Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

A cationic vaccine adjuvant based on a saturated quaternary ammonium lipid have different in vivo distribution kinetics and display a distinct CD4 T cell-inducing capacity compared to its unsaturated analog

Adjuvants are often composed of different constituents that can be divided into two groups based on their primary activity: the delivery system which carries and presents the vaccine antigen to antigen-presenting cells, and the immunostimulator that activates and modulates the ensuing immune response. Herein, we have investigated the importance of the delivery system and in particular its physical characteristics by comparing the delivery properties of two lipids which differ only in the degree of saturation of the acyl chains, rendering the liposomes either rigid (DDA, dimethyldioctadecylammonium) or highly fluid (DODA, dimethyldioleoylammonium) at physiological temperature. We show that these delivery systems are remarkably different in their ability to prime a Th1-directed immune response with the rigid DDA-based liposomes inducing a response more than 100 times higher compared to that obtained with the fluid DODA-based liposomes. Upon injection with a vaccine antigen, DDA-based liposomes form a vaccine depot that results in a continuous attraction of antigen-presenting cells that engulf a high amount of adjuvant and are subsequently efficiently activated as measured by an elevated expression of the co-stimulatory molecules CD40 and CD86. In contrast, the fluid DODA-based liposomes are more rapidly removed from the site of injection resulting in a lower up-regulation of co-stimulatory CD40 and CD86 molecules on adjuvant-positive antigen-presenting cells. Additionally, the vaccine antigen is readily dissociated from the DODA-based liposomes leading to a population of antigen-presenting cells that are antigen-positive but adjuvant-negative and consequently are not activated. These studies demonstrate the importance of studying in vivo characteristics of the vaccine components and furthermore show that physicochemical properties of the delivery system have a major impact on the vaccine-induced immune response. © 2012 Elsevier B.V. All rights reserved.