A periodicity result for a nonlinear functional integral equation

In this paper, we study the effect of introducing a delay in a model of cell proliferation considered originally by O. Arino and M. Kimmel (J. Math. Biol. 27, 341–354 (1989)). We prove that slow oscillations take place and periodic oscillations appear for appropriate values of a parameter.     

阔叶树的叶形曲线方程：—适于叶面积计算的数学模型

树木的叶形可以看作一个平面几何图形。这种几何图形可用解析方程给予表达,我们把这种解析方程称为叶形曲线方程。由于叶形是一个左右对称,而上下不对称的图形,也就是说叶的最宽处绝大多数不在叶的中部,少数在     

Alterations in the structure of the electrical double layer adjacent to a charged membrane arising from electromagnetically induced changes in the activity of membrane bound enzymes

Electromagnetic fields of very low amplitude have been reported to influence a number of cellular functions. Many of these effects have a high degree of frequency specificity. Herein it is suggested that some of these reported results could be explained by a fieldinduced alteration in the enzymic activity of integral membrane proteins. It is shown that such a field-induced transition from an initial nonequilibrium steady-state to a final nonequilibrium steady-state can lead to an alteration in the concentration profiles of those charged species in the cell's ambient electrolyte that comprise the so-called electrical double layer. Examples of variations in the concentration profiles of those ions that react with a membrane-bound enzyme, as well as nonreacting ionic species, are given. The modulation of such effects by systematic variations in extracellular pH and ionic strength is discussed.     

Numerical solution of a nonlinear advance-delay-differential equation from nerve conduction theory

A functional differential equation which is nonlinear and involves forward and backward deviating arguments is solved numerically. The equation models conduction in a myelinated nerve axon in which the myelin completely insulates the membrane, so that the potential change jumps from node to node. The equation is of first order with boundary values given at t=±. The problem is approximated via a difference scheme which solves the problem on a finite interval by utilizing an asymptotic representation at the endpoints, cubic interpolation and iterative techniques to approximate the delays, and a continuation method to start the procedure. The procedure is tested on a class of problems which are solvable analytically to access the scheme's accuracy and stability, then applied to the problem that models propagation in a myelinated axon. The solution's dependence on various model parameters of physical interest is studied. This is the first numerical study of myelinated nerve conduction in which the advance and delay terms are treated explicitly.Supported in part by NSF Grant MCS8301724 and by a Biomedical Research Support Grant 2SO7RR0706618 from NIH     

一类阔叶树叶面积的通用公式测算法

本文在观察和测算的基础上,提出了一类阔叶树的叶形方程,并对方程进行积分,求出了计算这类阔叶树叶面积的通用公式。从1980年应用至今证明,用这个通用公式计算这类阔叶树的面积,方便、简捷、精度高,现介绍如下。     

Resetting biological oscillators—A stochastic approach

We present a stochastic approach to phase-resetting of an ensemble of oscillators. In order to describe stimulation-induced dynamical phenomena we develop a stochastic model which consists of an ensemble of phase oscillators interacting via random forces. Every single oscillator is submitted to a phase stimulus. The ensemble's dynamics is determined by a Fokker-Planck equation. The stationary states are calculated explicitly, whereas the transients are analysed numerically. If the stimulus of a given (non-vanishing) intensity is administered at a critical initial cluster phase for a critical duration T _crit the ensemble's synchronized oscillation is annihilated. A transition from type 1 resetting to type 0 resetting occurs when the stimulation duration exceeds T _crit. Stimulation causes a shift of the mean frequency of every single oscillator. This frequency shift is explicitly calculated by deriving the mean first passage time. The model shows that there is a subcritical intensity which is connected with an enhanced vulnerability to stimulation. The desynchronized states, the so-called black holes, are typically associated with a double peak in the ensemble's phase distribution. This is important for analysing experimental data because simple peak-detection algorithms are not able to extract the underlying dynamics.Our results are discussed from the experimentator's point of view so that the insights derived from our model can improve data analysis and design of stimulation experiments.     

EFFECTS OF FLOWING WATER ON NITROGEN- AND PHOSPHORUS-LIMITED PHOTOSYNTHESIS AND OPTIMUM N:P RATIOS BY SPIROGYRA FLUVIATILIS (CHAROPHYCEAE)1,2

The effects of flowing water on net photosynthesis, dark respiration, specific growth rate, and optimum N:P ratios by Spirogyra fluviatilis Hilse were assessed. The alga was cultivated under nitrogen or phosphorus limitation in laboratory streams at three flow velocities: 3, 12, and 30 cm·s^?1. The Droop equation adequately described respiration and photosynthesis (PS_net) as a function of N or P cell quota (Q^N or Q^p). The data show that for N- or P-limited Spirogyra fluviatilis, flowing water is physiologically costly. Generally, flowing water had little effect on respiration rates; however, the proportion of gross photosynthesis devoted to dark respiration did increase with flow velocity. For photosynthesis, the minimum N and P cell quotas increased with velocity, and the theoretical PS_net maxima for N and P both appeared greatest at 12 cm·s^?1. The Droop models showed that for any given Q^N or Q^p, PS_net, was reduced by the 30-cm·s^?1 treatment. Consistent with this finding, independent estimates of specific growth rates for P-limited S. fluviatilis in the laboratory streams were inversely related to flow velocity when ambient PO₄^?3 was undetectable. However, growth was not diminished at the fastest velocity when PO₄^?3 was available for uptake. Thus, the increase in cellular phosphorus demand can be offset by flow-enhanced P uptake when conditions permit; otherwise, growth will be impaired. The optimum N:P ratios for S. fluviatilis at 3, 12, and 30 cm·s^?1 were 50, 58, and 52 by atoms, respectively, when calculated for PS_net= 0. The optimum ratios were inversely related to PS_net and decreased to approximately 20 when PS_net was near maximum. The potential for flowing water to mediate nutrient partitioning among lotic algae by altering growth rates and optimum nutrient ratios is discussed.     

Do salt bridges stabilize proteins? A continuum electrostatic analysis

The electrostatic contribution to the free energy of folding was calculated for 21 salt bridges in 9 protein X-ray crystal structures using a continuum electrostatic approach with the DELPHI computer-program package. The majority (17) were found to be electrostatically destabilizing; the average free energy change, which is analogous to mutation of salt bridging side chains to hydrophobic isosteres, was calculated to be 3.5 kcal/mol. This is fundamentally different from stability measurements using pKa shifts, which effectively measure the strength of a salt bridge relative to 1 or more charged hydrogen bonds. The calculated effect was due to a large, unfavorable desolvation contribution that was not fully compensated by favorable interactions within the salt bridge and between salt-bridge partners and other polar and charged groups in the folded protein. Some of the salt bridges were studied in further detail to determine the effect of the choice of values for atomic radii, internal protein dielectric constant, and ionic strength used in the calculations. Increased ionic strength resulted in little or no change in calculated stability for 3 of 4 salt bridges over a range of 0.1-0.9 M. The results suggest that mutation of salt bridges, particularly those that are buried, to "hydrophobic bridges" (that pack at least as well as wild type) can result in proteins with increased stability. Due to the large penalty for burying uncompensated ionizable groups, salt bridges could help to limit the number of low free energy conformations of a molecule or complex and thus play a role in determining specificity (i.e., the uniqueness of a protein fold or protein-ligand binding geometry).