A neutral model with fluctuating population size and its effective size

We consider a diffusion model with neutral alleles whose population size is fluctuating randomly. For this model, the effects of fluctuation of population size on the effective size are investigated. The effective size defined by the equilibrium average heterozygosity is larger than the harmonic mean of population size but smaller than the arithmetic mean of population size. To see explicitly the effects of fluctuation of population size on the effective size, we investigate a special case where population size fluctuates between two distinct states. In some cases, the effective size is very different from the harmonic mean. For this concrete model, we also obtain the stationary distribution of the average heterozygosity. Asymptotic behavior of the effective size is obtained when the population size is large and/or autocorrelation of the fluctuation is weak or strong.     

A competition model for a seasonally fluctuating nutrient

A model of two species consuming a single, limited, periodically added resource is discussed. The model is based on chemostat-type equations, which differ from the classical models of Lotka and Volterra. The model incorporates nonlinear functional response curves of the Holling or Michaelis-Menten type to describe the dependence of the resource-exploitation rate on the amount of resource. Coexistence of two species due to seasonal variation is indicated by numerical studies.     

Alamethicin. A rich model for channel behavior.

Alamethicin, a 20-amino acid peptide, has been studied for a number of years as a model for voltage-gated channels. Recently both the x-ray structure of alamethicin in crystal and an NMR solution structure have been published (Fox and Richards, 1982. Bannerjee et al., 1983). Both structures show that the amino end of the molecule forms a stable alpha-helix nine or 10 residues in length and that the COOH-terminal ends exhibits a variable hydrogen bonding pattern. We have used synthetic analogues of alamethicin to test various hypotheses of its mode of action. As a result of these studies we propose a channel structure in which the COOH-terminal residues bond together as a beta-barrel, leaving the alpha- helices free to rotate under the influence of the electric field and gate the channel. Though the number of monomers per channel varies with experimental conditions, the gating charge per monomer stays close to that expected from an alpha-helical gate. We can also alter the sign of the voltage which turns on a channel by varying the charge on the alamethicin analogue. Channels are always slightly cation-selective even though formed by monomers with negative, positive, or zero formal charge. Channels are less stable in low ionic strength solutions than high. Finally, alamethicin conductance parameters vary systematically with changes in membrane thickness. We show how these results and others in the literature can be explained by a fairly detailed structural model. The model can be easily generalized to a form more suited to high molecular weight single-peptide-chain proteins.     

A chemically driven fluctuating ratchet model for actomyosin interaction

With reference to the experimental observations by Yanagida and his co-workers on actomyosin interaction, a Brownian motor of fluctuating ratchet kind is designed with the aim to describe the interaction between a Myosin II head and a neighboring actin filament. Our motor combines the dynamics of the myosin head with a chemical external system related to the ATP cycle, whose role is to provide the energy supply necessary to bias the motion. Analytical expressions for the duration of the ATP cycle, for the Gibbs free energy and for the net displacement of the myosin head are obtained. Finally, by exploiting a method due to Sekimoto [J. Phys. Soc. Jpn. 66 (1997) 1234], a formula is worked out for the amount of energy consumed during the ATP cycle.     

Prediction of alternative RNA secondary structures based on fluctuating thermodynamic parameters.

In this paper we present a new method for predicting a set of RNA secondary structures that are thermodynamically favored in RNA folding simulations. This method uses a large number of 'simulated energy rules' (SER) generated by perturbing the free energy parameters derived experimentally within the range of the experimental errors. The structure with the lowest free energy is computed for each SER. Structural comparisons are used to avoid multiple generation of similar structures. Computed structures are evaluated using the energy distribution of the lowest free energy structures derived in the simulation. Predicted be graphically displayed with their occurring frequencies in the simulation by dot-plot representations. On average, about 90% of phylogenetic helixes in the known models of tRNA, Group I self-splicing intron, and Escherichia coli 16 S rRNA, were predicted using the method.     

Potassium channel structures

The molecular basis of K+ channel function is universally conserved. K+ channels allow K+ flux and are essential for the generation of electric current across excitable membranes. K+ channels are also the targets of various intracellular control mechanisms, such that the suboptimal regulation of channel function might be related to pathological conditions. Because of the fundamental role of K+ channels in controlling membrane excitability, a structural understanding of their function and regulation will provide a useful framework for understanding neuronal physiology. Many recent physiological and crystallographic studies have led to new insights into the workings of K+ channels.     

Implicit solvent model estimates of the stability of model structures of the alamethicin channel

Alamethicin is a hydrophobic helical peptide of 20 residues, which oligomerizes to form ion-conducting channels in membranes. The behavior of an intact alamethicin channel in POPC bilayers was recently studied, using 2 ns molecular dynamics (MD) simulations of a model hexameric channel. These simulations produced numerous conformations of the channel. In the present study, we used 11 of these channel conformations and carried out continuum-solvent model calculations, similar to those used for the monomers in our previous studies, to investigate the energetics of the channel inside the lipid bilayer. Our results suggest that, out of the 11 channel conformations produced by the MD simulations, only four are stable inside the lipid bilayer, with water-to-membrane free energies of transfer ranging from ~–6 to ~–10 kcal/mol. Analysis of the results suggests two causes for the apparent instability of the remainder of the structures inside the lipid bilayer, both resulting from the desolvation of channel polar groups (i.e. their transfer from the aqueous phase into the bilayer). The first is specific, uncompensated backbone hydrogen bonds, which exist in the region of the channel exposed to the hydrocarbon of the lipid bilayer. The second is exposure of intra-pore water molecules to the surrounding lipid. Thus, the association of these structures with the membrane involves a large electrostatic desolvation free-energy penalty. The apparent conflict between continuum-solvent and MD calculations, and its significance for the interpretation of membrane proteins simulations, are discussed.     

A model of morphogenesis for protein secondary structures.

This paper proposes a model for the expected probability distribution for a certain class of biological structures. In particular, a model is derived for the distribution of lengths of helices, sheets, turns, and coils as a function of the length of the structure divided by the length of the protein it is contained in. A fit between the derived lognormal function and the structures for some proteins whose three-dimensional structure is known was significant. The fit produces fundamental parameters particular to each structure type that are related to the underlying structure and its morphogenesis. The importance of the result is that a universal mathematical distribution can be used to explain certain protein morphogeneses. Also, these fundamental parameters can be used as an aid in predicting whether a given sequence is a particular secondary structure or not, without a knowledge of its three-dimensional structure.     

A microscopic electrostatic model for the amphotericin B channel.

A microscopic model of an amphotericin B channel is proposed. The structure of the pores is generated using the atomic coordinates of the molecule in the structure determined experimentally by X-ray diffraction. The net charges of the atoms are determined by Mulliken analysis. With these charges the electrostatic energy profiles are calculated for a monovalent ion passing through the channels formed by different number of antibiotic molecules having different radii. The water inside the channel was considered through a continuum medium using the dielectric constant of the bulk, and the membrane contribution was included using the virtual images of the pore in a dielectric slab of epsilon = 3. The model satisfactorily explains the permeability and selectivity characteristics as well as other observations yet unexplained. The electrostatic profiles obtained reinforce the hypothesis of the existence of channels formed by a variable number of units.     

A simple model for diffusion in independent, temporally fluctuating pores

A simple model is presented for one-dimensional diffusion in an ensemble of semi-infinite and finite pores or capillaries in which the boundary at one end of each capillary is allowed to fluctuate randomly between a perfectly reflecting barrier and a perfectly absorbing barrier. The model is independent of the spatial distribution of the capillaries; it is only assumed that there are a large number of them and that they are noninteracting. Exact solutions are possible and results are obtained, in terms of the fluctuation parameters, for the total amount per unit area of solute passed through the capillary system in the semi-infinite case, and for a permeability coefficient and time lag to steady state in the finite system. Applications of the model to diffusion in biological membranes are discussed.     

Primary uroepithelial cultures. A model system to analyze umbrella cell barrier function.

Despite almost 25 years of effort, the development of a highly differentiated and functionally equivalent cell culture model of uroepithelial cells has eluded investigators. We have developed a primary cell culture model of rabbit uroepithelium that consists of an underlying cell layer that interacts with a collagen substratum, an intermediate cell layer, and an upper cell layer of large (25-100 micrometer) superficial cells. When examined at the ultrastructural level, the superficial cells formed junctional complexes and had an asymmetric unit membrane, a hallmark of terminal differentiation in bladder umbrella cells. These cultured "umbrella" cells expressed uroplakins and a 27-kDa uroepithelial specific antigen that assembled into detergent-resistant asymmetric unit membrane particles. The cultures had low diffusive permeabilities for water (2.8 x 10(-4) cm/s) and urea (3.0 x 10(-7) cm/s) and high transepithelial resistance (>8000 Omega cm2) was achieved when 1 mM CaCl2 was included in the culture medium. The cell cultures expressed an amiloride-sensitive sodium transport pathway and increases in apical membrane capacitance were observed when the cultures were osmotically stretched. The described primary rabbit cell culture model mimics many of the characteristics of uroepithelium found in vivo and should serve as a useful tool to explore normal uroepithelial function as well as dysfunction as a result of disease.     

Highly fluctuating protein structures revealed by variable-pressure nuclear magnetic resonance

Although our knowledge of basic folded structures of proteins has dramatically improved, the extent of our corresponding knowledge of higher-energy conformers remains extremely slim. The latter information is crucial for advancing our understanding of mechanisms of protein function, folding, and conformational diseases. Direct spectroscopic detection and analysis of structures of higher-energy conformers are limited, particularly under physiological conditions, either because their equilibrium populations are small or because they exist only transiently in the folding process. A new experimental strategy using pressure perturbation in conjunction with multidimensional NMR spectroscopy is being used to overcome this difficulty. A number of rare conformers are detected under pressure for a variety of proteins such as the Ras-binding domain of RalGDS, beta-lactoglobulin, dihydrofolate reductase, ubiquitin, apomyoglobin, p13(MTCP1), and prion, which disclose a rich world of protein structure between basically folded and globally unfolded states. Specific structures suggest that these conformers are designed for function and are closely identical to kinetic intermediates. Detailed structural determination of higher-energy conformers with variable-pressure NMR will extend our knowledge of protein structure and conformational fluctuation over most of the biologically relevant conformational space.     

A minimal gating model for the cardiac calcium release channel.

A Markovian model of the cardiac Ca release channel, based on experimental single-channel gating data, was constructed to understand the transient nature of Ca release. The rate constants for a minimal gating scheme with one Ca-free resting state, and with two open and three closed states with one bound Ca2+, were optimized to simulate the following experimental findings. In steady state the channel displays three modes of activity: inactivated 1 mode without openings, low-activity L mode with single openings, and high-activity H mode with bursts of openings. At the onset of a Ca2+ step, the channel first activates in H mode and then slowly relaxes to a mixture of all three modes, the distribution of which depends on the new Ca2+. The corresponding ensemble current shows rapid activation, which is followed by a slow partial inactivation. The transient reactivation of the channel (increment detection) in response to successive additions of Ca2+ is then explained by the model as a gradual recruitment of channels from the extant pool of channels in the resting state. For channels in a living cell, the model predicts a high level of peak activation, a high extent of inactivation, and rapid deactivation, which could underlie the observed characteristics of the elementary release events (calcium sparks).     

A simple model for surface charge on ion channel proteins.

We present a simple two-parameter model for surface charge directly associated with ion channels. A spherically symmetric "charged shell" models a distribution of surface charge arrayed about the channel entrance, with a corresponding set of image charges behind the plane of the membrane. The transition between a regime of buffered conductance and a regime of rapidly falling conductance at very low ionic strength is found to depend on the magnitude of the surface charge as well as the separation between the charge and the channel entrance. This resolves an apparent discrepancy between the experimental findings of Naranjo and Latorre (1993. Biophys. J. 64:1038-1050) and previous theoretical computations. The charged-shell model is used in a comparative study of the toad skeletal muscle conductance data of Naranjo and Latorre, the rat skeletal muscle conductances of Ravindran et al. (1992. Biophys. J. 61:494-508), and a second set of rat muscle conductances presented in this paper.     

A cell culture model of the blood-brain barrier

Endothelial cells that make up brain capillaries and constitute the blood-brain barrier become different from peripheral endothelial cells in response to inductive factors found in the nervous system. We have established a cell culture model of the blood-brain barrier by treating brain endothelial cells with a combination of astrocyte-conditioned medium and agents that elevate intracellular cAMP. These cells form high resistance tight junctions and exhibit low rates of paracellular leakage and fluid-phase endocytosis. They also undergo a dramatic structural reorganization as they form tight junctions. Results from these studies suggest modes of manipulating the permeability of the blood-brain barrier, potentially providing the basis for increasing the penetration of drugs into the central nervous system.     

A model of growing vascular structures

Increasing attention is being paid to the configuration and development of vascular structures and their possible correlations with physiological events. The study of angiogenesis in normal and pathological states as well as in the embryo and adult has provided new insights into the mechanism of vessel growth and organization of the vasculature. Various mathematical branching models have been developed. These constructions are mainly geometrical and only involve a branching phenomenon. We propose the use of a deterministic non-linear model based on physiological laws and hydrodynamics. Growth, branching and anastomosis, the three actual main events occurring in vascular growth, are included in this model. Space growth, including cells and vessels, is defined by a decreasing transformation. Space density and the length of new sprouts are controlled by a set of parameters. The conditions on these parameters are well established, which allows the production of realistic patterns.