Structural changes and fluctuations of proteins. II. Analysis of the denaturation of globular proteins.

The statistical thermodynamic model of protein structure proposed in paper I is developed with special attention to the hydrophobic interaction. Calorimetric measurements of the thermal denaturation of five globular proteins, ribonuclease A, lysozyme, alpha-chymotrypsin, cytochrome c, and myoglobin, are quantitatively analyzed using the model. The thermodynamic parameters obtained by the least squares method reflect the global, average properties of proteins and are in good agreement with the expected values estimated from experimental and theoretical studies for model peptides. The average bond energy epsilon is well related to the tertiary structure of each protein. However, the difference in the parameters between different proteins is not observed for the cooperative energy ZJ and the chain entropy alpha. The individuality of a protein as far as its structural stability is concerned, is mainly reflected by the parameter gamma specifying the hydrophobic nature of a protein. The model is further applied in the analysis of several aspects of the structural stability of globular proteins. Denaturation induced by denaturants, salts, and pH are also explained by the model in a unified manner.     

Hydrodynamic calculations on the movements of cilia and flagella. II. Opalina.

Two different theoretical models are used to represent the propulsive mechanisms of Opalina. One model uses the concept of an envelope over all the cilia, while the other considers an array of elongated rods, similar to the model used in part 1. The envelope model shows a correlation between the motion of the cilium tip and the type of metachronism exhibited by the organism but under-predicts the velocities of propulsion. Calculations of the velocity profile, force and bending moment are carried out on the three-dimensional beat of a cilium of Opalina ranarum using the cilia sublayer model. The mean velocity profile is found to be twisted in form: in a clockwise direction at the top of the cilia sublayer relative to the effective stroke. Calculations of the force and rate of working emphasize the approximately equal duration of the effective and recovery strokes. Overall the sublayer model is found to be a more informative and useful approach than the envelope model which is limited to small amplitude motions.     

The behaviour of transporting epithelial cells. I. Computer analysis of a basic model.

We analyse the non-steady state behaviour of a computer model representing functional epithelial cells. The results show that a simple model of an epithelium, containing the essential ion transport asymmetries of the original Koefoed-Johnsen-Ussing model, predicts much of the observed behaviour of 'tight-type' epithelia under various well characterized experimental conditions.     

Biophysical models of protein denaturation. II. Effects of denaturants and of pH.

In order to broaden the scope and increase the utility of differential scanning calorimetry, a theoretical model of calorimetric thermograms is presently proposed which facilitates their biophysical interpretation and accounts explicitly for their modifications induced by denaturing agents and/or pH. The model rests mainly on statistical-physical considerations, the denaturation-linked increase of the number of binding sites for denaturants (including H+) serving as the conceptual basis for thermogram modelling. Denaturants were envisioned as contributing indirectly to thermal denaturation by forming complexes preferentially with unfolded protein molecules, shifting thus the equilibrium towards the denatured phase. After postulating the probability of complex formation, mean numbers of the relevant molecular species were computed by ensemble averaging. Finally, an eight-parameter expression has been derived defining protein heat capacity as a function of both temperature and denaturant concentration (or pH), each of the eight parameters having a distinct biophysical meaning. The model has been tested by applying it to the prediction of the pH-dependence of thermograms. Four proteins have been considered (lysozyme, myoglobin, apomyoglobin, and ribonuclease A), each represented by a series of three to four published thermograms recorded under different pH conditions. Model equations, fitted simultaneously to all thermograms in a pH series, reproduced correctly experimental tracings. Parameter values obtained as best-fit requirements (particularly those representing the number of binding sites unmasked by denaturation and the free energy of ion binding) were in close agreement with empirical, mainly potentiometric, data from literature. The empirically established pH-independence of the total enthalpy of denaturation, the phenomenon of cold denaturation, the pH-dependence of the Gibbs free energy of denaturation, of the melting temperature and of the temperature of cold denaturation, were all correctly predicted by the model. Combined effects of multiple denaturants, including the effects of pH in the presence of denaturants other than protons, are also predictable by the model.     

The kinetics of colloid osmotic hemolysis. I. Nystatin-induced lysis

A kinetic model of colloid osmotic hemolysis for cation-permeable cells has been developed. The model consists of three essential components. The first is a set of flux equations, under the assumption that the membrane potential is equal to the chloride equilibrium potential and that cation fluxes are described by the Goldman flux equation. The second is the osmotic equilibrium model of Freedman and Hoffman that takes into account the non-ideal osmotic behavior of erythrocytes. The third is an empirical relation between hemolysis and cell volume, developed from the lysis behavior in hypoosmotic media. Model simulations are compared with lysis experiments using the antibiotic nystatin to raise cation permeability. The form of the kinetics and inhibition of lysis by sucrose are described well by the model. In additional lysis experiments at different external pH the small pH dependence is accounted for by the model.     

Modeling of intraorgan arterial vasculature. II. Propagation of pressure waves

The dependence of the wave conductance in self-similar dichotomous models of intraorgan arterial vasculatures on the model parameters was studied. It was found that, with different sets of parameters, it is possible to simulate the suction effect induced by negative reflections of waves from arterial branchings and to model the resonance properties of arterial beds. It was shown that the choice of an adequate model for a given intraorgan arterial vasculature should be based on agreement between the biophysical characteristics of the model and the bed that characterize the propagation and reflection of pulse waves.     

The energetics of embryonic growth and development. I. Oxygen consumption, biomass growth, and heat production.

A quantitative phenomenological model to describe the relationships between biomass growth rate, oxygen consumption, and heat production in developing embryos has been developed and tested using a wide range of experimental data. The model employs generalized material and energy balances, principles of enzyme kinetics, and an overall metabolic model scheme based on known biochemical principles. The phosphorylation concentration ratio of ATP and ADP occurs naturally and becomes a significant parameter in the analysis. The model is applied to the growth of Escherichia coli, Oryzias latipes, chick spinal cord, and whole chicken eggs. Excellent agreement between the model and the experimental data is obtained. In a succeeding paper (Part II) environmental effects and growth efficiency are discussed.     

Lipid-cholesterol interactions in the P beta' phase. Application of a statistical mechanical model.

We describe a statistical mechanical model for lipid-cholesterol mixtures in the P beta' (ripple) phase of lipid bilayers. The model is a simple extension of an earlier model for the ripple phase in pure lipid bilayers. The extension consists of adding a degree of freedom to allow for the occupation of underlying lattice sites by cholesterol molecules, and adding a lipid-cholesterol interaction term to the model Hamiltonian. The interaction term was constructed based on numerical calculations of lipid-cholesterol energies for several different packing juxtapositions of the two molecules. Other than the lipid-cholesterol interactions, the extended model uses the same parameter set as the earlier model, so that comparison of the properties of the extended model with experimental data serves as a test of the validity of the original model. Properties of the model were calculated using the Monte Carlo method. Results are displayed as snapshots of the ripple configurations at different cholesterol concentrations. The spacing of the ripples increases with increasing cholesterol concentration and the rate of increase compares very well with experimental data. The success of this model supports the conclusion drawn earlier that frustration arising from anisotropic packing interactions is responsible for the ripple phase in lipid bilayers. In the extended model these packing interactions are responsible for the selective partitioning of cholesterol in the regions between the ripples.     

Lateral organisation of membrane lipids. The superlattice view.

Most biological membranes are extremely complex structures consisting of hundreds or even thousands of different lipid and protein molecules. The prevailing view regarding the organisation of these membranes is based on the fluid-mosaic model proposed by Singer and Nicholson in 1972. According to this model, phospholipids together with some other lipids form a fluid bilayer in which these lipids are diffusing very rapidly laterally. The idea of rapid lateral diffusion implies that, in general, the different lipid species would be randomly distributed in the plain of the membrane. However, there are recent data indicating that the components tend to adopt regular (superlattice-like) distributions in fluid, mixed bilayers. Based on this, a superlattice model of membranes has been proposed. This superlattice model is intriguing because it allows only a limited certain number of 'critical' compositions. These critical compositions could play a key role in the regulation of the lipid compositions of biological membranes. Furthermore, such putative critical compositions could explain how compositionally distinct organelles can exist despite of rapid inter-organelle membrane traffic. In this review, these intriguing predictions are discussed along with the basic principles of the model and the evidence supporting it.     

Gating current harmonics. II. Model simulations of axonal gating currents

A kinetic model of sodium activation gating is presented. The kinetics are based on harmonic analysis of gating current data obtained during large-amplitude sinusoidal voltage clamp in dynamic steady state. The technique classifies gating kinetic schemes into groups based on patterns of the harmonic content in the periodic gating current records. The kinetics that simulate the experimental data contain two independently constrained processes. The model predicts (a) sizable gating currents in response to hyperpolarizing voltage steps from rest; (b) a substantial increase in the initial peak of the gating current following voltage steps from prehyperpolarized potentials; (c) a small delay in the onset of sodium ion current following voltage steps from prehyperpolarized potentials; and (d) flickering during the open state in single channel current records. Although fundamentally different in kinetic structure from the Hodgkin-Huxley model, the present model reproduces the phenomenological development of Na conductance during the initiation and development of action potentials. The implications for possible gating mechanisms are discussed. A model gate is presented.     

Computer simulation of flagellar movement. IV. Properties of an oscillatory two-state cross-bridge model.

A stochastic computational method is used to examine the properties of a simple two-state cross-bridge model, of a type which has been shown previously to self-oscillate without requiring any feedback control of the active process. The force transients obtained with this model show the major features observed with oscillatory insect fibrillar flight muscle. The effects of viscosity and cross-bridge detachment rate on the frequency of oscillation of the model resemble the effects of viscosity and ATP concentration on flagellar oscillation, and the relationship between turnover rate and frequency of oscillation is also consistent with observations on flagella. However, the amplitude of oscillation of the model does not show the degree of frequency-independence which is typical of flagella.     

Intracranial pressure. III. Trial generalized theory]

The authors reported previously an elementary mathematical model of intracranial pressure (ICP) as well as result from an experimental verification of the model. The experimental tests revealed that certain factors had been neglected in the theoretical formation, and the present article offers an expanded version of model which takes into account those factors: changes in the formation of the CSF as a function of ICP; cerebral vasomotricity; cortical and sinusal venous pressures, and variations of the filtration coefficient of the subarachnoidal spaces. A generalized mathematical model of ICP, in the form of four equations, is proposed. The major aspects of both normal and pathological ICP are studied in the light of this model, and are integrated into a generalized theory.     

Computer simulation of flagellar movement. VI. Simple curvature-controlled models are incompletely specified.

Computer simulation is used to examine a simple flagellar model that will initiate and propagate bending waves in the absence of viscous resistances. The model contains only an elastic bending resistance and an active sliding mechanism that generates reduced active shear moment with increasing sliding velocity. Oscillation results from a distributed control mechanism that reverses the direction of operation of the active sliding mechanism when the curvature reaches critical magnitudes in either direction. Bend propagation by curvature-controlled flagellar models therefore does not require interaction with the viscous resistance of an external fluid. An analytical examination of moment balance during bend propagation by this model yields a solution curve giving values of frequency and wavelength that satisfy the moment balance equation and give uniform bend propagation, suggesting that the model is underdetermined. At 0 viscosity, the boundary condition of 0 shear rate at the basal end of the flagellum during the development of new bends selects the particular solution that is obtained by computer simulations. Therefore, the details of the pattern of bend initiation at the basal end of a flagellum can be of major significance in determining the properties of propagated bending waves in the distal portion of a flagellum. At high values of external viscosity, the model oscillates at frequencies and wavelengths that give approximately integral numbers of waves on the flagellum. These operating points are selected because they facilitate the balance of bending moments at the ends of the model, where the external viscous moment approaches 0. These mode preferences can be overridden by forcing the model to operate at a predetermined frequency. The strong mode preferences shown by curvature-controlled flagellar models, in contrast to the weak or absent mode preferences shown by real flagella, therefore do not demonstrate the inapplicability of the moment-balance approach to real flagella. Instead, they indicate a need to specify additional properties of real flagella that are responsible for selecting particular operating points.     

Subsite mapping of enzymes. Depolymerase computer modelling.

We have developed a depolymerase computer model that uses a minimization routine. The model is designed so that, given experimental bond-cleavage frequencies for oligomeric substrates and experimental Michaelis parameters as a function of substrate chain length, the optimum subsite map is generated. The minimized sum of the weighted-squared residuals of the experimental and calculated data is used as a criterion of the goodness-of-fit for the optimized subsite map. The application of the minimization procedure to subsite mapping is explored through the use of simulated data. A procedure is developed whereby the minimization model can be used to determine the number of subsites in the enzymic binding region and to locate the position of the catalytic amino acids among these subsites. The degree of propagation of experimental variance into the subsite-binding energies is estimated. The question of whether hydrolytic rate coefficients are constant or a function of the number of filled subsites is examined.     

The interaction of plant alkaloids with DNA. II. Berberinium chloride.

The interaction of berberinium chloride with DNA has been investigated using spectrophotometry, viscometric titrations with sonicated and closed circular superhelical DNA, and flow polarized fluorescence. The binding results for berberinium were found to fit the neighbor exclusion model. The two viscometric titrations and flow polarized fluorescence results exclusion model. The two viscometric titrations and flow polarized fluorescence results also indicated that berberinium binds to DNA by intercalation. Titration of sonicated DNA with berberinium produced viscosity increases which were less than those obtained with quinacrine and the titration of superhelical DNA indicated a significantly smaller unwinding angle for intercalation of berberinium than for quinacrine. These results can be interpreted in terms of a model in which (i) berberinium is partially intercalated into the double helix, or (ii) the alkaloid is more completely intercalated into the double helix, but causes bending of the helix due to the slight nonplanarity of the berberinium ring system, or (iii) a combination of (i) and (22).     

The tricarboxylic acid cycle in Dictyostelium discoideum. II. Evaluation of model consistency and robustness.

When kinetic models of complex biochemical systems are reconstructed from knowledge of the component reactions that have been characterized in vitro, or when values must be assumed for some of the parameters, errors are invariably encountered, and, as a consequence, the resulting model is frequently internally inconsistent. The simplest and most basic manifestations of such logical inconsistency are the failure of the model to exhibit a steady state or to yield a steady state that is in agreement with the actual steady state of the integrated system, or to yield a steady state that is dynamically stable. Models that are consistent may nonetheless be lacking in robustness, which is manifested as a pathological sensitivity to small changes in the values of their parameters. In this paper, we examine the current model of the tricarboxylic acid cycle in Dictyostelium discoideum (see Shiraishi, F., and Savageau, M. A. (1992) J. Biol. Chem. 267, 22912-22918) with regard to these basic indicators of model quality. This may be viewed as a preliminary analysis; the object is to determine whether or not the model is reasonable and worthy of a more refined analysis and, if not, to diagnose the areas in need of modification before further analysis is undertaken. The results demonstrate that the current model of the tricarboxylic acid cycle is self-consistent and possesses a steady state that is in agreement with experimental evidence. However, the results also suggest that this model is not very robust. The high sensitivities of parameters influencing pyruvate metabolism indicate that the experimental characterization of these reactions might be fruitfully re-examined. These high sensitivities lead us to predict that this model of the tricarboxylic acid cycle should be accurate only over a very narrow range in variation of the independent variables. This is verified by the results presented in the following paper (Shiraishi, F., and Savageau, M. A. (1992) J. Biol. Chem. 267, 22926-22933).     

Bioelectrorheological model of the cell. 1. Analysis of stresses and deformations

An electrorheological model of a cell in alternating electric field is proposed. The model relates changes in the spherical cell's shape to the field conditions, electric parameters of cytoplasm, cell membrane and external medium, and to the rheological parameters of the membrane. Stresses were determined using Maxwell's stress tensor for isotropic media. Shear stresses in the cell membrane were analyzed. Predictions of the model for variations of shear stress in cellular membranes subjected to an external periodic electric field are presented and related to the conditions prevailing in electrobiological research.