Lattice and continuum modelling of a bioactive porous tissue scaffold.

A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for tissue engineering applications make use of spatially homogeneous or spatially continuous equations to model cell growth, flow of culture medium, nutrient transport and their interactions. The network structure of the physical porous scaffold is often incorporated through parameters in these models, either phenomenologically or through techniques like mathematical homogenization. We derive a model on a square grid lattice to demonstrate the importance of explicitly modelling the network structure of the porous scaffold and compare results from this model with those from a modified continuum model from the literature. We capture two-way coupling between cell growth and fluid flow by allowing cells to block pores, and by allowing the shear stress of the fluid to affect cell growth and death. We explore a range of parameters for both models and demonstrate quantitative and qualitative differences between predictions from each of these approaches, including spatial pattern formation and local oscillations in cell density present only in the lattice model. These differences suggest that for some parameter regimes, corresponding to specific cell types and scaffold geometries, the lattice model gives qualitatively different model predictions than typical continuum models. Our results inform model selection for bioactive porous tissue scaffolds, aiding in the development of successful tissue engineering experiments and eventually clinically successful technologies.

Volume distribution of nodal domains of random band-limited functions.

We study the volume distribution of nodal domains of families of naturally arising Gaussian random fields on generic manifolds, namely random band-limited functions. It is found that in the high energy limit a typical instance obeys a deterministic universal law, independent of the manifold. Some of the basic qualitative properties of this law, such as its support, monotonicity and continuity of the cumulative probability function, are established.

How nanoscale protein interactions determine the mesoscale dynamic organisation of bacterial outer membrane proteins.

The spatiotemporal organisation of membranes is often characterised by the formation of large protein clusters. In Escherichia coli, outer membrane protein (OMP) clustering leads to OMP islands, the formation of which underpins OMP turnover and drives organisation across the cell envelope. Modelling how OMP islands form in order to understand their origin and outer membrane behaviour has been confounded by the inherent difficulties of simulating large numbers of OMPs over meaningful timescales. Here, we overcome these problems by training a mesoscale model incorporating thousands of OMPs on coarse-grained molecular dynamics simulations. We achieve simulations over timescales that allow direct comparison to experimental data of OMP behaviour. We show that specific interaction surfaces between OMPs are key to the formation of OMP clusters, that OMP clusters present a mesh of moving barriers that confine newly inserted proteins within islands, and that mesoscale simulations recapitulate the restricted diffusion characteristics of OMPs.

How anisotropy beats fractality in two-dimensional on-lattice diffusion-limited-aggregation growth.

We study the fractal structure of diffusion-limited aggregation (DLA) clusters on a square lattice by extensive numerical simulations (with clusters having up to 10^{8} particles). We observe that DLA clusters undergo strongly anisotropic growth, with the maximal growth rate along the axes. The naive scaling limit of a DLA cluster by its diameter is thus deterministic and one-dimensional. At the same time, on all scales from the particle size to the size of the entire cluster it has a nontrivial box-counting fractal dimension which corresponds to the overall growth rate, which, in turn, is smaller than the growth rate along the axes. This suggests that the fractal nature of the lattice DLA should be understood in terms of fluctuations around the one-dimensional backbone of the cluster.