Collective Fluctuations in the Dynamics of Adaptation and Other Traveling Waves

The dynamics of adaptation are difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from random genetic drift arising in a vanguard of particularly fit individuals of the population. Several approaches have been developed to analyze the crucial role of genetic drift on the expected dynamics of adaptation, including the mean fitness of the entire population, or the fate of newly arising beneficial deleterious mutations. However, little is known about how genetic drift causes fluctuations to emerge on the population level, where it becomes palpable as variations in the adaptation speed and the fitness distribution. Yet these phenomena control the decay of genetic diversity and variability in evolution experiments and are key to a truly predictive understanding of evolutionary processes. Here, we show that correlations induced by these emergent fluctuations can be computed at any arbitrary order by a suitable choice of a dynamical constraint. The resulting linear equations exhibit fluctuation-induced terms that amplify short-distance correlations and suppress long-distance ones. These terms, which are in general not small, control the decay of genetic diversity and, for wave-tip dominated (“pulled”) waves, lead to anticorrelations between the tip of the wave and the lagging bulk of the population. While it is natural to consider the process of adaptation as a branching random walk in fitness space subject to a constraint (due to finite resources), we show that other traveling wave phenomena in ecology and evolution likewise fall into this class of constrained branching random walks. Our methods, therefore, provide a systematic approach toward analyzing fluctuations in a wide range of population biological processes, such as adaptation, genetic meltdown, species invasions, or epidemics.     

Continuous Traveling Waves for Prey-Taxis

Spatially moving predators are often considered for biological control of invasive species. The question arises as to whether introduced predators are able to stop an advancing pest or foreign population. In recent studies of reaction–diffusion models, it has been shown that the prey invasion can only be stopped if the prey dynamics observes an Allee effect. In this paper, we include prey-taxis into the model. Prey-taxis describe the active movement of predators to regions of high prey density. This effect leads to the observation that predators are drawn away from the leading edge of a prey invasion where its density is low. This leads to counterintuitive result that prey-taxis can actually reduce the likelihood of effective biocontrol.     

Calcium Oscillations and Waves Generated by Multiple Release Mechanisms in Pancreatic Acinar Cells

We explore the dynamic behavior of a model of calcium oscillations and wave propagation in the basal region of pancreatic acinar cells [Sneyd, J., et al., Biophys. J. 85: 1392–1405, 2003]. Since it is known that two principal calcium release pathways are involved, inositol trisphosphate receptors (IPR) and ryanodine receptors (RyR), we study how the model behavior depends on the density of each receptor type. Calcium oscillations can be mediated either by IPR or RyR. Continuous increases in either RyR or IPR density can lead to the appearance and disappearance of oscillations multiple times, and the two receptor types interact via their common effect on cytoplasmic calcium concentration and the subsequent effect on the total amount of calcium inside the cell. Increases in agonist concentration can stimulate oscillations via the RyR by increasing calcium influx. Using a two time-scale approach, we explain these complex behaviors by treating the total amount of cellular calcium as a slow parameter. Oscillations are controlled by the shape of the slow manifold and where it intersects the nullcline of the slow variable. When calcium diffusion is included, the existence of traveling waves in the model equation is strongly dependent on the interplay between the total amount of calcium in the cell and membrane transport, a feature that can be experimentally tested. Our results help us understand the behavior of a model that includes both receptors in comparison to the properties of each receptor type in isolation.     

The Architecture of Traveling Actin Waves Revealed by Cryo-Electron Tomography

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Traveling Waves and Spread Rates for a West Nile Virus Model

A reaction–diffusion model for the spatial spread of West Nile virus is developed and analysed. Infection dynamics are based on a modified version of a model for cross infection between birds and mosquitoes (Wonham et al., 2004, An epidemiological model for West-Nile virus: Invasion analysis and control application. Proc. R. Soc. Lond. B 271), and diffusion terms describe movement of birds and mosquitoes. Working with a simplified version of the model, the cooperative nature of cross-infection dynamics is utilized to prove the existence of traveling waves and to calculate the spatial spread rate of infection. Comparison theorem results are used to show that the spread rate of the simplified model may provide an upper bound for the spread rate of a more realistic and complex version of the model.     

Traveling waves in a chemotactic model

A model for chemotaxis in a bacteria-substrate mixture introduced by Keller and Segel, which is described by nonlinear partial differential equations, is studied analytically. The existence of traveling waves is shown for the system in which the substrate diffusion is taken into account and the chemotactic coefficient is greater than the motility one, and the instability of traveling waves is discussed.     

The dynamic structure underlying subthreshold oscillatory activity and the onset of spikes in a model of medial entorhinal cortex stellate cells

Medial entorhinal cortex layer II stellate cells display subthreshold oscillations (STOs). We study a single compartment biophysical model of such cells which qualitatively reproduces these STOs. We argue that in the subthreshold interval (STI) the seven-dimensional model can be reduced to a three-dimensional system of equations with well differentiated times scales. Using dynamical systems arguments we provide a mechanism for generations of STOs. This mechanism is based on the “canard structure,” in which relevant trajectories stay close to repelling manifolds for a significant interval of time. We also show that the transition from subthreshold oscillatory activity to spiking (“canard explosion”) is controlled in the STI by the same structure. A similar mechanism is invoked to explain why noise increases the robustness of the STO regime. Taking advantage of the reduction of the dimensionality of the full stellate cell system, we propose a nonlinear artificially spiking (NAS) model in which the STI reduced system is supplemented with a threshold for spiking and a reset voltage. We show that the synchronization properties in networks made up of the NAS cells are similar to those of networks using the full stellate cell models. In memory of Angel A. Alonso     

混合拟单调系统行波解的存在性

运用单调迭代方法,证明了混合拟单调系统的行波解的存在性．当反应扩散系。统的反应函数是混合拟单调函数时,如果选取一对合适的耦合上下解作为迭代初值,则迭代序列将收敛到一对拟解．而且在这对拟解之间存在系统的行波解．     

Porosity Controls Spread of Excitation in Tectorial Membrane Traveling Waves

Cochlear frequency selectivity plays a key role in our ability to understand speech, and is widely believed to be associated with cochlear amplification. However, genetic studies targeting the tectorial membrane (TM) have demonstrated both sharper and broader tuning with no obvious changes in hair bundle or somatic motility mechanisms. For example, cochlear tuning of Tectb^–/– mice is significantly sharper than that of Tecta^Y1870C/+ mice, even though TM stiffnesses are similarly reduced relative to wild-type TMs. Here we show that differences in TM viscosity can account for these differences in tuning. In the basal cochlear turn, nanoscale pores of Tecta^Y1870C/+ TMs are significantly larger than those of Tectb^–/– TMs. The larger pore size reduces shear viscosity (by ∼70%), thereby reducing traveling wave speed and increasing spread of excitation. These results demonstrate the previously unrecognized importance of TM porosity in cochlear and neural tuning.     

Porosity Controls Spread of Excitation in Tectorial Membrane Traveling Waves

Cochlear frequency selectivity plays a key role in our ability to understand speech, and is widely believed to be associated with cochlear amplification. However, genetic studies targeting the tectorial membrane (TM) have demonstrated both sharper and broader tuning with no obvious changes in hair bundle or somatic motility mechanisms. For example, cochlear tuning of Tectb^–/– mice is significantly sharper than that of Tecta^Y1870C/+ mice, even though TM stiffnesses are similarly reduced relative to wild-type TMs. Here we show that differences in TM viscosity can account for these differences in tuning. In the basal cochlear turn, nanoscale pores of Tecta^Y1870C/+ TMs are significantly larger than those of Tectb^–/– TMs. The larger pore size reduces shear viscosity (by ∼70%), thereby reducing traveling wave speed and increasing spread of excitation. These results demonstrate the previously unrecognized importance of TM porosity in cochlear and neural tuning.     

Do neurons have a voltage or a current threshold for action potential initiation?

The majority of neural network models consider the output of single neurons to be a continuous, positive, and saturating firing ratef(t), while a minority treat neuronal output as a series of delta pulses (t — t _i ). We here argue that the issue of the proper output representation relates to the biophysics of the cells in question and, in particular, to whether initiation of somatic action potentials occurs when a certain thresholdvoltage or a thresholdcurrent is exceeded. We approach this issue using numerical simulations of the electrical behavior of a layer 5 pyramidal cell from cat visual cortex. The dendritic tree is passive while the cell body includes eight voltage- and calcium-dependent membrane conductances.We compute both the steady-state (I ^static (V _m )) and the instantaneous (I _o (V_m)) I–V relationships and argue that the amplitude of the local maximum inI ^static (V _m ) corresponds to the current thresholdI _th for sustained inputs, while the location of the middle zero-crossing ofI _o corresponds to a fixed voltage thresholdV _th for rapid inputs. We confirm this using numerical simulations: for rapid synaptic inputs, spikes are initiated if the somatic potential exceedsV _th, while for slowly varying inputI _th must be exceeded. Due to the presence of the large dendritic tree, no charge thresholdQ _th exists for physiological input.Introducing the temporal average of the somatic membrane potential (V _m) while the cell is spiking repetitively, allows us to define a dynamic I-V relationship ^dynamic ((V _m)). We find an exponential relationship between (V _m) and the net current sunk by the somatic membrane during spiking (diode-like behavior). The slope ofI/dynamic((V _m)) allows us to define a dynamic input conductance and a time constant that characterizes how rapidly the cell changes its output firing frequency in response to a change in its input.     

Estimating clear-day solar radiation: An evaluation of three models

Three models for estimating clear-day solar radiation were compared to one another and to values of solar radiation measured at Ft Collins, Colo. The models of Campbell (1977), Gates (1962) and McCullough and Porter (1971) all correlate closely with measurements of clear-day solar radiation. The Campbell and the Gates models require less technical expertise and less expensive computations to produce estimates of the direct component of solar radiation. All of the models appear to require calibration in order to correct estimates of the input variables to measured values of irradiance so that accurate calculations of direct solar radiation can subsequently be made. The best estimates of the diffuse component of solar radiation are obtained from the model of McCullough and Porter. The easiest and most accurate predictions of total solar radiation can be obtained from the direct-radiation models of Campbell (1977) and Gates (1962) and a modification of the diffuse-component model of McCullough and Porter (1971).     

带时滞互惠模型的稳定性和行波解的存在性

本文建立了一类空间非局部带时滞影响的互惠生物种群系统模型.前部分利用线性化方法证明了该模型的简单动力学行为,即证明了零平衡点和两个边界平衡点都是不稳定的,唯一的正平衡点是稳定的,同时还用Redlinger上下解方法得出了该模型的初边值问题存在唯一的正则解;后部分则证明了该反应扩散系统连接零平衡点和正平衡点的行波解的存在性.     

具时滞的人口模型的行波解

研究具时滞的人口模型的行波解存在性问题,利用[5]中的方法,鹕行波解的存在性问题转化为寻找上下解的问题。     

Traveling Theta Waves along the Entire Septotemporal Axis of the Hippocampus

A topographical relationship exists between the hippocampus-entorhinal cortex and the neocortex. However, it is not known how these anatomical connections are utilized during information exchange and behavior. We recorded theta oscillations along the entire extent of the septotemporal axis of the hippocampal CA1 pyramidal layer. While the frequency of theta oscillation remained same along the entire long axis, the amplitude and coherence between recording sites decreased from dorsal to ventral hippocampus (VH). Theta phase shifted monotonically with distance along the longitudinal axis, reaching ～180° between the septal and temporal poles. The majority of concurrently recorded units were phase-locked to the local field theta at all dorsoventral segments. The power of VH theta had only a weak correlation with locomotion velocity, and its amplitude varied largely independently from theta in the dorsal part. Thus, theta oscillations can temporally combine or segregate neocortical representations along the septotemporal axis of the hippocampus.     

Possible mechanisms of synaptic plasticity modulation by extremely low-frequency magnetic fields

Understanding the biological mechanisms by which extremely low-frequency (ELF, < 300 Hz) magnetic fields (MFs) interact with human brain activity is an active field of research. Such knowledge is required by international agencies providing guidelines for general public and workers exposure to ELF MFs (such as ICNIRP, the International Commission on Non-Ionizing Radiation Protection). The identification of these interaction mechanisms is extremely challenging, since the effects of ELF MF exposure need to be monitored and understood at very different spatial (from micrometers to centimeters) and temporal (from milliseconds to minutes) scales. One possibility to overcome these issues is to develop biophysical models, based on the systems of mathematical equations describing the electric or metabolic activity of the brain tissue. Biophysical models of the brain activity offer the possibility to simulate how the brain tissue interacts with ELF MFs, in order to gain new insights into experimental data, and to test novel hypotheses regarding interaction mechanisms. This paper presents novel hypotheses regarding the effects of power line (60 Hz in North America) MFs on human brain activity, with arguments from biophysical models. We suggest a hypothetic chain of events that could bridge MF exposure with detectable effects on human neurophysiology. We also suggest novel directions of research in order to reach a convergence of biophysical models of brain activity and corresponding experimental data to identify interaction mechanisms.     

Biophysical limits on athermal effects of RF and microwave radiation

Using biophysical criteria, I show that continuous radiofrequency (RF) and microwave radiation with intensity less than 10 mW/cm(2) are unlikely to affect physiology significantly through athermal mechanisms. Biological systems are fundamentally noisy on the molecular scale as a consequence of thermal agitation and are noisy macroscopically as a consequence of physiological functions and animal behavior. If electromagnetic fields are to significantly affect physiology, their direct physical effect must be greater than that from the ubiquitous endogenous noise. Using that criterion, I show that none of a set of interactions of weak fields, which I argue is nearly complete on dimensional grounds, can affect biology on the molecular scale. Moreover, I conclude that such weak fields are quite unlikely to generate significant effects in their interactions with larger biological elements such as cells. In the course of that analysis, I examine important special examples of electromagnetic interactions: "direct" interactions where biology is modified simply by the motion of charged elements generated by the electric field; resonance interactions; the effects of electrostrictive forces and induced dipole moments; and modifications of radical pair recombination probabilities. In each case, I show that it is unlikely that low intensity fields can generate significant physiological consequences.     

Efficient search,mapping, and optimization of multi‐protein genetic systems in diverse bacteria

Developing predictive models of multi‐protein genetic systems to understand and optimize their behavior remains a combinatorial challenge, particularly when measurement throughput is limited. We developed a computational approach to build predictive models and identify optimal sequences and expression levels, while circumventing combinatorial explosion. Maximally informative genetic system variants were first designed by the RBS Library Calculator, an algorithm to design sequences for efficiently searching a multi‐protein expression space across a > 10,000‐fold range with tailored search parameters and well‐predicted translation rates. We validated the algorithm's predictions by characterizing 646 genetic system variants, encoded in plasmids and genomes, expressed in six gram‐positive and gram‐negative bacterial hosts. We then combined the search algorithm with system‐level kinetic modeling, requiring the construction and characterization of 73 variants to build a sequence‐expression‐activity map (SEAMAP) for a biosynthesis pathway. Using model predictions, we designed and characterized 47 additional pathway variants to navigate its activity space, find optimal expression regions with desired activity response curves, and relieve rate‐limiting steps in metabolism. Creating sequence‐expression‐activity maps accelerates the optimization of many protein systems and allows previous measurements to quantitatively inform future designs.     

一类具有时空时滞的单种群模型行波解的存在性

通过单调迭代和上下解技术,研究了一类具有时空时滞的单物种种群模型行波解的存在性,证明了当时滞充分小时,方程具有连接两个平衡点的波前解,并得到了一些新的结果.