An Experimental and Computational Study of the Effect of ActA Polarity on the Speed of Listeria monocytogenes Actin-based Motility

Listeria monocytogenes is a pathogenic bacterium that moves within infected cells and spreads directly between cells by harnessing the cell's dendritic actin machinery. This motility is dependent on expression of a single bacterial surface protein, ActA, a constitutively active Arp2,3 activator, and has been widely studied as a biochemical and biophysical model system for actin-based motility. Dendritic actin network dynamics are important for cell processes including eukaryotic cell motility, cytokinesis, and endocytosis. Here we experimentally altered the degree of ActA polarity on a population of bacteria and made use of an ActA-RFP fusion to determine the relationship between ActA distribution and speed of bacterial motion. We found a positive linear relationship for both ActA intensity and polarity with speed. We explored the underlying mechanisms of this dependence with two distinctly different quantitative models: a detailed agent-based model in which each actin filament and branched network is explicitly simulated, and a three-state continuum model that describes a simplified relationship between bacterial speed and barbed-end actin populations. In silico bacterial motility required a cooperative restraining mechanism to reconstitute our observed speed-polarity relationship, suggesting that kinetic friction between actin filaments and the bacterial surface, a restraining force previously neglected in motility models, is important in determining the effect of ActA polarity on bacterial motility. The continuum model was less restrictive, requiring only a filament number-dependent restraining mechanism to reproduce our experimental observations. However, seemingly rational assumptions in the continuum model, e.g. an average propulsive force per filament, were invalidated by further analysis with the agent-based model. We found that the average contribution to motility from side-interacting filaments was actually a function of the ActA distribution. This ActA-dependence would be difficult to intuit but emerges naturally from the nanoscale interactions in the agent-based representation.     

Travelling Waves in Hybrid Chemotaxis Models

Hybrid models of chemotaxis combine agent-based models of cells with partial differential equation models of extracellular chemical signals. In this paper, travelling wave properties of hybrid models of bacterial chemotaxis are investigated. Bacteria are modelled using an agent-based (individual-based) approach with internal dynamics describing signal transduction. In addition to the chemotactic behaviour of the bacteria, the individual-based model also includes cell proliferation and death. Cells consume the extracellular nutrient field (chemoattractant), which is modelled using a partial differential equation. Mesoscopic and macroscopic equations representing the behaviour of the hybrid model are derived and the existence of travelling wave solutions for these models is established. It is shown that cell proliferation is necessary for the existence of non-transient (stationary) travelling waves in hybrid models. Additionally, a numerical comparison between the wave speeds of the continuum models and the hybrid models shows good agreement in the case of weak chemotaxis and qualitative agreement for the strong chemotaxis case. In the case of slow cell adaptation, we detect oscillating behaviour of the wave, which cannot be explained by mean-field approximations.     

Reproduction of patterns in melanocytic proliferations by agent-based simulation and geometric modeling

Spatio-temporal patterns of melanocytic proliferations observed in vivo are important for diagnosis but the mechanisms that produce them are poorly understood. Here we present an agent-based model for simulating the emergence of the main biologic patterns found in melanocytic proliferations. Our model portrays the extracellular matrix of the dermo-epidermal junction as a two-dimensional manifold and we simulate cellular migration in terms of geometric translations driven by adhesive, repulsive and random forces. Abstracted cellular functions and melanocyte-matrix interactions are modeled as stochastic events. For identification and validation we use visual renderings of simulated cell populations in a horizontal perspective that reproduce growth patterns observed in vivo by sequential dermatoscopy and corresponding vertical views that reproduce the arrangement of melanocytes observed in histopathologic sections. Our results show that a balanced interplay of proliferation and migration produces the typical reticular pattern of nevi, whereas the globular pattern involves additional cellular mechanisms. We further demonstrate that slight variations in the three basic cellular properties proliferation, migration, and adhesion are sufficient to produce a large variety of morphological appearances of nevi. We anticipate our model to be a starting point for the reproduction of more complex scenarios that will help to establish functional connections between abstracted microscopic behavior and macroscopic patterns in all types of melanocytic proliferations including melanoma.     

Rule-Based Model of Vein Graft Remodeling

When vein segments are implanted into the arterial system for use in arterial bypass grafting, adaptation to the higher pressure and flow of the arterial system is accomplished thorough wall thickening and expansion. These early remodeling events have been found to be closely coupled to the local hemodynamic forces, such as shear stress and wall tension, and are believed to be the foundation for later vein graft failure. To further our mechanistic understanding of the cellular and extracellular interactions that lead to global changes in tissue architecture, a rule-based modeling method is developed through the application of basic rules of behaviors for these molecular and cellular activities. In the current method, smooth muscle cell (SMC), extracellular matrix (ECM), and monocytes are selected as the three components that occupy the elements of a grid system that comprise the developing vein graft intima. The probabilities of the cellular behaviors are developed based on data extracted from in vivo experiments. At each time step, the various probabilities are computed and applied to the SMC and ECM elements to determine their next physical state and behavior. One- and two-dimensional models are developed to test and validate the computational approach. The importance of monocyte infiltration, and the associated effect in augmenting extracellular matrix deposition, was evaluated and found to be an important component in model development. Final model validation is performed using an independent set of experiments, where model predictions of intimal growth are evaluated against experimental data obtained from the complex geometry and shear stress patterns offered by a mid-graft focal stenosis, where simulation results show good agreements with the experimental data.     

Strategies of Eradicating Glioma Cells: A Multi-Scale Mathematical Model with MiR-451-AMPK-mTOR Control

The cellular dispersion and therapeutic control of glioblastoma, the most aggressive type of primary brain cancer, depends critically on the migration patterns after surgery and intracellular responses of the individual cancer cells in response to external biochemical and biomechanical cues in the microenvironment. Recent studies have shown that a particular microRNA, miR-451, regulates downstream molecules including AMPK and mTOR to determine the balance between rapid proliferation and invasion in response to metabolic stress in the harsh tumor microenvironment. Surgical removal of main tumor is inevitably followed by recurrence of the tumor due to inaccessibility of dispersed tumor cells in normal brain tissue. In order to address this multi-scale nature of glioblastoma proliferation and invasion and its response to conventional treatment, we propose a hybrid model of glioblastoma that analyses spatio-temporal dynamics at the cellular level, linking individual tumor cells with the macroscopic behaviour of cell organization and the microenvironment, and with the intracellular dynamics of miR-451-AMPK-mTOR signaling within a tumour cell. The model identifies a key mechanism underlying the molecular switches between proliferative phase and migratory phase in response to metabolic stress and biophysical interaction between cells in response to fluctuating glucose levels in the presence of blood vessels (BVs). The model predicts that cell migration, therefore efficacy of the treatment, not only depends on oxygen and glucose availability but also on the relative balance between random motility and strength of chemoattractants. Effective control of growing cells near BV sites in addition to relocalization of invisible migratory cells back to the resection site was suggested as a way of eradicating these migratory cells.     

AgentCell: a digital single-cell assay for bacterial chemotaxis

MOTIVATION: In recent years, single-cell biology has focused on the relationship between the stochastic nature of molecular interactions and variability of cellular behavior. To describe this relationship, it is necessary to develop new computational approaches at the single-cell level. RESULTS: We have developed AgentCell, a model using agent-based technology to study the relationship between stochastic intracellular processes and behavior of individual cells. As a test-bed for our approach we use bacterial chemotaxis, one of the best characterized biological systems. In this model, each bacterium is an agent equipped with its own chemotaxis network, motors and flagella. Swimming cells are free to move in a 3D environment. Digital chemotaxis assays reproduce experimental data obtained from both single cells and bacterial populations.     

A Tissue-Level Electromechanical Model of the Left Ventricle: Application to the Analysis of Intraventricular Pressure

The ventricular pressure profile is characteristic of the cardiac contraction progress and is useful to evaluate the cardiac performance. In this contribution, a tissue-level electromechanical model of the left ventricle is proposed, to assist the interpretation of left ventricular pressure waveforms. The left ventricle has been modeled as an ellipsoid composed of twelve mechano-hydraulic sub-systems. The asynchronous contraction of these twelve myocardial segments has been represented in order to reproduce a realistic pressure profiles. To take into account the different energy domains involved, the tissue-level scale and to facilitate the building of a modular model, multiple formalisms have been used: Bond Graph formalism for the mechano-hydraulic aspects and cellular automata for the electrical activation. An experimental protocol has been defined to acquire ventricular pressure signals from three pigs, with different afterload conditions. Evolutionary Algorithms have been used to identify the model parameters in order to minimize the error between experimental and simulated ventricular pressure signals. Simulation results show that the model is able to reproduce experimental ventricular pressure. In addition, electro-mechanical activation times have been determined in the identification process. For example, the maximum electrical activation time is reached, respectively, 96.5, 139.3 and 131.5 ms for the first, second, and third pigs. These preliminary results are encouraging for the application of the model on non-invasive data like ECG, arterial pressure or myocardial strain.     

BIO-LGCA: A cellular automaton modelling class for analysing collective cell migration

Collective dynamics in multicellular systems such as biological organs and tissues plays a key role in biological development, regeneration, and pathological conditions. Collective tissue dynamics—understood as population behaviour arising from the interplay of the constituting discrete cells—can be studied with on- and off-lattice agent-based models. However, classical on-lattice agent-based models, also known as cellular automata, fail to replicate key aspects of collective migration, which is a central instance of collective behaviour in multicellular systems. To overcome drawbacks of classical on-lattice models, we introduce an on-lattice, agent-based modelling class for collective cell migration, which we call biological lattice-gas cellular automaton (BIO-LGCA). The BIO-LGCA is characterised by synchronous time updates, and the explicit consideration of individual cell velocities. While rules in classical cellular automata are typically chosen ad hoc, rules for cell-cell and cell-environment interactions in the BIO-LGCA can also be derived from experimental cell migration data or biophysical laws for individual cell migration. We introduce elementary BIO-LGCA models of fundamental cell interactions, which may be combined in a modular fashion to model complex multicellular phenomena. We exemplify the mathematical mean-field analysis of specific BIO-LGCA models, which allows to explain collective behaviour. The first example predicts the formation of clusters in adhesively interacting cells. The second example is based on a novel BIO-LGCA combining adhesive interactions and alignment. For this model, our analysis clarifies the nature of the recently discovered invasion plasticity of breast cancer cells in heterogeneous environments.     

Effectiveness of Hair Bundle Motility as the Cochlear Amplifier

The effectiveness of hair bundle motility in mammalian and avian ears is studied by examining energy balance for a small sinusoidal displacement of the hair bundle. The condition that the energy generated by a hair bundle must be greater than energy loss due to the shear in the subtectorial gap per hair bundle leads to a limiting frequency that can be supported by hair-bundle motility. Limiting frequencies are obtained for two motile mechanisms for fast adaptation, the channel re-closure model and a model that assumes that fast adaptation is an interplay between gating of the channel and the myosin motor. The limiting frequency obtained for each of these models is an increasing function of a factor that is determined by the morphology of hair bundles and the cochlea. Primarily due to the higher density of hair cells in the avian inner ear, this factor is ∼10-fold greater for the avian ear than the mammalian ear, which has much higher auditory frequency limit. This result is consistent with a much greater significance of hair bundle motility in the avian ear than that in the mammalian ear.     

Emergence of Bursting Activity in Connected Neuronal Sub-Populations

Uniform and modular primary hippocampal cultures from embryonic rats were grown on commercially available micro-electrode arrays to investigate network activity with respect to development and integration of different neuronal populations. Modular networks consisting of two confined active and inter-connected sub-populations of neurons were realized by means of bi-compartmental polydimethylsiloxane structures. Spontaneous activity in both uniform and modular cultures was periodically monitored, from three up to eight weeks after plating. Compared to uniform cultures and despite lower cellular density, modular networks interestingly showed higher firing rates at earlier developmental stages, and network-wide firing and bursting statistics were less variable over time. Although globally less correlated than uniform cultures, modular networks exhibited also higher intra-cluster than inter-cluster correlations, thus demonstrating that segregation and integration of activity coexisted in this simple yet powerful in vitro model. Finally, the peculiar synchronized bursting activity shown by confined modular networks preferentially propagated within one of the two compartments (‘dominant’), even in cases of perfect balance of firing rate between the two sub-populations. This dominance was generally maintained during the entire monitored developmental frame, thus suggesting that the implementation of this hierarchy arose from early network development.     

Agent-based model provides insight into the mechanisms behind failed regeneration following volumetric muscle loss injury

Skeletal muscle possesses a remarkable capacity for repair and regeneration following a variety of injuries. When successful, this highly orchestrated regenerative process requires the contribution of several muscle resident cell populations including satellite stem cells (SSCs), fibroblasts, macrophages and vascular cells. However, volumetric muscle loss injuries (VML) involve simultaneous destruction of multiple tissue components (e.g., as a result of battlefield injuries or vehicular accidents) and are so extensive that they exceed the intrinsic capability for scarless wound healing and result in permanent cosmetic and functional deficits. In this scenario, the regenerative process fails and is dominated by an unproductive inflammatory response and accompanying fibrosis. The failure of current regenerative therapeutics to completely restore functional muscle tissue is not surprising considering the incomplete understanding of the cellular mechanisms that drive the regeneration response in the setting of VML injury. To begin to address this profound knowledge gap, we developed an agent-based model to predict the tissue remodeling response following surgical creation of a VML injury. Once the model was able to recapitulate key aspects of the tissue remodeling response in the absence of repair, we validated the model by simulating the tissue remodeling response to VML injury following implantation of either a decellularized extracellular matrix scaffold or a minced muscle graft. The model suggested that the SSC microenvironment and absence of pro-differentiation SSC signals were the most important aspects of failed muscle regeneration in VML injuries. The major implication of this work is that agent-based models may provide a much-needed predictive tool to optimize the design of new therapies, and thereby, accelerate the clinical translation of regenerative therapeutics for VML injuries.     

闽楠叶形态与叶脉网络性状关系对城市生长环境的响应

植物叶形态与叶脉网络功能性状的协同变异与权衡关系,对深入理解植物叶脉网络功能性状对环境变异的生态适应,以及预测植物物种生活习性对城市化过程的响应具有重要意义。闽楠作为珍贵的常绿阔叶树种,正在城市绿化中逐步推广。针对不同生长环境中（行道与植物园混交林）的闽楠,开展了叶形态与叶脉网络功能性状关系对城市生长环境的响应研究。研究结果表明：闽楠叶性状值基本满足正态分布,各性状变异系数保持在10%-20%之间,群体内性状变异较为丰富,单因素方差分析表明两种环境对叶形态性状的影响比叶脉网络系统的影响更明显;两种生长环境下闽楠叶形态性状组与叶脉网络功能性状组都具有极显著相关性,行道和植物园混交林典型性相关系数分别为0.804和0.795,叶形态性状与叶脉直径呈显著正相关,形态性状、叶脉直径与初级脉密度呈显著负相关;闽楠在响应城市生长环境的过程中呈现出相应的经济权衡机制,行道环境中闽楠以较大的初级脉密度和较小叶面积来确保水分获取和光合之间的平衡,植物园闽楠则采用较低初级叶脉密度、较高叶面积和叶脉直径的叶形态和叶脉网络构建模式。在选择闽楠作为城市绿化树种时,可将叶片形态性状组与叶脉网络功能性状组的协同变化和权衡关系作为选种依据,以提高闽楠在城市环境中的成活率和适应性。     

Bridging cell-scale simulations and radiologic images to explain short-time intratumoral oxygen fluctuations

Radiologic images provide a way to monitor tumor development and its response to therapies in a longitudinal and minimally invasive fashion. However, they operate on a macroscopic scale (average value per voxel) and are not able to capture microscopic scale (cell-level) phenomena. Nevertheless, to examine the causes of frequent fast fluctuations in tissue oxygenation, models simulating individual cells’ behavior are needed. Here, we provide a link between the average data values recorded for radiologic images and the cellular and vascular architecture of the corresponding tissues. Using hybrid agent-based modeling, we generate a set of tissue morphologies capable of reproducing oxygenation levels observed in radiologic images. We then use these in silico tissues to investigate whether oxygen fluctuations can be explained by changes in vascular oxygen supply or by modulations in cellular oxygen absorption. Our studies show that intravascular changes in oxygen supply reproduce the observed fluctuations in tissue oxygenation in all considered regions of interest. However, larger-magnitude fluctuations cannot be recreated by modifications in cellular absorption of oxygen in a biologically feasible manner. Additionally, we develop a procedure to identify plausible tissue morphologies for a given temporal series of average data from radiology images. In future applications, this approach can be used to generate a set of tissues comparable with radiology images and to simulate tumor responses to various anti-cancer treatments at the tissue-scale level.     

The role of cell proliferation and migration in the development of a neo-intimal layer in veins grafted into arteries,in rats

Summary The development of a thickened (hyperplastic) fibro-cellular neo-intima is a significant event in the adaptation of a vein grafted into an artery. The histogenesis of tissues in vein grafts was explored in a rat model where the source of endothelial and smooth muscle cells was from the adjacent artery. Cell proliferation was assessed by the incorporation of tritiated thymidine and autoradiography, up to 18 months after grafting. Cell migration was detected by prelabelling in the first 5 days after grafting and sampling at later times. The proliferation of cells in the arterial media adjacent to the graft was elevated above control levels as early as 2 days after grafting; it was maximal at 3 days and returned to low levels by day 21. During the first week, prelabelled smooth muscle cells in the tunica media of the adjacent artery migrated to the subendothelial space, where they continued to proliferate to produce arterial intimal hyperplasia. The migration of endothelial and smooth muscle cells proceeded across the anastomosis to populate the vein graft neo-intima, where smooth muscle cells continued to proliferate until 28 days after grafting. Cell migration and proliferation were significant factors in the histogenesis of vein graft neo-intimal hyperplasia in this model. These processes were controlled, perhaps by local regulatory factors, to form a vein graft, the wall of which was similar in thickness and structure to that of the host artery.     

Simple rules for a “simple” nervous system? Molecular and biomathematical approaches to enteric nervous system formation and malformation

We review morphogenesis of the enteric nervous system from migratory neural crest cells, and defects of this process such as Hirschsprung disease, centering on cell motility and assembly, and cell adhesion and extracellular matrix molecules, along with cell proliferation and growth factors. We then review continuum and agent-based (cellular automata) models with rules of cell movement and logistical proliferation. Both movement and proliferation at the individual cell level are modeled with stochastic components from which stereotyped outcomes emerge at the population level. These models reproduced the wave-like colonization of the intestine by enteric neural crest cells, and several new properties emerged, such as colonization by frontal expansion, which were later confirmed biologically. These models predict a surprising level of clonal heterogeneity both in terms of number and distribution of daughter cells. Biologically, migrating cells form stable chains made up of unstable cells, but this is not seen in the initial model. We outline additional rules for cell differentiation into neurons, axon extension, cell-axon and cell–cell adhesions, chemotaxis and repulsion which can reproduce chain migration. After the migration stage, the cells re-arrange as a network of ganglia. Changes in cell adhesion molecules parallel this, and we describe additional rules based on Steinberg's Differential Adhesion Hypothesis, reflecting changing levels of adhesion in neural crest cells and neurons. This was able to reproduce enteric ganglionation in a model. Mouse mutants with disturbances of enteric nervous system morphogenesis are discussed, and these suggest future refinement of the models. The modeling suggests a relatively simple set of cell behavioral rules could account for complex patterns of morphogenesis. The model has allowed the proposal that Hirschsprung disease is mostly an enteric neural crest cell proliferation defect, not a defect of cell migration. In addition, the model suggests an explanations for zonal and skip segment variants of Hirschsprung disease, and also gives a novel stochastic explanation for the observed discordancy of Hirschsprung disease in identical twins.     

TGF-beta- and CTGF-mediated fibroblast recruitment influences early outward vein graft remodeling

Luminal shearing forces have been shown to impact both geometric remodeling and the development of intimal hyperplasia. Less well studied is the influence of intramural wall stresses on vessel growth and adaptation. Using a vein graft-fistula configuration to isolate the impact of circumferential wall stress, we identify the reorganization of adventitial myofibroblasts as the dominant histological event that limits early outward remodeling of vein grafts in response to elevated wall stress. We hypothesize that increased production of transforming growth factor-beta (TGF-beta) and connective tissue growth factor (CTGF) induces recruitment of myofibroblasts, promotes adventitial reorganization, and limits early outward remodeling in response to increased intramural wall stress. Vein grafts with a distal arteriovenous fistula in the neck of rabbits were constructed, resulting in a fourfold differential in circumferential wall stress. Using this model, we demonstrate 1) elevated wall stress augments the production of TGF-beta and CTGF, 2) increased TGF-beta expression and CTGF expression are correlated with the enhanced differentiation from fibroblasts to myofibroblasts, as evidenced by the significant increase in the alpha-actin-positive cells in adventitia, and 3) the levels of TGF-beta, CTGF, and alpha-actin are inversely correlated with the magnitude of outward remodeling of the graft wall. Increased wall stress after vein graft implantation appears to induce a TGF-beta- and CTGF-mediated recruitment of adventitial fibroblasts and a conversion to a myofibroblast phenotype. Although important in the maintenance of wall stability in the face of an increased mechanical load, this adventitial adaptation limits early outward remodeling of the vein conduit and may prove deleterious in maintaining long-term vein graft patency.     

Cellular, molecular and immunological mechanisms in the pathophysiology of vein graft intimal hyperplasia

Coronary artery disease, leading to myocardial infarction and ischaemia, affects millions of persons and is one of the leading causes of morbidity and mortality worldwide. Invasive techniques such as coronary artery bypass grafting are used to alleviate the sequelae of arterial occlusion. Unfortunately, restenosis or occlusion of the grafted conduit occurs over a time frame of months to years with a gradual reduction in patency, especially in vein grafts. The events leading to intimal hyperplasia (IH) formation involve numerous cellular and molecular components. Various cellular elements of the vessel wall are involved as are leucocyte-endothelial interactions that trigger the coagulation cascade leading to localized thrombus formation. Subsequent phenotypic modification of the medial smooth muscle cells and their intimal migration is the basis of the lesion formation that is thought to be propagated by an immune-mediated reaction. Despite intense scrutiny, the pathophysiology of IH remains an enigma. Although several growth factors, cytokines and numerous other biomolecules have been implicated and their relationship to prohyperplasia pathways such as the phosphatidyl-inositol 3-kinase (PI3K)-Akt pathway has been established, many pieces of the puzzle are still missing. An in-depth understanding of early vein graft adaptation and progression is necessary to improve the long-term prognosis and develop more effective therapeutic measures. In this review, we have critically evaluated and summarized the literature to elucidate and interlink the numerous established and emerging factors that play a key role in the development of IH leading to vein graft restenosis.     

In silico leaf venation networks: Growth and reorganization driven by mechanical forces

Development commonly involves an interplay between signaling, genetic expression and biophysical forces. However, the relative importance of these mechanisms during the different stages of development is unclear. Leaf venation networks provide a fitting context for the examination of these questions. In mature leaves, venation patterns are extremely diverse, yet their local structure satisfies a universal property: at junctions between veins, angles and diameters are related by a vectorial equation analogous to a force balance. Using a cell proliferation model, we reproduce in silico the salient features of venation patterns. Provided that vein cells are given different mechanical properties, tensile forces develop along the veins during growth, causing the network to deform progressively. Our results suggest that the local structure of venation networks results from a reorganization driven by mechanical forces, independently of how veins form. This conclusion is supported by recent observations of vein development in young leaves and by the good quantitative agreement between our simulations and data from mature leaves.