Emergence of orientation-selective inhibition in the primary visual cortex: a Bayes–Markov computational model

The recent consensus is that virtually all aspects of response selectivity exhibited by the primary visual cortex are either created or sharpened by cortical inhibitory interneurons. Experimental studies have shown that there are cortical inhibitory cells that are driven by geniculate cells and that, like their cortical excitatory counterparts, are orientation selective, though less sharply tuned. The main goal of this article is to demonstrate how orientation-selective inhibition might be created by the circuitry of the primary visual cortex (striate cortex, V1) from its nonoriented geniculate inputs. To fulfill this goal, first, a Bayes–Markov computational model is developed for the V1 area dedicated to foveal vision. The developed model consists of three parts: (i) a two-layered hierarchical Markov random field that is assumed to generate the activity patterns of the geniculate and cortical inhibitory cells, (ii) a Bayesian computational goal that is formulated based on the maximum a posteriori (MAP) estimation principle, and (iii) an iterative, deterministic, parallel algorithm that leads the cortical circuitry to achieve its assigned computational goal. The developed model is not fully LGN driven and it is not implementable by the neural machinery of V1. The model, then, is transformed into a fully LGN-driven and physiologically plausible form. Computer simulation is used to demonstrate the performance of the developed models.     

Giant squid-hidden canard: the 3D geometry of the Hodgkin–Huxley model

This work is motivated by the observation of remarkably slow firing in the uncoupled Hodgkin-Huxley model, depending on parameters tau( h ), tau( n ) that scale the rates of change of the gating variables. After reducing the model to an appropriate nondimensionalized form featuring one fast and two slow variables, we use geometric singular perturbation theory to analyze the model's dynamics under systematic variation of the parameters tau( h ), tau( n ), and applied current I. As expected, we find that for fixed (tau( h ), tau( n )), the model undergoes a transition from excitable, with a stable resting equilibrium state, to oscillatory, featuring classical relaxation oscillations, as I increases. Interestingly, mixed-mode oscillations (MMO's), featuring slow action potential generation, arise for an intermediate range of I values, if tau( h ) or tau( n ) is sufficiently large. Our analysis explains in detail the geometric mechanisms underlying these results, which depend crucially on the presence of two slow variables, and allows for the quantitative estimation of transitional parameter values, in the singular limit. In particular, we show that the subthreshold oscillations in the observed MMO patterns arise through a generalized canard phenomenon. Finally, we discuss the relation of results obtained in the singular limit to the behavior observed away from, but near, this limit.     

A hybrid model of intercellular tension and cell–matrix mechanical interactions in a multicellular geometry

Biomechanics and Modeling in Mechanobiology - Epithelial cells form continuous sheets of cells that exist in tensional homeostasis. Homeostasis is maintained through cell-to-cell junctions that...     

Origins and suppression of oscillations in a computational model of Parkinson’s disease

Efficacy of deep brain stimulation (DBS) for motor signs of Parkinson’s disease (PD) depends in part on post-operative programming of stimulus parameters. There is a need for a systematic approach to tuning parameters based on patient physiology. We used a physiologically realistic computational model of the basal ganglia network to investigate the emergence of a 34 Hz oscillation in the PD state and its optimal suppression with DBS. Discrete time transfer functions were fit to post-stimulus time histograms (PSTHs) collected in open-loop, by simulating the pharmacological block of synaptic connections, to describe the behavior of the basal ganglia nuclei. These functions were then connected to create a mean-field model of the closed-loop system, which was analyzed to determine the origin of the emergent 34 Hz pathological oscillation. This analysis determined that the oscillation could emerge from the coupling between the globus pallidus external (GPe) and subthalamic nucleus (STN). When coupled, the two resonate with each other in the PD state but not in the healthy state. By characterizing how this oscillation is affected by subthreshold DBS pulses, we hypothesize that it is possible to predict stimulus frequencies capable of suppressing this oscillation. To characterize the response to the stimulus, we developed a new method for estimating phase response curves (PRCs) from population data. Using the population PRC we were able to predict frequencies that enhance and suppress the 34 Hz pathological oscillation. This provides a systematic approach to tuning DBS frequencies and could enable closed-loop tuning of stimulation parameters.     

A model of a MAPK•substrate complex in an active conformation: a computational and experimental approach

The mechanisms by which MAP kinases recognize and phosphorylate substrates are not completely understood. Efforts to understand the mechanisms have been compromised by the lack of MAPK-substrate structures. While MAPK-substrate docking is well established as a viable mechanism for bringing MAPKs and substrates into close proximity the molecular details of how such docking promotes phosphorylation is an unresolved issue. In the present study computer modeling approaches, with restraints derived from experimentally known interactions, were used to predict how the N-terminus of Ets-1 associates with ERK2. Interestingly, the N-terminus does not contain a consensus-docking site ((R/K)_2-3-X_2-6-Φ_A-X-Φ_B, where Φ is aliphatic hydrophobic) for ERK2. The modeling predicts that the N-terminus of Ets-1 makes important contributions to the stabilization of the complex, but remains largely disordered. The computer-generated model was used to guide mutagenesis experiments, which support the notion that Leu-11 and possibly Ile-13 and Ile-14 of Ets-1 1-138 (Ets) make contributions through binding to the hydrophobic groove of the ERK2 D-recruiting site (DRS). Based on the modeling, a consensus-docking site was introduced through the introduction of an arginine at residue 7, to give the consensus ⁷RK-X₂-Φ_A-X-Φ_B ¹³. This results in a 2-fold increase in k _cat/K _m for the phosphorylation of Ets by ERK2. Similarly, the substitution of the N-terminus for two different consensus docking sites derived from Elk-1 and MKK1 also improves k _cat/K _m by two-fold compared to Ets. Disruption of the N-terminal docking through deletion of residues 1-23 of Ets results in a 14-fold decrease in k _cat/K _m, with little apparent change in k _cat. A peptide that binds to the DRS of ERK2 affects K _m, but not k _cat. Our kinetic analysis suggests that the unstructured N-terminus provides 10-fold uniform stabilization of the ground state ERK2•Ets•MgATP complex and intermediates of the enzymatic reaction.     

A computational study of amoeboid motility in 3D: the role of extracellular matrix geometry,cell deformability,and cell–matrix adhesion

Biomechanics and Modeling in Mechanobiology - Amoeboid cells often migrate using pseudopods, which are membrane protrusions that grow, bifurcate, and retract dynamically, resulting in a net cell...     

A coarse-grain MD (molecular dynamic) simulation of PCL–PEG and PLA–PEG aggregation as a computational model for prediction of the drug-loading efficacy of doxorubicin

Abstract

Formulating a hydrophobic drug that is water-soluble is a pharmaceutical challenge. One way is to incorporate the drug in an amphiphilic micelle composed from an aggregation of block copolymers. Design of a good nano-micelle requires many trial-and-error attempts. In this article, we developed a computational model based on a coarse-grained molecular dynamic (MD) simulation and correlated outputs with previous studies. A good correlation shows that this model reliably simulates poly-lactic acid–poly-ethylene glycol (PLA–PEG) and poly-caprolactone (PCL)–PEG aggregation in water with and without the presence of doxorubicin.

Communicated by Ramaswamy H. Sarma     

Comparative chondrogenesis of human cells in a 3D integrated experimental–computational mechanobiology model

We present an integrated experimental–computational mechanobiology model of chondrogenesis. The response of human articular chondrocytes to culture medium perfusion, versus perfusion associated with cyclic pressurisation, versus non-perfused culture, was compared in a pellet culture model, and multiphysic computation was used to quantify oxygen transport and flow dynamics in the various culture conditions. At 2 weeks of culture, the measured cell metabolic activity and the matrix content in collagen type II and aggrecan were greatest in the perfused+pressurised pellets. The main effects of perfusion alone, relative to static controls, were to suppress collagen type I and GAG contents, which were greatest in the non-perfused pellets. All pellets showed a peripheral layer of proliferating cells, which was thickest in the perfused pellets, and most pellets showed internal gradients in cell density and matrix composition. In perfused pellets, the computed lowest oxygen concentration was 0.075 mM (7.5% tension), the maximal oxygen flux was 477.5 nmol/m²/s and the maximal fluid shear stress, acting on the pellet surface, was 1.8 mPa (0.018 dyn/cm²). In the non-perfused pellets, the lowest oxygen concentration was 0.003 mM (0.3% tension) and the maximal oxygen flux was 102.4 nmol/m²/s. A local correlation was observed, between the gradients in pellet properties obtained from histology, and the oxygen fields calculated with multiphysic simulation. Our results show up-regulation of hyaline matrix protein production by human chondrocytes in response to perfusion associated with cyclic pressurisation. These results could be favourably exploited in tissue engineering applications.     

Structure of the UreD–UreF–UreG–UreE complex in Helicobacter pylori: a model study

The molecular details of the protein complex formed by UreD, UreF, UreG, and UreE, accessory proteins for urease activation in the carcinogenic bacterium Helicobacter pylori, have been elucidated using computational modeling. The calculated structure of the complex supports the hypothesis of UreF acting as a GTPase activation protein that facilitates GTP hydrolysis by UreG during urease maturation, and provides a rationale for the design of new drugs against infections by ureolytic bacterial pathogens.     

Evolution of conditional dispersal: a reaction–diffusion–advection model

To study evolution of conditional dispersal, a Lotka-Volterra reaction-diffusion-advection model for two competing species in a heterogeneous environment is proposed and investigated. The two species are assumed to be identical except their dispersal strategies: both species disperse by random diffusion and advection along environmental gradients, but one species has stronger biased movement (i.e., advection along the environmental gradients) than the other one. It is shown that at least two scenarios can occur: if only one species has a strong tendency to move upward the environmental gradients, the two species can coexist since one species mainly pursues resources at places of locally most favorable environments while the other relies on resources from other parts of the habitat; if both species have such strong biased movements, it can lead to overcrowding of the whole population at places of locally most favorable environments, which causes the extinction of the species with stronger biased movement. These results provide a new mechanism for the coexistence of competing species, and they also imply that selection is against excessive advection along environmental gradients, and an intermediate biased movement rate may evolve.     

A fast computational model for circulatory dynamics: effects of left ventricle–aorta coupling

The course of diseases such as hypertension, systolic heart failure and heart failure with a preserved ejection fraction is affected by interactions between the left ventricle (LV) and the vasculature. To study these interactions, a computationally efficient, biophysically based mathematical model for the circulatory system is presented. In a four-chamber model of the heart, the LV is represented by a previously described low-order, wall volume-preserving model that includes torsion and base-to-apex and circumferential wall shortening and lengthening, and the other chambers are represented using spherical geometries. Active and passive myocardial mechanics of all four chambers are included. The cardiac model is coupled with a wave propagation model for the aorta and a closed lumped-parameter circulation model. Parameters for the normal heart and aorta are determined by fitting to experimental data. Changes in the timing and magnitude of pulse wave reflections by the aorta are demonstrated with changes in compliance and taper of the aorta as seen in aging (decreased compliance, increased diameter and length), and resulting effects on LV pressure–volume loops and LV fiber stress and sarcomere shortening are predicted. Effects of aging of the aorta combined with reduced LV contractile force (failing heart) are examined. In the failing heart, changes in aortic properties with aging affect stroke volume and sarcomere shortening without appreciable augmentation of aortic pressure, and the reflected pressure wave contributes an increased proportion of aortic pressure.

     

Which factors influence the ability of a computational model to predict the in vivo deformation behaviour of skeletal muscle?

Deep tissue injury (DTI) is a severe form of pressure ulcer where tissue damage starts in deep tissues underneath intact skin. Tissue deformation may play an important role in the aetiology, which can be investigated using an experimental–numerical approach. Recently, an animal-specific finite element model has been developed to simulate experiments in which muscle tissue was compressed with an indenter. In this study, the material behaviour and boundary conditions were adapted to improve the agreement between model and experiment and to investigate the influence of these adaptations on the predicted strain distribution. The use of a highly nonlinear material law and including friction between the indenter and the muscle both improved the quality of the model and considerably influenced the estimated strain distribution. With the improved model, the required sample size to detect significant differences between loading conditions can be diminished, which is clearly relevant in experiments involving animals.     

On a biophysical and mathematical model of Pgp-mediated multidrug resistance: understanding the “space–time” dimension of MDR

Multidrug resistance (MDR) is explained by drug transporters with a drug-handling activity. Despite much work, MDR remains multifaceted, and several conditions are required to generate drug resistance. The drug pumping was conceptually described using a kinetic, i.e., temporal, approach. The re-emergence of physical biology has allowed us to take into account new parameters focusing on the notion of space. This, in turn, has given us important clues regarding the process whereby drug and transporter interact. We will demonstrate that the likelihood of drug-transporter meeting (i.e., the affinity) and thus interaction are also driven by the mechanical interaction between drug molecular weight (MW) and the membrane mechanical properties. This should allow us to mechanically control drug delivery.     

Anhydrobiosis: the model worm as a model?

New work now shows that the dauer larvae of Caenorhabditis elegans can survive anhydrobiotically. The genetic tractability of this model organism may be useful in studying how organisms survive when losing most or all of their water.     

The dynamics of the lynx–hare system: an application of the Lotka–Volterra model

The Lotka–Volterra model of predator–prey dynamics was used for approximation of the wellknown empirical time series on the lynx–hare system in Canada that was collected by the Hudson Bay Company in 1845–1935. The model was assumed to demonstrate satisfactory data approximation if the sets of deviations of the model and empirical data for both time series satisfied a number of statistical criteria (for the selected significance level). The frequency distributions of deviations between the theoretical (model) trajectories and empirical datasets were tested for symmetry (with respect to the Y-axis; the Kolmogorov–Smirnov and Lehmann–Rosenblatt tests) and the presence or absence of serial correlation (the Swed–Eisenhart and “jumps up–jumps down” tests). The numerical calculations show that the set of points of the space of model parameters, when the deviations satisfy the statistical criteria, is not empty and, consequently, the model is suitable for describing empirical data.     

Mechanobiology of soft skeletal tissue differentiation—a computational approach of a fiber-reinforced poroelastic model based on homogeneous and isotropic simplifications

The material properties of multipotent mesenchymal tissue change dramatically during the differentiation process associated with skeletal regeneration. Using a mechanobiological tissue differentiation concept, and homogeneous and isotropic simplifications of a fiber-reinforced poroelastic model of soft skeletal tissues, we have developed a mathematical approach for describing time-dependent material property changes during the formation of cartilage, fibrocartilage, and fibrous tissue under various loading histories. In this approach, intermittently imposed fluid pressure and tensile strain regulate proteoglycan synthesis and collagen fibrillogenesis, assembly, cross-linking, and alignment to cause changes in tissue permeability (k), compressive aggregate modulus (H_A), and tensile elastic modulus (E). In our isotropic model, k represents the permeability in the least permeable direction (perpendicular to the fibers) and E represents the tensile elastic modulus in the stiffest direction (parallel to the fibers). Cyclic fluid pressure causes an increase in proteoglycan synthesis, resulting in a decrease in k and increase in H_A caused by the hydrophilic nature and large size of the aggregating proteoglycans. It further causes a slight increase in E owing to the stiffness added by newly synthesized type II collagen. Tensile strain increases the density, size, alignment, and cross-linking of collagen fibers thereby increasing E while also decreasing k as a result of an increased flow path length. The Poisson's ratio of the solid matrix, _s, is assumed to remain constant (near zero) for all soft tissues. Implementing a computer algorithm based on these concepts, we simulate progressive changes in material properties for differentiating tissues. Beginning with initial values of E=0.05 MPa, H_A=0 MPa, and k=1×10^–13 m⁴/Ns for multipotent mesenchymal tissue, we predict final values of E=11 MPa, H_A=1 MPa, and k=4.8×10^–15 m⁴/Ns for articular cartilage, E=339 MPa, H_A=1 MPa, and k=9.5×10^–16 m⁴/Ns for fibrocartilage, and E=1,000 MPa, H_A=0 MPa, and k=7.5×10^–16 m⁴/Ns for fibrous tissue. These final values are consistent with the values reported by other investigators and the time-dependent acquisition of these values is consistent with current knowledge of the differentiation process.     

Do cortical maps depend on the timing of sensory input? Experimental evidence and computational model

Fast adaptations in the functional organization of primary sensory cortex are generally assumed to result from changes of network connectivity. However, the effects of intrinsic neuronal excitability alterations due to the activation of neighboring cortical representational zones, which might as well account for the changes of cortical representative maps, have been paid little attention to. In a recent experiment (Braun et al. 2000b) we showed by neuromagnetic source imaging that random or fixed sequence stimulation of three digits of both hands led to stimulation-timing-induced changes in primary somatosensory (SI) cortical maps. The distance between the cortical representation of thumb and middle finger became significantly shorter during the fixed sequence stimulation. The analysis on the time course of the cortical map changes revealed that these reorganizations occurred within minutes and were fully reversible. The previously reported results were interpreted as the involvement of a superordinate center responsible for detecting and activating the appropriate maps. Here we present an alternative parsimonious explanation that is supported by a computational model. Based on the experimental evidence, we developed a simple model that took intrinsic neuronal excitability together with subthreshold activation into account and assumed partial cortical overlap of the representational zones of neighboring digits. Furthermore, in the model the neuronal excitability decayed slowly with respect to the stimulation frequency. The observed cortical map changes in the experiment could be reproduced by the two-layer feed-forward computational network. Our model thus suggests that the dynamic shifts of cortical maps can be explained by the state and time course of intrinsic neuronal excitability and subthreshold activation, without involving changes in network connectivity.     

Analysis and forecasting of airborne pollen–induced symptoms with the aid of computational intelligence methods

Allergies due to airborne pollen affect a considerable percentage of Europeans; thus, the provision of health-related information services concerning pollen-induced symptoms can improve the overall quality of life. In this paper, we demonstrate the development of personalized, health-related, quality-of-life information services by adopting a data-driven approach. The data we use consist of allergic symptoms reported by people as well as detailed pollen count information of the most allergenic taxa. We apply computational intelligence methods in order to analyze symptoms, identify possible interrelationships with several pollen taxa and develop models that associate pollen count levels with allergic symptoms on a personal level. The results for the case of Austria show that this approach can lead to accurate personalized symptom forecasting models; we report an average correlation coefficient of r = 0.70 for a sample of 102 users of the Patients Hayfever Diary. We conclude that some of these models could serve as the basis for personalized health information services.     

A decision-making Fokker–Planck model in computational neuroscience

In computational neuroscience, decision-making may be explained analyzing models based on the evolution of the average firing rates of two interacting neuron populations, e.g., in bistable visual perception problems. These models typically lead to a multi-stable scenario for the concerned dynamical systems. Nevertheless, noise is an important feature of the model taking into account both the finite-size effects and the decision’s robustness. These stochastic dynamical systems can be analyzed by studying carefully their associated Fokker–Planck partial differential equation. In particular, in the Fokker–Planck setting, we analytically discuss the asymptotic behavior for large times towards a unique probability distribution, and we propose a numerical scheme capturing this convergence. These simulations are used to validate deterministic moment methods recently applied to the stochastic differential system. Further, proving the existence, positivity and uniqueness of the probability density solution for the stationary equation, as well as for the time evolving problem, we show that this stabilization does happen. Finally, we discuss the convergence of the solution for large times to the stationary state. Our approach leads to a more detailed analytical and numerical study of decision-making models applied in computational neuroscience.     

On the accuracy of a diffusion approximation to a discrete state–space Markovian model of a population

The traditional Kolmogorov equations treat the size of a population as a discrete random variable. A model is introduced that extends these equations to incorporate environmental variability. Difficulties with this discrete model motivate approximating the population size as a continuous random variable through the use of diffusion processes. The set of cumulants for both the population size and the environmental factors affecting the population size characterize the population–environmental system. The evolution of this set, as predicted by the diffusion approximation, closely matches the corresponding predictions for the discrete model. It is also noted that the simulation estimates of the cumulants against which the predictions of the diffusion model are checked can vary considerably between simulations — despite averaging over a large number of simulation runs. The precision of the simulation estimates–both over time and with differing cumulant order–is discussed.