A new computational growth model for sea urchin skeletons

A new computational model has been developed to simulate growth of regular sea urchin skeletons. The model incorporates the processes of plate addition and individual plate growth into a composite model of whole-body (somatic) growth. A simple developmental model based on hypothetical morphogens underlies the assumptions used to define the simulated growth processes. The data model is based on a Delaunay triangulation of plate growth center points, using the dual Voronoi polygons to define plate topologies. A spherical frame of reference is used for growth calculations, with affine deformation of the sphere (based on a Young-Laplace membrane model) to result in an urchin-like three-dimensional form. The model verifies that the patterns of coronal plates in general meet the criteria of Voronoi polygonalization, that a morphogen/threshold inhibition model for plate addition results in the alternating plate addition pattern characteristic of sea urchins, and that application of the Bertalanffy growth model to individual plates results in simulated somatic growth that approximates that seen in living urchins. The model suggests avenues of research that could explain some of the distinctions between modern sea urchins and the much more disparate groups of forms that characterized the Paleozoic Era.     

Identifying Optimal Models to Represent Biochemical Systems

Biochemical systems involving a high number of components with intricate interactions often lead to complex models containing a large number of parameters. Although a large model could describe in detail the mechanisms that underlie the system, its very large size may hinder us in understanding the key elements of the system. Also in terms of parameter identification, large models are often problematic. Therefore, a reduced model may be preferred to represent the system. Yet, in order to efficaciously replace the large model, the reduced model should have the same ability as the large model to produce reliable predictions for a broad set of testable experimental conditions. We present a novel method to extract an “optimal” reduced model from a large model to represent biochemical systems by combining a reduction method and a model discrimination method. The former assures that the reduced model contains only those components that are important to produce the dynamics observed in given experiments, whereas the latter ensures that the reduced model gives a good prediction for any feasible experimental conditions that are relevant to answer questions at hand. These two techniques are applied iteratively. The method reveals the biological core of a model mathematically, indicating the processes that are likely to be responsible for certain behavior. We demonstrate the algorithm on two realistic model examples. We show that in both cases the core is substantially smaller than the full model.     

Mathematical modelling of anisotropy in fibrous connective tissue

We present two modelling frameworks for studying dynamic anistropy in connective tissue, motivated by the problem of fibre alignment in wound healing. The first model is a system of partial differential equations operating on a macroscopic scale. We show that a model consisting of a single extracellular matrix material aligned by fibroblasts via flux and stress exhibits behaviour that is incompatible with experimental observations. We extend the model to two matrix types and show that the results of this extended model are robust and consistent with experiment. The second model represents cells as discrete objects in a continuum of ECM. We show that this model predicts patterns of alignment on macroscopic length scales that are lost in a continuum model of the cell population.     

选择方向强化学习的神经网络模型

提出了神经网络模型的一种选择方向强化学习规则,定义并导出了新模型与Hopfield模型两种不同的筛选曲线,由此表明新模型对相关图样的分辨力优于Hopfield模型。在微机上模拟了由100个神经元构成的网络,结果显示新模型具有重复记忆这一神经生理学特点。定义并分行了记忆强度因子,模拟结果表明记忆强度因子愈大的记忆态,联想性能愈好,学习周期愈短。     

Charles Bonnet Syndrome: Evidence for a Generative Model in the Cortex?

Several theories propose that the cortex implements an internal model to explain, predict, and learn about sensory data, but the nature of this model is unclear. One condition that could be highly informative here is Charles Bonnet syndrome (CBS), where loss of vision leads to complex, vivid visual hallucinations of objects, people, and whole scenes. CBS could be taken as indication that there is a generative model in the brain, specifically one that can synthesise rich, consistent visual representations even in the absence of actual visual input. The processes that lead to CBS are poorly understood. Here, we argue that a model recently introduced in machine learning, the deep Boltzmann machine (DBM), could capture the relevant aspects of (hypothetical) generative processing in the cortex. The DBM carries both the semantics of a probabilistic generative model and of a neural network. The latter allows us to model a concrete neural mechanism that could underlie CBS, namely, homeostatic regulation of neuronal activity. We show that homeostatic plasticity could serve to make the learnt internal model robust against e.g. degradation of sensory input, but overcompensate in the case of CBS, leading to hallucinations. We demonstrate how a wide range of features of CBS can be explained in the model and suggest a potential role for the neuromodulator acetylcholine. This work constitutes the first concrete computational model of CBS and the first application of the DBM as a model in computational neuroscience. Our results lend further credence to the hypothesis of a generative model in the brain.     

A goodness-of-fit test for multinomial logistic regression

This article presents a score test to check the fit of a logistic regression model with two or more outcome categories. The null hypothesis that the model fits well is tested against the alternative that residuals of samples close to each other in covariate space tend to deviate from the model in the same direction. We propose a test statistic that is a sum of squared smoothed residuals, and show that it can be interpreted as a score test in a random effects model. By specifying the distance metric in covariate space, users can choose the alternative against which the test is directed, making it either an omnibus goodness-of-fit test or a test for lack of fit of specific model variables or outcome categories.     

The species-area relation III. A third model for a delimited community

Summary A mathematical model of the species-area relation is described for a group of limited species. This model is a modification of that proposed earlier (Kobayashi, 1975), being assumed that the limited species are expected to occur in a habitat under consideration. The model equation gives a sigmoid species-log area curve implying that few rare species are found in a group of species. The good agreement between observation and this model is exemplified with the data of plant and arthropod communities. The implication of parameters involved are examined in connection with those of the preceding model, and the underlying ecology of the model is discussed. Contribution from the Laboratory of Applied Zoology, Yamagata University, No. 83.     

A Push-Pull CORF Model of a Simple Cell with Antiphase Inhibition Improves SNR and Contour Detection

We propose a computational model of a simple cell with push-pull inhibition, a property that is observed in many real simple cells. It is based on an existing model called Combination of Receptive Fields or CORF for brevity. A CORF model uses as afferent inputs the responses of model LGN cells with appropriately aligned center-surround receptive fields, and combines their output with a weighted geometric mean. The output of the proposed model simple cell with push-pull inhibition, which we call push-pull CORF, is computed as the response of a CORF model cell that is selective for a stimulus with preferred orientation and preferred contrast minus a fraction of the response of a CORF model cell that responds to the same stimulus but of opposite contrast. We demonstrate that the proposed push-pull CORF model improves signal-to-noise ratio (SNR) and achieves further properties that are observed in real simple cells, namely separability of spatial frequency and orientation as well as contrast-dependent changes in spatial frequency tuning. We also demonstrate the effectiveness of the proposed push-pull CORF model in contour detection, which is believed to be the primary biological role of simple cells. We use the RuG (40 images) and Berkeley (500 images) benchmark data sets of images with natural scenes and show that the proposed model outperforms, with very high statistical significance, the basic CORF model without inhibition, Gabor-based models with isotropic surround inhibition, and the Canny edge detector. The push-pull CORF model that we propose is a contribution to a better understanding of how visual information is processed in the brain as it provides the ability to reproduce a wider range of properties exhibited by real simple cells. As a result of push-pull inhibition a CORF model exhibits an improved SNR, which is the reason for a more effective contour detection.     

A flexible B-spline model for multiple longitudinal biomarkers and survival

Often when jointly modeling longitudinal and survival data, we are interested in a multivariate longitudinal measure that may not fit well by linear models. To overcome this problem, we propose a joint longitudinal and survival model that has a nonparametric model for the longitudinal markers. We use cubic B-splines to specify the longitudinal model and a proportional hazards model to link the longitudinal measures to the hazard. To fit the model, we use a Markov chain Monte Carlo algorithm. We select the number of knots for the cubic B-spline model using the Conditional Predictive Ordinate (CPO) and the Deviance Information Criterion (DIC). The method and model selection approach are validated in a simulation. We apply this method to examine the link between viral load, CD4 count, and time to event in data from an AIDS clinical trial. The cubic B-spline model provides a good fit to the longitudinal data that could not be obtained with simple parametric models.     

Stochastic Petri Net extension of a yeast cell cycle model

This paper presents the definition, solution and validation of a stochastic model of the budding yeast cell cycle, based on Stochastic Petri Nets (SPN). A specific family of SPNs is selected for building a stochastic version of a well-established deterministic model. We describe the procedure followed in defining the SPN model from the deterministic ODE model, a procedure that can be largely automated. The validation of the SPN model is conducted with respect to both the results provided by the deterministic one and the experimental results available from literature. The SPN model catches the behavior of the wild type budding yeast cells and a variety of mutants. We show that the stochastic model matches some characteristics of budding yeast cells that cannot be found with the deterministic model. The SPN model fine-tunes the simulation results, enriching the breadth and the quality of its outcome.     

Patient-derived orthotopic xenograft (PDOX) mouse model of adult rhabdomyosarcoma invades and recurs after resection in contrast to the subcutaneous ectopic model

Rhabdomyosarcoma (RMS) is a rare mesenchymal tumor. The aim of the present study was to develop a patient-derived orthotopic xenograft (PDOX) mouse model of RMS and compare the PDOX model to a subcutaneous (s.c.)-transplant model. A patient RMS from a striated muscle was grown orthotopically in the right biceps femoris muscle and right quadriceps muscle of nude mice to establish a PDOX model, as well as under the skin to establish an s.c. model. PDOX tumors grew at a statistically-significant faster rate compared to the s.c. tumors. Recurrence after surgical resection occurred only in PDOX tumors, not in the s.c. model. Histologically, only the PDOX model was shown to be invasive. In conclusion, these results indicate that the PDOX model of adult RMS is malignant and the subcutaneous model is benign. These results emphasize that a proper tumor microenvironment is necessary for patient-like behavior of a tumor in a mouse model.     

Dissection and reduction of a modeled bursting neuron

An 11-variable Hodgkin-Huxley type model of a bursting neuron was investigated using numerical bifurcation analysis and computer simulations. The results were applied to develop a reduced model of the underlying subthreshold oscillations (slow-wave) in membrane potential. Two different low-order models were developed: one 3-variable model, which mimicked the slow-wave of the full model in the absence of action potentials and a second 4-variable model, which included expressions accounting for the perturbational effects of action potentials on the slow-wave. The 4-variable model predicted more accurately the activity mode (bursting, beating, or silence) in response to application of extrinsic stimulus current or modulatory agents. The 4-variable model also possessed a phase-response curve that was very similar to that of the original 11-variable model. The results suggest that low-order models of bursting cells that do not consider the effects of action potentials may erroneously predict modes of activity and transient responses of the full model on which the reductions are based. These results also show that it is possible to develop low-order models that retain many of the characteristics of the activity of the higher-order system.     

Towards the development of a minimal cell model by generalization of a model of Escherichia coli: use of dimensionless rate parameters.

A model of a minimal cell would be a valuable tool in identifying the organizing principles that relate the static sequence information of the genome to the dynamic functioning of the living cell. Our approach for developing a minimal cell model is to first generalize an existing model of Escherichia coli by expressing reaction rates as ratios to a set of reference parameters. This generalized model is a prototype minimal cell model that will be developed by adding detail to explicitly include each chemical species. We tested the concept of a generalized model by testing the effect of scaling all enzyme-catalyzed reactions in the E. coli model. The scaling has little effect on cellular function for a wide range of kinetic ratios, where the kinetic ratio is defined as the rate of all enzyme-catalyzed reactions in a given model relative to those in the E. coli model.     

Capturing the Dynamics of a Hybrid Multiscale Cancer Model with a Continuum Model

Cancer is a complex disease involving processes at spatial scales from subcellular, like cell signalling, to tissue scale, such as vascular network formation. A number of multiscale models have been developed to study the dynamics that emerge from the coupling between the intracellular, cellular and tissue scales. Here, we develop a continuum partial differential equation model to capture the dynamics of a particular multiscale model (a hybrid cellular automaton with discrete cells, diffusible factors and an explicit vascular network). The purpose is to test under which circumstances such a continuum model gives equivalent predictions to the original multiscale model, in the knowledge that the system details are known, and differences in model results can be explained in terms of model features (rather than unknown experimental confounding factors). The continuum model qualitatively replicates the dynamics from the multiscale model, with certain discrepancies observed owing to the differences in the modelling of certain processes. The continuum model admits travelling wave solutions for normal tissue growth and tumour invasion, with similar behaviour observed in the multiscale model. However, the continuum model enables us to analyse the spatially homogeneous steady states of the system, and hence to analyse these waves in more detail. We show that the tumour microenvironmental effects from the multiscale model mean that tumour invasion exhibits a so-called pushed wave when the carrying capacity for tumour cell proliferation is less than the total cell density at the tumour wave front. These pushed waves of tumour invasion propagate by triggering apoptosis of normal cells at the wave front. Otherwise, numerical evidence suggests that the wave speed can be predicted from linear analysis about the normal tissue steady state.     

Direct competition results from strong competition for limited resource

We study a model of competition for resource through a chemostat-type model where species consume the common resource that is constantly supplied. We assume that the species and resources are characterized by a continuous trait. As already proved, this model, although more complicated than the usual Lotka–Volterra direct competition model, describes competitive interactions leading to concentrated distributions of species in continuous trait space. Here we assume a very fast dynamics for the supply of the resource and a fast dynamics for death and uptake rates. In this regime we show that factors that are independent of the resource competition become as important as the competition efficiency and that the direct competition model is a good approximation of the chemostat. Assuming these two timescales allows us to establish a mathematically rigorous proof showing that our resource-competition model with continuous traits converges to a direct competition model. We also show that the two timescales assumption is required to mathematically justify the corresponding classic result on a model consisting of only finite number of species and resources (MacArthur in, Theor Popul Biol 1:1–11, 1970). This is performed through asymptotic analysis, introducing different scales for the resource renewal rate and the uptake rate. The mathematical difficulty relies in a possible initial layer for the resource dynamics. The chemostat model comes with a global convex Lyapunov functional. We show that the particular form of the competition kernel derived from the uptake kernel, satisfies a positivity property which is known to be necessary for the direct competition model to enjoy the related Lyapunov functional.     

Closing the larval loop: linking larval ecology to the population dynamics of marine benthic invertebrates

The majority of marine benthic invertebrates exhibit a complex life cycle that includes separate planktonic larval, and bottom-dwelling juvenile and adult phases. To understand and predict changes in the spatial and temporal distributions, abundances, population growth rate, and population structure of a species with such a complex life cycle, it is necessary to understand the relative importance of the physical, chemical and biological properties and processes that affect individuals within both the planktonic and benthic phases. To accomplish this goal, it is necessary to study both phases within a common, quantitative framework defined in terms of some common currency. This can be done efficiently through construction and evaluation of a population dynamics model that describes the complete life cycle.

Two forms that such a model might assume are reviewed: a stage-based, population matrix model, and a model that specifies discrete stages of the population, on the bottom and in the water column, in terms of simultaneous differential equations that may be solved in both space and time. Terms to be incorporated in each type of model can be formulated to describe the critical properties and processes that can affect populations within each stage of the life cycle. For both types of model it is shown how this might be accomplished using an idealized balanomorph barnacle as an example species. The critical properties and processes that affect the planktonic and benthic phases are reviewed. For larvae, these include benthic adult fecundity and fertilization success, growth and larval stage duration, mortality, larval behavior, dispersal by currents and turbulence, and larval settlement. It is possible to predict or estimate empirically all of the key terms that should be built into the larval and benthic components of the model. Thus, the challenge of formulating and evaluating a full life cycle model is achievable. Development and evaluation of such a model will be challenging because of the diverse processes which must be considered, and because of the disparities in the spatial and temporal scales appropriate to the benthic and planktonic larval phases. In evaluating model predictions it is critical that sampling schemes be matched to the spatial and temporal scales of model resolution.     

A Model of a Segmental Oscillator in the Leech Heartbeat Neuronal Network

We modeled a segmental oscillator of the timing network that paces the heartbeat of the leech. This model represents a network of six heart interneurons that comprise the basic rhythm-generating network within a single ganglion. This model builds on a previous two cell model (Nadim et al., 1995) by incorporating modifications of intrinsic and synaptic currents based on the results of a realistic waveform voltage-clamp study (Olsen and Calabrese, 1996). Due to these modifications, the new model behaves more similarly to the biological system than the previous model. For example, the slow-wave oscillation of membrane potential that underlies bursting is similar in form and amplitude to that of the biological system. Furthermore, the new model with its expanded architecture demonstrates how coordinating interneurons contribute to the oscillations within a single ganglion, in addition to their role of intersegmental coordination.     

Probability of response models and DNA repair: a statistical-biological approach

This paper develops a simple statistical model, the weighted hazard model, which incorporates the toxicological idea of DNA repair and its role in chemical carcinogenesis. We restrict attention to a small segment of DNA that migrates in and out of the high risk states; it is shown that random hazard functions play an important role in the distributional properties of the time to first detectable tumor. Included in the many shapes of the weighted hazard model is one that has a shape in the low dose region similar to that of the probit model, a model that many toxicologists favor. The analyses of two data sets are presented and interpreted, and suggestions for further research are given.