Directed cell migration in the presence of obstacles

BACKGROUND: Chemotactic movement is a common feature of many cells and microscopic organisms. In vivo, chemotactic cells have to follow a chemotactic gradient and simultaneously avoid the numerous obstacles present in their migratory path towards the chemotactic source. It is not clear how cells detect and avoid obstacles, in particular whether they need a specialized biological mechanism to do so. RESULTS: We propose that cells can sense the presence of obstacles and avoid them because obstacles interfere with the chemical field. We build a model to test this hypothesis and find that this naturally enables efficient at-a-distance sensing to be achieved with no need for a specific and active obstacle-sensing mechanism. We find that (i) the efficiency of obstacle avoidance depends strongly on whether the chemotactic chemical reacts or remains unabsorbed at the obstacle surface. In particular, it is found that chemotactic cells generally avoid absorbing barriers much more easily than non-absorbing ones. (ii) The typically low noise in a cell's motion hinders the ability to avoid obstacles. We also derive an expression estimating the typical distance traveled by chemotactic cells in a 3D random distribution of obstacles before capture; this is a measure of the distance over which chemotaxis is viable as a means of directing cells from one point to another in vivo. CONCLUSION: Chemotactic cells, in many cases, can avoid obstacles by simply following the spatially perturbed chemical gradients around obstacles. It is thus unlikely that they have developed specialized mechanisms to cope with environments having low to moderate concentrations of obstacles

Modeling Robustness Tradeoffs in Yeast Cell Polarization Induced by Spatial Gradients

Cells localize (polarize) internal components to specific locations in response to external signals such as spatial gradients. For example, yeast cells form a mating projection toward the source of mating pheromone. There are specific challenges associated with cell polarization including amplification of shallow external gradients of ligand to produce steep internal gradients of protein components (e.g. localized distribution), response over a broad range of ligand concentrations, and tracking of moving signal sources. In this work, we investigated the tradeoffs among these performance objectives using a generic model that captures the basic spatial dynamics of polarization in yeast cells, which are small. We varied the positive feedback, cooperativity, and diffusion coefficients in the model to explore the nature of this tradeoff. Increasing the positive feedback gain resulted in better amplification, but also produced multiple steady-states and hysteresis that prevented the tracking of directional changes of the gradient. Feedforward/feedback coincidence detection in the positive feedback loop and multi-stage amplification both improved tracking with only a modest loss of amplification. Surprisingly, we found that introducing lateral surface diffusion increased the robustness of polarization and collapsed the multiple steady-states to a single steady-state at the cost of a reduction in polarization. Finally, in a more mechanistic model of yeast cell polarization, a surface diffusion coefficient between 0.01 and 0.001 µm2/s produced the best polarization performance, and this range is close to the measured value. The model also showed good gradient-sensitivity and dynamic range. This research is significant because it provides an in-depth analysis of the performance tradeoffs that confront biological systems that sense and respond to chemical spatial gradients, proposes strategies for balancing this tradeoff, highlights the critical role of lateral diffusion of proteins in the membrane on the robustness of polarization, and furnishes a framework for future spatial models of yeast cell polarization

Coordination of Cell Differentiation and Migration in Mathematical Models of Caudal Embryonic Axis Extension

Vertebrate embryos display a predominant head-to-tail body axis whose formation is associated with the progressive development of post-cranial structures from a pool of caudal undifferentiated cells. This involves the maintenance of active FGF signaling in this caudal region as a consequence of the restricted production of the secreted factor FGF8. FGF8 is transcribed specifically in the caudal precursor region and is down-regulated as cells differentiate and the embryo extends caudally. We are interested in understanding the progressive down-regulation of FGF8 and its coordination with the caudal movement of cells which is also known to be FGF-signaling dependent. Our study is performed using mathematical modeling and computer simulations. We use an individual-based hybrid model as well as a caricature continuous model for the simulation of experimental observations (ours and those known from the literature) in order to examine possible mechanisms that drive differentiation and cell movement during the axis elongation. Using these models we have identified a possible gene regulatory network involving self-repression of a caudal morphogen coupled to directional domain movement that may account for progressive down-regulation of FGF8 and conservation of the FGF8 domain of expression. Furthermore, we have shown that chemotaxis driven by molecules, such as FGF8 secreted in the stem zone, could underlie the migration of the caudal precursor zone and, therefore, embryonic axis extension. These mechanisms may also be at play in other developmental processes displaying a similar mode of axis extension coupled to cell differentiation

Computational Models of HIV-1 Resistance to Gene Therapy Elucidate Therapy Design Principles

Gene therapy is an emerging alternative to conventional anti-HIV-1 drugs, and can potentially control the virus while alleviating major limitations of current approaches. Yet, HIV-1's ability to rapidly acquire mutations and escape therapy presents a critical challenge to any novel treatment paradigm. Viral escape is thus a key consideration in the design of any gene-based technique. We develop a computational model of HIV's evolutionary dynamics in vivo in the presence of a genetic therapy to explore the impact of therapy parameters and strategies on the development of resistance. Our model is generic and captures the properties of a broad class of gene-based agents that inhibit early stages of the viral life cycle. We highlight the differences in viral resistance dynamics between gene and standard antiretroviral therapies, and identify key factors that impact long-term viral suppression. In particular, we underscore the importance of mutationally-induced viral fitness losses in cells that are not genetically modified, as these can severely constrain the replication of resistant virus. We also propose and investigate a novel treatment strategy that leverages upon gene therapy's unique capacity to deliver different genes to distinct cell populations, and we find that such a strategy can dramatically improve efficacy when used judiciously within a certain parametric regime. Finally, we revisit a previously-suggested idea of improving clinical outcomes by boosting the proliferation of the genetically-modified cells, but we find that such an approach has mixed effects on resistance dynamics. Our results provide insights into the short- and long-term effects of gene therapy and the role of its key properties in the evolution of resistance, which can serve as guidelines for the choice and optimization of effective therapeutic agents

Hybrid models of tumor growth

Cancer is a complex, multiscale process, in which genetic mutations occurring at a subcellular level manifest themselves as functional changes at the cellular and tissue scale. The multiscale nature of cancer requires mathematical modeling approaches that can handle multiple intra- and extracellular factors acting on different time and space scales. Hybrid models provide a way to integrate both discrete and continuous variables that are used to represent individual cells and concentration or density fields, respectively. Each discrete cell can also be equipped with sub-models that drive cell behavior in response to microenvironmental cues. Moreover, the individual cells can interact with one another to form and act as an integrated tissue. Hybrid models form part of a larger class of individual-based-models that can naturally connect with tumor cell biology and allow for the integration of multiple interacting variables both intrinsically and extrinsically and are therefore perfectly suited to a systems biology approach to tumor growth

Modelling of Yeast Mating Reveals Robustness Strategies for Cell-Cell Interactions

Mating of budding yeast cells is a model system for studying cell-cell interactions. Haploid yeast cells secrete mating pheromones that are sensed by the partner which responds by growing a mating projection toward the source. The two projections meet and fuse to form the diploid. Successful mating relies on precise coordination of dynamic extracellular signals, signaling pathways, and cell shape changes in a noisy background. It remains elusive how cells mate accurately and efficiently in a natural multi-cell environment. Here we present the first stochastic model of multiple mating cells whose morphologies are driven by pheromone gradients and intracellular signals. Our novel computational framework encompassed a moving boundary method for modeling both a-cells and α-cells and their cell shape changes, the extracellular diffusion of mating pheromones dynamically coupled with cell polarization, and both external and internal noise. Quantification of mating efficiency was developed and tested for different model parameters. Computer simulations revealed important robustness strategies for mating in the presence of noise. These strategies included the polarized secretion of pheromone, the presence of the α-factor protease Bar1, and the regulation of sensing sensitivity; all were consistent with data in the literature. In addition, we investigated mating discrimination, the ability of an a-cell to distinguish between α-cells either making or not making α-factor, and mating competition, in which multiple a-cells compete to mate with one α-cell. Our simulations were consistent with previous experimental results. Moreover, we performed a combination of simulations and experiments to estimate the diffusion rate of the pheromone a-factor. In summary, we constructed a framework for simulating yeast mating with multiple cells in a noisy environment, and used this framework to reproduce mating behaviors and to identify strategies for robust cell-cell interactions

Gravity Sensing, Graviorientation and Microgravity

Gravity has constantly governed the evolution of life on Earth over the last 3.5 billion years while the magnetic field of the Earth has fluctuated over the eons, temperatures constantly change, and the light intensity undergoes seasonal and daily cycles. All forms of life are permanently exposed to gravity and it can be assumed that almost all organisms have developed sensors and respond in one way or the other to the unidirectional acceleration force. Here we summarize what is currently known about gravity sensing and response mechanisms in microorganisms, lower and higher plants starting from the historical eye-opening experiments from the nineteenth century up to today’s extremely rapidly advancing cellular, molecular and biotechnological research. In addition to high-tech methods, in particular experimentation in the microgravity environment of parabolic flights and in the low Earth orbit as well as in “microgravity simulators” have considerably improved our knowledge of the fascinating sensing and response mechanisms which enable organisms to explore and exploit the environment on, above and below the surface of the Earth and which was fundamental for evolution of life on Earth

Advances in experiments and modeling in micro-and nano-biomechanics: A mini review

10.1007/s12195-011-0183-xCellular and Molecular Bioengineering43327-33