Organization of receptive fields in networks with Hebbian learning: the connection between synaptic and phenomenological models

In this paper we address the question of how interactions affect the formation and organization of receptive fields in a network composed of interacting neurons with Hebbian-type learning. We show how to partially decouple single cell effects from network effects, and how some phenomenological models can be seen as approximations to these learning networks. We show that the interaction affects the structure of receptive fields. We also demonstrate how the organization of different receptive fields across the cortex is influenced by the interaction term, and that the type of singularities depends on the symmetries of the receptive fields.     

Cell motion, contractile networks, and the physics of interpenetrating reactive flow.

In this paper we propose a physical model of contractile biological polymer networks based on the notion of reactive interpenetrating flow. We show how our model leads to a mathematical formulation of the dynamical laws governing the behavior of contractile networks. We also develop estimates of the various parameters that appear in our equations, and we discuss some elementary predictions of the model concerning the general scaling principles that pertain to the motions of contractile networks.     

Effects of directional environmental change on extinction dynamics in experimental microbial communities are predicted by a simple model

Global temperatures are expected to rise between 1.1 and 6.4°C over the next 100 years, although the exact rate will depend on future greenhouse emissions, and will vary spatially. Temperature can alter an individual's metabolic rate, and consequently birth and death rates. In declining populations, these alterations may manifest as changes in the rate of that population's decline, and subsequently the timing of extinction events. Predicting such events could therefore be of considerable use. We use a small‐scale experimental system to investigate how the rate of temperature change can alter a population's time to extinction, and whether it is possible to predict this event using a simple phenomenological model that incorporates information about population dynamics at a constant temperature, published scaling of metabolic rates, and temperature. In addition, we examine 1) the relative importance of the direct effects of temperature on metabolic rate, and the indirect effects (via temperature driven changes in body size), on predictive accuracy (defined as the proximity of the predicted date of extinction to the mean observed date of extinction), 2) the combinations of model parameters that maximise accuracy of predictions, and 3) whether substituting temperature change through time with mean temperature produces accurate predictions. We find that extinction occurs earlier in environments that warm faster, and this can be accurately predicted (R² > 0.84). Increasing the number of parameters that were temperature‐dependent increased the model's accuracy, as did scaling these temperature‐dependent parameters with either the direct effects of temperature alone, or with the direct and indirect effects. Using mean temperature through time instead of actual temperature produces less accurate predictions of extinction. These results suggest that simple phenomenological models, incorporating metabolic theory, may be useful in understanding how environmental change can alter a population's rate of extinction. Synthesis Understanding how populations will respond to future climatic change is a key goal in ecology, however the exact rate of future warming will vary both spatially and temporally. Consequently, mathematical models must be used to understand the potential range of future population dynamics under various warming scenarios. We use a combination of experimentation and modelling to show that the effects of varying rates of environmental change on population dynamics can be predicted by a simple model. However, the accuracy of these predictions depends upon, amongst other things, a detailed knowledge of how temperature will change over time, rather than approximating this change to mean temperature.     

Coordinated Optimization of Visual Cortical Maps (I) Symmetry-based Analysis

In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of orientation columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about a hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference. From basic symmetry assumptions we obtain a comprehensive phenomenological classification of possible inter-map coupling energies and examine representative examples. We show that each individual coupling energy leads to a different class of OP solutions with different correlations among the maps such that inferences about the optimization principle from map layout appear viable. We systematically assess whether quantitative laws resembling experimental observations can result from the coordinated optimization of orientation columns with other feature maps.     

Internal transport properties of macroporous sugar polyacrylate hydrogels: microsphere diffusion described by phenomenological laws

We have determined the internal transport properties of heterogeneous, macroporous hydrogels based on the regioregular sugar polyacrylate poly(6-acryloyl-beta-O-methyl-galactopyranoside). This was accomplished by measuring the diffusive flux of variously sized polystyrene microspheres and combining these results with solutions of phenomenological transport laws (the Navier-Stokes equations and Fick's Law with an assumption of first-order irreversible sphere capture by the gel polymer). This enabled calculation of gel properties such as average pore diameters (ca. 11.76 microm) and the diffusivities of the polystyrene spheres in the gel. These values range from 76% to 83% of that in free solution and correlate closely with the equilibrium solution content of the gel (82.3%). This approach has also enabled calculation of the sphere capture rates (2.4 x 10(-3) to 9.6 x 10(-5) s(-1)). These low capture rates indicate that the gel is extremely non-adhesive towards the spheres, and a linear correlation with sphere form drag area (r(2) = 1) was found. The pore sizes of the hydrated gel were observed via DIC light microscopy and the visible effective diameters corresponded very closely to the calculated values (11.66 vs. 11.76 microm). The diffusion/capture of inert spheres in the hydrogel can thus be described in a non-destructive manner by straightforward application of phenomenological transport laws. This result is significant in that these laws were intended to describe macroscopic ensembles of very large numbers of particles in continuous media, not small numbers (i.e., hundreds) in discontinuous media.     

Stigma and Self-Stigma in Addiction

Addictions are commonly accompanied by a sense of shame or self-stigmatization. Self-stigmatization results from public stigmatization in a process leading to the internalization of the social opprobrium attaching to the negative stereotypes associated with addiction. We offer an account of how this process works in terms of a range of looping effects, and this leads to our main claim that for a significant range of cases public stigma figures in the social construction of addiction. This rests on a social constructivist account in which those affected by public stigmatization internalize its norms. Stigma figures as part-constituent of the dynamic process in which addiction is formed. Our thesis is partly theoretical, partly empirical, as we source our claims about the process of internalization from interviews with people in treatment for substance use problems.     

Tissue morphogenesis: a surface buckling mechanism

Surface patterns can emerge during growth of anisotropic tissues because of surface buckling. This morphogenetic scenario is examined in the present paper based on a simple phenomenological theory of tissue growth. In particular, we show that constrained growth can lead to tissue compression, which in turn may result in surface buckling of the tissue. The latter means the appearance of wavy patterns on the surface. These patterns decay away from the surface. It is interesting that the critical magnitude of the parameter of mass supply, which corresponds to surface buckling, is independent of the pattern wavelength and various patterns can generally be generated in growth. Results of theoretical analysis show that the surface buckling scenario is realistic if the growing tissue matches the following two conditions. First, compression should appear during tissue growth. Second, the tissue should exhibit strong anisotropy. The former condition does not necessarily mean geometric constraints: inhomogeneous growth or material inhomogeneity and anisotropy can lead to the appearance of compressive stresses. The latter condition is typical of some tissues with fiber reinforcement in planes parallel to the surface. In the latter case, the tissue material is much softer in the out-of-plane direction than in plane. The creation of patterns by restraining tissue growth and forcing the surface to buckle represents a challenging experimental problem.     

Systematic Construction of Kinetic Models from Genome-Scale Metabolic Networks

The quantitative effects of environmental and genetic perturbations on metabolism can be studied in silico using kinetic models. We present a strategy for large-scale model construction based on a logical layering of data such as reaction fluxes, metabolite concentrations, and kinetic constants. The resulting models contain realistic standard rate laws and plausible parameters, adhere to the laws of thermodynamics, and reproduce a predefined steady state. These features have not been simultaneously achieved by previous workflows. We demonstrate the advantages and limitations of the workflow by translating the yeast consensus metabolic network into a kinetic model. Despite crudely selected data, the model shows realistic control behaviour, a stable dynamic, and realistic response to perturbations in extracellular glucose concentrations. The paper concludes by outlining how new data can continuously be fed into the workflow and how iterative model building can assist in directing experiments.     

A mathematical and statistical framework for modelling dispersal

Mechanistic and phenomenological dispersal modelling of organisms has long been an area of intensive research. Recently, there has been an increased interest in intermediate models between the two. Intermediate models include major mechanisms that affect dispersal, in addition to the dispersal curve of a phenomenological model. Here we review and describe the mathematical and statistical framework for phenomenological dispersal modelling. In the mathematical development we describe modelling of dispersal in two dimensions from a point source, and in one dimension from a line or area source. In the statistical development we describe applicable observation distributions, and the procedures of model fitting, comparison, checking, and prediction. The procedures are also demonstrated using data from dispersal experiments. The data are hierarchically structured, and hence, we fit hierarchical models. The Bayesian modelling approach is applied, which allows us to show the uncertainty in the parameter estimates and in predictions. Finally, we show how to account for the effect of wind speed on the estimates of the dispersal parameters. This serves as an example of how to strengthen the coupling in the modelling between the phenomenon observed in an experiment and the underlying process – something that should be striven for in the statistical modelling of dispersal.     

Magnetoreception in microorganisms and fungi

The ability to respond to magnetic fields is ubiquitous among the five kingdoms of organisms. Apart from the mechanisms that are at work in bacterial magnetotaxis, none of the innumerable magnetobiological effects are as yet completely understood in terms of their underlying physical principles. Physical theories on magnetoreception, which draw on classical electrodynamics as well as on quantum electrodynamics, have greatly advanced during the past twenty years, and provide a basis for biological experimentation. This review places major emphasis on theories, and magnetobiological effects that occur in response to weak and moderate magnetic fields, and that are not related to magnetotaxis and magnetosomes. While knowledge relating to bacterial magnetotaxis has advanced considerably during the past 27 years, the biology of other magnetic effects has remained largely on a phenomenological level, a fact that is partly due to a lack of model organisms and model responses; and in great part also to the circumstance that the biological community at large takes little notice of the field, and in particular of the available physical theories. We review the known magnetobiological effects for bacteria, protists and fungi, and try to show how the variegated empirical material could be approached in the framework of the available physical models.     

Continuum model of fibroblast-driven wound contraction: inflammation-mediation.

We propose a mathematical model to aid the understanding of how events in wound healing are orchestrated to result in wound contraction. Ultimately, a validated model could provide a predictive means for enhancing or mitigating contraction as is appropriate for managing a particular wound. The complex nature of wound healing and the lack of a modeling framework which can account for both the relevant cell biology and biomechanics are major reasons for the absence of models to date. Here we adapt a model originally proposed by Murray and co-workers to show how cell traction forces can result in spatial patterns of cell aggregates since it offers a framework for understanding how traction exerted by wound fibroblasts drives wound contraction. Since it is a continuum model based on conservation laws which reflect assumed cell and tissue properties, it is readily extended to account for emerging understanding of the cell biology of wound healing and its relationship to inflammation. We consider various sets of assumed properties, based on current knowledge, within a base model of dermal wound healing and compare predictions of the rate and extent of wound contraction to published experimental results.     

A homeostatic model of neuronal firing governed by feedback signals from the extracellular matrix

Molecules of the extracellular matrix (ECM) can modulate the efficacy of synaptic transmission and neuronal excitability. These mechanisms are crucial for the homeostatic regulation of neuronal firing over extended timescales. In this study, we introduce a simple mathematical model of neuronal spiking balanced by the influence of the ECM. We consider a neuron receiving random synaptic input in the form of Poisson spike trains and the ECM, which is modeled by a phenomenological variable involved in two feedback mechanisms. One feedback mechanism scales the values of the input synaptic conductance to compensate for changes in firing rate. The second feedback accounts for slow fluctuations of the excitation threshold and depends on the ECM concentration. We show that the ECM-mediated feedback acts as a robust mechanism to provide a homeostatic adjustment of the average firing rate. Interestingly, the activation of feedback mechanisms may lead to a bistability in which two different stable levels of average firing rates can coexist in a spiking network. We discuss the mechanisms of the bistability and how they may be related to memory function.     

Extinction,diversity and survivorship of taxa in the fossil record

Using data drawn from large-scale databases, a number of interesting trends in the fossil record have been observed in recent years. These include the average decline in extinction rates throughout the Phanerozoic, the average increase in standing diversity, correlations between rates of origination and extinction, and simple laws governing the form of survivorship curves and the distribution of the lifetimes of taxa. In this paper we derive a number of mathematical relationships between these quantities and show how these different trends are interrelated. We also derive a variety of constraints on the possible forms of these trends, such as limits on the rate at which extinction may decline and limits on the allowed difference between extinction and origination rates at any given time.     

Twinstar, the Drosophila homolog of cofilin/ADF, is required for planar cell polarity patterning

Planar cell polarity (PCP) is a level of tissue organization in which cells adopt a uniform orientation within the plane of an epithelium. The process of tissue polarization is likely to be initiated by an extracellular gradient. Thus, determining how cells decode and convert this graded information into subcellular asymmetries is key to determining how cells direct the reorganization of the cytoskeleton to produce uniformly oriented structures. Twinstar (Tsr), the Drosophila homolog of Cofilin/ADF (actin depolymerization factor), is a component of the cytoskeleton that regulates actin dynamics. We show here that various alleles of tsr produce PCP defects in the wing, eye and several other epithelia. In wings mutant for tsr, Frizzled (Fz) and Flamingo (Fmi) proteins do not properly localize to the proximodistal boundaries of cells. The correct asymmetric localization of these proteins instructs the actin cytoskeleton to produce one actin-rich wing hair at the distal-most vertex of each cell. These results argue that actin remodeling is not only required in the manufacture of wing hairs, but also in the PCP read-out that directs where a wing hair will be secreted.     

Stochastic E2F Activation and Reconciliation of Phenomenological Cell-Cycle Models

The transition of the mammalian cell from quiescence to proliferation is a highly variable process. Over the last four decades, two lines of apparently contradictory, phenomenological models have been proposed to account for such temporal variability. These include various forms of the transition probability (TP) model and the growth control (GC) model, which lack mechanistic details. The GC model was further proposed as an alternative explanation for the concept of the restriction point, which we recently demonstrated as being controlled by a bistable Rb-E2F switch. Here, through a combination of modeling and experiments, we show that these different lines of models in essence reflect different aspects of stochastic dynamics in cell cycle entry. In particular, we show that the variable activation of E2F can be described by stochastic activation of the bistable Rb-E2F switch, which in turn may account for the temporal variability in cell cycle entry. Moreover, we show that temporal dynamics of E2F activation can be recast into the frameworks of both the TP model and the GC model via parameter mapping. This mapping suggests that the two lines of phenomenological models can be reconciled through the stochastic dynamics of the Rb-E2F switch. It also suggests a potential utility of the TP or GC models in defining concise, quantitative phenotypes of cell physiology. This may have implications in classifying cell types or states.     

Phenomenological vs. biophysical models of thermal stress in aquatic eggs

Predicting species responses to climate change is a central challenge in ecology. These predictions are often based on lab‐derived phenomenological relationships between temperature and fitness metrics. We tested one of these relationships using the embryonic stage of a Chinook salmon population. We parameterised the model with laboratory data, applied it to predict survival in the field, and found that it significantly underestimated field‐derived estimates of thermal mortality. We used a biophysical model based on mass transfer theory to show that the discrepancy was due to the differences in water flow velocities between the lab and the field. This mechanistic approach provides testable predictions for how the thermal tolerance of embryos depends on egg size and flow velocity of the surrounding water. We found support for these predictions across more than 180 fish species, suggesting that flow and temperature mediated oxygen limitation is a general mechanism underlying the thermal tolerance of embryos.     

Three-dimensional image analysis of cells in reflexion contrast—I. Methods for determination of surface,volume and angle of declivity of human erythrocytes

In reflexion contrast (RC) microscopy, cells with plane contact to the glass surface show interference lines which correspond to lines of equal altitude or thickness. Between two neighbouring dissimilar interference lines the thickness of layer is about 0.1 μm (depending on refractive index and wavelength). The interference lines of RC are evaluated by means of semi-automatic image analysis and used for both three-dimensional reconstruction of the cells and calculation of the surface, volume and angle of climb of surface structures. Determination of the absolute thickness of cells is carried out either by measuring the shadows at one-sided illumination or by the two-filter method at different wavelengths. Equations for various simple reference figures of normocytes and a layer method are given which allow the three-dimensional analysis of optionally formed structures. The methods were tested using erythrocytes.     

Maternal effects as the cause of parent-of-origin effects that mimic genomic imprinting

Epigenetic effects are increasingly recognized as an important source of variation in complex traits and have emerged as the focus of a rapidly expanding area of research. Principle among these effects is genomic imprinting, which has generally been examined in analyses of complex traits by testing for parent-of-origin-dependent effects of alleles. However, in most of these analyses maternal effects are confounded with genomic imprinting because they can produce the same patterns of phenotypic variation expected for various forms of imprinting. Distinguishing between the two is critical for genetic and evolutionary studies because they have entirely different patterns of gene expression and evolutionary dynamics. Using a simple single-locus model, we show that maternal genetic effects can result in patterns that mimic those expected under genomic imprinting. We further demonstrate how maternal effects and imprinting effects can be distinguished using genomic data from parents and offspring. The model results are applied to a genome scan for quantitative trait loci (QTL) affecting growth- and weight-related traits in mice to illustrate how maternal effects can mimic imprinting. This genome scan revealed five separate maternal-effect loci that caused a diversity of patterns mimicking those expected under various modes of genomic imprinting. These results demonstrate that the appearance of parent-of-origin-dependent effects (POEs) of alleles at a locus cannot be taken as direct evidence that the locus is imprinted. Moreover, they show that, in gene mapping studies, genetic data from both parents and offspring are required to successfully differentiate between imprinting and maternal effects as the cause of apparent parent-of-origin effects of alleles.     

Acidification and release of nutrients from organic matter — a model analysis

A simple, phenomenological model is proposed to describe the behaviour of nett mineralization of nitrogen from the soil organic matter.Experimental evidence shows that nett mineralization of nitrogen is increased following artificial acidification of soil forests. The model seems to describe appropriately this phenomenon and some testable predictions are derived from it. These predictions seem to give a clue to the intriguing difficulty of establishing effects of acid rain in coniferous forest ecosystems.A discussion is also given on how the model can be extended to nutrient elements other than nitrogen.