Simultaneous quantification of cell motility and protein-membrane-association using active contours

We present a new method for the quantification of dynamic changes in fluorescence intensities at the cell membrane of moving cells. It is based on an active contour method for cell-edge detection, which allows tracking of changes in cell shape and position. Fluorescence intensities at specific cortical subregions can be followed in space and time and correlated with cell motility. The translocation of two GFP tagged proteins (CRAC and GRP1) from the cytosol to the membrane in response to stimulation with the chemoattractant cAMP during chemotaxis of Dictyostelium cells and studies of the spatio-temporal dynamics of this process exemplify the method: We show that the translocation can be correlated with motility parameters and that quantitative differences in the rate of association and dissociation from the membrane can be observed for the two PH domain containing proteins. The analysis of periodic CRAC translocation to the leading edge of a cell responding to natural cAMP waves in a mound demonstrates the power of this approach. It is not only capable of tracking the outline of cells within aggregates in front of a noisy background, but furthermore allows the construction of spatio-temporal polar plots, capturing the dynamics of the protein distribution at the cell membrane within the cells' moving co-ordinate system. Compilation of data by means of normalised polar plots is suggested as a future tool, which promises the so-far impossible practicability of extensive statistical studies and automated comparison of complex spatio-temporal protein distribution patterns.     

Individual‐based and stochastic modeling of cell population dynamics considering substrate dependency

In this article, we propose an individual‐based and stochastic modeling approach that is capable of describing the bacterial cell population dynamics during a batch culture. All stochastic nature inherent in intracellular molecular level reactions and cell division processes were considered in a single model framework by embedding a sub‐model describing individual cell's growth kinetics in a discrete event simulation algorithm. The resultant unique feature of the model is that the effects of the stochasticities on the cell population dynamics can be investigated for different substrate‐dependent cell growth kinetics. When Monod kinetics was used as the sub‐model, the stochasticities only slightly affected the cell mass increase and substrate consumption profiles during the batch culture although they were still important in describing the changes of cell population distributions. When Andrews substrate inhibition kinetics was used, however, it was revealed that the overall cell population dynamics could be seriously influenced by the stochasticities. Under a critical initial substrate level, the cell population could proliferate against the substrate inhibition only when the stochasticities were considered. Biotechnol. Bioeng. 2009;103: 891–899. © 2009 Wiley Periodicals, Inc.     

Stem cell dynamics in sebaceous gland morphogenesis in mouse skin

The hair follicle (HF) and the sebaceous gland (SG) constitute the two integral parts of the pilosebaceous unit and significantly contribute to the barrier function of mammalian skin. Considerable progress has been made in our understanding how HF formation is regulated. However, the development of the SG is poorly understood, both at the molecular and cellular level. Here, we investigate the process of SG morphogenesis and the dynamics of its cellular organisation in more detail. The spatial and temporal organisation of distinct stem and progenitor compartments was analysed during morphogenesis of the pilosebaceous unit in mouse tail epidermis. Our experiments reveal a dynamic expression pattern for diverse HF stem cell marker molecules including Sox9 and Lrig1. Surprisingly, Sox9 and Lrig1 are initially coexpressed by epidermal progenitor cells and are confined to different regions within the pilosebaceous unit when the specification of the sebocyte cell lineage takes place. We demonstrate that SG development at the distal part of the HF is driven by asymmetric cell fate decision of Lrig1 positive stem cells, whereas MTS24/Plet1 positive precursor cells seem not to play a role in this process. Importantly, our data clearly show that distinct stem and progenitor compartments are established at different time points of development. By studying the process of SG morphogenesis more precisely, we discovered that the two prominent SGs attached to one tail HF originate from one small cluster of sebocyte cells. Finally, we show regional specificity for HF patterning and spatio-temporal control of the underlying molecular signals initiating the development of the pilosebaceous unit.     

Mathematically modeling dynamics of T cell responses: predictions concerning the generation of memory cells

Mathematical models of T cell population dynamics after infection typically assume that T cells differentiate according to a linear process in which they first become effector cells, and then after some time, differentiate further into memory cells. In this paper, we offer a different mathematical model which can equally well capture T cell dynamics, using data from lymphocytic choriomeningitis (LCMV) infection. Our model assumes that memory cells are intermediates that further differentiate into effector cells only from additional or stronger antigenic stimulation. Our assumption naturally leads to a testable prediction about the generation of T cell memory-that the memory phenotype of T cells should be present in detectable numbers during the expansion phase of the response. We use our model to estimate a rate of differentiation from memory type cells to effectors. We argue that this differentiation assumption, where memory cells are intermediates, captures recent experimental work on T cell differentiation, and hence this new mathematical model could be helpful in doing further studies of T cell population dynamics. We also propose a method of distinguishing the models by examining the ratio of memory T cells detectable long after an infection to the peak numbers of T cells at the end of the expansion phase.     

Superstability of the yeast cell-cycle dynamics: ensuring causality in the presence of biochemical stochasticity

Gene regulatory dynamics are governed by molecular processes and therefore exhibits an inherent stochasticity. However, for the survival of an organism it is a strict necessity that this intrinsic noise does not prevent robust functioning of the system. It is still an open question how dynamical stability is achieved in biological systems despite the omnipresent fluctuations. In this paper we investigate the cell cycle of the budding yeast Saccharomyces cerevisiae as an example of a well-studied organism. We study a genetic network model of 11 genes that coordinate the cell-cycle dynamics using a modeling framework which generalizes the concept of discrete threshold dynamics. By allowing for fluctuations in the process times, we introduce noise into the model, accounting for the effects of biochemical stochasticity. We study the dynamical attractor of the cell cycle and find a remarkable robustness against fluctuations of this kind. We identify mechanisms that ensure reliability in spite of fluctuations: 'Catcher states' and persistence of activity levels contribute significantly to the stability of the yeast cell cycle despite the inherent stochasticity.     

Cross-scale sensitivity analysis of a non-small cell lung cancer model: linking molecular signaling properties to cellular behavior

Sensitivity analysis is an effective tool for systematically identifying specific perturbations in parameters that have significant effects on the behavior of a given biosystem, at the scale investigated. In this work, using a two-dimensional, multiscale non-small cell lung cancer (NSCLC) model, we examine the effects of perturbations in system parameters which span both molecular and cellular levels, i.e. across scales of interest. This is achieved by first linking molecular and cellular activities and then assessing the influence of parameters at the molecular level on the tumor's spatio-temporal expansion rate, which serves as the output behavior at the cellular level. Overall, the algorithm operated reliably over relatively large variations of most parameters, hence confirming the robustness of the model. However, three pathway components (proteins PKC, MEK, and ERK) and eleven reaction steps were determined to be of critical importance by employing a sensitivity coefficient as an evaluation index. Each of these sensitive parameters exhibited a similar changing pattern in that a relatively larger increase or decrease in its value resulted in a lesser influence on the system's cellular performance. This study provides a novel cross-scaled approach to analyzing sensitivities of computational model parameters and proposes its application to interdisciplinary biomarker studies.     

Molecular phenotyping of aging in single yeast cells using a novel microfluidic device

Budding yeast has served as an important model organism for aging research, and previous genetic studies have led to the discovery of conserved genes/pathways that regulate lifespan across species. However, the molecular causes of aging and death remain elusive, because it is very difficult to directly observe the cellular and molecular events accompanying aging in single yeast cells by the traditional approach based on micromanipulation. We have developed a microfluidic system to track individual mother cells throughout their lifespan, allowing automated lifespan measurement and direct observation of cell cycle dynamics, cell/organelle morphologies, and various molecular markers. We found that aging of the wild-type cells is characterized by an increased general stress and a progressive lengthening of the cell cycle for the last few cell divisions; these features are much less apparent in the long-lived FOB1 deletion mutant. Following the fate of individual cells revealed that there are different forms of cell death that are characterized by different terminal cell morphologies, and associated with different levels of stress and lifespan. We have identified a molecular marker - the level of the expression of Hsp104, as a good predictor for the lifespan of individual cells. Our approach allows detailed molecular phenotyping of single cells in the process of aging and thus provides new insight into its mechanism.     

Spatio-temporal dynamics of glycolysis in cell layers. A mathematical model

Glycolytic oscillations occur in many cell types and have been intensively studied in yeast. Recent experimental and theoretical research has been focussed on the oscillatory dynamics and the synchronisation mechanism in stirred yeast cell suspensions. Here we are interested in the spatio-temporal organisation of glycolysis in cell layers. To this end we study a grid of a few thousand compartments each containing a cell. The intracellular dynamics is described by a core model of glycolysis. The compartments can exchange metabolites via diffusion. The conditions for oscillatory dynamics in a single compartment are investigated by bifurcation analysis. The spatio-temporal behaviour of the cell layer is studied by simulations. The model predicts the propagation of repetitive wave fronts induced by a substrate gradient. The formation of these waves crucially depends on the diffusive exchange of the reaction product between cells. Depending on the kinetic parameters complex spatio-temporal behaviour such as periodic termination of waves can arise. In these cases the cellular oscillation characteristics depend on the location of the cell in the array.     

The effects of EGF-receptor density on multiscale tumor growth patterns

We studied the effects of epidermal growth factor receptor (EGFR) density on tumor growth dynamics, both on the sub- and the multi-cellular level using our previously developed model. This algorithm simulates the growth of a brain tumor using a multi-scale two-dimensional agent-based approach with an integrated transforming growth factor alpha (TGFalpha) induced EGFR-gene-protein interaction network. The results confirm that increasing cell receptor density correlates with an acceleration of the tumor system's spatio-temporal expansion dynamics. This multicellular behavior cannot be explained solely on the basis of spatial sub-cellular dynamics, which remain qualitatively similar amongst the three glioma cell lines investigated here in silico. Rather, we find that cells with higher EGFR density show an early increase in the phenotypic switching activity between proliferative and migratory traits, linked to a higher level of initial auto-stimulation by the PLCgamma-mediated TGFalpha-EGFR autocrine network. This indicates a more active protein level interaction in these chemotactically acting tumor systems and supports the role of post-translational regulation for the implemented EGFR pathway. Implications of these results for experimental cancer research are discussed.     

Molecular dynamics simulations of the interaction of phospholipid bilayers with polycaprolactone

The molecular interaction between common polymer chains and the cell membrane is unknown. Molecular dynamics simulations offer an emerging tool to characterise the nature of the interaction between common degradable polymer chains used in biomedical applications, such as polycaprolactone, and model cell membranes. Herein we characterise with all-atomistic and coarse-grained molecular dynamics simulations the interaction between single polycaprolactone chains of varying chain lengths with a phospholipid membrane. We find that the length of the polymer chain greatly affects the nature of interaction with the membrane, as well as the membrane properties. Furthermore, we next utilise advanced sampling techniques in molecular dynamics to characterise the two-dimensional free energy surface for the interaction of varying polymer chain lengths (short, intermediate, and long) with model cell membranes. We find that the free energy minimum shifts from the membrane-water interface to the hydrophobic core of the phospholipid membrane as a function of chain length. Finally, we perform coarse-grained molecular dynamics simulations of slightly larger membranes with polymers of the same length and characterise the results as compared with all-atomistic molecular dynamics simulations. These results can be used to design polymer chain lengths and chemistries to optimise their interaction with cell membranes at the molecular level.     

A 3-D model of tumor progression based on complex automata driven by particle dynamics

The dynamics of a growing tumor involving mechanical remodeling of healthy tissue and vasculature is neglected in most of the existing tumor models. This is due to the lack of efficient computational framework allowing for simulation of mechanical interactions. Meanwhile, just these interactions trigger critical changes in tumor growth dynamics and are responsible for its volumetric and directional progression. We describe here a novel 3-D model of tumor growth, which combines particle dynamics with cellular automata concept. The particles represent both tissue cells and fragments of the vascular network. They interact with their closest neighbors via semi-harmonic central forces simulating mechanical resistance of the cell walls. The particle dynamics is governed by both the Newtonian laws of motion and the cellular automata rules. These rules can represent cell life-cycle and other biological interactions involving smaller spatio-temporal scales. We show that our complex automata, particle based model can reproduce realistic 3-D dynamics of the entire system consisting of the tumor, normal tissue cells, blood vessels and blood flow. It can explain phenomena such as the inward cell motion in avascular tumor, stabilization of tumor growth by the external pressure, tumor vascularization due to the process of angiogenesis, trapping of healthy cells by invading tumor, and influence of external (boundary) conditions on the direction of tumor progression. We conclude that the particle model can serve as a general framework for designing advanced multiscale models of tumor dynamics and it is very competitive to the modeling approaches presented before.     

Formal modeling with multistate neurones and multidimensional synapses

Multistate neurones, a generalization of the popular McCulloch-Pitts binary neurones, are described; they are intended to model the fact that neurones may be in several different states of activity, while McCulloch-Pitts neurones model two states only: active or inactive. We show that as a consequence, multidimensional synapses are necessary to describe the dynamics of the model. As an illustration, we show how to derive the parameters of formal multistate neurones and their associated multidimensional synapses from simulations involving Hodgkin-Huxley neurones. Our approach opens the way to solve in a more biologically plausible way, two problems that were addressed previously: (1) the resolution of 'inverse problems', i.e. the construction of formal networks, whose dynamics follows a pre-defined spatio-temporal binary sequence, (2) the generation of spatio-temporal patterns that reproduce exactly the 'code' extracted from experimental recordings (olfactory codes at the glomerular level).     

Purification of pseudopodia from polarized cells reveals redistribution and activation of Rac through assembly of a CAS/Crk scaffold

Initiation of cell migration requires morphological polarization with formation of a dominant leading pseudopodium and rear compartment. A molecular understanding of this process has been limited, due to the inability to biochemically separate the leading pseudopodium from the rear of the cell. Here we examine the spatio-temporal localization and activation of cytoskeletal-associated signals in purified pseudopodia directed to undergo growth or retraction. Pseudopodia growth requires assembly of a p130Crk-associated substrate (CAS)/c-CrkII (Crk) scaffold, which facilitates translocation and activation of Rac1. Interestingly, Rac1 activation then serves as a positive-feedback loop to maintain CAS/Crk coupling and pseudopodia extension. Conversely, disassembly of this molecular scaffold is critical for export and down regulation of Rac1 activity and induction of pseudopodia retraction. Surprisingly, the uncoupling of Crk from CAS during pseudopodium retraction is independent of changes in focal adhesion kinase activity and CAS tyrosine phosphorylation. These findings establish CAS/Crk as an essential scaffold for Rac1-mediated pseudopodia growth and retraction, and illustrate spatio-temporal segregation of cytoskeletal signals during cell polarization.     

Mathematical Model for Spatial Segregation of the Rho-Family GTPases Based on Inhibitory Crosstalk

Cdc42, Rac, and Rho are small GTPases known to play a central role in signal transduction to the actin cytoskeleton. These proteins regulate cell motility, by affecting nucleation, uncapping, and depolymerization of actin filaments, and acto-myosin contractility. Studies of crosstalk and mutual feedbacks in these three proteins have led to a number of proposals for their interaction. At the same time, observations of the spatio-temporal dynamics of Rho-family proteins give evidence of spatial polarization and mutual exclusion between Cdc42/Rac and Rho. In this paper, we formulate a mathematical model to account for such observations, based on the known underlying biology of these proteins. We first investigate which of the crosstalk schemes proposed in the literature is consistent with observed dynamics, and then derive a simple model that can correctly describe these dynamics (assuming crosstalk is mediated via Rho GEFs). We show that cooperativity is an essential ingredient in the interactions of the proteins. The co-occurrence of a stable rest state with the possibility of fast spatial segregation can be related to bistability in a set of underlying ODEs in which the inactive forms of these proteins are fixed at a constant level. We show that the fast diffusion of the inactive forms is essential for stabilizing the transition fronts in the PDE formulation of the model, leading to robust spatial polarization, rather than traveling waves.     

Combining mechanical and optical approaches to dissect cellular mechanobiology

Mechanical force modulates a wide array of cell physiological processes. Cells sense and respond to mechanical stimuli using a hierarchy of structural complexes spanning multiple length scales, including force-sensitive molecules and cytoskeletal networks. Understanding mechanotransduction, i.e., the process by which cells convert mechanical inputs into biochemical signals, has required the development of novel biophysical tools that allow for probing of cellular and subcellular components at requisite time, length, and force scales and technologies that track the spatio-temporal dynamics of relevant biomolecules. In this review, we begin by discussing the underlying principles and recent applications of atomic force microscopy, magnetic twisting cytometry, and traction force microscopy, three tools that have been widely used for measuring the mechanical properties of cells and for probing the molecular basis of cellular mechanotransduction. We then discuss how such tools can be combined with advanced fluorescence methods for imaging biochemical processes in living cells in the context of three specific problem spaces. We first focus on fluorescence resonance energy transfer, which has enabled imaging of intra- and inter-molecular interactions and enzymatic activity in real time based on conformational changes in sensor molecules. Next, we examine the use of fluorescence methods to probe force-dependent dynamics of focal adhesion proteins. Finally, we discuss the use of calcium ratiometric signaling to track fast mechanotransductive signaling dynamics. Together, these studies demonstrate how single-cell biomechanical tools can be effectively combined with molecular imaging technologies for elucidating mechanotransduction processes and identifying mechanosensitive proteins.     

Fission yeast cytoskeletons and cell polarity factors: connecting at the cortex

Cell polarity is a fundamental property of cells from unicellular to multicellular organisms. Most of the time, it is essential so that the cells can achieve their function. The fission yeast Schizosaccharomyces pombe is a powerful genetic model organism for studying the molecular mechanisms of the cell polarity process. Indeed, S. pombe cells are rod-shaped and cell growth is restricted at the poles. The accurate localization of the cell growth machinery at the cell cortex, which involves the actin cytoskeleton, depends on cell polarity pathways that are temporally and spatially regulated. The importance of interphase microtubules and cell polarity factors acting at the cortex of cell ends in this process has been shown. Here, we review recent advances in knowledge of molecular pathways leading to the establishment of a cellular axis in fission yeast. We also describe the role of cortical proteins and mitotic cytoskeletal rearrangements that control the symmetry of cell division.     

Mixing of nanofluids: molecular dynamics simulations and modelling

In this paper we study a mixing scheme, which has recently been proposed for microfluids, on the nanoscale. We do this by performing a series of nonequilibrium molecular dynamics simulations. On the nanoscale the chaotic mixing regime is captured. We discover a new phenomenon where the two mixing fluids exchange positions after leaving the mixing intersection. The results from the molecular dynamics simulations also reveal complex spatio-temporal stream velocity profiles generated by the mixing device. We find that these profiles can be modelled through an approximate analytical solution to the Navier–Stokes equation.     

A pharmacologically based multiscale mathematical model of angiogenesis and its use in investigating the efficacy of a new cancer treatment strategy

Tumor angiogenesis is the process by which new blood vessels are formed and enhance the oxygenation and growth of tumors. As angiogenesis is recognized as being a critical event in cancer development, considerable efforts have been made to identify inhibitors of this process. Cytostatic treatments that target the molecular events of the angiogenesis process have been developed, and have met with some success. However, it is usually difficult to preclinically assess the effectiveness of targeted therapies, and apparently promising compounds sometimes fail in clinical trials.We have developed a multiscale mathematical model of angiogenesis and tumor growth. At the molecular level, the model focuses on molecular competition between pro- and anti-angiogenic substances modeled on the basis of pharmacological laws. At the tissue scale, the model uses partial differential equations to describe the spatio-temporal changes in cancer cells during three stages of the cell cycle, as well as those of the endothelial cells that constitute the blood vessel walls.This model is used to qualitatively assess how efficient endostatin gene therapy is. Endostatin is an anti-angiogenic endogenous substance. The gene therapy entails overexpressing endostatin in the tumor and in the surrounding tissue. Simulations show that there is a critical treatment dose below which increasing the duration of treatment leads to a loss of efficacy.This theoretical model may be useful to evaluate the efficacy of therapies targeting angiogenesis, and could therefore contribute to designing prospective clinical trials.