On the phase transition in a monolayer adsorbed on graphite at temperatures below the 2D-critical temperature

Monte Carlo simulations in the grand ensemble and meso-canonical ensemble in which the adsorbent is connected to a finite reservoir have been used to study adsorption isotherms for monolayer argon adsorption on graphite at temperatures below the 2D-critical temperature in order to elucidate the microscopic details of the 2D-transitions: vapour–solid, vapour–liquid and liquid–solid. An S-shaped van der Waals (vdW) loop was found when a small square surface was used; however, for large square surfaces and rectangular surfaces the isotherms exhibit a vdW-type loop with a vertical segment which indicates the coexistence of two phases separated by a boundary that changes its shape with the loading. This coexistence occurs at the same chemical potential as determined by the mid-density scheme, developed by Do and co-workers (Z. Liu, L. Herrera, V.T. Nguyen, D.D. Do, and D. Nicholson, A Monte Carlo scheme based on mid-density in a hysteresis loop to determine equilibrium phase transition. Mol Simul. 37(11):932–939, 2011; Z. Liu, D.D. Do, and D. Nicholson, A thermodynamic study of the mid-density scheme to determine the equilibrium phase transition in cylindrical pores. Mol Simul. 38(3):189–199, 2011).     

Reconciliation of different simulation methods in the determination of the equilibrium branch for adsorption in pores

The recently proposed mid-density scheme [Liu Z, Herrera L, Nguyen VT, Do DD, Nicholson D. A Monte Carlo scheme based on mid-density in a hysteresis loop to determine equilibrium phase transition. Mol Simul. 2011; 37(11):932–939, Liu Z, Do DD, Nicholson D. A thermodynamic study of the mid-density scheme to determine the equilibrium phase transition in cylindrical pores. Mol Simul. 2012; 38(3):189–199] is tested against a method 2V-NVT (similar to the well-established gauge cell method) and the canonical ensemble (CE) method, using argon adsorption at 87 K in graphitic slit pores of infinite and finite length. In infinitely long pores, the equilibrium transition is vertical that is expected for an infinite system to have a first-order transition and this vertical transition was found to lie at the middle of the hysteresis loop and satisfies the well-known Maxwell rule of equal area. For pores of finite length, the equilibrium transitions are steep and are close to, but not exactly identical to, the desorption branch. This lends support to the conventional view that the desorption branch is nearest to equilibrium, although both adsorption and desorption branches are strictly speaking metastable; a view proposed originally by Everett [Everett DH. Capillary condensation and adsorption hysteresis. Berichte Der Bunsen-Gesellschaft [Phys Chem Chem Phys]. 1975; 79(9):732–734]. As a consequence, the Maxwell rule of equal area does not apply to finite systems. As the widely accepted CE and gauge cell methods do not falsify the mid-density scheme, this study lends strong support to the validity of this technique for the study of equilibria.     

Adsorption of polypeptides on solid surfaces. I. Effect of chain stiffness

The general method of obtaining the partition function and thermodynamic characteristics of polymer chains near an adsorbing surface, simulated by random walks on a lattice, is developed. The method takes into account the effect of short-range interactions in polymer chains, in particular, the chain stiffness and secondary structure. The theory of adsorption of chains of different stiffness is developed, and the process of adsorption which occurs when the external conditions change is shown to be always a second-order phase transition. The critical adsorption energy decreases and the sharpness of transition grows when the chain stiffness increases. A simple model of a chain with “virtual” steps is proposed which simplifies the treatment; the results obtained are in good agreement with exact theories. A general scheme of analysis of adsorption of chains with a given secondary structure is set forth and the analogy between the stiffness of a noncooperative chain and the presence of helical segments in a polypeptide chain is discussed.     

Direct Determination of Fluid Phase Equilibria by Simulation in the Gibbs Ensemble: A Review

This paper provides an extensive review of the literature on the Gibbs ensemble Monte Carlo method for direct determination of phase coexistence in fluids. The Gibbs ensemble technique is based on performing a simulation in two distinct regions in a way that ensures that the conditions of phase coexistence are satisfied in a statistical sense. Contrary to most other available techniques for this purpose, such as thermodynamic integration, grand canonical Monte Carlo or Widom test particle insertions, the Gibbs ensemble technique involves only a single simulation per coexistence point. A significant body of literature now exists on the method, its theoretical foundations, and proposed modifications for efficient determination of equilibria involving dense fluids and complex intermolecular potentials. Some practical aspects of Gibbs ensemble simulation are also discussed in this review. Applications of the technique to date range from studies of simple model potentials (for example Lennard–Jones, square-well or Yukawa fluids) to calculations of equilibria in mixtures with components described by realistic potentials. We conclude by discussing the limitations of the technique and potential future applications.     

Co-dominance and succession in forest dynamics: the role of interspecific differences in crown transmissivity

Forests that are composed of two or more tree species with similar ecological strategies appear to contradict the competitive exclusion principle. Beech-maple communities are a well-known example of such a system. On a local scale, a number of mechanisms have been proposed to explain the coexistence of these two species. These are reciprocal replacement, external factors that favour alternatively one or the other species and demographic stochasticity. This paper presents and analyses a simple mathematical model that shows that external factors are not an essential requirement for coexistence. Rather, coexistence requires interspecific differences in light transmissivity through the crowns of adult trees. However, all the three mechanisms mentioned above can be interpreted within the framework of the model. Furthermore, many models of forest dynamics make use of shade tolerance as a key feature in describing successional dynamics. Despite its importance, however, shade tolerance does not have a commonly accepted quantitative definition. Here, a simple scheme is proposed where the relationship between shade tolerance, individual traits (growth and survival) and successional status is defined. This might have important implications in understanding the overall dynamics. Theoretical results have been compared with a number of studies carried out in North American forests. In particular, coexistence in beech-maple communities and the relation between shade tolerance and successional status in a beech-hemlock-birch community have been discussed.     

Coexistence of competitive species with a stage-structured life cycle

Ecological theory provides explanations for exclusion or coexistence of competing species. Most theoretical works on competition dynamics that have shaped current perspectives on coexistence assume a simple life cycle. This simplification, however, may omit important realities. We present a simple two-stage structured competition model to investigate the effects of life-history characteristics on coexistence. The achievement and the stability of coexistence depend not only on competition coefficients but also on a set of life-history parameters that reflect the viability of an individual, namely, adult death rate, maturation rate, and birth rate. High individual viability is necessary for a species to persist, but it does not necessarily facilitate coexistence. Intense competition at the juvenile or adult stage may require higher or lower viability, respectively, for stable coexistence to be possible. The stability mechanism can be explained by the refuge effect of the less competitive stage, and the birth performance, which preserves the less competitive stage as a refuge. Coexistence might readily collapse if the life-history characteristics, which together constitute individual viability, change, even though two species have an inherent competitive relation conducive to stable coexistence.     

An efficient algorithm in the grand canonical ensemble: constructing adsorption isotherms

A new computational method is presented that efficiently describes open thermodynamic systems within the grand canonical ensemble formalism. The method is based on the j-walking algorithm, which circumvent sampling difficulties by coupling random walkers in different thermodynamic states. By imposing detailed balance, a new acceptance probability is derived and applied to the construction of adsorption isotherms for atomic monolayers. The method converges much faster than the standard grand canonical Monte Carlo method and permits the construction of accurate adsorption isotherms and the identification of phase transitions occurring in the adsorbed material.     

Concurrent Codes: A Holographic-Type Encoding Robust against Noise and Loss

Concurrent coding is an encoding scheme with ‘holographic’ type properties that are shown here to be robust against a significant amount of noise and signal loss. This single encoding scheme is able to correct for random errors and burst errors simultaneously, but does not rely on cyclic codes. A simple and practical scheme has been tested that displays perfect decoding when the signal to noise ratio is of order -18dB. The same scheme also displays perfect reconstruction when a contiguous block of 40% of the transmission is missing. In addition this scheme is 50% more efficient in terms of transmitted power requirements than equivalent cyclic codes. A simple model is presented that describes the process of decoding and can determine the computational load that would be expected, as well as describing the critical levels of noise and missing data at which false messages begin to be generated.     

Molecular weight dependence of the depletion attraction and its effects on the competitive adsorption of lung surfactant

Albumin competes with lung surfactant for the air-water interface, resulting in decreased surfactant adsorption and increased surface tension. Polyethylene glycol (PEG) and other hydrophilic polymers restore the normal rate of surfactant adsorption to the interface, which re-establishes low surface tensions on compression. PEG does so by generating an entropic depletion attraction between the surfactant aggregates and interface, reducing the energy barrier to adsorption imposed by the albumin. For a fixed composition of 10 g/L (1% wt.), surfactant adsorption increases with the 0.1 power of PEG molecular weight from 6 kDa-35 kDa as predicted by simple excluded volume models of the depletion attraction. The range of the depletion attraction for PEG with a molecular weight below 6 kDa is less than the dimensions of albumin and there is no effect on surfactant adsorption. PEG greater than 35 kDa reaches the overlap concentration at 1% wt. resulting in both decreased depletion attraction and decreased surfactant adsorption. Fluorescence images reveal that the depletion attraction causes the surfactant to break through the albumin film at the air-water interface to spread as a monolayer. During this transition, there is a coexistence of immiscible albumin and surfactant domains. Surface pressures well above the normal equilibrium surface pressure of albumin are necessary to force the albumin from the interface during film compression.     

Complex food webs prevent competitive exclusion among producer species

Herbivorous top-down forces and bottom-up competition for nutrients determine the coexistence and relative biomass patterns of producer species. Combining models of predator-prey and producer-nutrient interactions with a structural model of complex food webs, I investigated these two aspects in a dynamic food-web model. While competitive exclusion leads to persistence of only one producer species in 99.7% of the simulated simple producer communities without consumers, embedding the same producer communities in complex food webs generally yields producer coexistence. In simple producer communities, the producers with the most efficient nutrient-intake rates increase in biomass until they competitively exclude inferior producers. In food webs, herbivory predominantly reduces the biomass density of those producers that dominated in producer communities, which yields a more even biomass distribution. In contrast to prior analyses of simple modules, this facilitation of producer coexistence by herbivory does not require a trade-off between the nutrient-intake efficiency and the resistance to herbivory. The local network structure of food webs (top-down effects of the number of herbivores and the herbivores' maximum consumption rates) and the nutrient supply (bottom-up effect) interactively determine the relative biomass densities of the producer species. A strong negative feedback loop emerges in food webs: factors that increase producer biomasses also increase herbivory, which reduces producer biomasses. This negative feedback loop regulates the coexistence and biomass patterns of the producers by balancing biomass increases of producers and biomass fluxes to herbivores, which prevents competitive exclusion.     

A Monte Carlo study of equilibrium transition in finite cylindrical pores

In this paper, we report a comprehensive analysis of the adsorption of argon in cylindrical pores of finite length having different dimensions and adsorbent energies. We determine the mechanisms of adsorption and desorption in the hysteresis region, and use the recently introduced mid-density scheme, as an approximate method, to determine the equilibrium transition, which is found to lie wholly within the loop and closer to the desorption branch. For a given loading in the hysteresis region, we determine the microscopic behaviour of two metastable states (one on the adsorption branch and the other on the desorption branch) and the stable equilibrium state. The adsorption metastable state is characterised by a bulging adsorbed layer, while the desorption metastable state is characterised by a liquid bridge with a meniscus at each end in the shape of a long elliptical cone. The equilibrium state has a configuration that displays a liquid bridge with hemispherically shaped menisci having areas less than those of the two menisci in the desorption metastable state.     

The invisible niche: Weakly density-dependent mortality and the coexistence of species

Weakly density-dependent effects, characterized by fractional scaling exponents close to one, are rarely studied in the ecological literature. Here, we consider the effect of an additional weakly density-dependent term on a simple competition model. Our investigation reveals that weak density-dependence opens up an “invisible niche”. This niche does not constitute a new mechanism for coexistence, but is a previously unexplored consequence of known mechanisms. In the invisible niche a weaker competitor can survive at very low density. Coexistence thus requires large habitat size. Such niches, if found in nature, would have a direct impact on species-area laws and species-abundance curves and should therefore receive more attention.     

A directed approach for engineering conditional protein stability using biologically silent small molecules

The ability to regulate the function of specific proteins using cell-permeable molecules can be a powerful method for interrogating biological systems. To bring this type of "chemical genetic" control to a wide range of proteins, we recently developed an experimental system in which the stability of a small protein domain expressed in mammalian cells depends on the presence of a high affinity ligand. This ligand-dependent stability is conferred to any fused partner protein. The FK506- and rapamycin-binding protein (FKBP12) has been the subject of extensive biophysical analyses, including both kinetic and thermodynamic studies of the wild-type protein as well as dozens of mutants. The goal of this study was to determine if the thermodynamic stabilities (DeltaDeltaG(U-F)) of various amino acid substitutions within a given protein are predictive for engineering additional ligand-dependent destabilizing domains. We used FKBP12 as a model system and found that in vitro thermodynamic stability correlates weakly with intracellular degradation rates of the mutants and that the ability of a given mutation to destabilize the protein is context-dependent. We evaluated several new FKBP12 ligands for their ability to stabilize these mutants and found that a cell-permeable molecule called Shield-1 is the most effective stabilizing ligand. We then performed an unbiased microarray analysis of NIH3T3 cells treated with various concentrations of Shield-1. These studies show that Shield-1 does not elicit appreciable cellular responses.     

A weighted test-area method for calculating surface tension

In this paper, we propose a weighted test-area method to calculate surface tension by incorporating the weighting factor from the Bennett method into the free energy perturbation scheme of the test-area method. This new method was tested by comparing against the results of the Bennett and test-area methods for simulations of square well (SW), Lennard-Jones and point charge fluid models. It is seen that the new method is accurate for all these simulations, giving the same results as the Bennett method, in contrast to the test-area method which cannot calculate the surface tension of a SW fluid. The new method converges as quickly, on the basis of computational time required, as the test-area method and almost twice as quickly as the Bennett method. This combination of speed and accuracy means that the weighted test-area method should be used in preference to the test-area method and Bennett method for surface tension and other macroscopic thermodynamic quantities that can be calculated through perturbation methods.     

Morphometric Image Analysis of Giant Vesicles: A New Tool for Quantitative Thermodynamics Studies of Phase Separation in Lipid Membranes

We have developed a strategy to determine lengths and orientations of tie lines in the coexistence region of liquid-ordered and liquid-disordered phases of cholesterol containing ternary lipid mixtures. The method combines confocal-fluorescence-microscopy image stacks of giant unilamellar vesicles (GUVs), a dedicated 3D-image analysis, and a quantitative analysis based in equilibrium thermodynamic considerations. This approach was tested in GUVs composed of 1,2-dioleoyl-sn-glycero-3-phosphocholine/1,2-palmitoyl-sn-glycero-3-phosphocholine/cholesterol. In general, our results show a reasonable agreement with previously reported data obtained by other methods. For example, our computed tie lines were found to be nonhorizontal, indicating a difference in cholesterol content in the coexisting phases. This new, to our knowledge, analytical strategy offers a way to further exploit fluorescence-microscopy experiments in GUVs, particularly retrieving quantitative data for the construction of three lipid-component-phase diagrams containing cholesterol.     

Analysis of ligand binding curves on basis of mean intrinsic thermodynamic quantities

The mean intrinsic thermodynamic quantity can be defined by considering the relative population of complex species in the solution and the value of intrinsic thermodynamic quantity corresponds to each step of ligation. In the present study a new method is introduced for analysis of experimental ligand binding data on basis of mean intrinsic thermodynamic quantities. In this regard, a deviation parameter was defined by comparing the non-interacting system with the cooperative interactive one. This parameter can be calculated just by estimation of the first binding constant. A set of relations between this deviation parameter and other binding characteristics, such as mean intrinsic Gibbs free energy of binding and mean Gibbs free energy of site-site interaction, have been developed. This model presents binding mechanism in a unified way that is simple, yet stringent, more straightforward, more reliable and informative. This analyzing method has been successfully applied for evaluation of various systems such as oxygen binding to hemoglobin, laurate and warfarin binding to human serum albumin, and reveals some new biological features of these binding systems.     

Calorimetry for studying the adsorption of proteins in hydrophobic interaction chromatography

Hydrophobic interaction chromatography is a very popular chromatography method for purification of proteins and plasmids in all scales from analytical to industrial manufacturing. Despite this frequent use, the complex interaction mechanism and the thermodynamic aspects of adsorption in hydrophobic interaction chromatography are still not well understood. Calorimetric methods such as isothermal titration calorimetry and flow calorimetry can help to gain a deeper understanding of the adsorption strength, the influence of salt type and temperature. They can be used to study conformational changes of proteins, which are often associated with the adsorption in hydrophobic interaction chromatography. This review offers a detailed introduction into the thermodynamic fundamentals of adsorption in hydrophobic interaction chromatography with a special focus on the potential applications of isothermal titration calorimetry and flow calorimetry for studying specific problems and relationships of the adsorption behavior of proteins and its various influencing factors. Models for characterizing conformational changes upon adsorption are presented together with methods for assessing this problem for different proteins and stationary phases. All of this knowledge can contribute greatly to forming a sound basis for method development, process optimization and finding modelling strategies in hydrophobic interaction chromatography.     

Wetting of Planar Surfaces by a Gay-Berne Liquid Crystal

Molecular simulation of the wetting of an unstructured attractive wall by Gay-Berne liquid crystals are reported. Simulations are performed in the grand canonical ensemble on a wide pore at constant temperatures of T *=0.53 and 0.56, corresponding to temperatures below and above the nematic-isotropic-vapor triple point. Close to the coexistence chemical potential, a thick liquid film wets the solid surface. The film is composed of stratified layers of molecules parallel to the solid surface, which follow to a nematic domain at the lower temperature and an isotropic one at the higher temperature. In both cases, the film is in equilibrium with the corresponding vapor phase. Close to the liquid-vapor interface there is a manifest tendency for the molecules to orient themselves parallel to the interface. The adsorption on the wall varies continuously with the thermodynamic parameters considered and no evidence of a first order prewetting transition is observed.     

Direct Evaluation of Vapour-Liquid Equilibria of Mixtures by Molecular Dynamics Using Gibbs-Duhem Integration

Abstract

We present an extension of the Gibbs-Duhem integration method that permits direct evaluation of vapour-liquid equilibria of mixtures by molecular dynamics. The Gibbs-Duhem integration combines the best elements of the Gibbs ensemble Monte Carlo technique and thermodynamic integration. Given conditions of coexistence of pure substances, simultaneous but independent molecular dynamics simulations of each phase at constant number of particles, constant pressure, constant temperature and constant fugacity fraction of species 2 are carried out in succession along coexistence lines. In each simulation, the coexistence pressure is adjusted to satisfy the Clapeyron-type equation. The Clapeyron-type equation is a first-order nonlinear differential equation that prescribes how the pressure must change with the fugacity fraction of species 2 to maintain coexistence at constant temperature. The Clapeyron-type equation is solved by the predictor-corrector method. Running averages of mole fraction and compressibility factor for the two phases are used to evaluate the right-hand side of the Clapeyron-type equation. The Gibbs-Duhem integration method is applied to three prototypes of binary mixtures of the two-centre Lennard-Jones fluid having various elongations. The starting points on the coexistence curve were taken from published data.