Generalized binomial Tau-leap method for biochemical kinetics incorporating both delay and intrinsic noise

The delay stochastic simulation algorithm (DSSA) by Barrio et al. [Plos Comput. Biol.2, 117–E (2006)] was developed to simulate delayed processes in cell biology in the presence of intrinsic noise, that is, when there are small-to-moderate numbers of certain key molecules present in a chemical reaction system. These delayed processes can faithfully represent complex interactions and mechanisms that imply a number of spatiotemporal processes often not explicitly modeled such as transcription and translation, basic in the modeling of cell signaling pathways. However, for systems with widely varying reaction rate constants or large numbers of molecules, the simulation time steps of both the stochastic simulation algorithm (SSA) and the DSSA can become very small causing considerable computational overheads. In order to overcome the limit of small step sizes, various τ-leap strategies have been suggested for improving computational performance of the SSA. In this paper, we present a binomial τ- DSSA method that extends the τ-leap idea to the delay setting and avoids drawing insufficient numbers of reactions, a common shortcoming of existing binomial τ-leap methods that becomes evident when dealing with complex chemical interactions. The resulting inaccuracies are most evident in the delayed case, even when considering reaction products as potential reactants within the same time step in which they are produced. Moreover, we extend the framework to account for multicellular systems with different degrees of intercellular communication. We apply these ideas to two important genetic regulatory models, namely, the hes1 gene, implicated as a molecular clock, and a Her1/Her 7 model for coupled oscillating cells.

Prospective association between physical activity and falls in community-dwelling older women

Abstract Objective: To explore associations between physical activity and risk of falls and broken or fractured bones in community-dwelling older women. Design, setting and participants: This was a prospective observational survey with 3- and 6-year follow-ups. The sample included 8562 healthy, community-dwelling women, aged 70-75 years in 1996, who completed surveys as participants in the Australian Longitudinal Study on Women’s Health. Outcomes were reports of a fall to the ground, injury from a fall, and broken or fractured bones in 1999 and 2002. The main predictor variable was physical activity level in 1996, categorized based on weekly frequency as none/very low, low, moderate, high, and very high. Covariates were demographic and health-related variables. Logistic regression models were computed separately for each outcome in 1999 and 2002. Main results: In multivariable models, very high physical activity was associated with decreased risk of a fall in 1999 (odds ratio 0.67, 95% CI 0.48 to 0.93) and in 2002 (odds ratio 0.62, 95% CI 0.42 to 0.92). High/very high physical activity was associated with decreased risk of broken or fractured bones in 2002 (odds ratio 0.64, 95% CI 0.42 to 0.96). No significant association was found between physical activity and injury from a fall. Conclusions: The results suggest that at least daily moderate to vigorous physical activity is required for the primary prevention of falls to the ground and broken or fractured bones in women aged 70-75 years.

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.

Oscillatory regulation of Hes1: Discrete stochastic delay modelling and simulation

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

Correlates of Pedometer Use: Results from a Community-based Physical Activity Intervention Trial (10,000 Steps Rockhampton)

Background Pedometers have become common place in physical activity promotion, yet little information exists on who is using them. The multi-strategy, community-based 10,000 Steps Rockhampton physical activity intervention trial provided an opportunity to examine correlates of pedometer use at the population level. Methods Pedometer use was promoted across all intervention strategies including: local media, pedometer loan schemes through general practice, other health professionals and libraries, direct mail posted to dog owners, walking trail signage, and workplace competitions. Data on pedometer use were collected during the 2-year follow-up telephone interviews from random population samples in Rockhampton, Australia, and a matched comparison community (Mackay). Logistic regression analyses were used to determine the independent influence of interpersonal characteristics and program exposure variables on pedometer use. Results Data from 2478 participants indicated that 18.1% of Rockhampton and 5.6% of Mackay participants used a pedometer in the previous 18-months. Rockhampton pedometer users (n = 222) were more likely to be female (OR = 1.59, 95% CI: 1.11, 2.23), aged 45 or older (OR = 1.69, 95% CI: 1.16, 2.46) and to have higher levels of education (university degree OR = 4.23, 95% CI: 1.86, 9.6). Respondents with a BMI > 30 were more likely to report using a pedometer (OR = 1.68, 95% CI: 1.11, 2.54) than those in the healthy weight range. Compared with those in full-time paid work, respondents in 'home duties' were significantly less likely to report pedometer use (OR = 0.18, 95% CI: 0.06, 0.53). Exposure to individual program components, in particular seeing 10,000 Steps street signage and walking trails or visiting the website, was also significantly associated with greater pedometer use. Conclusion Pedometer use varies between population subgroups, and alternate strategies need to be investigated to engage men, people with lower levels of education and those in full-time 'home duties', when using pedometers in community-based physical activity promotion initiatives.