pH control of the third virial coefficient of hyaluronate solutions calculated from van der Waals forces by means of the Lifshitz-McLachlan susceptibility theory

Positive third virial coefficients and osmotic coefficients have been calculated for human umbilical cord hyaluronic acid solutions at pHs 6.0, 6.5, 7.0, 7.5, 8.0, and 8.5 and constant ionic strength 0.1. The calculations are based on experimental axial flow birefringence and radial linear dichroism data previously reported and the Lifshitz-McLachlan field theory of van der Waals forces. The second virial coefficients are negative, according to both this analysis and light scattering evidence, and reflect the tendency of hyaluronic acid to associate. This negativity denies the assumption of force additivity required by virial expansion theory.The results are in reasonable agreement with those of light scattering studies, and indicate the extreme nonideality of hyaluronate solutions with a high degree of pH control of osmotic pressure. The data are explained within the context of statistical mechanical and field theories of van der Waals forces, and the osmotic pressure of a solution is related to its optical properties. The numerical method used offers a way of exploring the applicability of modern interparticle force theory to biological systems.     

An efficient method for calculation of dynamic logarithmic gains in biochemical systems theory

Biochemical systems theory (BST) characterizes a given biochemical system based on the logarithmic gains, rate-constant sensitivities and kinetic-order sensitivities defined at a steady state. This paper describes an efficient method for calculation of the time courses of logarithmic gains, i.e. dynamic logarithmic gains L(Xi, Xj; t), which expresses the percentage change in the value of a dependent variable Xi at a time t in response to an infinitesimal percentage change in the value of an independent variable Xj at t=0. In this method, one first recasts the ordinary differential equations for the dependent variables into an exact canonical nonlinear representation (GMA system) through appropriate transformations of variables. Owing to the structured mathematical form of this representation, the recast system can be fully described by a set of numeric parameters, and the differential equations for the dynamic logarithmic gains can be set up automatically without resource to computer algebra. A simple general-purpose computer program can thus be written that requires only the relevant numeric parameters as input to calculate the time courses of the variables and of the dynamic logarithmic gains for both concentrations and fluxes. Unlike other methods, the proposed method does not require to derive any expression for the partial differentiation of flux expressions with respect to each independent variable. The proposed method has been applied to two kinds of reaction models to elucidate its usefulness.     

Organismic supercategories: I. Proposals for a general unitary theory of systems

The present paper is an attempt to outline an abstract unitary theory of systems. In the introduction some of the previous abstract representations of systems are discussed. Also a possible connection of abstract representations of systems with a general theory of measure is proposed. Then follow some necessary definitions and authors' proposals for an axiomatic theory of systems. Finally some concrete examples are analyzed in the light of the proposed theory.     

X-ray diffraction reconstruction of the inverted hexagonal (HII) phase in lipid-water systems.

The structure of the inverted hexagonal (HII) phase in biological lipid-water systems is studied to examine the physical interactions which drive the polymorphic phase behavior and which are also thought to play a relevant role in biological membrane function. A method is derived which yields the complex phase factors of the HII phase diffraction amplitudes from examination of a single sample. This method is applied to a low-resolution Fourier reconstruction of the HII phase in dioleoylphosphatidylethanolamine (DOPE) + water, specifically to examine deviations from the presumed circular model of the HII phase. It is found that the average radius of the water core, Rw, as determined from a Fourier reconstruction, is in good agreement with previously measured values of Rw obtained from more time-consuming traditional methods [Tate, M. W., & Gruner, S. M. (1989) Biochemistry 28, 4245]. In addition to the average value of Rw, the Fourier reconstruction also can be used to determine the true shape of the water core. It is found that the water core is circular to within 5% of Rw when the unit cell size is less than approximately 75 A. Above 75 A, however, a definite shape deformation becomes apparent, with radial noncircularities of 5-10%, probably in response to the increased entropic cost of packing the hydrocarbon chains into the anisotropic environment of the HII unit cell [Kirk, G. L., Gruner, S. M., & Stein D. E. (1984) Biochemistry 23, 1093]. As a more direct probe of the packing anisotropy, Fourier reconstructions of DOPE + dodecane and DOPE + squalene systems were compared with the reconstruction of DOPE. These oils are known to promote the low temperature occurrence of the HII phase, presumably by a reduction in the hydrocarbon packing stress. In support of this hypothesis, the alkanes were observed to relax the water core to a circular shape for even large lattices. In addition, anisotropy of the electron density near the end of the lipid chains is reduced when alkane is added, implying a more uniform hydrocarbon packing environment, consistent with the results of neutron diffraction upon the addition of deuterated decane [Turner, D. C., Gruner, S. M., & Huang, J. (1992) Biochemistry (following paper in this issue)].     

Role of substrate binding forces in exchange-only transport systems: I. Transition-state theory

Summary An analysis of transition-state models for exchange-only transport shows that substrate binding forces, carrier conformational changes, and coupled substrate flow are interrelated. For a system to catalyze exchange but not net transport, addition of the substrate must convert the carrier from an immobile to a mobile form. The reduction in the energy barrier to movement is necessarily paid for out of the intrinsic binding energy between the substrate and the transport site, and is dependent on the formation of two different types of complex: a loose complex initially and a tight complex in the transition state in carrier movement. Hence the site should at first be incompletely organized for optimal binding but, following a conformational change, complementary to the substrate structure in the transition state. The conformational change, which may involve the whole protein, would be induced by cooperative interactions between the substrate and several groups within the site, involving a chelate effect. The tightness of coupling, i.e., the ratio of exchange to net transport, is directly proportional to the increased binding energy in the transition state, a relationship which allows the virtual substrate dissociation constant in the transition state to be calculated from experimental rate and half-saturation constants. Because the transition state is present in minute amount, strong bonding here does not enhance the substrate's affinity, and specificity may, therefore, be expressed in maximum exchange rates alone. However, where substrates largely convert the carrier to a transport intermediate whose mobility is the same with all substrates, specificity is also expressed in affinity. Hence the expression of substrate specificity provides evidence on the translocation mechanism.     

A new approach for the calculation of the energy of van der Waals interactions in macromolecules of globular proteins

Van der Waals interaction energy in globular proteins is presented by the interaction energies between regions of protein spatial structure with homogenous medium density distribution. We introduce a notion of the local medium permittivity as a function of absorptance of molecular groups with particular conformation. Proposed theory avoids shortcomings which are typical for the calculations on the basis of the pairwise additive approximation. The approach takes into account local peculiarities of protein spatial structure and physical-chemical characteristics of amino acid residues and molecular groups.     

A new approach to calculation of the energy from van der Waals interactions in macromolecular proteins. Dielectric permeability as a physical parameter for calculations

The problem in the calculation of Van der Waals interactions in protein globules based on the theory of condensed media was considered. The Van der Waals interactions are represented as energies of interaction of regions with a uniform density distribution. A definition of the local dielectric constant as a function of coefficients of absorption of molecular groups with a particular conformation was introduced. The applicability of this approach was estimated. The theory enables one to circumvent the problems arising in calculations based on pairwise additive approximation. The methods provides a high accuracy in determining the local features of spatial structures of globular proteins and physicochemical characteristics of their constituent amino acids and molecular groups.     

Evolution of adhesive mechanisms in cribellar spider prey capture thread: evidence for van der Waals and hygroscopic forces

Sticky prey capture threads are produced by many members of the spider infraorder Araneomorphae. Cribellar threads are plesiomorphic for this clade, and viscous threads are apomorphic. The outer surface of cribellar thread is formed of thousands of fine, looped fibrils. Basal araneomorphs produce non-noded cribellar fibrils, whereas more derived members produce noded fibrils. Cribellar fibrils snag and hold rough surfaces, but other forces are required to explain their adherence to smooth surfaces. Threads of Hypochilus pococki (Hypochilidae) formed of non-noded fibrils held to a smooth plastic surface with the same force under low and high humidities. In contrast, threads of Hyptiotes cavatus and Uloborus glomosus (Uloboridae) formed of noded fibrils held with greater force to the same surface at intermediate and high humidities. This supports the hypothesis that van der Waals forces allow non-noded cribellar fibrils to adhere to smooth surfaces, whereas noded fibrils, owing to the hydrophilic properties of their nodes, add hygroscopic forces at intermediate and high humidities. Thus, there appear to have been two major events in the evolution of adhesive mechanisms in spider prey capture thread: the addition of hydrophilic nodes to the fibrils of cribellar threads and the replacement of cribellar fibrils by viscous material and glycoprotein glue.  © 2002 The Linnean Society of London, Biological Journal of the Linnean Society , 2002, 77 , 1–8.     

Implementation of a gene expression index calculation method based on the PDNN model

SUMMARY: Gene expression index calculations from Affymetrix GeneChips have been dominated by the Affymetrix MAS, dChip, and RMA methods. A new method to estimate the gene expression value utilizing the probe sequence information named position-dependent nearest-neighbor (PDNN) has been suggested by Zhang et al. (2003). Here we describe an open source implementation of the PDNN method for the statistical language R. AVAILABILITY: The package can be downloaded from http://www.bioconductor.org/repository/devel/package/html/affypdnn.html CONTACT: hbjorn@cbs.dtu.dk.     

2D calculation method based on composite beam theory for the determination of local homogenised stiffnesses of long bones

A calculation method using the finite element technique is presented. Its main objective was to determine strains, stresses and more particularly stiffnesses in any cross section of a tibia, thus enabling the localisation of tibial torsion in vivo. Each tibial cross section was considered to be a non-uniform cross section of a composite beam with arbitrary orientation of fibres. The determination of stresses, strains and stiffnesses within a composite beam cross section has been defined by solving a variational problem. The validation of this method was performed on a tibial diaphysis of which each cross section was assumed to be the cross section of a composite beam made of orthotropic materials with orthotropic axes of any orientation with respect to the principal axis of the bone. The comparison of the results, from our model and that of a three-dimensional one, was performed on each nodal value (strains, stresses) of the meshed cross section as it was impossible to obtain local stiffnesses by experimentation. The good agreement between the results has validated our finite element program. Actually, this method has enabled to treat directly 2D geometric reconstructions from CT scan images with a good accuracy to determine locally the homogenised mechanical characteristics of human tibia in vivo, and particularly to quantify torsional tibial abnormalities of children without approximation of the shape of the cross section and by calculating the real moment of inertia J. The importance of the fibre orientation with regards to the stiffness values has been emphasised. This 2D method has also allowed to reduce CPU time of the 3D modelling and calculation.     

Towards a general theory of neural computation based on prediction by single neurons

Although there has been tremendous progress in understanding the mechanics of the nervous system, there has not been a general theory of its computational function. Here I present a theory that relates the established biophysical properties of single generic neurons to principles of Bayesian probability theory, reinforcement learning and efficient coding. I suggest that this theory addresses the general computational problem facing the nervous system. Each neuron is proposed to mirror the function of the whole system in learning to predict aspects of the world related to future reward. According to the model, a typical neuron receives current information about the state of the world from a subset of its excitatory synaptic inputs, and prior information from its other inputs. Prior information would be contributed by synaptic inputs representing distinct regions of space, and by different types of non-synaptic, voltage-regulated channels representing distinct periods of the past. The neuron's membrane voltage is proposed to signal the difference between current and prior information ("prediction error" or "surprise"). A neuron would apply a Hebbian plasticity rule to select those excitatory inputs that are the most closely correlated with reward but are the least predictable, since unpredictable inputs provide the neuron with the most "new" information about future reward. To minimize the error in its predictions and to respond only when excitation is "new and surprising," the neuron selects amongst its prior information sources through an anti-Hebbian rule. The unique inputs of a mature neuron would therefore result from learning about spatial and temporal patterns in its local environment, and by extension, the external world. Thus the theory describes how the structure of the mature nervous system could reflect the structure of the external world, and how the complexity and intelligence of the system might develop from a population of undifferentiated neurons, each implementing similar learning algorithms.     

A two-dimensional gas of interacting electric dipoles with hard cores: Van der Waals isotherms and their possible application in lipid phase transitions

We calculate the thermodynamic properties of a two-dimensional fluid of hard disks with embedded dipoles. Our attention is centered on the isotherms in the neighborhood of the critical point. Evaluating the canonical partition function by the "factor cluster expansion", we exhibit the Van der Waals loops obtained considering the exact two-body clusters and the "hard core" contribution of the three-body clusters. The Van der Waals isotherms can be scaled as universal functions of the parameter =p²/4r ₀ ³ kT, where p, r₀, , are the dipole moment, hard core radius, and permittivity which characterize the interaction. The model is applied to the lipid phase transition found in natural and synthetic membranes. The typical critical parameters (T_c300K, _C50 dyne/cm) reflect a physically reasonable value for the dipole moment of a polar head group of a lipid but a much-too-small value for the hard core radius.     

基于混沌理论的蛋白质序列特性的研究

蛋白质序列特性的研究对于蛋白质的结构及功能具有重要意义。该文为了研究蛋白质序列是否具有混沌行为,先将蛋白质序列通过氨基酸电子离子相互作用势(electron interaction potential,EIIP)转化为时间序列,再根据混沌理论对其进行相空间重构,利用去偏自相关系数,经典G-P算法确定系统的时间延迟t和嵌入维数m,系统的最大Lyapunov指数则用改进的最大Lyapunov指数计算方法计算,其结果绝大多数为正,从而确认了蛋白质时间序列的混沌行为,并对特例进行了说明。     

A model for the recognition of protein kinases based on the entropy of 3D van der Waals interactions

The study and prediction of kinase function (kinomics) is of major importance for proteome research due to the widespread distribution of kinases. However, the prediction of protein function based on the similarity between a functionally annotated 3D template and a query structure may fail, for instance, if a similar protein structure cannot be identified. Alternatively, function can be assigned using 3D-structural empirical parameters. In previous studies, we introduced parameters based on electrostatic entropy (Proteins 2004, 56, 715) and molecular vibration entropy (Bioinformatics 2003, 19, 2079) but ignored other important factors such as van der Waals (vdw) interactions. In the work described here, we define 3D-vdw entropies (degrees theta(k)) and use them for the first time to derive a classifier for protein kinases. The model classifies correctly 88.0% of proteins in training and more than 85.0% of proteins in validation studies. Principal components analysis of heterogeneous proteins demonstrated that degrees theta(k) codify information that is different to that described by other bulk or folding parameters. In additional validation experiments, the model recognized 129 out of 142 kinases (90.8%) and 592 out of 677 non-kinases (87.4%) not used above. This study provides a basis for further consideration of degrees theta(k) as parameters for the empirical search for structure-function relationships.     

A general theory of life table construction and a precise abridged life table method

"In this paper we lay the foundation of life table construction by unifying the existing life table methods. We also present a new method of constructing current (period) abridged life tables.... The development includes (1) a careful formulation and computation of age-specific death rates, (2) derivation of a new set of formulas for computing the survivorship function from the observed age-specific death rates and populations, (3) estimation of the main life table functions by spline interpolation, integration and differentiation, and (4) use of a quadratic and a Gompertz function to close the life table.... The method is illustrated with construction of abridged life tables using Canadian data."     

Evolution of structure,order and complexity in biological systems: Part III of a general theory

In this, Part III of a general theory, the large-scale features of evolution of structure, order, and complexity are considered as characteristic features of the biological state of matter. This starts with a rigorous formal definition of structure, classes of structural order, complexity, measures of complexity, and how these arise through evolution by a cumulative process of storing information in memory systems. Three such memory systems have evolved: the genetic memory, the immune memory, and the memories of the nervous system. The evolution, characteristic parameters and the limitations of these memory systems are explored. From these considerations emerge the large-scale features of the evolutionary pathways of biological structure, function, and complexity.     

Effects of electric field on alamethicin bound at the lipid-water interface: a molecular mechanics study.

A systematic molecular mechanics study of the alamethicin molecule was made to determine a set of low-energy conformers in vacuo and in aqueous environment. The behavior of these conformers was investigated at the phase boundary which was modeled as a plane dividing two compartments with solvation properties of water and octanol with a constant electric field applied normal to the boundary. The calculations were performed with a molecular mechanics program for calculation of stable conformations at the phase boundary utilizing the Empiric Conformational Energy Program for Peptides force field and the Hopfinger-Scheraga solvation model. 371 minimum energy conformers of alamethicin, determined in vacuo with the build-up procedure, were used as starting conformations for energy minimization in aqueous environment and at the phase boundary. Only 49 interphase-bound structures were within 12 kcal/mol of the minima which was found. No helical structures having values close to the canonical parameters for an alpha- or 3(10)-helix were found despite the presence of eight alpha-methylalanine residues which favor the formation of these helices; four helix-like structures were found, having all negative phi, psi values. All the helical conformers have very high energies in water (approximately 14 kcal/mol), but are quite stable at the phase boundary (3.7-6.8 kcal/mol above the lowest minima found). The implications of these results for proposed mechanisms for membrane-binding and voltage-dependent gating are considered.