Bayesian inference on a microstructural, hyperelastic model of tendon deformation.

Microstructural models of soft-tissue deformation are important in applications including artificial tissue design and surgical planning. The basis of these models, and their advantage over their phenomenological counterparts, is that they incorporate parameters that are directly linked to the tissue's microscale structure and constitutive behaviour and can therefore be used to predict the effects of structural changes to the tissue. Although studies have attempted to determine such parameters using diverse, state-of-the-art, experimental techniques, values ranging over several orders of magnitude have been reported, leading to uncertainty in the true parameter values and creating a need for models that can handle such uncertainty. We derive a new microstructural, hyperelastic model for transversely isotropic soft tissues and use it to model the mechanical behaviour of tendons. To account for parameter uncertainty, we employ a Bayesian approach and apply an adaptive Markov chain Monte Carlo algorithm to determine posterior probability distributions for the model parameters. The obtained posterior distributions are consistent with parameter measurements previously reported and enable us to quantify the uncertainty in their values for each tendon sample that was modelled. This approach could serve as a prototype for quantifying parameter uncertainty in other soft tissues.

IVEN: A quantitative tool to describe 3D cell position and neighbourhood reveals architectural changes in FGF4-treated preimplantation embryos.

Architectural changes at the cellular and organism level are integral and necessary to successful development and growth. During mammalian preimplantation development, cells reduce in size and the architecture of the embryo changes significantly. Such changes must be coordinated correctly to ensure continued development of the embryo and, ultimately, a successful pregnancy. However, the nature of such transformations is poorly defined during mammalian preimplantation development. In order to quantitatively describe changes in cell environment and organism architecture, we designed Internal Versus External Neighbourhood (IVEN). IVEN is a user-interactive, open-source pipeline that classifies cells into different populations based on their position and quantifies the number of neighbours of every cell within a dataset in a 3D environment. Through IVEN-driven analyses, we show how transformations in cell environment, defined here as changes in cell neighbourhood, are related to changes in embryo geometry and major developmental events during preimplantation mammalian development. Moreover, we demonstrate that modulation of the FGF pathway alters spatial relations of inner cells and neighbourhood distributions, leading to overall changes in embryo architecture. In conjunction with IVEN-driven analyses, we uncover differences in the dynamic of cell size changes over the preimplantation period and determine that cells within the mammalian embryo initiate growth phase only at the time of implantation.

Cell Cycle Heterogeneity Can Generate Robust Cell Type Proportioning.

Cell-cell heterogeneity can facilitate lineage choice during embryonic development because it primes cells to respond to differentiation cues. However, remarkably little is known about the origin of heterogeneity or whether intrinsic and extrinsic variation can be controlled to generate reproducible cell type proportioning seen in vivo. Here, we use experimentation and modeling in D. discoideum to demonstrate that population-level cell cycle heterogeneity can be optimized to generate robust cell fate proportioning. First, cell cycle position is quantitatively linked to responsiveness to differentiation-inducing signals. Second, intrinsic variation in cell cycle length ensures cells are randomly distributed throughout the cell cycle at the onset of multicellular development. Finally, extrinsic perturbation of optimal cell cycle heterogeneity is buffered by compensatory changes in global signal responsiveness. These studies thus illustrate key regulatory principles underlying cell-cell heterogeneity optimization and the generation of robust and reproducible fate choice in development.

Product-Form Stationary Distributions for Deficiency Zero Networks with Non-mass Action Kinetics.

In many applications, for example when computing statistics of fast subsystems in a multiscale setting, we wish to find the stationary distributions of systems of continuous-time Markov chains. Here we present a class of models that appears naturally in certain averaging approaches whose stationary distributions can be computed explicitly. In particular, we study continuous-time Markov chain models for biochemical interaction systems with non-mass action kinetics whose network satisfies a certain constraint. Analogous with previous related results, the distributions can be written in product form.

A stochastic model for early placental development.

In the human, placental structure is closely related to placental function and consequent pregnancy outcome. Studies have noted abnormal placental shape in small-for-gestational-age infants which extends to increased lifetime risk of cardiovascular disease. The origins and determinants of placental shape are incompletely understood and are difficult to study in vivo. In this paper, we model the early development of the human placenta, based on the hypothesis that this is driven by a chemoattractant effect emanating from proximal spiral arteries in the decidua. We derive and explore a two-dimensional stochastic model, and investigate the effects of loss of spiral arteries in regions near to the cord insertion on the shape of the placenta. This model demonstrates that disruption of spiral arteries can exert profound effects on placental shape, particularly if this is close to the cord insertion. Thus, placental shape reflects the underlying maternal vascular bed. Abnormal placental shape may reflect an abnormal uterine environment, predisposing to pregnancy complications. Through statistical analysis of model placentas, we are able to characterize the probability that a given placenta grew in a disrupted environment, and even able to distinguish between different disruptions.

A constrained approach to multiscale stochastic simulation of chemically reacting systems.

Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper, we introduce a multiscale methodology suitable to address this problem, assuming that the evolution of the slow species in the system is well approximated by a Langevin process. It is based on the conditional stochastic simulation algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the constrained multiscale algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Fokker-Planck equation approximation, we can in turn approximate average switching times in stochastic chemical systems.