Uniformisation techniques for stochastic simulation of chemical reaction networks

This work considers the method of uniformisation for continuous-time Markov chains in the context of chemical reaction networks. Previous work in the literature has shown that uniformisation can be beneficial in the context of time-inhomogeneous models, such as chemical reaction networks incorporating extrinsic noise. This paper lays focus on the understanding of uniformisation from the viewpoint of sample paths of chemical reaction networks. In particular, an efficient pathwise stochastic simulation algorithm for time-homogeneous models is presented which is complexity-wise equal to Gillespie's direct method. This new approach therefore enlarges the class of problems for which the uniformisation approach forms a computationally attractive choice. Furthermore, as a new application of the uniformisation method, we provide a novel variance reduction method for (raw) moment estimators of chemical reaction networks based upon the combination of stratification and uniformisation

Exact solution of stochastic gene expression models with bursting, cell cycle and replication dynamics

The bulk of stochastic gene expression models in the literature do not have an explicit description of the age of a cell within a generation and hence they cannot capture events such as cell division and DNA replication. Instead, many models incorporate cell cycle implicitly by assuming that dilution due to cell division can be described by an effective decay reaction with first-order kinetics. If it is further assumed that protein production occurs in bursts then the stationary protein distribution is a negative binomial. Here we seek to understand how accurate these implicit models are when compared with more detailed models of stochastic gene expression. We derive the exact stationary solution of the chemical master equation describing bursty protein dynamics, binomial partitioning at mitosis, age-dependent transcription dynamics including replication, and random interdivision times sampled from Erlang or more general distributions; the solution is different for single lineage and population snapshot settings. We show that protein distributions are well approximated by the solution of implicit models (a negative binomial) when the mean number of mRNAs produced per cycle is low and the cell cycle length variability is large. When these conditions are not met, the distributions are either almost bimodal or else display very flat regions near the mode and cannot be described by implicit models. We also show that for genes with low transcription rates, the size of protein noise has a strong dependence on the replication time, it is almost independent of cell cycle variability for lineage measurements and increases with cell cycle variability for population snapshot measurements. In contrast for large transcription rates, the size of protein noise is independent of replication time and increases with cell cycle variability for both lineage and population measurements.Comment: 7 figure

Effects of cell cycle variability on lineage and population measurements of mRNA abundance

Many models of gene expression do not explicitly incorporate a cell cycle description. Here, we derive a theory describing how messenger RNA (mRNA) fluctuations for constitutive and bursty gene expression are influenced by stochasticity in the duration of the cell cycle and the timing of DNA replication. Analytical expressions for the moments show that omitting cell cycle duration introduces an error in the predicted mean number of mRNAs that is a monotonically decreasing function of η, which is proportional to the ratio of the mean cell cycle duration and the mRNA lifetime. By contrast, the error in the variance of the mRNA distribution is highest for intermediate values of η consistent with genome-wide measurements in many organisms. Using eukaryotic cell data, we estimate the errors in the mean and variance to be at most 3% and 25%, respectively. Furthermore, we derive an accurate negative binomial mixture approximation to the mRNA distribution. This indicates that stochasticity in the cell cycle can introduce fluctuations in mRNA numbers that are similar to the effect of bursty transcription. Finally, we show that for real experimental data, disregarding cell cycle stochasticity can introduce errors in the inference of transcription rates larger than 10%

Equalizing the Cost of Health Insurance

The Dutch government compensates health insurance companies when insuringindividuals who are estimated to have high health care costs. This is necessaryto avoid insurers not offering services to certain groups or not providing themwith a high quality of service. It is, however, unknown to what extent thedifferences in health care expenses by different groups of people are truly due toa poorer or better health status. We explore several statistical approaches thatfacilitate explaining the cause of these differences

Equalizing the Cost of Health Insurance

The Dutch government compensates health insurance companies when insuring individuals who are estimated to have high health care costs. This is necessary to avoid insurers not offering services to certain groups or not providing them with a high quality of service. It is, however, unknown to what extent the differences in health care expenses by different groups of people are truly due to a poorer or better health status. We explore several statistical approaches that facilitate explaining the cause of these differences

Equalizing the Cost of Health Insurance

The Dutch government compensates health insurance companies when insuring individuals who are estimated to have high health care costs. This is necessary to avoid insurers not offering services to certain groups or not providing them with a high quality of service. It is, however, unknown to what extent the differences in health care expenses by different groups of people are truly due to a poorer or better health status. We explore several statistical approaches that facilitate explaining the cause of these differences