Simulation methods with extended stability for stiff biochemical Kinetics

Background  

With increasing computer power, simulating the dynamics of complex systems in chemistry and biology is becoming increasingly routine. The modelling of individual reactions in (bio)chemical systems involves a large number of random events that can be simulated by the stochastic simulation algorithm (SSA). The key quantity is the step size, or waiting time, τ, whose value inversely depends on the size of the propensities of the different channel reactions and which needs to be re-evaluated after every firing event. Such a discrete event simulation may be extremely expensive, in particular for stiff systems where τ can be very short due to the fast kinetics of some of the channel reactions. Several alternative methods have been put forward to increase the integration step size. The so-called τ-leap approach takes a larger step size by allowing all the reactions to fire, from a Poisson or Binomial distribution, within that step. Although the expected value for the different species in the reactive system is maintained with respect to more precise methods, the variance at steady state can suffer from large errors as τ grows.     

The cell cycle modulated glycoprotein GP115 is one of the major yeast proteins containing glycosylphosphatidylinositol

The cell cycle modulated protein gp115 (115 kDa, isoelectric point about 4.8-5) of Saccharomyces cerevisiae undergoes various post-translational modifications. It is N-glycosylated during its maturation along the secretory pathway where an intermediary precursor of 100 kDa (p100), dynamically related to the mature gp115 protein, is detected at the level of endoplasmic reticulum. Moreover, we have shown by the use of metabolic labeling with [35S]methionine, [3H]palmitic acid and myo-[3H]inositol combined with high resolution two-dimensional gel electrophoresis and immunoprecipitation with a specific antiserum, that gp115 is one of the major palmitate- and inositol-containing proteins in yeast. These results, and the susceptibility of gp115 to phosphatidylinositol-specific phospholipase C treatment strongly indicate that gp115 contains the glycosylphosphatidylinositol (GPI) structure as membrane anchor domain. The two-dimensional analysis of the palmitate- and inositol-labeled proteins has also allowed the characterization of other polypeptides which possibly contain a GPI structure.     

Use of Wishart Prior and Simple Extensions for Sparse Precision Matrix Estimation

A conjugate Wishart prior is used to present a simple and rapid procedure for computing the analytic posterior (mode and uncertainty) of the precision matrix elements of a Gaussian distribution. An interpretation of covariance estimates in terms of eigenvalues is presented, along with a simple decision-rule step to improve the performance of the estimation of sparse precision matrices and associated graphs. In this, elements of the estimated precision matrix that are zero or near zero can be detected and shrunk to zero. Simulated data sets are used to compare posterior estimation with decision-rule with two other Wishart-based approaches and with graphical lasso. Furthermore, an empirical Bayes procedure is used to select prior hyperparameters in high dimensional cases with extension to sparsity.