Finding Transition Pathways on Manifolds

We consider noise-induced transition paths in randomly perturbed dynami- cal systems on a smooth manifold. The classical Freidlin-Wentzell large devia- tion theory in Euclidean spaces is generalized and new forms of action functionals are derived in the spaces of functions and the space of curves to accommodate the intrinsic constraints associated with the manifold. Numerical meth- ods are proposed to compute the minimum action paths for the systems with constraints. The examples of conformational transition paths for a single and double rod molecules arising in polymer science are numerically investigated

Precision shooting: Sampling long transition pathways

The kinetics of collective rearrangements in solution, such as protein folding and nanocrystal phase transitions, often involve free energy barriers that are both long and rough. Applying methods of transition path sampling to harvest simulated trajectories that exemplify such processes is typically made difficult by a very low acceptance rate for newly generated trajectories. We address this problem by introducing a new generation algorithm based on the linear short-time behavior of small disturbances in phase space. Using this ``precision shooting'' technique, arbitrarily small disturbances can be propagated in time, and any desired acceptance ratio of shooting moves can be obtained. We demonstrate the method for a simple but computationally problematic isomerization process in a dense liquid of soft spheres. We also discuss its applicability to barrier crossing events involving metastable intermediate states.Comment: 9 pages, 12 figures, submitted to J. Chem. Phy

Multiple Folding Pathways of the SH3 domain

Experimental observations suggest that proteins follow different pathways under different environmental conditions. We perform molecular dynamics simulations of a model of the SH3 domain over a broad range of temperatures, and identify distinct pathways in the folding transition. We determine the kinetic partition temperature --the temperature for which the SH3 domain undergoes a rapid folding transition with minimal kinetic barriers-- and observe that below this temperature the model protein may undergo a folding transition via multiple folding pathways. The folding kinetics is characterized by slow and fast pathways and the presence of only one or two intermediates. Our findings suggest the hypothesis that the SH3 domain, a protein for which only two-state folding kinetics was observed in previous experiments, may exhibit intermediates states under extreme experimental conditions, such as very low temperatures. A very recent report (Viguera et al., Proc. Natl. Acad. Sci. USA, 100:5730--5735, 2003) of an intermediate in the folding transition of the Bergerac mutant of the alpha-spectrin SH3 domain protein supports this hypothesis.Comment: 16 pages, 4 figures To be published in the "Journal of Molecular Biology

Modelling Socio-Technical Transition Patterns and Pathways

We report on research that is developing a simulation model for assessing systemic innovations, or 'transitions', of societal systems towards a more sustainable development. Our overall aim is to outline design principles for models that can offer new insights into tackling persistent problems in large-scale systems, such as the European road transport system or the regional management of water resources. The systemic nature of these problems is associated with them being complex, uncertain and cutting across a number of sectors, and indicates a need for radical technological and behavioural solutions that address changes at the systems level rather than offering incremental changes within sub-systems. Model design is inspired by recent research into transitions, an emerging paradigm which provides a framework for tackling persistent problems. We use concepts from the literature on transitions to develop a prototype of a generic 'transition model'. Our prototype aims to capture different types of transition pathways, using historical examples such as the transition from horse-drawn carriages to cars or that from sailing ships to steam ships. The model combines agent-based modelling techniques and system dynamics, and includes interactions of individual agents and sub-systems, as well as cumulative effects on system structures. We show success in simulating different historical transition pathways by adapting the model's parameters and rules for each example. Finally, we discuss the improvements necessary for systematically exploring and detailing transition pathways in empirical case-study applications to current and future transitions such as the transition to a sustainable transport system in Europe.Complex Systems, Agent-Based Modelling, Social Simulation, Transitions, Transition Theory

Tipping the balance: theoretical interrogation of divergent extended heterolytic fragmentations.

Herein we interrogate a type of heterolytic fragmentation reaction called a 'divergent fragmentation' using density functional theory (DFT), natural bond orbital (NBO) analysis, ab initio molecular dynamics (AIMD), and external electric field (EEF) calculations. We demonstrate that substituents, electrostatic environment and non-statistical dynamic effects all influence product selectivity in reactions that involve divergent fragmentation pathways. Direct dynamics simulations reveal an unexpected post-transition state bifurcation (PTSB), and EEF calculations suggest that some transition states for divergent pathways can, in principle, be selectively stabilized if an electric field of the correct magnitude is oriented appropriately

Cryptic post-transition state bifurcations that reduce the efficiency of lactone-forming Rh-carbenoid C-H insertions.

Byproducts of chemical reactions are generally thought to result from the competition between two reaction pathways, each with its own rate-determining transition state structure. We show here, however, that pathways with a single transition state structure followed by a post-transition state bifurcation may also be a source of undesired products, especially those whose appearance is unexpected. The viability of this scenario for intramolecular C-H insertion reactions affording β-lactones via Rh-carbenoid intermediates is assessed through quantum chemical calculations on potential energy surfaces and quasi-classical molecular dynamics simulations. It appears that, in these cases, the rhodium catalyst is to blame for the accessibility of a second, unintended, pathway following the transition state structure for β-lactone formation that leads to fragmentation to a ketene and carbonyl compound. If an unexpected product is formed via a post-transition state bifurcation, conventional strategies for suppressing its formation are unlikely to succeed. Guidelines for recognizing the presence of a post-transition state bifurcation are described here, along with hints at means for controlling product distributions