Stochastic simulation of chemical reactions in spatially complex media

Discrete stochastic simulations, via techniques such as the Stochastic Simulation Algorithm (SSA) are a powerful tool for understanding the dynamics of chemical kinetics when there are low numbers of certain molecular species. However, an important constraint is the assumption of well-mixedness and homogeneity. In this paper, we show how to use Monte Carlo simulations to estimate an anomalous diffusion parameter that encapsulates the crowdedness of the spatial environment. We then use this parameter to replace the rate constants of bimolecular reactions by a time-dependent power law to produce an SSA valid in cases where anomalous diffusion occurs or the system is not well-mixed (ASSA). Simulations then show that ASSA can successfully predict the temporal dynamics of chemical kinetics in a spatially constrained environment.

Nitrone [2]rotaxanes: Simultaneous chemical protection and electrochemical activation of a functional group

We report on the use of the hydrogen bond accepting properties of neutral nitrone moieties to prepare benzylic-amide-macrocycle-containing [2]rotaxanes in yields as high as 70 %. X-Ray crystallography shows the presence of up to four intercomponent hydrogen bonds between the amide groups of the macrocycle and the two nitrone groups of the thread. Dynamic 1H NMR studies of the rates of macrocycle pirouetting in nonpolar solutions indicate that amide-nitrone hydrogen bonds are particularly strong, ~1.3 and ~0.2 kcal mol-1 stronger than similar amide-ester and amide-amide interactions, respectively. In addition to polarizing the N-O bond through hydrogen bonding, the rotaxane structure affects the chemistry of the nitrone groups in two significant ways: The intercomponent hydrogen bonding activates the nitrone groups to electrochemical reduction, a one electron reduction of the rotaxane being stablized by a remarkable 400 mV (8.1 kcal mol-1) with respect to the same process in the thread; encapsulation, however, protects the same functional groups from chemical reduction with an external reagent (and slows down electron transfer to and from the electroactive groups in cyclicvoltammetry experiments). Mechanical interlocking with a hydrogen bonding molecular sheath thus provides a route to an encapsulated polarized functional group and radical anions of significant kinetic and thermodynamic stability.

Modeling intrinsic noise and delays in chemical kinetics of coupled autoregulated oscillating cells

Delays are an important feature in temporal models of genetic regulation due to slow biochemical processes, such as transcription and translation. In this paper, we show how to model intrinsic noise effects in a delayed setting by either using a delay stochastic simulation algorithm (DSSA) or, for larger and more complex systems, a generalized Binomial τ-leap method (Bτ-DSSA). As a particular application, we apply these ideas to modeling somite segmentation in zebra fish across a number of cells in which two linked oscillatory genes (her1 and her7) are synchronized via Notch signaling between the cells.