A computational model for cell differentiation

In this paper, we present a word set generating mechanism, called cell-differentiation system, inspired by the tissue process formation in multicellular organisms, which might model some properties of evolving communities of living cells at the syntactical level. The tools utilized to model these biological phenomena belong to the formal language theory. In this context chromosomal mutations are defined as operations on strings and the differentiation according to the control of gene expression is represented by some random-context conditions in formal languages.In the presented formal framework we prove that in a simplified form of this formalism, with only one cell-type which is regular, one single cell and no mitosis involved, the problem of establishing whether or not the set of vectors of integers indicating the number of cells in each population, is finite, linear or semilinear, is recursively undecidable. However, one can algorithmically decide whether or not a cell-differentiation system of finite cell-type can produce a specific generation of cells.     

A computational model for feature binding

The "Binding Problem" is an important problem across many disciplines, including psychology, neuroscience, computational modeling, and even philosophy. In this work, we proposed a novel computational model, Bayesian Linking Field Model, for feature binding in visual perception, by combining the idea of noisy neuron model, Bayesian method, Linking Field Network and competitive mechanism. Simulation Experiments demonstrated that our model perfectly fulfilled the task of feature binding in visual perception and provided us some enlightening idea for future research.     

A mathematical model for dorsal closure

During embryogenesis, drosophila embryos undergo epithelial folding and unfolding, which leads to a hole in the dorsal epidermis, transiently covered by an extraembryonic tissue called the amnioserosa. Dorsal closure (DC) consists of the migration of lateral epidermis towards the midline, covering the amnioserosa. It has been extensively studied since numerous physical mechanisms and signaling pathways present in DC are conserved in other morphogenetic events and wound healing in many other species (including vertebrates).We present here a simple mathematical model for DC that involves a reduced number of parameters directly linked to the intensity of the forces in the presence and which is applicable to a wide range of geometries of the leading edge (LE). This model is a natural generalization of the very interesting model proposed in Hutson et al. (2003). Being based on an ordinary differential equation (ODE) approach, the previous model had the advantage of being even simpler, but this restricted significantly the variety of geometries that could be considered and thus the number of modified dorsal closures that could be studied.A partial differential equation (PDE) approach, as the one developed here, allows considering much more general situations that show up in genetically or physically perturbed embryos and whose study will be essential for a proper understanding of the different components of the DC process. Even for native embryos, our model has the advantage of being applicable since an early stages of DC when there is no antero-posterior symmetry (approximately verified only in the late phases of DC).We validate our model in a native setting and also test it further in embryos where the zipping force is perturbed through the expression of spastin (a microtubule severing protein). We obtain variations of the force coefficients that are consistent with what was previously described for this setting.     

A computational model for telomere-dependent cell-replicative aging

Telomere shortening provides a molecular basis for the Hayflick limit. Recent data suggest that telomere shortening also influence mitotic rate. We propose a stochastic growth model of this phenomena, assuming that cell division in each time interval is a random process which probability decreases linearly with telomere shortening. Computer simulations of the proposed stochastic telomere-regulated model provides good approximation of the qualitative growth of cultured human mesenchymal stem cells.     

A morphoelastic model for dermal wound closure

We develop a model of wound healing in the framework of finite elasticity, focussing our attention on the processes of growth and contraction in the dermal layer of the skin. The dermal tissue is treated as a hyperelastic cylinder that surrounds the wound and is subject to symmetric deformations. By considering the initial recoil that is observed upon the application of a circular wound, we estimate the degree of residual tension in the skin and build an evolution law for mechanosensitive growth of the dermal tissue. Contraction of the wound is governed by a phenomenological law in which radial pressure is prescribed at the wound edge. The model reproduces three main phases of the healing process. Initially, the wound recoils due to residual stress in the surrounding tissue; the wound then heals as a result of contraction and growth; and finally, healing slows as contraction and growth decrease. Over a longer time period, the surrounding tissue remodels, returning to the residually stressed state. We identify the steady state growth profile associated with this remodelled state. The model is then used to predict the outcome of rewounding experiments designed to quantify the amount of stress in the tissue, and also to simulate the application of pressure treatments.     

A hybrid computational model for collective cell durotaxis

Collective cell migration is regulated by a complex set of mechanical interactions and cellular mechanisms. Collective migration emerges from mechanisms occurring at single cell level, involving processes like contraction, polymerization and depolymerization, of cell–cell interactions and of cell–substrate adhesion. Here, we present a computational framework which simulates the dynamics of this emergent behavior conditioned by substrates with stiffness gradients. The computational model reproduces the cell’s ability to move toward the stiffer part of the substrate, process known as durotaxis. It combines the continuous formulation of truss elements and a particle-based approach to simulate the dynamics of cell–matrix adhesions and cell–cell interactions. Using this hybrid approach, researchers can quickly create a quantitative model to understand the regulatory role of different mechanical conditions on the dynamics of collective cell migration. Our model shows that durotaxis occurs due to the ability of cells to deform the substrate more in the part of lower stiffness than in the stiffer part. This effect explains why cell collective movement is more effective than single cell movement in stiffness gradient conditions. In addition, we numerically evaluate how gradient stiffness properties, cell monolayer size and force transmission between cells and extracellular matrix are crucial in regulating durotaxis.     

A computational model for populations of dividing cells.

A mathematical model of the cell movements due to cell division is presented. In the model we assume that every cell is a computational object with a given volume, and that the cell pushes the neighbouring cells in order to acquire the space for this volume. The Force that each cell exerts over the other cells is derived from a harmonic arbitrary Potential. The main parameter of the model is the average distance among the cells, that checks if the system is in spatial equilibrium or not. We show that just changing the physical constraints we can model two different systems, a two-dimensional culture on a plate and a three-dimensional early embryo. In both cases the patterns of the cell populations we obtain are similar to the real ones.     

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.     

A computational model of visual anisotropy

Visual anisotropy has been demonstrated in multiple tasks where performance differs between vertical, horizontal, and oblique orientations of the stimuli. We explain some principles of visual anisotropy by anisotropic smoothing, which is based on a variation on Koenderink's approach in [1]. We tested the theory by presenting gaussian elongated luminance profiles and measuring the perceived orientations by means of an adjustment task. Our framework is based on the smoothing of the image with elliptical gaussian kernels and it correctly predicted an illusory orientation bias towards the vertical axis. We discuss the scope of the theory in the context of other anisotropies in perception.     

A goodness-of-fit test for capture-recapture model Mt under closure

A new, fully efficient goodness-of-fit test for the time-specific closed-population capture-recapture model Mt is presented. This test is based on the residual distribution of the capture history data given the maximum likelihood parameter estimates under model Mt, is partitioned into informative components, and is based on chi-square statistics. Comparison of this test with Leslie's test (Leslie, 1958, Journal of Animal Ecology 27, 84-86) for model Mt, using Monte Carlo simulations, shows the new test generally outperforms Leslie's test. The new test is frequently computable when Leslie's test is not, has Type I error rates that are closer to nominal error rates than Leslie's test, and is sensitive to behavioral variation and heterogeneity in capture probabilities. Leslie's test is not sensitive to behavioral variation in capture probabilities but, when computable, has greater power to detect heterogeneity than the new test.     

A path-based computational model for long non-coding RNA-protein interaction prediction

Recently, lncRNAs have attracted accumulating attentions because more and more experimental researches have shown lncRNA can play critical roles in many biological processes. Predicting potential interactions between lncRNAs and proteins are key to understand the lncRNAs biological functions. But traditional biological experiments are expensive and time-consuming, network similarity methods provide a powerful solution to computationally predict lncRNA-protein interactions. In this work, a novel path-based lncRNA-protein interaction (PBLPI) prediction model is proposed by integrating protein semantic similarity, lncRNA functional similarity, known human lncRNA-protein interactions, and Gaussian interaction profile kernel similarity. PBLPI model utilizes three interlinked sub-graphs to construct a heterogeneous graph, and then infers potential lncRNA-protein interactions through depth-first search algorithm. Consequently, PBLPI achieves reliable performance in the frameworks of 5-fold cross validation (average AUC is 0.9244 and AUPR is 0.6478). In the case study, we use “Mus musculus” data to further validate the reliability of PBLPI method. It is anticipated that PBLPI would become a useful tool to identify potential lncRNA-protein interactions.     

A computational model for dynamic analysis of the human gait

Biomechanical models are important tools in the study of human motion. This work proposes a computational model to analyse the dynamics of lower limb motion using a kinematic chain to represent the body segments and rotational joints linked by viscoelastic elements. The model uses anthropometric parameters, ground reaction forces and joint Cardan angles from subjects to analyse lower limb motion during the gait. The model allows evaluating these data in each body plane. Six healthy subjects walked on a treadmill to record the kinematic and kinetic data. In addition, anthropometric parameters were recorded to construct the model. The viscoelastic parameter values were fitted for the model joints (hip, knee and ankle). The proposed model demonstrated that manipulating the viscoelastic parameters between the body segments could fit the amplitudes and frequencies of motion. The data collected in this work have viscoelastic parameter values that follow a normal distribution, indicating that these values are directly related to the gait pattern. To validate the model, we used the values of the joint angles to perform a comparison between the model results and previously published data. The model results show a same pattern and range of values found in the literature for the human gait motion.     

A real-time computational model for estimating kinematics of ankle ligaments

Background: An accurate assessment of ankle ligament kinematics is crucial in understanding the injury mechanisms and can help to improve the treatment of an injured ankle, especially when used in conjunction with robot-assisted therapy. A number of computational models have been developed and validated for assessing the kinematics of ankle ligaments. However, few of them can do real-time assessment to allow for an input into robotic rehabilitation programs. Method: An ankle computational model was proposed and validated to quantify the kinematics of ankle ligaments as the foot moves in real-time. This model consists of three bone segments with three rotational degrees of freedom (DOFs) and 12 ankle ligaments. This model uses inputs for three position variables that can be measured from sensors in many ankle robotic devices that detect postures within the foot–ankle environment and outputs the kinematics of ankle ligaments. Validation of this model in terms of ligament length and strain was conducted by comparing it with published data on cadaver anatomy and magnetic resonance imaging. Results: The model based on ligament lengths and strains is in concurrence with those from the published studies but is sensitive to ligament attachment positions. Conclusions: This ankle computational model has the potential to be used in robot-assisted therapy for real-time assessment of ligament kinematics. The results provide information regarding the quantification of kinematics associated with ankle ligaments related to the disability level and can be used for optimizing the robotic training trajectory.     

A computational model for the neurobiological substrates of visual attention

Two interesting and complex tasks are performed by the brain in the process of perception: the integration of characteristics leading to an easier recognition of a pattern as a whole (binding), and the extraction of properties that need to be detailed and analyzed (attention). Attention seems to have a reciprocal relation with binding, inasmuch as the latter promotes the composition of features and their dependencies, while the former selects a single characteristic independently of the remainder. Classically, binding is viewed as a process whereby sets of properties are gathered in representative entities, which are themselves linked to form higher level structures, in a sequence that culminates in the total integration of the pattern features in a localized construct. The convergent axonal projections from one cortical area to another would be the neurobiological mechanism through which binding is achieved. Attention comprises the selective excitation of neuronal networks or pathways that stand for specific pattern properties. The thalamus and its reticular nucleus would then be the anatomical substrate of the attentional focus. In this paper we propose a computational model aiming at bringing together the main (and apparently diverging) ideas about binding and attention. Based on experimental data, a neuronal network representing cortical pyramidal cells is assembled, and its structure and function are related to the binding and attention phenomena. Actually, the convergent projections that enlarge the visual receptive field are associated to binding, while a specific change in the pyramidal cell behavior is responsible for attention. Computer simulations are shown which reproduce the electrophysiology of pyramidal cells and mimic some interesting experimental results in visual attention. We conclude by conjecturing that attention is a driven interruption in the regular process of binding.     

A computational model of chemotaxis-based cell aggregation

We present a computational model that successfully captures the cell behaviors that play important roles in 2-D cell aggregation. A virtual cell in our model is designed as an independent, discrete unit with a set of parameters and actions. Each cell is defined by its location, size, rates of chemoattractant emission and response, age, life cycle stage, proliferation rate and number of attached cells. All cells are capable of emitting and sensing a chemoattractant chemical, moving, attaching to other cells, dividing, aging and dying. We validated and fine-tuned our in silico model by comparing simulated 24-h aggregation experiments with data derived from in vitro experiments using PC12 pheochromocytoma cells. Quantitative comparisons of the aggregate size distributions from the two experiments are produced using the Earth Mover's Distance (EMD) metric. We compared the two size distributions produced after 24 h of in vitro cell aggregation and the corresponding computer simulated process. Iteratively modifying the model's parameter values and measuring the difference between the in silico and in vitro results allow us to determine the optimal values that produce simulated aggregation outcomes closely matched to the PC12 experiments. Simulation results demonstrate the ability of the model to recreate large-scale aggregation behaviors seen in live cell experiments.     

A computational model of transmembrane integrin clustering

The presented work describes a structural model for integrin homooligomerization, focusing on the transmembrane domains. The two noncovalently linked integrin subunits, alpha and beta, were previously shown to homodimerize or homotrimerize, respectively. Our work is based on published mutational work that induced homotrimerization of beta3 integrins. The mutations provided structural restraints for the creation of a structural model of the beta3 homotrimer by a computational search of the conformational space of homomeric interactions of the beta3 integrin. Additionally, we explored possible conformations of the alphaIIb integrin homodimer, for which no unique solution was found. Two possible models of signal transduction, involving two different alphaIIb conformations, are discussed. One of the possible homodimeric alphaIIb conformations is GpA like, which is in line with experimental evidence. Based on our here-presented structural models and on recent experiments, we will argue that most probably the heteromeric alpha/beta transmembrane complex separates in the course of clustering.     

A computational model of the human thyroid

The thyroid, the largest gland in the endocrine system, secretes hormones that help promote bodily growth and development. This gland regulates hormonal secretion rate in spite of changes in dietary iodine which is a key ingredient in the hormone's biosynthesis. The thyroid relies on several feedback mechanisms for this regulation, and in this paper we use recent molecular-level and clinical observations to engineer a computational thyroid model. We use simulation and analysis to show that this models captures known aspects of thyroid physiology. We identify features in the model that are responsible for hormonal regulation, and use the model to identify and evaluate competing hypotheses associated with Wolff-Chaikoff escape.