Morphodynamics facilitate cancer cells to navigate 3D extracellular matrix

Cell shape is linked to cell function. The significance of cell morphodynamics, namely the temporal fluctuation of cell shape, is much less understood. Here we study the morphodynamics of MDA-MB-231 cells in type I collagen extracellular matrix (ECM). We systematically vary ECM physical properties by tuning collagen concentrations, alignment, and gelation temperatures. We find that morphodynamics of 3D migrating cells are externally controlled by ECM mechanics and internally modulated by Rho/ROCK-signaling. We employ machine learning to classify cell shape into four different morphological phenotypes, each corresponding to a distinct migration mode. As a result, we map cell morphodynamics at mesoscale into the temporal evolution of morphological phenotypes. We characterize the mesoscale dynamics including occurrence probability, dwell time and transition matrix at varying ECM conditions, which demonstrate the complex phenotype landscape and optimal pathways for phenotype transitions. In light of the mesoscale dynamics, we show that 3D cancer cell motility is a hidden Markov process whereby the step size distributions of cell migration are coupled with simultaneous cell morphodynamics. Morphological phenotype transitions also facilitate cancer cells to navigate non-uniform ECM such as traversing the interface between matrices of two distinct microstructures. In conclusion, we demonstrate that 3D migrating cancer cells exhibit rich morphodynamics that is controlled by ECM mechanics, Rho/ROCK-signaling, and regulate cell motility. Our results pave the way to the functional understanding and mechanical programming of cell morphodynamics as a route to predict and control 3D cell motility.

Variational Inference for Coupled Hidden Markov Models Applied to the Joint Detection of Copy Number Variations

Hidden Markov models provide a natural statistical framework for the detection of the copy number variations (CNV) in genomics. In this context, we define a hidden Markov process that underlies all individuals jointly in order to detect and to classify genomics regions in different states (typically, deletion, normal or amplification). Structural variations from different individuals may be dependent. It is the case in agronomy where varietal selection program exists and species share a common phylogenetic past. We propose to take into account these dependencies inthe HMM model. When dealing with a large number of series, maximum likelihood inference (performed classically using the EM algorithm) becomes intractable. We thus propose an approximate inference algorithm based on a variational approach (VEM), implemented in the CHMM R package. A simulation study is performed to assess the performance of the proposed method and an application to the detection of structural variations in plant genomes is presented.

PRICING SOVEREIGN CONTINGENT CONVERTIBLE DEBT

We develop a pricing model for Sovereign Contingent Convertible bonds (S-CoCo) with payment standstills triggered by a sovereign’s Credit Default Swap (CDS) spread. We model CDS spread regime switching, which is prevalent during crises, as a hidden Markov process, coupled with a mean-reverting stochastic process of spread levels under fixed regimes, in order to obtain S-CoCo prices through simulation. The paper uses the pricing model in a Longstaff–Schwartz American option pricing framework to compute future state contingent S-CoCo prices for risk management. Dual trigger pricing is also discussed using the idiosyncratic CDS spread for the sovereign debt together with a broad market index. Numerical results are reported using S-CoCo designs for Greece, Italy and Germany with both the pricing and contingent pricing models.

Estimating Density and Temperature Dependence of Juvenile Vital Rates Using a Hidden Markov Model

Organisms in the wild have cryptic life stages that are sensitive to changing environmental conditions and can be difficult to survey. In this study, I used mark-recapture methods to repeatedly survey Anaea aidea (Nymphalidae) caterpillars in nature, then modeled caterpillar demography as a hidden Markov process to assess if temporal variability in temperature and density influence the survival and growth of A. aidea over time. Individual encounter histories result from the joint likelihood of being alive and observed in a particular stage, and I included hidden states by separating demography and observations into parallel and independent processes. I constructed a demographic matrix containing the probabilities of all possible fates for each stage, including hidden states, e.g., eggs and pupae. I observed both dead and live caterpillars with high probability. Peak caterpillar abundance attracted multiple predators, and survival of fifth instars declined as per capita predation rate increased through spring. A time lag between predator and prey abundance was likely the cause of improved fifth instar survival estimated at high density. Growth rates showed an increase with temperature, but the most likely model did not include temperature. This work illustrates how state-space models can include unobservable stages and hidden state processes to evaluate how environmental factors influence vital rates of cryptic life stages in the wild.

Understanding melanopsin using bayesian generative models − an Introduction

Understanding biological processes implies a quantitative description. In recent years a new tool set, Bayesian hierarchical modeling, has seen rapid development. We use these methods to model kinetics of a specific protein in a neuroscience context: melanopsin. Melanopsin is a photoactive protein in retinal ganglion cells. Due to its photoactivity, melanopsin is widely used in optogenetic experiments and an important component in the elucidation of neuronal interactions. Thus it is important to understand the relevant processes and develop mechanistic models. Here, with a focus on methodological aspects, we develop, implement, fit and discuss Bayesian generative models of melanopsin dynamics. We start with a sketch of a basic model and then translate it into formal probabilistic language. As melanopsin occurs in at least two states, a resting and a firing state, a basic model is defined by a non-stationary two state hidden Markov process. Subsequently we add complexities in the form of (1) an hierarchical extension to fit multiple cells; (2) a wavelength dependency, to investigate the response at different color of light stimulation; (3) an additional third state to investigate whether melanopsin is bi- or tri-stable; (4) differences between different sub-types of melanopsin as found in different species. This application of modeling melanopsin dynamics demonstrates several benefits of Bayesian methods. They directly model uncertainty of parameters, are flexible in the distributions and relations of parameters in the modeling, and allow including prior knowledge, for example parameter values based on biochemical data.