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.

Measuring and decomposing changes in agricultural productivity, nitrogen use efficiency and cumulative exergy efficiency: Application to OECD agriculture

This paper uses an aggregate quantity space to decompose the temporal changes in nitrogen use efficiency and cumulative exergy use efficiency into changes of Moorsteen–Bjurek (MB) Total Factor Productivity (TFP) changes and changes in the aggregate nitrogen and cumulative exergy contents. Changes in productivity can be broken into technical change and changes in various efficiency measures such as technical efficiency, scale efficiency and residual mix efficiency. Changes in the aggregate nitrogen and cumulative exergy contents can be driven by changes in the quality of inputs and outputs and changes in the mixes of inputs and outputs. Also with cumulative exergy content analysis, changes in the efficiency in input production can increase or decrease the cumulative exergy transformity of agricultural production. The empirical study in 30 member countries of the Organisation for Economic Co-operation Development from 1990 to 2003 yielded some important findings. The production technology progressed but there were reductions in technical efficiency, scale efficiency and residual mix efficiency levels. This result suggests that the production frontier had shifted up but there existed lags in the responses of member countries to the technological change. Given TFP growth, improvements in nutrient use efficiency and cumulative exergy use efficiency were counteracted by reductions in the changes of the aggregate nitrogen contents ratio and aggregate cumulative exergy contents ratio. The empirical results also confirmed that different combinations of inputs and outputs as well as the quality of inputs and outputs could have more influence on the growth of nutrient and cumulative exergy use efficiency than factors that had driven productivity change. Keywords: Nutrient use efficiency; Cumulative exergy use efficiency; Thermodynamic efficiency change; Productivity growth; OECD agriculture; Sustainability