The general membrane equilibrium equation: Its simple derivation and some of its biological implications

On the basis of thermodynamic considerations, expressions for the relation between thei-th andj-th ions and solvent separated into subsystems by a semi-permeable membrane are derived. From this basic equation expressions for the transfer of solvent attending solute changes are developed. The application of these expressions to biological systems involving solvent transfer, as in cellular growth, chloride shift in the red blood cell, imbibition of water into cells is discussed.     

The survival rate of irradiated cells as a solution of a stochastic differential equation. A general description

The survival rate function is described as a solution of some stochastic differential equation. Two main reasons for the formation of dispersion of irradiated cell survival were analysed: accidental changes in reactivity of individual cells during irradiation and differences in reactivity of individual cells within the exposed ensemble. It was shown that in both cases dose response of the survival dispersion was different.     

Parameter optimization by using differential elimination: a general approach for introducing constraints into objective functions

Background

The investigation of network dynamics is a major issue in systems and synthetic biology. One of the essential steps in a dynamics investigation is the parameter estimation in the model that expresses biological phenomena. Indeed, various techniques for parameter optimization have been devised and implemented in both free and commercial software. While the computational time for parameter estimation has been greatly reduced, due to improvements in calculation algorithms and the advent of high performance computers, the accuracy of parameter estimation has not been addressed.

Results

We propose a new approach for parameter optimization by using differential elimination, to estimate kinetic parameter values with a high degree of accuracy. First, we utilize differential elimination, which is an algebraic approach for rewriting a system of differential equations into another equivalent system, to derive the constraints between kinetic parameters from differential equations. Second, we estimate the kinetic parameters introducing these constraints into an objective function, in addition to the error function of the square difference between the measured and estimated data, in the standard parameter optimization method. To evaluate the ability of our method, we performed a simulation study by using the objective function with and without the newly developed constraints: the parameters in two models of linear and non-linear equations, under the assumption that only one molecule in each model can be measured, were estimated by using a genetic algorithm (GA) and particle swarm optimization (PSO). As a result, the introduction of new constraints was dramatically effective: the GA and PSO with new constraints could successfully estimate the kinetic parameters in the simulated models, with a high degree of accuracy, while the conventional GA and PSO methods without them frequently failed.

Conclusions

The introduction of new constraints in an objective function by using differential elimination resulted in the drastic improvement of the estimation accuracy in parameter optimization methods. The performance of our approach was illustrated by simulations of the parameter optimization for two models of linear and non-linear equations, which included unmeasured molecules, by two types of optimization techniques. As a result, our method is a promising development in parameter optimization.

     

Behavior of a viscoelastic valveless pump: a simple theory with experimental validation

Background  

A valveless pump generates a unidirectional net flow of fluid around a closed loop of soft viscoelastic tubing that is rhythmically compressed at one point. The tubing must have at least two sections with two different stiffnesses. When a short segment of the tube is squeezed asymmetrically at certain frequencies, net flow of fluid around the loop can occur without valves.     

Stochastic prey-predator relationships: A random differential equation approach

A stochastic model describing two interacting populations is considered. The model involves a random differential equation of the form dX/dt=A(t)X+Y(t) where the random matrixA and vectorY represent the interactions and growth rates respectively andX is a (random) vector the components of which are the logarithms of the population's sizes. An expression for the solution of the above equation is obtained whence its statistical properties can be determined. Alternatively, a method based on Liouville's theorem is used to obtain the probability distribution of the solution. Application of both methods to simple cases indicates that the random solution is asymptotically stable in the mean even when the solution to the associated deterministic equation is not, viz. in the absence of self interactions.     

DNA sequence analysis: a general, simple and rapid method for sequencing large oligodeoxyribonucleotide fragments by mapping

Several electrophoretic and chromatographic systems have been investigated and compared for sequence analysis of oligodeoxyribonucleotides. Three systems were found to be useful for the separation of a series of sequential degradation products resulting from a labeled oligonucleotide: (I) 2-D electrophoresis†; (II) 2-D PEI-cellulose; and (III) 2-D homochromatography. System (III) proved generally most informative regardless of base composition and sequence. Furthermore, only in this system will the omission of an oligonucleotide in a series of oligonucleotides be self-evident from the two-dimensional map. The sequence of up to fifteen nucleotides can be determined solely by the characteristic mobility shifts of its sequential degradation products distributed on the two-dimensional map. With this method, ten nucleotides from the double-stranded region adjacent to the left-hand 3′-terminus and seven from the right-hand 3′-terminus of bacteriophage λ DNA have been sequenced. Similarly, nine nucleotides from the double-stranded region adjacent to the left-hand 3′-terminus and five nucleotides from the right-hand terminus of bacteriophage 80 DNA have also been sequenced. The advantages and disadvantages of each separation system with respect to sequence analysis are discussed.     

Ordered differential display: a simple method for systematic comparison of gene expression profiles.

A method for display of 3'-end restriction fragments of cDNAs is proposed, extending the idea reported recently. First, representative pools of such fragments are selectively amplified using PCR suppression effect. Then, simplified subsets of these fragments suitable for comparison by PAGE are amplified by adapter-specific primers extended by two randomly picked bases at their 3'ends. By testing all possible combinations of extended primers the whole mRNA pool may be systematically investigated. The method was applied to search for molecular regional markers of freshwater planarian Dugesia tigrina .     

Bisexual sterility conferred by the differential expression of Barnase and Barstar: a simple and efficient method of transgene containment

To establish a simple and an efficient system to minimize the environmental risk of genetically modified plants, we tested the applicability of the barnase/barstar system in conferring bisexual sterility; that is, in preventing plants setting seeds by self-fertilization and out-crossing. Transgenic tobacco plants were generated to express barnase, a cell death inducing ribonuclease, under the control of the gamete-specific AtDMC1 promoter, and barstar, a specific inhibitor of barnase, under the control of the ACT2 promoter, which is constitutively active in almost all tissues except gametes. In contrast to control plants harboring the barstar expression unit only, which set seeds normally with self-pollination, all transformants harboring both barnase and barstar were bisexually sterile. They produced aberrant anthers containing no detectable pollen and failed to set seeds even after pollination with wild-type tobacco pollen.An erratum to this article can be found at     

Apparent first-order behavior under second-order kinetic conditions: a general concept illustrated by the reversible binding of hydrogen peroxide to cytochrome c oxidase.

The theory of the second-order reversible reaction, A + B<-->A.B, has been extensively discussed. Apparent first-order behavior is observed when, for example, [B] > [A]. If the reaction exhibits second-order behavior then it is presumed that the concentrations of A and B were initially equal and that they remain equal during the reaction. However, in the case of hydrogen peroxide binding to cytochrome c oxidase, Weng & Baker (1991, Biochemistry 30, 5727-5733) showed that the observed rate was rigorously first order over a broad concentration range of ligand, including the stoichiometric case. It was further shown that kobs increased linearly with [H2O2], precluding the possibility of a rate-limiting, unimolecular pre-step. The current work examines the theoretical rate equation for the bimolecular, reversible reaction when [A] = [B]. Simulations show that this equimolar condition resulted in rigorous exponential binding as kd, the equilibrium dissociation constant for the A.B complex, approached the initial concentration of A (or B). In particular, the second-order simulation was rigorously exponential when [A]o/Kd = 0.5, and showed only minor deviations when the ratio was increased to 25. These results demonstrate that a reversible, bimolecular reaction can appear first order even under second order conditions, without the need for more complicated mechanisms.     

Dynamics of a delay differential equation model of hepatitis B virus infection

We formulate and systematically study the global dynamics of a simple model of hepatitis B virus in terms of delay differential equations. This model has two important and novel features compared to the well-known basic virus model in the literature. Specifically, it makes use of the more realistic standard incidence function and explicitly incorporates a time delay in virus production. As a result, the infection reproduction number is no longer dependent on the patient liver size (number of initial healthy liver cells). For this model, the existence and the component values of the endemic steady state are explicitly dependent on the time delay. In certain biologically interesting limiting scenarios, a globally attractive endemic equilibrium can exist regardless of the time delay length.     

A differential equation model for functional mapping of a virus-cell dynamic system

The dynamic pattern of viral load in a patient’s body critically depends on the host’s genes. For this reason, the identification of those genes responsible for virus dynamics, although difficult, is of fundamental importance to design an optimal drug therapy based on patients’ genetic makeup. Here, we present a differential equation (DE) model for characterizing specific genes or quantitative trait loci (QTLs) that affect viral load trajectories within the framework of a dynamic system. The model is formulated with the principle of functional mapping, originally derived to map dynamic QTLs, and implemented with a Markov chain process. The DE-integrated model enhances the mathematical robustness of functional mapping, its quantitative prediction about the temporal pattern of genetic expression, and therefore its practical utilization and effectiveness for gene discovery in clinical settings. The model was used to analyze simulated data for viral dynamics, aimed to investigate its statistical properties and validate its usefulness. With an increasing availability of genetic polymorphic data, the model will have great implications for probing the molecular genetic mechanism of virus dynamics and disease progression.     

Stability analysis of a state-dependent delay differential equation for cell maturation: analytical and numerical methods

Journal of Mathematical Biology - We consider a mathematical model describing the maturation process of stem cells up to fully mature cells. The model is formulated as a differential equation with...     

Mechanical hemolysis in blood flow: user-independent predictions with the solution of a partial differential equation

This paper presents for the first time numerical predictions of mechanical blood hemolysis obtained by solving a hyperbolic partial differential equation (PDE) modelling the hemolysis in a Eulerian frame of reference. This provides hemolysis predictions over the entire computational domain as an alternative to the Lagrangian approach consisting in evaluating cell hemolysis along their trajectories. The solution of a PDE over a computational domain, such as in the approach presented herein, yields a unique solution. This is a clear advantage over the Lagrangian approach, which requires the human-made choice of a limited number of trajectories for integration and inevitably results in the incomplete coverage of the computational domain. The hyperbolic hemolysis model is solved with a Discontinuous Galerkin finite element method. The solution algorithm also includes adaptive remeshing to provide high accuracy simulations. Predictions of the modified index of hemolysis (MIH) are presented for flows in dialysis cannulae and sudden contractions. MIH predictions for cannulae differ significantly from those obtained by other authors using the Lagrangian approach. The predictions for flows in sudden contractions are used, along with our own experimental measurements, to assess the value of the threshold shear stress required for hemolysis that is included in the hemolysis model.