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Gibbs ensemble Monte Carlo simulations were used to test the ability of intermolecular pair potentials derived ab initio from quantum mechanical principles, enhanced by Axilrod-Teller triple-dipole interactions, to predict the vapor-liquid phase equilibria of pure neon, pure argon, and the binary mixtures neon-argon and argon-krypton. The interaction potentials for Ne-Ne, Ar-Ar, Kr-Kr, and Ne-Ar were taken from literature; fbr Ar-Kr a different potential has been developed. In all cases the quantum mechanical calculations had been carried out with the coupled-cluster approach [CCSD(T) level of theory] and with correlation consistent basis sets; furthermore an extrapolation scheme had been applied to obtain the basis set limit of the interaction energies. The ab initio pair potentials as well as the thermodynamic data based on them are found to he in excellent agreement with experimental data; the only exception is neon. It is shown, however, that in this case the deviations can be quantitatively explained by quantum effects. The interaction potentials that have been developed permit quantitative predictions of high-pressure phase equilibria of noble-gas mixtures. [ABSTRACT FROM AUTHOR]

Advancements in microscopy techniques and computing technologies have enabled researchers to digitally reconstruct brains at micron scale. As a result, community efforts like the BRAIN Initiative Cell Census Network (BICCN) have generated thousands of whole-brain imaging datasets to trace neuronal circuitry and comprehensively map cell types. This data holds valuable information that extends beyond initial analyses, opening avenues for variation studies and robust classification of cell types in specific brain regions. However, the size and heterogeneity of these imaging data have historically made storage, sharing, and analysis difficult for individual investigators and impractical on a broad community scale. Here, we introduce the Brain Image Library (BIL), a public resource serving the neuroscience community that provides a persistent centralized repository for brain microscopy data. BIL currently holds thousands of brain datasets and provides an integrated analysis ecosystem, allowing for exploration, visualization, and data access without the need to download, thus encouraging scientific discovery and data reuse., Competing Interests: Competing interests The authors declare no competing interests., (© 2024. The Author(s).)

Lambert-Eaton myasthenic syndrome (LEMS) is an autoimmune-mediated neuromuscular disease thought to be caused by autoantibodies against P/Q-type voltage-gated calcium channels (VGCCs), which attack and reduce the number of VGCCs within transmitter release sites (active zones; AZs) at the neuromuscular junction (NMJ), resulting in neuromuscular weakness. However, patients with LEMS also have antibodies to other neuronal proteins, and about 15% of patients with LEMS are seronegative for antibodies against VGCCs. We hypothesized that a reduction in the number of P/Q-type VGCCs alone is not sufficient to explain LEMS effects on transmitter release. Here, we used a computational model to study a variety of LEMS-mediated effects on AZ organization and transmitter release constrained by electron microscopic, pharmacological, immunohistochemical, voltage imaging, and electrophysiological observations. We show that models of healthy AZs can be modified to predict the transmitter release and short-term facilitation characteristics of LEMS and that in addition to a decrease in the number of AZ VGCCs, disruption in the organization of AZ proteins, a reduction in AZ number, a reduction in the amount of synaptotagmin, and the compensatory expression of L-type channels outside the remaining AZs are important contributors to LEMS-mediated effects on transmitter release. Furthermore, our models predict that antibody-mediated removal of synaptotagmin in combination with disruption in AZ organization alone could mimic LEMS effects without the removal of VGCCs (a seronegative model). Overall, our results suggest that LEMS pathophysiology may be caused by a collection of pathological alterations to AZs at the NMJ, rather than by a simple loss of VGCCs. NEW & NOTEWORTHY We used a computational model of the active zone (AZ) in the mammalian neuromuscular junction to investigate Lambert-Eaton myasthenic syndrome (LEMS) pathophysiology. This model suggests that disruptions in presynaptic active zone organization and protein content (particularly synaptotagmin), beyond the simple removal of presynaptic calcium channels, play an important role in LEMS pathophysiology.

We study the role of temperature on the structure of pure polymer brushes and their mixture with attractive nanoparticles in flat and cylindrical geometries. It has previously been established that the addition of such nanoparticles causes the polymer brush to collapse and the intensity of the collapse depends on the attraction strength, the nanoparticle diameter, and the grafting density. In this work, we carry out molecular dynamics simulation under good solvent conditions to show how the collapse transition is affected by the temperature, for both plane grafted and inside-cylinder grafted brushes. We first examine the pure brush morphology and verify that the brush height is insensitive to temperature changes in both planar and cylindrical geometries, as expected for a polymer brush in a good solvent. On the other hand, for both system geometries, the brush structure in the presence of attractive nanoparticles is quite responsive to temperature changes. Generally speaking, for a given nanoparticle concentration, increasing the temperature causes the brush height to increase. A brush which contracts when nanoparticles are added eventually swells beyond its pure brush height as the system temperature is increased. The combination of two easily controlled external parameters, namely, concentration of nanoparticles in solution and temperature, allows for sensitive and reversible adjustment of the polymer brush height, a feature which could be exploited in designing smart polymer devices.

The general mechanism of calcium-triggered chemical transmitter release from neuronal synapses has been intensely studied, is well-known, and highly conserved between species and synapses across the nervous system. However, the structural and functional details within each transmitter release site (or active zone) are difficult to study in living tissue using current experimental approaches owing to the small spatial compartment within the synapse where exocytosis occurs with a very rapid time course. Therefore, computer simulations offer the opportunity to explore these microphysiological environments of the synapse at nanometer spatial scales and on a sub-microsecond timescale. Because biological reactions and physiological processes at synapses occur under conditions where stochastic behavior is dominant, simulation approaches must be driven by such stochastic processes. MCell provides a powerful simulation approach that employs particle-based stochastic simulation tools to study presynaptic processes in realistic and complex (3D) geometries using optimized Monte Carlo algorithms to track finite numbers of molecules as they diffuse and interact in a complex cellular space with other molecules in solution and on surfaces (representing membranes, channels and binding sites). In this review we discuss MCell-based spatially realistic models of the mammalian and frog neuromuscular active zones that were developed to study presynaptic mechanisms that control transmitter release. In particular, these models focus on the role of presynaptic voltage-gated calcium channels, calcium sensors that control the probability of synaptic vesicle fusion, and the effects of action potential waveform shape on presynaptic calcium entry. With the development of these models, they can now be used in the future to predict disease-induced changes to the active zone, and the effects of candidate therapeutic approaches., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Laghaei and Meriney.)

The action potential (AP) waveform controls the opening of voltage-gated calcium channels and contributes to the driving force for calcium ion flux that triggers neurotransmission at presynaptic nerve terminals. Although the frog neuromuscular junction (NMJ) has long been a model synapse for the study of neurotransmission, its presynaptic AP waveform has never been directly studied, and thus the AP waveform shape and propagation through this long presynaptic nerve terminal are unknown. Using a fast voltage-sensitive dye, we have imaged the AP waveform from the presynaptic terminal of male and female frog NMJs and shown that the AP is very brief in duration and actively propagated along the entire length of the terminal. Furthermore, based on measured AP waveforms at different regions along the length of the nerve terminal, we show that the terminal is divided into three distinct electrical regions: A beginning region immediately after the last node of Ranvier where the AP is broadest, a middle region with a relatively consistent AP duration, and an end region near the tip of nerve terminal branches where the AP is briefer. We hypothesize that these measured changes in the AP waveform along the length of the motor nerve terminal may explain the proximal-distal gradient in transmitter release previously reported at the frog NMJ. SIGNIFICANCE STATEMENT The AP waveform plays an essential role in determining the behavior of neurotransmission at the presynaptic terminal. Although the frog NMJ is a model synapse for the study of synaptic transmission, there are many unknowns centered around the shape and propagation of its presynaptic AP waveform. Here, we demonstrate that the presynaptic terminal of the frog NMJ has a very brief AP waveform and that the motor nerve terminal contains three distinct electrical regions. We propose that the changes in the AP waveform as it propagates along the terminal can explain the proximal-distal gradient in transmitter release seen in electrophysiological studies., (Copyright © 2020 the authors.)

We have investigated the impact of transmitter release site (active zone; AZ) structure on synaptic function by physically rearranging the individual AZ elements in a previously published frog neuromuscular junction (NMJ) AZ model into the organization observed in a mouse NMJ AZ. We have used this strategy, purposefully without changing the properties of AZ elements between frog and mouse models (even though there are undoubtedly differences between frog and mouse AZ elements in vivo), to directly test how structure influences function at the level of an AZ. Despite a similarly ordered ion channel array substructure within both frog and mouse AZs, frog AZs are much longer and position docked vesicles in a different location relative to AZ ion channels. Physiologically, frog AZs have a lower probability of transmitter release compared with mouse AZs, and frog NMJs facilitate strongly during short stimulus trains in contrast with mouse NMJs that depress slightly. Using our computer modeling approach, we found that a simple rearrangement of the AZ building blocks of the frog model into a mouse AZ organization could recapitulate the physiological differences between these two synapses. These results highlight the importance of simple AZ protein organization to synaptic function. NEW & NOTEWORTHY A simple rearrangement of the basic building blocks in the frog neuromuscular junction model into a mouse transmitter release site configuration predicted the major physiological differences between these two synapses, suggesting that transmitter release site structure and organization is a strong predictor of function.

The spatiotemporal calcium dynamics within presynaptic neurotransmitter release sites (active zones, AZs) at the time of synaptic vesicle fusion is critical for shaping the dynamics of neurotransmitter release. Specifically, the relative arrangement and density of voltage-gated calcium channels (VGCCs) as well as the concentration of calcium buffering proteins can play a large role in the timing, magnitude, and plasticity of release by shaping the AZ calcium profile. However, a high-resolution understanding of the role of AZ structure in spatiotemporal calcium dynamics and how it may contribute to functional heterogeneity at an adult synapse is currently lacking. We demonstrate that synaptic delay varies considerably across, but not within, individual synapses at the frog neuromuscular junction (NMJ). To determine how elements of the AZ could contribute to this variability, we performed a parameter search using a spatially realistic diffusion reaction-based computational model of a frog NMJ AZ (Dittrich M, Pattillo JM, King JD, Cho S, Stiles JR, Meriney SD. Biophys J 104: 2751-2763, 2013; Ma J, Kelly L, Ingram J, Price TJ, Meriney SD, Dittrich M. J Neurophysiol 113: 71-87, 2015). We demonstrate with our model that synaptic delay is sensitive to significant alterations in the spatiotemporal calcium dynamics within an AZ at the time of release caused by manipulations of the density and organization of VGCCs or by the concentration of calcium buffering proteins. Furthermore, our data provide a framework for understanding how AZ organization and structure are important for understanding presynaptic function and plasticity. NEW & NOTEWORTHY The structure of presynaptic active zones (AZs) can play a large role in determining the dynamics of neurotransmitter release across many model preparations by influencing the spatiotemporal calcium dynamics within the AZ at the time of vesicle fusion. However, less is known about how different AZ structural schemes may influence the timing of neurotransmitter release. We demonstrate that variations in AZ structure create different spatiotemporal calcium profiles that, in turn, lead to differences in synaptic delay.

At present, the three-dimensional structure of the multimeric paracellular claudin pore is unknown. Using extant biophysical data concerning the size of the pore and permeation of water and cations through it, two three-dimensional models of the pore are constructed in silico. Molecular Dynamics (MD) calculations are then performed to compute water and sodium ion permeation fluxes under the influence of applied hydrostatic pressure. Comparison to experiment is made, under the assumption that the hydrostatic pressure applied in the simulations is equivalent to osmotic pressure induced in experimental measurements of water/ion permeability. One model, in which pore-lining charged is distributed evenly over a selectivity filter section 10-16 Å in length, is found to be generally consistent with experimental data concerning the dependence of water and ion permeation on channel pore diameter, pore length, and the sign and magnitude of pore lining charge. The molecular coupling mechanism between water and ion flow under conditions where hydrostatic pressure is applied is computationally elucidated., (© 2015 Wiley Periodicals, Inc.)

In recent years, much effort has focused on the early stages of aggregation and the formation of amyloid oligomers. Aggregation processes for these proteins are complex and their non-equilibrium nature makes any experimental study very difficult. Under these conditions, simulations provide a useful alternative for understanding the dynamics of the early stages of oligomerization. Here, we focus on the non-Aβ amyloid component (NAC) of the monomer, dimer, and trimer of α-synuclein, an important 35-residue sequence involved in the aggregation and fibrillation of this protein associated with Parkinson's disease. Using Hamiltonian and temperature replica exchange molecular dynamics simulations combined with the coarse grained Optimized Potential for Efficient peptide structure Prediction potential, we identify the role of the various regions and the secondary structures for the onset of oligomerization. For this sequence, we clearly observe the passage from α-helix to β-sheet, a characteristic transition of amyloid proteins. More precisely, we find that the NAC monomer is highly structured with two α-helical regions, between residues 2-13 and 19-25. As the dimer and trimer form, β-sheet structures between residues 2-14 and 26-34 appear and rapidly structure the system. The resulting conformations are much more structured than similar dimers and trimers of β-amyloid and amylin proteins and yet display a strong polymorphism at these early stages of aggregation. In addition to its inherent experimental interest, comparison with other sequences shows that NAC could be a very useful numerical model for understanding the onset of aggregation.

Influx of ferrous ions from the cytoplasm through 3-fold pores in the shell of ferritin protein is computed using a 3-dimensional Poisson-Nernst-Planck electrodiffusion model, with inputs such as the pore structure and the diffusivity profile of permeant Fe(2+) ions extracted from all-atom molecular dynamics (MD) simulations. These calculations successfully reproduce experimental estimates of the transit time of Fe(2+) through the ferritin coat, which is on the millisecond time scale and hence much too long to be directly simulated via all-atom MD. This is also much longer than the typical time scale for ion transit in standard membrane spanning ion channels whose pores bear structural similarity to that of the 3-fold ferritin pore. The slow time scale for Fe(2+) transport through ferritin pores is traced to two features that distinguish the ferritin pore system from standard ion channels, namely, (i) very low concentration of cytoplasmic Fe(2+) under physiological conditions and (ii) very small internal diffusion coefficients for ions inside the ferritin pore resulting from factors that include the divalent nature of Fe(2+) and two rings of negatively charged amino acids surrounding a narrow geometric obstruction within the ferritin pore interior.

We study via all atom classical molecular dynamics (MD) simulation the process of uptake of ferrous ions (Fe(2+)) into the human ferritin protein and the catalytic ferroxidase sites via pores ("channels") in the interior of the protein. We observe that the three-fold hydrophilic channels serve as the main entrance pathway for the Fe(2+) ions. The binding sites along the ion pathway are investigated. Two strong binding sites, at the Asp131 and Glu134 residues and two weak binding sites, at the His118 and Cys130 are observed inside the three-fold channel. We also identify an explicit pathway for an ion exiting the channel into the central core of the protein as it moves to the ferroxidase site. The diffusion of an Fe(2+) ion from the inner opening of the channel to a ferroxidase site located in the interior region of the protein coat is assisted by Thr135, His136 and Tyr137. The Fe(2+) ion binds preferentially to site A of the ferroxidase site., (Copyright © 2013 Wiley Periodicals, Inc.)

We study the mechanism of vacancy migration and phase transitions of 3D crystalline colloidal arrays (CCA) using Langevin dynamics simulations. We calculate the self-diffusion coefficient of the colloid particles and the diffusion constant for vacancies as a function of temperature and DLVO potential parameters. We investigate the phase behavior of several systems with different interaction potential parameters using Voronoi analysis. Voronoi polyhedra tessellation, which is a useful method for characterizing the nearest neighbor environment around each atom, provides an efficient and effective way to identify phase transitions as well as geometrical changes in crystals. Using Voronoi analysis, we show that several neighboring particles are involved in the vacancy migration process that causes the vacancy to diffuse.

The Amyloid-beta protein is related to Alzheimer's disease, and various experiments have shown that oligomers as small as the dimer are cytotoxic. Two alloforms are mainly produced: Aβ(1-40) and Aβ(1-42). They have very different oligomer distributions, and it was recently suggested, from experimental studies, that this variation may originate from structural differences in their dimer structures. Little structural information is available on the Aβ dimer, however, and to complement experimental observations, we simulated the folding of the wild-type Aβ(1-40) and Aβ(1-42) dimers as well as the mutated Aβ(1-40)(D23N) dimer using an accurate coarse-grained force field coupled to Hamiltonian-temperature replica exchange molecular dynamics. The D23N variant impedes the salt-bridge formation between D23 and K28 seen in the wild-type Aβ, leading to very different fibrillation properties and final amyloid fibrils. Our results show that the Aβ(1-42) dimer has a higher propensity than the Aβ(1-40) dimer to form β-strands at the central hydrophobic core (residues 17-21) and at the C-terminal (residues 30-42), which are two segments crucial to the oligomerization of Aβ. The free energy landscape of the Aβ(1-42) dimer is also broader and more complex than that of the Aβ(1-40) dimer. Interestingly, D23N also impacts the free energy landscape by increasing the population of configurations with higher β-strand propensities when compared against Aβ(40). In addition, while Aβ(1-40)(D23N) displays a higher β-strand propensity at the C-terminal, its solvent accessibility does not change with respect to the wild-type sequence. Overall, our results show the strong impact of the two amino acids Ile41-Ala42 and the salt-bridge D23-K28 on the folding of the Aβ dimer.

The loss of the insulin-producing β-cells in the pancreatic islets of Langerhans, responsible for type-II diabetes, is associated with islet amyloid deposits. The main component of these deposits is the amyloid fibrils formed by the 37-residue human islet amyloid polypeptide (hIAPP also known as amylin). Although the fibrils are well characterized by cross β structure, the structure of the transient oligomers formed in the early stage of aggregation remains elusive. In this study, we apply the Hamiltonian-temperature replica exchange molecular dynamics to characterize the structure and thermodynamics of a full-length hIAPP dimer in both the presence and the absence of the Cys2-Cys7 disulfide bond. We compare these results with those obtained on the monomeric and dimeric forms of rat IAPP (rIAPP) with a disulfide bridge which differ from the hIAPP by 6 amino acids in the C-terminal region, but it is unable to form fibrils. Using a coarse-grained protein force field (OPEP-the Optimized Potential for Efficient peptide structure Prediction) running for a total of 10-28 μs per system studied, we show that sequences sample α-helical structure in the N-terminal region but that the length of this secondary element is shorter and less stable for the chains without the disulfide bridge (residues 5-16 for hIAPP with the bridge vs 10-16 for hIAPP without the bridge). This α-helix is known to be an important transient stage in the formation of oligomers. In the C-terminal, the amyloidogenic region of hIAPP, β-strands are seen for residues 17-26 and 30-35. On the contrary, no significant β-sheet content in the C-terminal is observed for either the monomeric or the dimeric rIAPP. These numerical results are fully consistent with recent experimental findings that the N-terminal residues are not part of the fibril by forming α-helical structure but rather play a significant role in stabilizing the amyloidogenic region available for the fibrillation.

The human Islet amyloid polypeptide (hIAPP or amylin) is a 37-residue peptide hormone that is normally cosecreted with insulin by the pancreatic beta-cells. In patients with type 2 diabetes, hIAPP deposits as amyloid fibrils in the extracellular spaces of the pancreatic islets. Recent experimental studies show that the intramolecular disulfide bond between Cys2 and Cys7 plays a central role in the process of fibril formation. However, the effect of the disulfide bond on the intrinsic structural properties of monomeric hIAPP is yet to be determined. In this study, we characterize the atomic structure and the thermodynamics of full-length hIAPP in the presence and absence of a disulfide bond using extensive combined Hamiltonian and temperature replica exchange molecular dynamics simulations (HT-REMD) with a coarse grained protein force field. Our simulations show that HT-REMD is more efficient in sampling than temperature REMD. On the basis of a total simulation time of 28 mus, we find that, although native hIAPP (in the presence of a disulfide bond) essentially adopts a disordered conformation in solution, consistent with the signal measured by ultraviolet-circular dichroism (UV-CD) spectroscopy, it also transiently samples alpha-helical structure for residues 5-16. In comparison with the N-terminal region, the C-terminal region is highly disordered and populates a much lesser content of isolated beta-strand conformation for residues 22-26 and 30-35. Moreover, the absence of the disulfide bond greatly decreases the extent of helix formed throughout residues 5-9 in favor of random coil and beta-sheet structure. Implications of the stabilization of N-terminal helical structure by disulfide bond on the initialization of hIAPP amyloid formation are discussed.

Expansion of polyglutamine (polyQ) beyond the pathogenic threshold (35-40 Gln) is associated with several neurodegenerative diseases including Huntington's disease, several forms of spinocerebellar ataxias and spinobulbar muscular atrophy. To determine the structure of polyglutamine aggregates we perform replica-exchange molecular dynamics simulations coupled with the optimized potential for effective peptide forcefield. Using a range of temperatures from 250 to 700 K, we study the aggregation kinetics of the polyglutamine monomer and dimer with chain lengths from 30 to 50 residues. All monomers show a similar structural change at the same temperature from alpha-helical structure to random coil, without indication of any significant beta-strand. For dimers, by contrast, starting from random structures, we observe spontaneous formation of antiparallel beta-sheets and triangular and circular beta-helical structures for polyglutamine with 40 residues in a 400 ns 50 temperature replica-exchange molecular dynamics simulation (total integrated time 20 micros). This approximately 32 A diameter structure reorganizes further into a tight antiparallel double-stranded approximately 22 A nanotube with 22 residues per turn close to Perutz' model for amyloid fibers as water-filled nanotubes. This diversity of structures suggests the existence of polymorphism for polyglutamine with possibly different pathways leading to the formation of toxic oligomers and to fibrils.

Current approaches aimed at determining the free energy surface of all-atom medium-size proteins in explicit solvent are slow and are not sufficient to converge to equilibrium properties. To ensure a proper sampling of the configurational space, it is preferable to use reduced representations such as implicit solvent and/or coarse-grained protein models, which are much lighter computationally. Each model must be verified, however, to ensure that it can recover experimental structures and thermodynamics. Here we test the coarse-grained implicit solvent OPEP model with replica exchange molecular dynamics (REMD) on six peptides ranging in length from 10 to 28 residues: two alanine-based peptides, the second beta-hairpin from protein G, the Trp-cage and zinc-finger motif, and a dimer of a coiled coil peptide. We show that REMD-OPEP recovers the proper thermodynamics of the systems studied, with accurate structural description of the beta-hairpin and Trp-cage peptides (within 1-2 A from experiments). The light computational burden of REMD-OPEP, which enables us to generate many hundred nanoseconds at each temperature and fully assess convergence to equilibrium ensemble, opens the door to the determination of the free energy surface of larger proteins and assemblies.

A newly proposed theory [R. Laghaei et al., J. Chem. Phys. 124, 154502 (2006)] was extended to polyatomics and applied to compute the density and temperature dependence of the effective site diameters of carbon disulfide fluids. The generic van der Waals (GvdW) theory was also extended to polyatomics in order to calculate the GvdW parameters and the molecular free volume using the effective site diameters as the repulsion-attraction separation distance. A three-site Lennard-Jones potential available in the literature was slightly modified and used in Monte Carlo simulations to obtain the functions appearing in the effective site diameter and GvdW expressions. The interaction potential was examined to reproduce the fluid phase thermodynamic properties using Gibbs ensemble Monte Carlo simulations and also the equation of state in the liquid phase using NVT Monte Carlo (NVT-MC) simulations. Comparison between the simulation results and experimental data shows excellent agreement for the densities of the coexisting phases, the vapor pressure, properties of the predicted critical point, and the equation of state. NVT-MC simulations were performed over a wide range of densities and temperatures in sub- and supercritical regions to compute the effective site diameters, the GvdW parameters, and the molecular free volume. The molecular structure in terms of the site-site pair correlation functions, the density dependence of the effective site diameters, and the density and temperature dependence of the GvdW parameters and molecular free volume were studied and discussed. The GvdW parameters were fitted to empirical expressions as a function of density and temperature. The computed molecular free volume will be used in future investigations to study the transport properties of carbon disulfide.

A quantum mechanical derived ab initio interaction potential for the argon dimer was tested in molecular simulations to reproduce the thermophysical properties of the vapor-liquid phase equilibria using the Gibbs ensemble Monte Carlo simulations as well as the liquid and supercritical equation of state using the NVT Monte Carlo simulations. The ab initio interaction potential was taken from the literature. A recently developed theory [R. Laghaei et al., J. Chem. Phys. 124, 154502 (2006)] was used to compute the effective diameters of argon in fluid phases and the results were subsequently applied in the generic van der Waals theory to compute the free volume of argon. The calculated densities of the coexisting phases, the vapor pressure, and the equation of state show excellent agreement with experimental values. The effective diameters and free volumes of argon are given over a wide range of densities and temperatures. An empirical formula was used to fit the effective diameters as a function of density and temperature. The computed free volume will be used in future investigations to calculate the transport properties of argon.

In the previous papers applying the generic van der Waals equation of state the mean excluded volume was defined with the contact diameter of particles at which the potential energy is equal to zero-the size parameter in the case of the Lennard-Jones potential. This parameter appears as the upper limit of the integral for the generic van der Waals parameter B (mean excluded volume divided by the density) in the generic van der Waals equation of state. Since the choice is not unique, in this paper we reexamine the manner of defining the upper limit and propose another choice for the upper limit. We also propose an interpretation of the free volume overlap factor alpha appearing in the free volume theory of diffusion and a method of estimating it in terms of the intermolecular potential energy only. It is shown that with the so-estimated free volume overlap factor and the new choice of the upper limit of the integral for B the self-diffusion coefficient in the modified free volume theory of diffusion not only acquires a better accuracy than before, but also becomes calculable in terms of only the intermolecular interaction potential without an adjustable parameter. We also assess some of effective diameters of molecules proposed in the literature for their ability to predict the self-diffusion coefficient within the framework of the modified free volume theory of diffusion.

In this paper the thermal conductivity of the Lennard-Jones fluid is calculated by applying the combination of the density-fluctuation theory, the modified free volume theory of diffusion, and the generic van der Waals equation of state. A Monte Carlo simulation method is used to compute the equilibrium pair-correlation function necessary for computing the mean free volume and the coefficient in the potential-energy and virial contributions to the thermal conductivity. The theoretical results are compared with our own molecular dynamics simulation results and with those reported in the literature. They agree in good accuracy over wide ranges of density and temperature examined in molecular dynamics simulations. Thus the combined theory represents a molecular theory of thermal conductivity of the Lennard-Jones fluid and by extension simple fluids, which enables us to compute the nonequilibrium quantity by means of the Monte Carlo simulations for the equilibrium pair-correlation function.

The generalized Boltzmann equation for simple dense fluids gives rise to the stress tensor evolution equation as a constitutive equation of generalized hydrodynamics for fluids far removed from equilibrium. It is possible to derive a formula for the non-Newtonian shear viscosity of the simple fluid from the stress tensor evolution equation in a suitable flow configuration. The non-Newtonian viscosity formula derived is applied to calculate the non-Newtonian viscosity as a function of the shear rate by means of statistical mechanics in the case of the Lennard-Jones fluid. For that purpose we have used the density-fluctuation theory for the Newtonian viscosity, the modified free volume theory for the self-diffusion coefficient, and the generic van der Waals equation of state to compute the mean free volume appearing in the modified free volume theory. Monte Carlo simulations are used to calculate the pair-correlation function appearing in the generic van der Waals equation of state and shear viscosity formula. To validate the Newtonian viscosity formula obtained we first have examined the density and temperature dependences of the shear viscosity in both subcritical and supercritical regions and compared them with molecular-dynamic simulation results. With the Newtonian shear viscosity and thermodynamic quantities so computed we then have calculated the shear rate dependence of the non-Newtonian shear viscosity and compared it with molecular-dynamics simulation results. The non-Newtonian viscosity formula is a universal function of the product of reduced shear rate (gamma*) times reduced relaxation time (taue*) that is independent of the material parameters, suggesting a possibility of the existence of rheological corresponding states of reduced density, temperature, and shear rate. When the simulation data are reduced appropriately and plotted against taue*gamma* they are found clustered around the reduced (universal) non-Newtonian viscosity formula. Thus we now have a molecular theory of non-Newtonian shear viscosity for the Lennard-Jones fluid, which can be implemented with a Monte Carlo simulation method for the pair-correlation function.

In this paper, we apply the Matteoli-Mansoori empirical formula for the pair correlation function of simple fluids obeying the Lennard-Jones potential to calculate reduced self-diffusion coefficients on the basis of the modified free volume theory. The self-diffusion coefficient thus computed as functions of temperature and density is compared with the molecular dynamics simulation data and the self-diffusion coefficient obtained by the modified free volume theory implemented with the Monte Carlo simulation method for the pair correlation function. We show that the Matteoli-Mansoori empirical formula yields sufficiently accurate self-diffusion coefficients in the supercritical regime, provided that the minimum free volume activating diffusion is estimated with the classical turning point of binary collision at the mean relative kinetic energy 3k(B)T/2, where k(B) is the Boltzmann constant and T is the temperature. In the subcritical regime, the empirical formula yields qualitatively correct, but lower values for the self-diffusion coefficients compared with computer simulation values and those from the modified free volume theory implemented with the Monte Carlo simulations for the pair correlation function. However, with a slightly modified critical free volume, the results can be made quite acceptable.

In previous work on the density fluctuation theory of transport coefficients of liquids, it was necessary to use empirical self-diffusion coefficients to calculate the transport coefficients (e.g., shear viscosity of carbon dioxide). In this work, the necessity of empirical input of the self-diffusion coefficients in the calculation of shear viscosity is removed, and the theory is thus made a self-contained molecular theory of transport coefficients of liquids, albeit it contains an empirical parameter in the subcritical regime. The required self-diffusion coefficients of liquid carbon dioxide are calculated by using the modified free volume theory for which the generic van der Waals equation of state and Monte Carlo simulations are combined to accurately compute the mean free volume by means of statistical mechanics. They have been computed as a function of density along four different isotherms and isobars. A Lennard-Jones site-site interaction potential was used to model the molecular carbon dioxide interaction. The density and temperature dependence of the theoretical self-diffusion coefficients are shown to be in excellent agreement with experimental data when the minimum critical free volume is identified with the molecular volume. The self-diffusion coefficients thus computed are then used to compute the density and temperature dependence of the shear viscosity of liquid carbon dioxide by employing the density fluctuation theory formula for shear viscosity as reported in an earlier paper (J. Chem. Phys. 2000, 112, 7118). The theoretical shear viscosity is shown to be robust and yields excellent density and temperature dependence for carbon dioxide. The pair correlation function appearing in the theory has been computed by Monte Carlo simulations.

The shear viscosity formula derived by the density fluctuation theory in previous papers is computed for argon, krypton, and methane by using the self-diffusion coefficients derived in the modified free volume theory with the help of the generic van der Waals equation of state. In the temperature regime near or above the critical temperature, the density dependence of the shear viscosity can be accounted for by ab initio calculations with the self-diffusion coefficients provided by the modified free volume theory if the minimum (critical) free volume is set equal to the molecular volume and the volume overlap parameter (alpha) is taken about unity in the expression for the self-diffusion coefficient. In the subcritical temperature regime, if the density fluctuation range parameter is chosen appropriately at a temperature, then the resulting expression for the shear viscosity can well account for its density and temperature dependence over the ranges of density and temperature experimentally studied. In the sense that once the density fluctuation range is fixed at a temperature, the theory can account for the experimental data at other subcritical temperatures on the basis of the intermolecular force only; the theory is predictive even in the subcritical regime of temperature. Theory is successfully tested in comparison with experimental data for self-diffusion coefficients and shear viscosity for argon, krypton, and methane.