Roles of positive and negative feedback in biological systems

We discuss the influence of positive and negative feedback on the stability of a system, which is not clear-cut, and involves complex, mathematical problems. We show in particular that positive feedback can have a stabilising effect on some systems. We also point out the role that positive feedback plays in the digital treatment of signals required by cellular signalling, drawing on analogies from electronics, and the role that negative feedback plays in making a system robust against alteration of its parameters. Both positive and negative feedback can be seen as important enhancers of the properties of biological systems.     

A theoretical model of sinusoidal forearm tracking with delayed visual feedback

We present a phenomenological model to an experiment, where a person is systematically confronted with a delayed effect of her or his reaction to a time-periodic external signal. The model equations are derived from purely macroscopic considerations. Applying methods developed in the realm of synergetics we can analyze the first instability in the person's behaviour semi-analytically. A careful numerical study is devoted to the higher order instabilities and a comparison between experiment and the results obtained from our model is performed in detail.     

On the stability of equilibria in metabolic feedback systems

A sufficient criterion for the stability of the equilibrium of a metabolic feedback system will be constructed.     

Generalized transition state method and continuous diffusion in multi-dimensional systems with relation to ion transport in channels of biological membranes

An exact expression for the escape rate of a particle in a multi-dimensional system, with respect to an arbitrary reaction coordinate, is derived from first principles according to the transition state method, using a simple geometrical argument. It is shown how the mutual coupling of all degrees of freedom due to the interaction forces leads to the appearance of an effective mass and the potential of the mean force. The same relevant quantities dominate the effective one-particle Fokker-Planck equation, which is derived by a similar projection procedure from the multi-dimensional transport equation. In the limit of a large, position-dependent friction the respective effective Smoluchowski equation is obtained. It allows for the discussion of a diffusing particle which is subject to a temperature bath only through the coupled motion with the constituent lattice particles, or ligands in the case of a molecular ion channel. This treatment is of particular importance for the analysis of ion transport in membrane pores in which the ionic motion is mediated by internal ligand motion.     

Parameter estimation in a stochastic model of the tubuloglomerular feedback mechanism in a rat nephron

A key parameter in the understanding of renal hemodynamics is the gain of the feedback function in the tubuloglomerular feedback mechanism. A dynamic model of autoregulation of renal blood flow and glomerular filtration rate has been extended to include a stochastic differential equations model of one of the main parameters that determines feedback gain. The model reproduces fluctuations and irregularities in the tubular pressure oscillations that the former deterministic models failed to describe. This approach assumes that the gain exhibits spontaneous erratic variations that can be explained by a variety of influences, which change over time (blood pressure, hormone levels, etc.). To estimate the key parameters of the model we have developed a new estimation method based on the oscillatory behavior of the data. The dynamics is characterized by the spectral density, which has been estimated for the observed time series, and numerically approximated for the model. The parameters have then been estimated by the least squares distance between data and model spectral densities. To evaluate the estimation procedure measurements of the proximal tubular pressure from 35 nephrons in 16 rat kidneys have been analyzed, and the parameters characterizing the gain and the delay have been estimated. There was good agreement between the estimated values, and the values obtained for the same parameters in independent, previously published experiments.     

The role of cortical feedback in the generation of the temporal receptive field responses of lateral geniculate nucleus neurons: a computational modelling study

The influence of cortical feedback on thalamic visual responses has been a source of much discussion in recent years. In this study we examine the possible role of cortical feedback in shaping the spatiotemporal receptive field (STRF) responses of thalamocortical (TC) cells in the lateral geniculate nucleus (LGN) of the thalamus. A population-based computational model of the thalamocortical network is used to generate a representation of the STRF response of LGN TC cells within the corticothalamic feedback circuit. The cortical feedback is shown to have little influence on the spatial response properties of the STRF organization. However, the model suggests that cortical feedback may play a key role in modifying the experimentally observed biphasic temporal response property of the STRF, that is, the reversal over time of the polarity of ON and OFF responses of the centre and surround of the receptive field, in particular accounting for the experimentally observed mismatch between retinal cells and TC cells in respect of the magnitude of the second (rebound) phase of the temporal response. The model results also show that this mismatch may result from an anti-phase corticothalamic feedback mechanism.     

Regulation of release factor expression using a translational negative feedback loop: A systems analysis

The essential eukaryote release factor eRF1, encoded by the yeast SUP45 gene, recognizes stop codons during ribosomal translation. SUP45 nonsense alleles are, however, viable due to the establishment of feedback-regulated readthrough of the premature termination codon; reductions in full-length eRF1 promote tRNA-mediated stop codon readthrough, which, in turn, drives partial production of full-length eRF1. A deterministic mathematical model of this eRF1 feedback loop was developed using a staged increase in model complexity. Model predictions matched the experimental observation that strains carrying the mutant SUQ5 tRNA (a weak UAA suppressor) in combination with any of the tested sup45^UAA nonsense alleles exhibit threefold more stop codon readthrough than that of an SUQ5 yeast strain. The model also successfully predicted that eRF1 feedback control in an SUQ5 sup45^UAA mutant would resist, but not completely prevent, imposed changes in eRF1 expression. In these experiments, the introduction of a plasmid-borne SUQ5 copy into a sup45^UAASUQ5 mutant directed additional readthrough and full-length eRF1 expression, despite feedback. Secondly, induction of additional sup45^UAA mRNA expression in a sup45^UAASUQ5 strain also directed increased full-length eRF1 expression. The autogenous sup45 control mechanism therefore acts not to precisely control eRF1 expression, but rather as a damping mechanism that only partially resists changes in release factor expression level. The validated model predicts that the degree of feedback damping (i.e., control precision) is proportional to eRF1 affinity for the premature stop codon. The validated model represents an important tool to analyze this and other translational negative feedback loops.     

On the limitations of standard statistical modeling in biological systems: A full Bayesian approach for biology

One of the most important scientific challenges today is the quantitative and predictive understanding of biological function. Classical mathematical and computational approaches have been enormously successful in modeling inert matter, but they may be inadequate to address inherent features of biological systems. We address the conceptual and methodological obstacles that lie in the inverse problem in biological systems modeling. We introduce a full Bayesian approach (FBA), a theoretical framework to study biological function, in which probability distributions are conditional on biophysical information that physically resides in the biological system that is studied by the scientist.     

一套研究机械电反馈的心室压力钳系统

在心脏机械电反馈的研究中准确控制机械刺激是非常重要的。本研究室构建了一套适用于离体家兔心脏的心室压力钳系统。该系统通过计算机控制压力钳,不仅能模拟正常生理条件下左心室的压力波形,还能在心室活动周期的特定时相、以适当波形对心室施加机械刺激。该系统集心脏灌流与起搏、表面心电图记录、单相动作电位记录、心室压力钳制与测定等多种功能于一体,特别适用于器官水平上观察机械电反馈现象并探讨其机制。     

棉株上烟粉虱若虫种群的垂直分布与统计方法研究

对烟粉虱Bemisiatabaci在棉花植株上的垂直分布调查发现 ,烟粉虱在棉株各部位均有分布 ,且分布极不均匀 ,统计分析表明棉株各部位间烟粉虱的种群数量存在显著的差异。棉花顶部烟粉虱的若虫数量约占全棉株若虫总量的 1 6%,通过对棉株各部位烟粉虱的若虫数量与整株若虫总量的回归分析 ,建立了相应的回归方程式     

A statistical method for determining the breakpoint of two lines

A method is presented for determining the breakpoint of a line which suddenly changes slope at some unknown point. A statistical test is given for testing whether the broken line is a significantly better fit to the data than a single straight line. An approximate confidence interval can be obtained for the position of the breakpoint.     

Ion-conformational interaction and charge transport through channels of biological membranes

This work proposes a theory of charge transport through channels in biological membranes, based on ion flow interaction with charged groups of protein macromolecules that form the channel. Displacements of the groups are due to conformational changes of the protein molecule, the relaxation times of which are much larger than the average time of ion ocurrence in the channel. Ion flow is assumed to depend on the conformational changes and vice-versa. The resulting self-organizing ion-conformational system is described by a set of nonlinear differential equations for conformational variables and average occupancy of the channel by ions. The system exhibits multistable behaviour in a certain range of control parameters (potential difference, input ion flow). The stationary states of the system may be identified with the states of discrete conductivity of the ionic channels.     

基于空间统计特征的城市热环境时空演化

利用遥感反演和GIS空间分析等工具,提出了一种基于空间统计特征的城市热岛范围界定方法,并应用该方法分析了1984-2010年杭州市城市热环境的时空演化规律.结果表明:1984-2010年间,杭州市的城市热岛面积增加了8.66倍;杭州城市热岛的空间形态日趋复杂,空间分布由单中心的聚集状态逐渐向多中心的扩散状态发展;杭州城市热环境呈现出由区域低温均衡向区域高温均衡发展的态势.城市热岛的动态变化检测表明,城市扩张是杭州城市热岛发育的主要原因.本文所提方法考虑了城市地表温度的空间相关关系,反映了城市地表温度的全局统计特征,提供的信息更多,也更为客观和准确.通过该方法的推广,有助于解决当前城市热岛研究中研究样本之间缺乏通用性和可比性的问题.     

Some statistical considerations in the determination of thresholds in ELISA

The presentation of quantitative results from ELISAs is very variable, and, in particular, the positive-negative threshold or critical value is poorly defined. A simple statistical model is presented which demonstrates how this value may be determined. Depending on what assumptions are made it is possible to estimate the necessary parameters in several different ways. These methods generally form a hierarchy, and greater precision can be achieved by combining variances from several plates. More problematical is the determination of the negative control, and indeed its definition. The results of a series of ELISAs taken from a study of polyphagous predators of the cereal aphid S. avenae are used to illustrate the methods. The ELISAs were done over a period of three months using 86 plates. Recommendations are made for the numbers and levels of controls to be used in future studies.     

Synthesis of an octupolar compound and its biological effects on serum albumin

A special rigid planar structural octupolar molecule titled 2,4,6-tris(p-methylstyryl)-s-triazine (TMT) was synthesized and its interaction with bovine serum albumin (BSA) were studied by molecular spectroscopy. The quenching mechanism of fluorescence of BSA by TMT was discussed. The thermodynamic parameters ΔH ^θ, ΔG ^θ, ΔS ^θ at different temperatures were calculated and the results indicate hydrogen bond forces played major role in the reaction and the reaction was mainly enthalpy-driven. The distance r between donor (BSA) and acceptor (TMT) was obtained according to Förster theory of non-radiation energy transfer. Circular dichroism (CD) spectra, synchronous and three-dimensional fluorescence spectra were used to investigate the structural change of BSA molecules with addition of TMT, the result indicates that the α-helical structures of BSA molecules reduced in the presence of TMT. Sketch map of the interaction process was analyzed at molecular level.     

Note on the interpretation of tracer experiments in biological systems

It is shown that the results of C. W. Sheppard and A. S. Householder (1951) can be modified to include open systems which may or may not be in the steady state. Some conditions are given under which simple chemical reactions can be included.     

等位基因多态性群体遗传结构的多元非线性分析方法

长期以来,对于多维基因多态性数据的多元统计分析,如计算遗传距离时昕用的聚类分析、分析群体遗传结构时所用的主成分分析、因子分析和典型相关分析等,一直应用为无约束条件数据而设计的经典多元线性分析方法,并没有注意基因多态性数据的“闭合效应”所带来的问题。从分析基因多态性数据的分布和结构特征入手,文中指出了基因多态性分布具有“闭合数据”的特点,分析了由于“闭合效应”的影响,经典多元线性方法用于群体遗传结构分析昕面临的困难。根据成分数据统计分析的理论和方法,提出了基因多态性群体遗传结构的多元非线性分析基本方法。并以主成分分析为例,通过实例比较和分析了经典线性主成分分析和“对数比”非线性主成分分析的结果,证明“对数比”非线性主成分分析方法是研究基因多态性群体遗传结构的良好方法,具有特异、灵敏等优点,其结果符合群体遗传学规律。     

Negative feedback of extracellular ADP on ATP release in goldfish hepatocytes: A theoretical study

A mathematical model was built to account for the kinetic of extracellular ATP (ATPe) and extracellular ADP (ADPe) concentrations from goldfish hepatocytes exposed to hypotonicity. The model was based on previous experimental results on the time course of ATPe accumulation, ectoATPase activity, and cell viability [Pafundo et al., 2008].The kinetic of ATPe is controlled by a lytic ATP flux, a non-lytic ATP flux, and ecto-ATPase activity, whereas ADPe kinetic is governed by a lytic ADP flux and both ecto-ATPase and ecto-ADPase activities. Non-lytic ATPe efflux was included as a diffusion equation modulated by ATPe activation (positive feedback) and ADPe inhibition (negative feedback).The model yielded physically meaningful and stable steady-state solutions, was able to fit the experimental time evolution of ATPe and simulated the concomitant kinetic of ADPe. According to the model during the first minute of hypotonicity the concentration of ATPe is mainly governed by both lytic and non-lytic ATP efflux, with almost no contribution from ecto-ATPase activity. Later on, ecto-ATPase activity becomes important in defining the time dependent decay of ATPe levels. ADPe inhibition of the non-lytic ATP efflux was strong, whereas ATPe activation was minimal. Finally, the model was able to predict the consequences of partial inhibition of ecto-ATPase activity on the ATPe kinetic, thus emulating the exposure of goldfish cells to hypotonic medium in the presence of the ATP analog AMP-PCP. The model predicts this analog to both inhibit ectoATPase activity and increase non-lytic ATP release.     

Host-specificity of AM fungal population growth rates can generate feedback on plant growth

While the mutualistic interaction between plants and AM fungi is of obvious importance to ecosystem processes, the factors influencing the ecological and evolutionary dynamics within this interaction are poorly understood. The mutual interdependence of plant and AM fungal relative growth rates could generate complex dynamics in which the composition of the AM fungal community changes due to association with host and this change in fungal composition then differentially feeds back on plant growth. I first review evidence for feedback dynamics and then present an approach to evaluating such complex dynamics. I specifically present evidence of host-specific differences in the population growth rates of AM fungi. Pure cultures of AM fungi were mixed to produce the initial fungal community. This community was then distributed into replicate pots and grown with one of four co-occurring plant species. Distinct compositions of AM fungal spores were produced on different host species. The AM fungal communities were then inoculated back onto their own host species and grown for a second growing season. The differentiation observed in the first generation was enhanced during this second generation, verifying that the measure of spore composition reflects host-specific differences in AM fungal population growth rates. In further work on this system, I have found evidence of negative feedback through two pairs of plant species. The dynamic within the AM fungal community can thereby contribute to the coexistence of plant species.