Complementary variational principles for the steady-state finite cable model of nerve membranes

Maximum and minimum principles for the steady-state finite cable model of nerve membranes are derived from the canonical theory of complementary variational principles. An accurate variational solution is obtained in an illustrative calculation.     

Complementary extremum principles for a nonlinear model of heat conduction in the human head

The theory of complementary variational principles is used to obtain maximum and minimum principles for a nonlinear model of heat conduction in the human head. Accurate variational solutions are obtained in illustrative calculations. The effect of nonlinearity is seen to be significant from a comparison with the linearized model.     

Extremum principles and the elastic and fluid mechanical behaviour of the human eye

Complementary variational principles are derived for the pressure boundary value problems in Weinbaum's (1965) model of the human eye. These principles can be used to obtain accurate solutions for the pressure.     

Analysis of a nonlinear diffusion problem With Michaelis-Menten kinetics by an integral equation method

A mathematical model for oxygen diffusion in a spherical cell with Michaelis-Menten oxygen uptake kinetics is analyzed by means of an intergral equation method. It is shown that an integral equation formulation can be used to obtain a numerical solution associated with this boundary and initial value problem. Through an illustrative numerical calculation we are able to obtain an accurate solution for both the steady and transient problems. Finally, a comparison is made with the numerical solution of McElwain and the variational solution of Anderson and Arthurs for the steady state and Lin's result concerning the unsteady state.     

Application of the osmotic virial equation in cryobiology

The multisolute osmotic virial equation is the only multisolute thermodynamic solution theory that has been derived from first principles and can make predictions of multisolute solution behaviour in the absence of multisolute solution data. Other solution theories either (i) include simplifying assumptions that do not take into account the interactions between different types of solute molecules or (ii) require fitting to multisolute data to obtain empirical parameters. The osmotic virial coefficients, which are obtained from single-solute data, can be used to make predictions of multisolute solution osmolality. The osmotic virial coefficients for a range of solutes of interest in cryobiology are provided in this paper, for use with concentration units of both molality and mole fraction, along with an explanation of the background and theory necessary to implement the multisolute osmotic virial equation.     

A Neuro-Muscular Elasto-Dynamic Model of the Human Arm Part 1: Model Development

In this paper we develop an elasto-dynamic model of the human arm for use in neuro-muscular control and dynamic interactionstudies.The motivation for this work is to present a case for developing and using non-quasistatic models of humanmusculo-skeletal biomechanics.The model is based on hybrid parameter multiple body system(HPMBS)variational projectionprinciples.In this paper,we present an overview of the HPMBS variational principle applied to the full elasto-dynamic model ofthe arm.The generality of the model allows one to incorporate muscle effects as either loads transmitted through the tendon atpoints of origin and insertion or as an effective torque at a joint.Though the technique is suitable for detailed bone and jointmodeling,we present in this initial effort only simple geometry with the bones discretized as Rayleigh beams with elongation,while allowing for large deflections.Simulations demonstrate the viability of the mcthod for use in the companion paper and infuture studies.     

Return current in encephalography. Variational principles.

The encephalographic problem of finding the electric potential V and the return current associated with any assumed primary current, Jp, is put in the form of a variational principle. With Jp and the conductivity specified, the correct V is one which makes an integral quantity P[V] a maximum. The terms in P[V] are related to the rates at which work is done by the electric field on the primary and return currents. It is shown that there is a unique solution for the electric field, and it satisfies the conservation of energy; this condition can serve as a check on any numerical solution. With the conductivity a different constant in different regions, the variational principle is recast in terms of the charge density on the surfaces of discontinuity. An iteration-variation method for finding the solution is outlined, and possible computational advantages over other approaches are discussed.     

Predictive power of "a minima" models in biology

Many apparently complex mechanisms in biology, especially in embryology and molecular biology, can be explained easily by reasoning at the level of the "efficient cause" of the observed phenomenology: the mechanism can then be explained by a simple geometrical argument or a variational principle, leading to the solution of an optimization problem, for example, via the co-existence of a minimization and a maximization problem (a min-max principle). Passing from a microscopic (or cellular) level (optimal min-max solution of the simple mechanistic system) to the macroscopic level often involves an averaging effect (linked to the repetition of a large number of such microscopic systems with possible random choice of the parameters of each of them) that gives birth to a global functional feature (e.g. at the tissue level). We will illustrate these general principles by building in four different domains of application "a minima" models and showing the main properties of their solutions: (1) extraction of a minimal RNA structure functioning as the first "peptidic machine," a kind of ancestral ribosome; (2) study of a genetic regulatory network of Drosophila centred on Engrailed gene and expressing successively two genes inside a limit cycle; (3) study of a genetic network regulating neural activity and proliferation in mammals; and (4) study of a simple geometric model of epiboly in zebrafish.     

Dynamic analysis of leaflet stresses and application to heart valve design

The problem is approached using an approximate and simple variational procedure. A comparison with results obtained by means of the finite element method reveals that the analytical solution is convenient from a practical engineering viewpoint. It is hoped that biomedical researchers and designers will find the present approach useful when dealing with more complex structural dynamic situations.     

Forward rate constants for receptor clusters. Variational methods for upper and lower bounds

We are interested in the effect of receptor clustering on k+, the diffusion-limited forward rate constant for the binding of a ligand to a cell surface receptor. Here we estimate the reduction in k+ when receptors are clustered in various configurations. We obtain two alternative expressions for the flux of ligands into receptors distributed on a surface. Next we show through a variational principle that these provide both upper and lower bounds on the flux when evaluated for trial concentration functions which satisfy only the boundary conditions of the Laplace equation. We use an analogy with electrostatics to calculate rigorous bounds within approx. 10% of the exact result for a variety of planar clusters of hemispherical receptor sites. We also obtain an exact result for the flux into a spheroidal receptor and use this result to obtain bounds on the flux into certain receptor clusters.     

Variational Principles in the Mechanics of Conformational Motions of Macromolecules in a Viscous Medium

The mechanics of the conformational motions of macromolecules due to rotations around the valence bonds in a viscous medium have been considered. The variational principles for the energy-dissipation rate during conformational motions in a viscous medium and the rate of the potential energy decrease of a macromolecule during conformational relaxation have been analyzed. The seeming contradiction between this principle and the principle of the minimum energy-dissipation rate is resolved. It is shown that the energy-dissipation rate must be optimal and minimal in order to simultaneously satisfy the conservation laws and fulfill the deterministic nature of classical trajectories. The generalization and analysis of the influence of thermal fluctuations and external forces on the variational principles for the conformational relaxation of macromolecules is carried out. A visual graphical geometric depiction has been developed using hyperspheres in the space of the velocities of chain nodes to describe conformational movements along many degrees of freedom in a viscous medium. The equipartition of the energy-dissipation rates (and the rates of potential energy decrease) among the conformational degrees of freedom is discussed.     

化学学科背景下细胞生物学课程教学的改革和实践

细胞生物学在大学生物相关专业的课程设置中占有重要地位,为提高化学优势学科背景下细胞生物学的教学质量,研究从学生知识掌握能力、知识融合能力和创新能力等三个方面进行相关教学的改革与实践。围绕教学内容和教学课件的优化,学生课外调研和科研写作的开展,学生创新热情的产生,学生动手解决问题及发现新问题的精神面貌转变等方面,阐述教改的主要内容。     

The existence of non-axisymmetric bilayer vesicle shapes predicted by the bilayer couple model

The existence of non-axisymmetric shapes with minimal bending energy is proved by means of a mathematical model. A parametric model is used; the shapes considered have an elliptical top view whilst their front view contour is described using Cassim ovals. Taking into account the bilayer couple model, the minimization of the membrane bending energy is performed at a constant membrane area A, a constant enclosed volume V and a constant difference between the two membrane leaflet areas A. It is shown that for certain sets of A, V and A the non-axisymmetric shapes calculated with the use of the parametric model have lower energy than the corresponding axisymmetric shapes obtained by the exact solution of the general variational problem. As an exact solution of the general variational problem for non-axisymmetric shapes would yield even lower energy, this indicates the existence of non-axisymmetric shapes with minimal bending energy in a region of the V/4A phase diagram.     

Metadynamic sampling of the free-energy landscapes of proteins coupled with a Monte Carlo algorithm

Metadynamics is a powerful computational tool to obtain the free-energy landscape of complex systems. The Monte Carlo algorithm has proven useful to calculate thermodynamic quantities associated with simplified models of proteins, and thus to gain an ever-increasing understanding on the general principles underlying the mechanism of protein folding. We show that it is possible to couple metadynamics and Monte Carlo algorithms to obtain the free energy of model proteins in a way which is computationally very economical.     

A general probabilistic model for group independent component analysis and its estimation methods

Independent component analysis (ICA) has become an important tool for analyzing data from functional magnetic resonance imaging (fMRI) studies. ICA has been successfully applied to single-subject fMRI data. The extension of ICA to group inferences in neuroimaging studies, however, is challenging due to the unavailability of a prespecified group design matrix and the uncertainty in between-subjects variability in fMRI data. We present a general probabilistic ICA (PICA) model that can accommodate varying group structures of multisubject spatiotemporal processes. An advantage of the proposed model is that it can flexibly model various types of group structures in different underlying neural source signals and under different experimental conditions in fMRI studies. A maximum likelihood (ML) method is used for estimating this general group ICA model. We propose two expectation-maximization (EM) algorithms to obtain the ML estimates. The first method is an exact EM algorithm, which provides an exact E-step and an explicit noniterative M-step. The second method is a variational approximation EM algorithm, which is computationally more efficient than the exact EM. In simulation studies, we first compare the performance of the proposed general group PICA model and the existing probabilistic group ICA approach. We then compare the two proposed EM algorithms and show the variational approximation EM achieves comparable accuracy to the exact EM with significantly less computation time. An fMRI data example is used to illustrate application of the proposed methods.     

Galerkin-Ritz procedures for approximate solutions to systems of reaction-diffusion equations

For any essentially nonlinear system of reaction-diffusion equations of the generic form ∂c_i/∂t=D_i∇²c_i+Q_i(c,x,t) supplemented with Robin type boundary conditions over the surface of a closed bounded three-dimensional region, it is demonstrated that all solutions for the concentration distributionn-tuple function c=(c ₁(x,t),...,c _n (x,t)) satisfy a differential variational condition. Approximate solutions to the reaction-diffusion intial-value boundary-value problem are obtainable by employing this variational condition in conjunction with a Galerkin-Ritz procedure. It is shown that the dynamical evolution from a prescribed initial concentrationn-tuple function to a final steady-state solution can be determined to desired accuracy by such an approximation method. The variational condition also admits a systematic Galerkin-Ritz procedure for obtaining approximate solutions to the multi-equation elliptic boundary-value problem for steady-state distributions c=−c(x). Other systems of phenomenological (non-Lagrangian) field equations can be treated by Galerkin-Ritz procedures based on analogues of the differential variational condition presented here. The method is applied to derive approximate nonconstant steady-state solutions for ann-species symbiosis model.     

Some exact solutions of a generalized Fisher equation related to the problem of biological invasion

The problem of biological invasion in a model single-species community is considered, the spatiotemporal dynamics of the system being described by a modified Fisher equation. For a special case, we obtain an exact solution describing self-similar growth of the initially inhabited domain. By comparison with numerical solutions, we show that this exact solution may be applicable to describe an early stage of a biological invasion preceding the propagation of the stationary travelling wave. Also, the exact solution is applied to the problem of critical aggregation to derive sufficient conditions of population extinction. Finally, we show that the solution we obtain is in agreement with some data from field observations.     

生姜辛辣部位的高效液相色谱(HPLC)指纹图谱研究

采用HPLC法分析了4个居群生姜丙酮回流-乙醚萃取物中的多酚类化合物,建立了有较好专属性的HPLC指纹图谱,比较了姜辣素含量及其得率。     

Microtubule stability studied by three-dimensional molecular theory of solvation

We study microtubular supramolecular architectures of tubulin dimers self-assembling into linear protofilaments, in turn forming a closed tube, which is an important component of the cytoskeleton. We identify the protofilament arrangements with the lowest free energy using molecular dynamics to optimize tubulin conformations. We then use the three-dimensional molecular theory of solvation to obtain the hydration structure of protofilaments built of optimized tubulins and the solvent-mediated effective potential between them. The latter theoretical method, based on first principles of statistical mechanics, is capable of predicting the structure and thermodynamics of solvation of supramolecular architectures. We obtained a set of profiles of the potential of mean force between protofilaments in a periodic two-dimensional sheet in aqueous solution. The profiles were calculated for a number of amino acid sequences, tubulin conformations, and spatial arrangements of protofilaments. The results indicate that the effective interaction between protofilaments in aqueous solution depends little on the isotypes studied; however, it strongly depends on the M loop conformation of beta-tubulin. Based on the analysis of the potential of mean force between adjacent protofilaments, we found the optimal arrangement of protofilaments, which is in good agreement with other studies. We also decomposed the potential of mean force into its energetic and entropic components, and found that both are considerable in the free-energy balance for the stabilized protofilament arrangements.     

On-line monitoring of monoclonal antibody formation in high density perfusion culture using FIA

An automated flow injection system for on-line analysis of proteins in real fermentation fluids was developed by combining the principles of stopped-flow, merging zones flow injection analysis (FIA) with antigen-antibody reactions. IgG in the sample reacted with its corresponding antibody (a-IgG) in the reagent solution. Formation of insoluble immunocomplexes resulted in an increase of the turbidity which was determined photometrically. This system was used to monitor monoclonal antibody production in high cell density perfusion culture of hybridoma cells. Perfusion was performed with a newly developed static filtration unit equipped with hydrophilic microporous tubular membranes. Different sampling devices were tested to obtain a cell-free sample stream for on-line product anlysis of high molecular weight (e.g., monoclonal antibodies) and low molecular weight (e.g., glucose, lactate) medium components. In fermentation fluids a good correlation (coefficient: 0.996) between the FIA method and an ELISA test was demonstrated. In a high density perfusion cultivation process mAb formation was succesfully monitored on-line over a period of 400 h using a reliable sampling system. Glucose and lactate were measured over the same period of time using a commercially available automatic analyser based on immobilized enzyme technology.Abbreviations TIA Turbidimetric immunoassay - mAb Monoclonal Antibody