Moment estimation for chemically reacting systems by extended Kalman filtering.

In stochastic models of chemically reacting systems that contain bimolecular reactions, the dynamics of the moments of order up to n of the species populations do not form a closed system, in the sense that their time-derivatives depend on moments of order n + 1. To close the dynamics, the moments of order n + 1 are generally approximated by nonlinear functions of the lower order moments. If the molecule counts of some of the species have a high probability of becoming zero, such approximations may lead to imprecise results and stochastic simulation is the only viable alternative for system analysis. Stochastic simulation can produce exact realizations of chemically reacting systems, but tends to become computationally expensive, especially for stiff systems that involve reactions at different time scales. Further, in some systems, important stochastic events can be very rare and many simulations are necessary to obtain accurate estimates. The computational cost of stochastic simulation can then be prohibitively large. In this paper, we propose a novel method for estimating the moments of chemically reacting systems. The method is based on closing the moment dynamics by replacing the moments of order n + 1 by estimates calculated from a small number of stochastic simulation runs. The resulting stochastic system is then used in an extended Kalman filter, where estimates of the moments of order up to n, obtained from the same simulation, serve as outputs of the system. While the initial motivation for the method was improving over the performance of stochastic simulation and moment closure methods, we also demonstrate that it can be used in an experimental setting to estimate moments of species that cannot be measured directly from time course measurements of the moments of other species.

Stochastic hybrid modeling of DNA replication across a complete genome.

DNA replication in eukaryotic cells initiates from hundreds of origins along their genomes, leading to complete duplication of genetic information before cell division. The large number of potential origins, coupled with system uncertainty, dictates the need for new analytical tools to capture spatial and temporal patterns of DNA replication genome-wide. We have developed a stochastic hybrid model that reproduces DNA replication throughout a complete genome. The model can capture different modes of DNA replication and is applicable to various organisms. Using genome-wide data on the location and firing efficiencies of origins in the fission yeast, we show how the DNA replication process evolves during S-phase in the presence of stochastic origin firing. Simulations reveal small regions of the genome that extend S-phase to three times its reported duration. The low levels of late replication predicted by the model are below the detection limit of techniques used to measure S-phase length. Parameter sensitivity analysis shows that increased replication fork speeds genome-wide, or additional origins are not sufficient to reduce S-phase to its reported length. We model the redistribution of a limiting initiation factor during S-phase and show that it could shorten S-phase to the reported duration. Alternatively, S-phase may be extended, and what has traditionally been defined as G2 may be occupied by low levels of DNA synthesis with the onset of mitosis delayed by activation of the G2/M checkpoint.