Rethinking causality: pattern as the science of change

In this book, Linda Glassop describes an integrative framework referred to as the SOP model of change. The SOP model is derived from the notion that structures (S) are organised (O) by processes (P). The concept of SOP is relevant to any real thing, at any level of analysis

Dissecting Ubiquitin Folding Using the Self-Organized Polymer Model

Folding of Ubiquitin (Ub), a functionally important protein found in eukaryotic organisms, is investigated at low and neutral pH at different temperatures using simulations of the coarse-grained self-organized-polymer model with side chains (SOP-SC). The melting temperatures (T-m's), identified with the peaks in the heat capacity curves, decrease as pH decreases, in qualitative agreement with experiments. The calculated radius of gyration, showing dramatic variations with pH, is in excellent agreement with scattering experiments. At T-m Ub folds in a two-state manner at low and neutral pH. Clustering analysis of the conformations sampled in equilibrium folding trajectories at T-m with multiple transitions between the folded and unfolded states, shows a network of metastable states connecting the native and unfolded states. At low and neutral pH, Ub folds with high probability through a preferred set of conformations resulting in a pH-dependent dominant folding pathway. Folding kinetics reveal that Ub assembly at low pH occurs by multiple pathways involving a combination of nucleation-collapse and diffusion collision mechanism. The mechanism by which Ub folds is dictated by the stability of the key secondary structural elements responsible for establishing long-range contacts and collapse of Ub. Nucleation collapse mechanism holds if the stability of these elements are marginal, as would be the case at elevated temperatures. If the lifetimes associated with these structured microdomains are on the order of hundreds of microseconds, then Ub folding follows the diffusion collision mechanism with intermediates, many of which coincide with those found in equilibrium. Folding at neutral pH is a sequential process with a populated intermediate resembling that sampled at equilibrium. The transition state structures, obtained using a P-fold analysis, are homogeneous and globular with most of the secondary and tertiary structures being native-like. Many of our findings for both the thermodynamics and kinetics of folding are not only in agreement with experiments but also provide missing details not resolvable in standard experiments. The key prediction that folding mechanism varies dramatically with pH is amenable to experimental tests.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.