食虫沟瘤蛛的饥饿耐受性

对我国多数稻区共享的优势种蜘蛛食虫沟瘤蛛进行饥饿耐受性测定,结果显示食虫沟瘤蛛的耐饥时间以及组内个体耐饥力的变异幅度与温度高低呈负相关。在35、25℃和15℃3种试验温度下,食虫沟瘤蛛的耐饥时间及变异幅度均与龄期呈正相关;在5℃时,耐饥时间极大延长,组内变异系幅度亦急剧增大,但此时耐饥时间和变异幅度均与龄期呈负相关。在高温35℃和低温5℃下,3个龄期组的耐饥时间差异不显著(p>0.05);但在适宜温度25℃和15℃时,3个龄期组之间的耐饥时间差异显著(p<0.05)。同一龄期组的食虫沟瘤蛛在任意两种不同的温度条件下,其耐饥时间的差异性均达到极显著水平(p<0.01)。4种试验温度条件下,处于饥饿状态的食虫沟瘤蛛各龄期组的阶段死亡率均具有正态分布特点,可用正态分布模型M=1σ2π.e-(T2-σ2μ)2进行拟合;并可根据正态分布的特点得出食虫沟瘤蛛的饥饿半致死时间(T50)和致死时间(T95)。     

Quantitative genetics of taura syndrome resistance in pacific white shrimp (penaeus vannamei): a cure model approach

Background

In aquaculture breeding, resistance against infectious diseases is commonly assessed as time until death under exposure to a pathogen. For some diseases, a fraction of the individuals may appear as "cured" (non-susceptible), and the resulting survival time may thus be a result of two confounded underlying traits, i.e., endurance (individual hazard) and susceptibility (whether at risk or not), which may be accounted for by fitting a cure survival model. We applied a cure model to survival data of Pacific white shrimp (Penaeus vannamei) challenged with the Taura syndrome virus, which is one of the major pathogens of Panaeid shrimp species.

Methods

In total, 15,261 individuals of 513 full-sib families from three generations were challenge-tested in 21 separate tests (tanks). All challenge-tests were run until mortality naturally ceased. Time-until-event data were analyzed with a mixed cure survival model using Gibbs sampling, treating susceptibility and endurance as separate genetic traits.

Results

Overall mortality at the end of test was 28%, while 38% of the population was considered susceptible to the disease. The estimated underlying heritability was high for susceptibility (0.41 ± 0.07), but low for endurance (0.07 ± 0.03). Furthermore, endurance and susceptibility were distinct genetic traits (r_g = 0.22 ± 0.25). Estimated breeding values for endurance and susceptibility were only moderately correlated (0.50), while estimated breeding values from classical models for analysis of challenge-test survival (ignoring the cured fraction) were closely correlated with estimated breeding values for susceptibility, but less correlated with estimated breeding values for endurance.

Conclusions

For Taura syndrome resistance, endurance and susceptibility are apparently distinct genetic traits. However, genetic evaluation of susceptibility based on the cure model showed clear associations with standard genetic evaluations that ignore the cure fraction for these data. Using the current testing design, genetic variation in observed survival time and absolute survival at the end of test were most likely dominated by genetic variation in susceptibility. If the aim is to reduce susceptibility, earlier termination of the challenge-test or back-truncation of the follow-up period should be avoided, as this may shift focus of selection towards endurance rather than susceptibility.     

Effect of exercise on muscle function decline with aging.

As people age, changes in muscle occur that are associated with a decrease in strength and endurance. These changes result in decreased functional capacity and quality of life. A substantial portion of this decrease is the result not of aging but of the sedentary life-style so frequently associated with aging. In "healthy old" persons and in older animals in experiments, an appropriate exercise program can result in increased strength and endurance. This is true both in longitudinal and short-term studies. As physical impairment increases, the exercise program must be individualized, and results are not as readily predictable. Much work remains before we may be certain how much exercise can be tolerated in these more impaired persons and what the effects may be.     

Solutions for transients in arbitrarily branching cables: I. Voltage recording with a somatic shunt.

An analytical solution is derived for voltage transients in an arbitrarily branching passive cable neurone model with a soma and somatic shunt. The response to injected currents can be represented as an infinite series of exponentially decaying components with different time constants and amplitudes. The time constants of a given model, obtained from the roots of a recursive transcendental equation, are independent of the stimulating and recording positions. Each amplitude is the product of three factors dependent on the corresponding root: one constant over the cell, one varying with the input site, and one with the recording site. The amplitudes are not altered by interchanging these sites. The solution reveals explicitly some of the parameter dependencies of the responses. An efficient recursive root-finding algorithm is described. Certain regular geometries lead to "lost" roots; difficulties associated with these can be avoided by making small changes to the lengths of affected segments. Complicated cells, such as a CA1 pyramid, produce many closely spaced time constants in the range of interest. Models with large somatic shunts and dendrites of unequal electrotonic lengths can produce large amplitude waveform components with surprisingly slow time constants. This analytic solution should complement existing passive neurone modeling techniques.     

The cylindrical cell with a time-variant membrane resistance. Measuring passive parameters.

The passive electrical properties of a cable can be measured by injecting a step of current at a point and fitting the resulting potentials at several positions along the cable with analytic solutions of the cable equation. An error analysis is presented for this method (which is based on constant membrane resistance) when the membrane resistance is not constant, but increases linearly with time. The increase of rm produces a "creep" in the membrane potential at long times, as observed in cardiac, skeletal, and smooth muscle. The partial differential equation describing the time-varying cable was solved numberically for a step of current and these "data" were fit by standard constant-resistance methods. Comparing the resulting parameter values with the known true values, we suggest that a correction of the standard methods is not satisfactory for resistance changes of the kind observed; instead, the cable equation must be solved again for the particular form of rm(t). The practical implementation of a method by Adrian and Peachey for measuring the membrane capacitance and an approximate method for estimating the rate-of-change of membrane resistance are discussed in appendices.     

A microscopic model of enzyme kinetics.

Many in vivo enzymatic processes, such as those of the tissue factor pathway of blood coagulation, occur in environments with facilitated substrate delivery or enzymes bound to cellular or lipid surfaces, which are quite different from the ideal fluid environment for which the Michaelis-Menten equation was derived. To describe the kinetics of such reactions, we propose a microscopic model that focuses on the kinetics of a single-enzyme molecule. This model provides the foundation for macroscopic models of the system kinetics of reactions occurring in both ideal and nonideal environments. For ideal reaction systems, the corresponding macroscopic models thus derived are consistent with the Michaelis-Menten equation. It is shown that the apparent Km is in fact a function of the mechanism of substrate delivery and should be interpreted as the substrate level at which the enzyme vacancy time equals the residence time of ES-complexes; it is suggested that our microscopic model parameters characterize more accurately an enzyme and its catalytic efficiency than does the classical Km. This model can also be incorporated into computer simulations of more complex reactions as an alternative to explicit analytical formulation of a macroscopic model.     

A fractional calculus approach to self-similar protein dynamics.

Relaxation processes and reaction kinetics of proteins deviate from exponential behavior because of their large amount of conformational substrates. The dynamics are governed by many time scales and, therefore, the decay of the relaxation function or reactant concentration is slower than exponential. Applying the idea of self-similar dynamics, we derive a fractal scaling model that results in an equation in which the time derivative is replaced by a differentiation (d/dt)beta of non-integer order beta. The fractional order differential equation is solved by a Mittag-Leffler function. It depends on two parameters, a fundamental time scale tau 0 and a fractional order beta that can be interpreted as a self-similarity dimension of the dynamics. Application of the fractal model to ligand rebinding and pressure release measurements of myoglobin is demonstrated, and the connection of the model to considerations of energy barrier height distributions is shown.     

Stochastic Gompertz model of tumour cell growth

In this communication, based upon the deterministic Gompertz law of cell growth, a stochastic model in tumour growth is proposed. This model takes account of both cell fission and mortality too. The corresponding density function of the size of the tumour cells obeys a functional Fokker--Planck equation which can be solved analytically. It is found that the density function exhibits an interesting "multi-peak" structure generated by cell fission as time evolves. Within this framework the action of therapy is also examined by simply incorporating a therapy term into the deterministic cell growth term.     

Modeling: optimal marathon performance on the basis of physiological factors

This paper examines current concepts concerning "limiting" factors in human endurance performance by modeling marathon running times on the basis of various combinations of previously reported values of maximal O2 uptake (VO2max), lactate threshold, and running economy in elite distance runners. The current concept is that VO2max sets the upper limit for aerobic metabolism while the blood lactate threshold is related to the fraction of VO2max that can be sustained in competitive events greater than approximately 3,000 m. Running economy then appears to interact with VO2max and blood lactate threshold to determine the actual running speed at lactate threshold, which is generally a speed similar to (or slightly slower than) that sustained by individual runners in the marathon. A variety of combinations of these variables from elite runners results in estimated running times that are significantly faster than the current world record (2:06:50). The fastest time for the marathon predicted by this model is 1:57:58 in a hypothetical subject with a VO2max of 84 ml.kg-1.min-1, a lactate threshold of 85% of VO2max, and exceptional running economy. This analysis suggests that substantial improvements in marathon performance are "physiologically" possible or that current concepts regarding limiting factors in endurance running need additional refinement and empirical testing.     

A metabolic limit on the ability to make up for lost time in endurance events.

It has been repeatedly demonstrated that the tolerable duration (t) of high-intensity cycling is well characterized as a hyperbolic function of power (P) with an asymptote that has been termed the "fatigue threshold" and with a curvature constant. This hyperbolic P-t relationship has also been confirmed in running and swimming, when speed (V) is used instead of P; that is, (V - V(F)). t = D', where V(F) is the V at the fatigue threshold, and D' is the curvature constant. Therefore, we theoretically analyzed herein the consequences of an athlete performing the initial part of an endurance event at a V different from the constant rate that would allow the performance time to be determined by the hyperbolic V-t relationship. We considered not only the V-t constraints that limit the athlete's ability to make up the time lost by too slow an early pace but also the consequences of a more rapid early pace. Our analysis demonstrates that both the V(F) and D' parameters of the athlete's V-t curve play an important role in the pace allocation strategy of the athlete. That is, 1) when the running V during any part of the whole running distance is below V(F), the athlete can never attain the goal of achieving the time equivalent to that of running the entire race at constant maximal V (i.e., that determined by one's own best V-t curve); and 2) the "endurance parameter ratio" D'/V(F) is especially important in determining the flexibility of the race pace that the athlete was able to choose intentionally.     

Factors affecting the distribution of benthic and littoral rotifers in a large marine lagoon,together with the description of a new species

Diffusion plays an important role in the exchange processes between lake sediments and the overlying water. Compounds entering the sediments usually have to penetrate through a certain mud thickness, where a reaction may then occur, while compounds being released have to diffuse through the interstitial water before escaping into the lake water.In this article mathematical functions are given which describe certain cases. They are all based on the differential diffusion equation of Fick, but for different boundary conditions different mathematical solutions of partial differential equations are needed. Four of these are presented in this paper, covering the cases of a compound diffusing into the sediments, with or without a chemical reaction occurring in the sediments, combined with either a constant or a non-constant concentration in the water.Furthermore a numerical approach is proposed in which the calculations are made by an iteration process over time and space. The results are presented as a series of concentrations as a function of time and depth in the sediment layer. It is shown in the first place that the time and the space steps must be sufficient small in agreement with the dimensions and time scale of the processes studied in order to obtain a satisfactory precision. The results can be fitted to a simplified exponential equation of the form (A · e^{–·t b} – B), which can be used for a quick assessment of special cases, depends on porosity, ratio between water and mud height; b 0.667. Furthermore this equation can be used to extrapolate from laboratory experiments with the sediments of a specific lake to results valid for the lake itself.The numerical model has also been used to describe the backward diffusion of an eventual product of a chemical reaction, which will diffuse further downward, but also upward. This is e.g. the case for the N₂O production during denitrification experiments when acetylene is applied as an inhibitor.Finally, the application of so called peepers and benthic chambers is discussed, while many of their disadvantages are explained.     

Neural networks with constrained inputs as models for pattern formation in primate visual cortex

We present a neural network model for the formation of ocular dominance stripes on primate visual cortex and examine the generic phase behavior and dynamics of the model. The dynamical equation of ocular dominance development can be identified with a class of Langevin equations with a nonconserved order parameter. We first set up and examine an Ising model with long-range interactions in an external field, which is equivalent to the model described by the Langevin equation. We use both mean-field theory and Monte-Carlo simulations to study the equilibrium phase diagram of this equivalent Ising model. The phase diagram comprises three phases: a striped phase, a hexagonal bubble phase, and a uniform paramagnetic phase. We then examine the dynamics of the striped phase by solving the Langevin equation both numerically and by singular perturbation theory. Finally, we compare the results of the model with physiological data. The typical striped structure of the ocular dominance columns corresponds to the zero-field configurations of the model. Monocular deprivation can be simulated by allowing the system to evolve in the absence of an external field at early times and then continuing the simulation in the presence of an external field. The physical and physiological applications of our model are discussed in the conclusion.     

Epidemiological Models with Non-Exponentially Distributed Disease Stages and Applications to Disease Control

SEIR epidemiological models with the inclusion of quarantine and isolation are used to study the control and intervention of infectious diseases. A simple ordinary differential equation (ODE) model that assumes exponential distribution for the latent and infectious stages is shown to be inadequate for assessing disease control strategies. By assuming arbitrarily distributed disease stages, a general integral equation model is developed, of which the simple ODE model is a special case. Analysis of the general model shows that the qualitative disease dynamics are determined by the reproductive number , which is a function of control measures. The integral equation model is shown to reduce to an ODE model when the disease stages are assumed to have a gamma distribution, which is more realistic than the exponential distribution. Outcomes of these models are compared regarding the effectiveness of various intervention policies. Numerical simulations suggest that models that assume exponential and non-exponential stage distribution assumptions can produce inconsistent predictions.     

Modelling human power and endurance

A generalised three component hydraulic model has been proposed to represent the human bioenergetic processes relating internal energy stores to performance during exercise, and into recovery. Further development of the model allows testable predictions to be made. In particular in this paper I examine certain hypotheses of chemical fuel shortage as a subgroup of the potential causes of fatigue, and their implications for maximal power and for endurance. The assumption that the limitation to sustainable power is direct proportionality to the glycogen store remaining, appears the most feasible. Based on this assumption, equations for the decline in maximum attainable power over time, the endurance at fixed workrates and the endurance at incremental tests (as a function of the increment slope) are obtained. Using published data for fit males, the maximum exertable power declines after about 6 s at 972 W to very low levels after about 2 min. For constant powers selected between 208 and 927 W, endurance declines from ad infinitum to only 6 s. Endurance at VO2max is predicted to be about 9 min. For incremental exercise tests of slope ranging from 30 W/min to 60 W/min, endurance lessens from 14 to 9 min. In these tests the anaerobic threshold is reached in times between 6 and 3 min. Although the power at termination of a test increases with incremental slope, terminal oxygen consumption is effectively constant. Almost all these model predictions are observed to correspond well with published experimental findings. These results suggest that the model can be used to represent an adequate overview of the operation of the human bioenergetic system.     

Ontogenetic change in blood oxygen capacity and maximum activity in garter snakes (Thamnophis sirtalis)

Summary There is an ontogenetic increase in the time that garter snakes (Thamnophis s. sirtalis) can maintain maximum activity at 25°C. Newborn snakes are exhausted by 3–5 min of activity while adults can be active for 20–25 min. The increased endurance of adult snakes results from ontogenetic increases in both aerobic and anaerobic energy generation. At rest juvenile and adult snakes have the same whole-body lactic acid concentrations, but at exhaustion adult lactic acid concentrations are 1.5 times those of juveniles. This increase in anaerobic energy production accounts for part of the endurance of adult snakes, but increased aerobic metabolism appears to be more important. Among the mechanisms increasing aerobic metabolism are more effective pulmonary ventilation and a 3-fold ontogenetic increase in blood oxygen capacity.The rapid exhaustion of small garter snakes probably limits the microhabitats they can occupy and the sorts of hunting methods they can employ. Small garter snakes feed only on small prey that are easily subdued. There is an ontogenetic increase in the relative size of prey eaten by garter snakes that parallels the ontogenetic increase in endurance. Adult feeding habits are adopted at the same body size at which adult blood oxygen capacity and endurance are attained.     

Quantification of conservative endurance times in thermally insulated cold-stressed digits.

The estimation of endurance times of the digits exposed to cold weather is performed by an analytical, one-dimensional cylindrical model. Blood perfusion effects are lumped into a volumetric heat-generation term. Cold-induced vasodilatation (CIVD) effects are not included in the present analysis. Endurance times, defined by a drop in cylinder tip temperature to 5 degrees C, were evaluated. Parameters included in this evaluation were 1) environmental temperatures, 2) thermal insulation applied on the cylinder, 3) length of the cylinder, and 4) diameter of the cylinder. It was found that the lower the ambient temperature, the longer the finger, and the smaller its diameter, then the shorter the endurance time for the same thermal insulation. Results of the model were compared with measured data for a subject not exhibiting CIVD response to cold stress. Conformity of results calculated for an adjusted value of the volumetric heat-generation term and measured data was very good, with a maximum deviation of less than 10% at only one particular point in time. This model facilitates the conservative estimation of lower bounds to thermally insulated fingers and toes exposed to cold stress.     

Models of dispersal in biological systems

In order to provide a general framework within which the dispersal of cells or organisms can be studied, we introduce two stochastic processes that model the major modes of dispersal that are observed in nature. In the first type of movement, which we call the position jump or kangaroo process, the process comprises a sequence of alternating pauses and jumps. The duration of a pause is governed by a waiting time distribution, and the direction and distance traveled during a jump is fixed by the kernel of an integral operator that governs the spatial redistribution. Under certain assumptions concerning the existence of limits as the mean step size goes to zero and the frequency of stepping goes to infinity the process is governed by a diffusion equation, but other partial differential equations may result under different assumptions. The second major type of movement leads to what we call a velocity jump process. In this case the motion consists of a sequence of runs separated by reorientations, during which a new velocity is chosen. We show that under certain assumptions this process leads to a damped wave equation called the telegrapher's equation. We derive explicit expressions for the mean squared displacement and other experimentally observable quantities. Several generalizations, including the incorporation of a resting time between movements, are also studied. The available data on the motion of cells and other organisms is reviewed, and it is shown how the analysis of such data within the framework provided here can be carried out.Supported in part by NIH Grant #GM 29123 and by NSF Grant #DMS-8301840Supported in part by NSF Grant #DMS-8301840Supported in part by the DFG Heisenberg Program     

Synaptic transmission in a model for stochastic neural activity.

A stochastic model equation for nerve membrane depolarization is derived which incorporates properties of synaptic transmission with a Rail-Eccles circuit for a trigger zone. If input processes are Poisson the depolarization is a Markov process for which equations for the moments of the interspike interval can be written down. An analytic result for the mean interval is obtained in a special case. The effect of the excitatory reversal potential is considerable if it is not too far from threshold and if the interspike interval is long. Computer simulations were performed when inhibitory and excitatory inputs are active. A substantial amount of inhibition leads to an exceedingly long tail in the density of the interspike time. With excitation only the interspike interval is often an approximately lognormal random variable. A coefficient of variation greater than one is often a consequence of relatively strong inhibition. Inferences can be made on the nature of the synaptic input from the statistics and density of the time between spikes. The inhibitory reversal potential usually has a relatively small effect except when the frequency of inhibition is large. An appendix contains the model equations in the case of an arbitrary distribution of postsynaptic potential amplitudes.     

Modelling conjugation with stochastic differential equations

Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared to the model without plate conjugation. The modelling approach described in this article can be applied generally when modelling dynamical systems.     

A nonlinear numerical model of percutaneous drug absorption.

A nonlinear mathematical model developed by Chandrasekaran et al. is examined to monitor pharmacokinetic profiles in percutaneous drug absorption and is addressed to several associated problems that could occur in the data analysis of in vitro experiments. The formulation of the model gives rise to a nonlinear partial differential equation (PDE) of parabolic type, and a family of finite-difference methods is developed for the numerical solution of the associated initial/boundary-value problem. The value given to a parameter in this family determines the stability properties of the resulting method and whether the solution is obtained explicitly or implicitly. In the case of implicit members of the family it is seen that the solution of the nonlinear PDE is obtained by solving a linear algebraic system, the coefficient matrix of which is tridiagonal. The behaviors of two methods of the family are examined in a series of numerical experiments. Numerical differentiation and integration procedures are combined to monitor the cumulative amount of drug eliminated into the receptor cell per unit area as time increases. It is found that the use of the equation for the simple membrane model to estimate the permeability coefficient and lag time is warranted even if the system should be described by the dual-sorption model, provided cumulative amount versus time data collected for a sufficiently long time are used. However, being different from the behavior in the simple membrane model, the lag time, which can be estimated in this way, is dose-dependent and decreases with increasing donor cell concentration. On the other hand, the permeability coefficient in the dual-sorption model remains constant irrespective of the donor cell concentrations as in the simple membrane model.