 nm, and for 50% loop formation we get a persistence length of 2.83 ± 0.63 nm. This estimation narrows the previously known persistence length and provides tools for finding the conformations of ssDNA.     

Distinct rhythmic locomotor patterns can be generated by a simple adaptive neural circuit: Biology,simulation, and VLSI implementation

Rhythmic motor patterns can be induced in leg motor neurons of isolated locust thoracic ganglia by bath application of pilocarpine. We observed that the relative phases of levators and depressors differed in the three thoracic ganglia. Assuming that the central pattern generating circuits underlying these three segmental rhythms are probably very similar, we developed a simple model circuit that can produce any one of the three activity patterns and characteristic phase relationships by modifying a single synaptic weight. We show results of a computer simulation of this circuit using the neuronal simulator NeuraLOG/Spike. We built and tested an analog VLSI circuit implementation of this model circuit that exhibits the same range of behaviors as the computer simulation. This multidisciplinary strategy will be useful to explore the dynamics of central pattern generating networks coupled to physical actuators, and ultimately should allow the design of biologically realistic walking robots.     

Dimensional reduction of a V1 ring model with simple and complex cells

In this paper, we extend a framework for constructing low-dimensional dynamical systems models of mammalian primary visual cortex to a cortical network model that incorporates the full nonlinear effects of complex cells. The procedure consists of capturing the essential dynamics in a low-dimensional subspace using empirical methods, then recasting the equations in the reduced vector space. Previously, we considered visual cortical network models consisting of only simple cells with nearly linear responses to external stimuli. Here we show that fully nonlinear effects can be incorporated by examining the dimensional reduction of an idealized ring model of V1 with both simple and complex cells. We found it expedient to divide the subspace into four separate neuronal populations: excitatory simple, excitatory complex, inhibitory simple and inhibitory complex. In order to reproduce the fluctuation-driven dynamics in this reduced space, we incorporated (1) white noises with different intensities into individual neuronal populations, and (2) firing rate estimates to capture the probability of firing due to subthreshold fluctuations. With a more accurate, fitted connectivity, our modified dimensional reduced models can reproduce the firing rates, circular variances and modulation ratios observed in the original ring model.     

Managing Free-energy Barriers in Nuclear Pore Transport

The Nuclear Pore Complexes (NPC) facilitate highly selective gateways for transport of macromolecules across the Nuclear Envelope (NE). Based on the current accumulated knowledge of the architecture of NPC we have established a minimal physical model of the pore and the transport mechanism. The barrier properties of the NPC model are analyzed by the recently established Wang–Landau Monte Carlo computer simulation technique and the transport properties are extracted by employing Kramers’ theory of reaction rates. We show that our physical model can account for a range of characteristics observed for nuclear pore transport.