Abstract: Spreading cell fronts are essential for embryonic development, tissue repair and cancer. Mathematical models used to describe the motion of cell fronts, such as Fisher’s equation and other partial differential equations, always invoke a mean-field assumption which implies that there is no spatial structure, such as cell clustering, present in the system. We test this ubiquitous assumption using a combination of in vitro cell migration assays, spatial statistics tools and discrete random walk simulations. In particular, we examine the conditions under which spatial structure can form in a spreading cell population. Our results highlight the importance of carefully examining these kinds of modelling assumptions that can be easily overlooked when applying partial differential equation models to describe the collective migration of a population of cells.

Abstract: Cell spreading process involves cell motility and cell proliferation, and is essential to developmental biology, wound healing and immune responses. Such process is inherently stochastic and should be modelled as such. Unfortunately, there is a lack of a general and principled technique to infer the parameters of these models and quantify the uncertainty associated with these estimates based on experimental data. In this talk we present a novel application of approximation Bayesian computation (ABC) that is able to achieve this goal in a coherent framework. We compare the parameter estimates based on two different implementations of the stochastic models. The first implementation uses the exact continuous time Gillespie (CTG) algorithm while the second is the discrete time approximate (DTA) algorithm. Our results indicate that the DTA algorithm provides very similar result to, but more computationally efficient than the CTG algorithm. The key parameter finding is that the posterior distribution of the time duration between motility events is highly correlated to the experimental time and the initial number of cells. That is, the more crowded cells or the longer experiment, the faster of cell motility rate. This trend also appears in the models with cell spreading driven by combined motility and proliferation. In similar studies, parameter estimates are typically based upon the size of the leading edge, since other sources of data from the experiments can be costly to collect. Our ABC analysis suggests that is possible to infer the time duration precisely from the leading edge but unfortunately brings very little information about the cell proliferation rate. This highlight the need to obtain more detailed information from the experimental observations of cell spreading, such as the cell density profile along a diameter, in order to quantify model parameters accurately.

Abstract: The mouse spermatogenic cycle describes the periodic development of male germ cells in the testicular tissue. Understanding the spermatogenic cycle has important clinical relevance, because disruption of the process leads to infertility or subfertility, and being able to regulate the process would provide new avenues to male contraceptives. However, the lengthy process prevents visualizing the cycle through dynamic imaging. Moreover, the precise action of germ cells that leads to the emergence of testicular tissue patterns remains uncharacterized. We develop an agent-based model to simulate the mouse spermatogenic cycle on a cross-section of the seminiferous tubule over a time scale of hours to years, taking consideration of multiple cellular behaviors including feedback regulation, mitotic and meiotic division, differentiation, apoptosis, and movement. The computer model is able to elaborate the temporal-spatial dynamics of germ cells in a time-lapse movie format, allowing us to trace individual cells as they change state and location. More importantly, the model provides the mechanistic understanding of the fundamentals of male fertility, namely, how testicular morphology and sperm production are achieved. By manipulating cellular behaviors either individually or collectively in silico, the model predicts the causal events to the altered arrangement of germ cells upon genetic and environmental perturbations. This in silico platform can serve as an interactive tool to perform long-term simulations and identify optimal approaches for infertility treatment and contraceptive development. Such approach may also be applicable to human spermatogenesis and, hence, may lay the foundation for increasing the effectiveness of male fertility regulation.