Computational model for autophagic vesicle dynamics in single cells

Macroautophagy (autophagy) is a cellular recycling program essential for homeostasis and survival during cytotoxic stress. This process, which has an emerging role in disease etiology and treatment, is executed in four stages through the coordinated action of more than 30 proteins. An effective strategy for studying complicated cellular processes, such as autophagy, involves the construction and analysis of mathematical or computational models. When developed and refined from experimental knowledge, these models can be used to interrogate signaling pathways, formulate novel hypotheses about systems, and make predictions about cell signaling changes induced by specific interventions. Here, we present the development of a computational model describing autophagic vesicle dynamics in a mammalian system. We used time-resolved, live-cell microscopy to measure the synthesis and turnover of autophagic vesicles in single cells. The stochastically simulated model was consistent with data acquired during conditions of both basal and chemically-induced autophagy. The model was tested by genetic modulation of autophagic machinery and found to accurately predict vesicle dynamics observed experimentally. Furthermore, the model generated an unforeseen prediction about vesicle size that is consistent with both published findings and our experimental observations. Taken together, this model is accurate and useful and can serve as the foundation for future efforts aimed at quantitative characterization of autophagy.     

Computational models of grid cells

Grid cells are space-modulated neurons with periodic firing fields. In moving animals, the multiple firing fields of an individual grid cell form a triangular pattern tiling the entire space available to the animal. Collectively, grid cells are thought to provide a context-independent metric representation of the local environment. Since the discovery of grid cells in 2005, a number of models have been proposed to explain the formation of spatially repetitive firing patterns as well as the conversion of these signals to place signals one synapse downstream in the hippocampus. The present article reviews the most recent developments in our understanding of how grid patterns are generated, maintained, and transformed, with particular emphasis on second-generation computational models that have emerged during the past 2-3 years in response to criticism and new data.     

Computational mechanical model studies on the spontaneous emergent morphogenesis of the cultured endothelial cells

To address questions concerning why and how the morphology of endothelial cells (ECs) forms under shear stress loading, a computational fluid dynamics (CFD) three-dimensional (3D) model of ECs simulating cell shape was designed. A full 3D non-linear CFD simulation was conducted to estimate the wall shear stress (WSS) distribution. The model cell was capable of random rotation, deformation, migration, and proliferation. Flow was computed after each update of the cell shape with infinitesimal configuration changes. After a finite interval of the flow computation, only the infinitesimal configuration changes that reduced the WSS were allowed to accumulate. As a result of the very long free-run computation experiment, starting with a sub-confluent pattern of cells, the model cells became confluent and were elongated and aligned, with a shape index (SI) very close to that reported for cells in vivo. The average WSS converged to the lowest value at the same time.     

A predictive model for the selective accumulation of chemicals in tumor cells

Cationic lipophilic dyes can accumulate in mitochondria, and especially in mitochondria of tumor cells. We investigated the chemical properties and the processes allowing selective uptake into tumor cells using the Fick–Nernst–Planck equation. The model simulates uptake into cytoplasm and mitochondria and is valid for neutral molecules and ions, and thus also for weak electrolytes. The differential equation system was analytically solved for the steady-state and the dynamic case. The parameterization was for a generic human cell, with a 60 mV more negative potential at the inner mitochondrial membrane of generic tumor cells. The chemical input data were the lipophilicity (logK_OW), the acid/base dissociation constant (pK_a) and the electric charge (z). Accumulation in mitochondria occurred for polar acids with pK_a between 5 and 9 owing to the ion trap, and for lipophilic bases with pK_a>11 or permanent cations owing to electrical attraction. Selective accumulation in tumor cells was found for monovalent cations or strong bases with logK_OW of the cation between –2 and 2, with the optimum near 0. The results are in agreement with experimental results for rhodamine 123, a series of cationic triarylmethane dyes, F16 and MKT-077, an anticancer drug targeting tumor mitochondria.     

Computational model for monitoring cholesterol metabolism

A non-deterministic finite automaton is designed to observe the cholesterol metabolism with the states of acceptance and rejection. The acceptance state of the automaton depicts the normal level of metabolism and production of good cholesterol as an end product. The rejection state of this machine shows the inhibition of enzymatic activity in cholesterol synthesis and removal of free fatty acids. The deficiency in human cholesterol metabolism pathway results in abnormal accumulation of cholesterol in plasma, arterial tissues leading to diseases such as hypercholesterolemia, atherosclerosis respectively and formation of gallstones. The designed machine can be used to monitor the cholesterol metabolism at molecular level through regulation of enzymes involved in the biosynthesis and metabolism of cholesterol for the treatment of diseases incident due to the respective metabolic disorder. In addition, an algorithm for this machine has been developed to compare the programmed string with the given string. This study demonstrates the construction of a machine that is used for the development of molecular targeted therapy for the disorders in cholesterol metabolism.     

Cinnamides as selective small-molecule inhibitors of a cellular model of breast cancer stem cells

A high-throughput screen (HTS) was conducted against stably propagated cancer stem cell (CSC)-enriched populations using a library of 300,718 compounds from the National Institutes of Health (NIH) Molecular Libraries Small Molecule Repository (MLSMR). A cinnamide analog displayed greater than 20-fold selective inhibition of the breast CSC-like cell line (HMLE_sh_Ecad) over the isogenic control cell line (HMLE_sh_eGFP). Herein, we report structure–activity relationships of this class of cinnamides for selective lethality towards CSC-enriched populations.     

Computational model of flow-tissue interactions in intussusceptive angiogenesis

Angiogenesis, the growth of vascular structures, is a complex biological process which has long puzzled scientists. Better physiological understanding of this phenomenon could result in many useful medical applications such as the development of new methods for cancer therapy. We report on the development of a simple computational model of micro-vascular structure formation in intussusceptive angiogenesis observed in vivo. The tissue is represented by a discrete set of basic structural entities and flow conditions within the resulting domain are obtained by solving the Navier-Stokes equations. The tissue is then remodelled according to the tangential shear stress while approximating advection by means of simple non-diffusive heuristics. The updated tissue geometry then becomes the input for the next remodelling step. The model, consisting of steady-state flow and a simple mechanistic tissue response, successfully predicts bifurcation formation and micro-vessel separation in a porous cellular medium. This opens new modelling possibilities in computational studies of the cellular transport involved in micro-vascular growth.     

Computational model for perception of objects and motions

Perception of objects and motions in the visual scene is one of the basic problems in the visual system. There exist ‘What’ and ‘Where’ pathways in the superior visual cortex, starting from the simple cells in the primary visual cortex. The former is able to perceive objects such as forms, color, and texture, and the latter perceives ‘where’, for example, velocity and direction of spatial movement of objects. This paper explores brain-like computational architectures of visual information processing. We propose a visual perceptual model and computational mechanism for training the perceptual model. The computational model is a three-layer network. The first layer is the input layer which is used to receive the stimuli from natural environments. The second layer is designed for representing the internal neural information. The connections between the first layer and the second layer, called the receptive fields of neurons, are self-adaptively learned based on principle of sparse neural representation. To this end, we introduce Kullback-Leibler divergence as the measure of independence between neural responses and derive the learning algorithm based on minimizing the cost function. The proposed algorithm is applied to train the basis functions, namely receptive fields, which are localized, oriented, and bandpassed. The resultant receptive fields of neurons in the second layer have the characteristics resembling that of simple cells in the primary visual cortex. Based on these basis functions, we further construct the third layer for perception of what and where in the superior visual cortex. The proposed model is able to perceive objects and their motions with a high accuracy and strong robustness against additive noise. Computer simulation results in the final section show the feasibility of the proposed perceptual model and high efficiency of the learning algorithm.     

Computational model of motor learning and perceptual change

Motor learning in the context of arm reaching movements has been frequently investigated using the paradigm of force-field learning. It has been recently shown that changes to somatosensory perception are likewise associated with motor learning. Changes in perceptual function may be the reason that when the perturbation is removed following motor learning, the hand trajectory does not return to a straight line path even after several dozen trials. To explain the computational mechanisms that produce these characteristics, we propose a motor control and learning scheme using a simplified two-link system in the horizontal plane: We represent learning as the adjustment of desired joint-angular trajectories so as to achieve the reference trajectory of the hand. The convergence of the actual hand movement to the reference trajectory is proved by using a Lyapunov-like lemma, and the result is confirmed using computer simulations. The model assumes that changes in the desired hand trajectory influence the perception of hand position and this in turn affects movement control. Our computer simulations support the idea that perceptual change may come as a result of adjustments to movement planning with motor learning.     

A mathematical model for selective differentiation of neural progenitor cells on micropatterned polymer substrates

The biological hypothesis that the astrocyte-secreted cytokine, interleukin-6 (IL6), stimulates differentiation of adult rat hippocampal progenitor cells (AHPCs) is considered from a mathematical perspective. The proposed mathematical model includes two different mechanisms for stimulation and is based on mass-action kinetics. Both biological mechanisms involve sequential binding, with one pathway solely utilizing surface receptors while the other pathway also involves soluble receptors. Choosing biologically-reasonable values for parameters, simulations of the mathematical model show good agreement with experimental results. A global sensitivity analysis is also conducted to determine both the most influential and non-influential parameters on cellular differentiation, providing additional insights into the biological mechanisms.     

Computational model of the fluid dynamics in systemic-to-pulmonary shunts

A systemic-to-pulmonary shunt is a connection created between the systemic and pulmonary arterial circulations in order to improve pulmonary perfusion in children with congenital heart diseases. Knowledge of the relationship between pressure and flow in this new, surgically created, cardiovascular district may be helpful in the clinical management of these patients, whose survival is critically dependent on the blood flow distribution between the pulmonary and systemic circulations. In this study a group of three-dimensional computational models of the shunt have been investigated under steady-state and pulsatile conditions by means of a finite element analysis. The model is used to quantify the effects of shunt diameter (D), curvature, angle, and pulsatility on the pressure-flow (DeltaP-Q) relationship of the shunt. Size of the shunt is the main regulator of pressure-flow relationship. Innominate arterial diameter and angles of insertion have less influence. Curvature of the shunt results in lower pressure drops. Inertial effects can be neglected. The following simplified formulae are derived: DeltaP=(0. 097Q+0.521Q(2))/D(4) and DeltaP=(0.096Q+0.393Q(2))/D(4) for the different shunt geometries investigated (straight and curved shunts, respectively).     

Computational model for cell migration in three-dimensional matrices

Although computational models for cell migration on two-dimensional (2D) substrata have described how various molecular and cellular properties and physiochemical processes are integrated to accomplish cell locomotion, the same issues, along with certain new ones, might contribute differently to a model for migration within three-dimensional (3D) matrices. To address this more complicated situation, we have developed a computational model for cell migration in 3D matrices using a force-based dynamics approach. This model determines an overall locomotion velocity vector, comprising speed and direction, for individual cells based on internally generated forces transmitted into external traction forces and considering a timescale during which multiple attachment and detachment events are integrated. Key parameters characterize cell and matrix properties, including cell/matrix adhesion and mechanical and steric properties of the matrix; critical underlying molecular properties are incorporated explicitly or implicitly. Model predictions agree well with experimental results for the limiting case of migration on 2D substrata as well as with recent experiments in 3D natural tissues and synthetic gels. Certain predicted features such as biphasic behavior of speed with density of matrix ligands for 3D migration are qualitatively similar to their 2D counterparts, but new effects generally absent in 2D systems, such as effects due to matrix sterics and mechanics, are now predicted to arise in many 3D situations. As one particular sample manifestation of these effects, the optimal levels of cell receptor expression and matrix ligand density yielding maximal migration are dependent on matrix mechanical compliance.     

A model of selective processing of auditory-nerve inputs by stellate cells of the antero-ventral cochlear nucleus

Stellate cells in the cat antero-ventral cochlear nucleus (AVCN) maintain a robust rate-place representation of vowel spectra over a wide range of stimulus levels. This rate-place representation resembles that of low threshold, high spontaneous rate (SR) auditory nerve fibers (ANFs)at low stimulus levels, and that of high threshold, lowmedium SR ANFsat high stimulus levels. One hypothesis accounting for this phenomenon is that AVCN stellate cells selectively process inputs from different SR population of ANFs in a level-dependent fashion. In this paper, we investigate a neural mechanism that can support selective processing of ANF inputs by stellate cells. We study a physiologically detailed compartmental model of stellate cells. The model reproduces PST histograms and rate-versus-level functions measured in real cells. These results indicate that simple and plausible distribution patterns of excitatory and inhibitory inputs within the stellate cell dendritic tree can support level dependent selective processing. Factors affecting selective processing are identified. This study thus represents a first step towards the development of a computational model of the AVCN stellate cell receptive field.     

A selective model of plasma protein catabolism

Recent data suggest that the catabolism of certain plasma protein could be a stepwise process, the actual breakdown selectively acting only on the molecules which have undergone a characteristic change. Based on this assumption a kinetic model of plasma protein catabolism is built up, giving the analytic expression for a catabolic curve. Assuming a relatively small fraction of the modified form, this expression fits the existing experimental data with the same accuracy range as the classical random breakdown curve. A testing criterion able to discriminate between the two possibilities is suggested and some particular cases are briefly discussed.     

Computational antisense oligo prediction with a neural network model

MOTIVATION: The expression of a gene can be selectively inhibited by antisense oligonucleotides (AOs) targeting the mRNA. However, if the target site in the mRNA is picked randomly, typically 20% or less of the AOs are effective inhibitors in vivo. The sequence properties that make an AO effective are not well understood, thus many AOs need to be tested to find good inhibitors, which is time consuming and costly. So far computational models have been based exclusively on RNA structure prediction or motif searches while ignoring information from other aspects of AO design into the model. RESULTS: We present a computational model for AO prediction based on a neural network approach using a broad range of input parameters. Collecting sequence and efficacy data from AO scanning experiments in the literature generated a database of 490 AO molecules. Using a set of derived parameters based on AO sequence properties we trained a neural network model. The best model, an ensemble of 10 networks, gave an overall correlation coefficient of 0.30 (p=10(-8)). This model can predict effective AOs (>50% inhibition of gene expression) with a success rate of 92%. Using these thresholds the model predicts on average 12 effective AOs per 1000 base pairs, making it a stringent yet practical method for AO prediction.     

Computational model of response maps in the dorsal cochlear nucleus

The neurons in the mammalian (gerbil, cat) dorsal cochlear nucleus (DCN) have responses to tones and noise that have been used to classify them into unit types. These types (I–V) are based on excitatory and inhibitory responses to tones organized into plots called response maps (RMs). Type I units show purely excitatory responses, while type V units are primarily inhibited. A computational model of the neural circuitry of the mammalian DCN, based on the MacGregor neuromime, was used to investigate RMs of the principal cells (P-cells) that represent the fusiform and giant cells. In gerbils, fusiform cells have been shown to have primarily type III unit response properties; however, fusiform cells in the cat DCN are thought to have type IV unit response properties. The DCN model is based on a previous computational model of the cat (Hancock and Voigt Ann Biomed Eng 27: 73–87, 1999) and gerbil (Zheng and Voigt Ann Biomed Eng 34: 697–708, 2006) DCN. The basic model for both species is architecturally the same, and to get either type III unit RMs or type IV unit RMs, connection parameters were adjusted. Interestingly, regardless of the RM type, these units in gerbils and cats show spectral notch sensitivity and are thought to play a role in sound localization in the median plane. In this study, further parameter adjustments were made to systematically explore their effect on P-cell RMs. Significantly, type I, type III, type III-i, type IV, type IV-T and type V unit RMs can be created for the modeled P-cells. Thus major RMs observed in the cat and gerbil DCN are recreated by the model. These results suggest that RMs of individual DCN projection neurons are the result of specific assortment of excitatory and inhibitory inputs to that neuron and that subtle differences in the complement of inputs can result in different RM types. Modulation of the efficacy of certain synapses suggests that RM type may change dynamically.     

Computational model of mesenchymal migration in 3D under chemotaxis

Cell chemotaxis is an important characteristic of cellular migration, which takes part in crucial aspects of life and development. In this work, we propose a novel in silico model of mesenchymal 3D migration with competing protrusions under a chemotactic gradient. Based on recent experimental observations, we identify three main stages that can regulate mesenchymal chemotaxis: chemosensing, dendritic protrusion dynamics and cell–matrix interactions. Therefore, each of these features is considered as a different module of the main regulatory computational algorithm. The numerical model was particularized for the case of fibroblast chemotaxis under a PDGF-bb gradient. Fibroblasts migration was simulated embedded in two different 3D matrices – collagen and fibrin – and under several PDGF-bb concentrations. Validation of the model results was provided through qualitative and quantitative comparison with in vitro studies. Our numerical predictions of cell trajectories and speeds were within the measured in vitro ranges in both collagen and fibrin matrices. Although in fibrin, the migration speed of fibroblasts is very low, because fibrin is a stiffer and more entangling matrix. Testing PDGF-bb concentrations, we noticed that an increment of this factor produces a speed increment. At 1 ng mL^?1 a speed peak is reached after which the migration speed diminishes again. Moreover, we observed that fibrin exerts a dampening behavior on migration, significantly affecting the migration efficiency.     

Computational model of blood flow in the aorto-coronary bypass graft

Background

Coronary artery bypass grafting surgery is an effective treatment modality for patients with severe coronary artery disease. The conduits used during the surgery include both the arterial and venous conduits. Long- term graft patency rate for the internal mammary arterial graft is superior, but the same is not true for the saphenous vein grafts. At 10 years, more than 50% of the vein grafts would have occluded and many of them are diseased. Why do the saphenous vein grafts fail the test of time? Many causes have been proposed for saphenous graft failure. Some are non-modifiable and the rest are modifiable. Non-modifiable causes include different histological structure of the vein compared to artery, size disparity between coronary artery and saphenous vein. However, researches are more interested in the modifiable causes, such as graft flow dynamics and wall shear stress distribution at the anastomotic sites. Formation of intimal hyperplasia at the anastomotic junction has been implicated as the root cause of long- term graft failure.Many researchers have analyzed the complex flow patterns in the distal sapheno-coronary anastomotic region, using various simulated model in an attempt to explain the site of preferential intimal hyperplasia based on the flow disturbances and differential wall stress distribution. In this paper, the geometrical bypass models (aorto-left coronary bypass graft model and aorto-right coronary bypass graft model) are based on real-life situations. In our models, the dimensions of the aorta, saphenous vein and the coronary artery simulate the actual dimensions at surgery. Both the proximal and distal anastomoses are considered at the same time, and we also take into the consideration the cross-sectional shape change of the venous conduit from circular to elliptical. Contrary to previous works, we have carried out computational fluid dynamics (CFD) study in the entire aorta-graft-perfused artery domain. The results reported here focus on (i) the complex flow patterns both at the proximal and distal anastomotic sites, and (ii) the wall shear stress distribution, which is an important factor that contributes to graft patency.

Methods

The three-dimensional coronary bypass models of the aorto-right coronary bypass and the aorto-left coronary bypass systems are constructed using computational fluid-dynamics software (Fluent 6.0.1). To have a better understanding of the flow dynamics at specific time instants of the cardiac cycle, quasi-steady flow simulations are performed, using a finite-volume approach. The data input to the models are the physiological measurements of flow-rates at (i) the aortic entrance, (ii) the ascending aorta, (iii) the left coronary artery, and (iv) the right coronary artery.

Results

The flow field and the wall shear stress are calculated throughout the cycle, but reported in this paper at two different instants of the cardiac cycle, one at the onset of ejection and the other during mid-diastole for both the right and left aorto-coronary bypass graft models. Plots of velocity-vector and the wall shear stress distributions are displayed in the aorto-graft-coronary arterial flow-field domain. We have shown (i) how the blocked coronary artery is being perfused in systole and diastole, (ii) the flow patterns at the two anastomotic junctions, proximal and distal anastomotic sites, and (iii) the shear stress distributions and their associations with arterial disease.

Conclusion

The computed results have revealed that (i) maximum perfusion of the occluded artery occurs during mid-diastole, and (ii) the maximum wall shear-stress variation is observed around the distal anastomotic region. These results can enable the clinicians to have a better understanding of vein graft disease, and hopefully we can offer a solution to alleviate or delay the occurrence of vein graft disease.

     

Computational model of aortic valve surgical repair using grafted pericardium

Aortic valve reconstruction using leaflet grafts made from autologous pericardium is an effective surgical treatment for some forms of aortic regurgitation. Despite favorable outcomes in the hands of skilled surgeons, the procedure is underutilized because of the difficulty of sizing grafts to effectively seal with the native leaflets. Difficulty is largely due to the complex geometry and function of the valve and the lower distensibility of the graft material relative to native leaflet tissue. We used a structural finite element model to explore how a pericardial leaflet graft of various sizes interacts with two native leaflets when the valve is closed and loaded. Native leaflets and pericardium are described by anisotropic, hyperelastic constitutive laws, and we model all three leaflets explicitly and resolve leaflet contact in order to simulate repair strategies that are asymmetrical with respect to valve geometry and leaflet properties. We ran simulations with pericardial leaflet grafts of various widths (increase of 0%, 7%, 14%, 21% and 27%) and heights (increase of 0%, 13%, 27% and 40%) relative to the native leaflets. Effectiveness of valve closure was quantified based on the overlap between coapting leaflets. Results showed that graft width and height must both be increased to achieve proper valve closure, and that a graft 21% wider and 27% higher than the native leaflet creates a seal similar to a valve with three normal leaflets. Experimental validation in excised porcine aortas (n=9) corroborates the results of simulations.