Soil carbon sequestration rates and associated economic costs for farming systems of south-eastern Australia

Soil organic carbon (C) sequestration rates based on the Intergovernmental Panel for Climate Change (IPCC) methodology were combined with local economic data to simulate the economic potential for C sequestration in response to conservation tillage in the six agro-ecological zones within the Southern Region of the Australian grains industry. The net C sequestration rate over 20 years for the Southern Region (which includes discounting for associated greenhouse gases) is estimated to be 3.6 or 6.3 Mg C/ha after converting to either minimum or no-tillage practices, respectively, with no-till practices estimated to return 75% more carbon on average than minimum tillage. The highest net gains in C per ha are realised when converting from conventional to no-tillage practices in the high-activity clay soils of the High Rainfall and Wimmera agro-ecological zones. On the basis of total area available for change, the Slopes agro-ecological zone offers the highest net returns, potentially sequestering an additional 7.1 Mt C under no-tillage scenario over 20 years. The economic analysis was summarised as C supply curves for each of the 6 zones expressing the total additional C accumulated over 20 years for a price per t C sequestered ranging from zero to AU$200. For a price of $50/Mg C, a total of 427 000 Mg C would be sequestered over 20 years across the Southern Region, <5% of the simulated C sequestration potential of 9.1 Mt for the region. The Wimmera and Mid-North offer the largest gains in C under minimum tillage over 20 years of all zones for all C prices. For the no-tillage scenario, for a price of $50/Mg C, 1.74 Mt C would be sequestered over 20 years across the Southern Region, <10% of the simulated C sequestration potential of 18.6 Mt for the region over 20 years. The Slopes agro-ecological zone offers the best return in C over 20 years under no-tillage for all C prices. The Mallee offers the least return for both minimum and no-tillage scenarios. At a price of $200/Mg C, the transition from conventional tillage to minimum or no-tillage practices will only realise 19% and 33%, respectively, of the total biogeochemical sequestration potential of crop and pasture systems of the Southern Region over a 20-year period.

Stochastic models for regulatory networks of the genetic toggle switch

Bistability arises within a wide range of biological systems from the λ phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. In this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

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.