On the Role of Physics in the Growth and Pattern Formation of Multi-Cellular Systems: What can we Learn from Individual-Cell Based Models?

We demonstrate that many collective phenomena in multi-cellular systems can be explained by models in which cells, despite their complexity, are represented as simple particles which are parameterized mainly by their physical properties. We mainly focus on two examples that nevertheless span a wide range of biological sub-disciplines: Unstructured cell populations growing in cell culture and growing cell layers in early animal development. While cultured unstructured cell populations would apriori been classified as particularly suited for a biophysical approach since the degree to which they are committed to a genetic program is expected to be modest, early animal development would be expected to mark the other extreme—here the degree of determinism according to a genetic program would be expected to be very high. We consider a number of phenomena such as the growth kinetics and spatial structure formation of monolayers and multicellular spheroids, the effect of the presence of another cell type surrounding the growing cell population, the effect of mutations and the critical surface dynamics of monolayers. Different from unstructured cell populations, cells in early development and at tissue interfaces usually form highly organized structures. An example are tissue layers. Under certain circumstances such layers are observed to fold. We show that folding pattern again can largely be explained by physical mechanisms either by a buckling instability or active cell shape changes. The paper combines new and published material and aims at an overview of a wide range of physical aspects in unstructured populations and growing tissue layers.     

A new polymorph of tetraphenyldiboroxane

A new polymorph of tetraphenyldiboroxane [or oxybis(diphenylborane)], C₂₄H₂₀B₂O, (Ia), has been found. It is monoclinic, like the already known form, (Ib), and can be refined in the same space group, namely P2₁/c, or in the equivalent setting P2₁/n. The molecular conformations of the two polymorphs differ in the rotations of two of the phenyl rings about the B—C bonds, leading to markedly different packing patterns and cell dimensions.     

Asymmetric hydrogenation of alkyl(vinyl)thioethers: a promising approach to α-chiral thioethers

This paper describes the enantioselective hydrogenation of vinylthioethers. We show that thioether derivatives of maleic esters can be hydrogenated with full conversion and up to 60% ee, and that α-thioether cinnamic acids can be hydrogenated in 51% ee with modest conversion.     

A Metropolis Monte Carlo Implementation of Bayesian Time-Domain Parameter Estimation: Application to Coupling Constant Estimation from Antiphase Multiplets

The Bayesian perspective on statistics asserts that it makes sense to speak of a probability of an unknown parameter having a particular value. Given a model for an observed, noise-corrupted signal, we may use Bayesian methods to estimate not only the most probable value for each parameter but also their distributions. We present an implementation of the Bayesian parameter estimation formalism developed by G. L. Bretthorst (1990,J. Magn. Reson.88, 533) using the Metropolis Monte Carlo sampling algorithm to perform the parameter and error estimation. This allows us to make very few assumptions about the shape of the posterior distribution, and allows the easy introduction of prior knowledge about constraints among the model parameters. We present evidence that the error estimates obtained in this manner are realistic, and that the Monte Carlo approach can be used to accurately estimate coupling constants from antiphase doublets in synthetic and experimental data.     

Determination of the Tolman cone angle from crystallographic parameters and a statistical analysis using the crystallographic data base

Summary A new method of evaluating the Tolman cone angle from X-ray structural data available from the Cambridge Crystallographic Data Base has been developed and a statistical analysis of the cone angles of the phosphines PPh₃, PMe₂Ph, PMePh₂, PMe₃, PEt₃ and PCy₃ (Cy = cyclohexyl) in transition metal complexes has been completed.     

A goal programming approach to strategic resource allocation in acute care hospitals

This paper describes a methodology for allocating resources in hospitals. The methodology uses two linear goal-programming models. One model sets case mix and volume for physicians, while holding service costs fixed; the other translates case mix decisions into a commensurate set of practice changes for physicians. The models allow decision makers to set case mix and case costs in such a way that the institution is able to break even, while preserving physician income and minimizing disturbance to practice. The models also permit investigation of trade-offs between case mix and physician practice parameters. Results are presented from a decision-making scenario facing the surgical division of Toronto's Mount Sinai Hospital after the announcement of a 3-year, 18% reduction in funding.     

Noise-induced asymptotic periodicity in a piecewise linear map

We examine asymptotically periodic density evolution in one-dimensional maps perturbed by noise, associating the macroscopic state of these dynamical systems with a phase space density. For asymptotically periodic systems density evolution becomes periodic in time, as do some macroscopic properties calculated from them. The general formalism of asymptotic periodicity is examined and used to calculate time correlations along trajectories of these maps as well as their limiting conditional entropy. The time correlation is shown to naturally decouple into periodic and stochastic components. Finally, asymptotic periodicity is studied in a noise-perturbed piecewise linear map, focusing on how the variation of noise amplitude can cause a transition from asymptotic periodicity to asymptotic stability in the density evolution of this system.     

Finite Abelian actions on surfaces

Edmonds showed that two free orientation preserving smooth actions φ₁ and φ₂ of a finite Abelian group G on a closed connected oriented smooth surface M are equivalent by an equivariant orientation preserving diffeomorphism iff they have the same bordism class [M,φ₁]=[M,φ₂] in the oriented bordism group Ω₂(G) of the group G. In this paper, we compute the bordism class [M,φ] for any such action of G on M and we determine for a given M, the bordism classes in Ω₂(G) that are representable by such actions of G on M. This will enable us to obtain a formula for the number of inequivalent such actions of G on M. We also determine the “weak” equivalence classes of such actions of G on M when all the p-Sylow subgroups of G are homocyclic (i.e. of the form n(Z/pαZ)).