Time scale and dimension analysis of a budding yeast cell cycle model

The progress through the eukaryotic cell division cycle is driven by an underlying molecular regulatory network. Cell cycle progression can be considered as a series of irreversible transitions from one steady state to another in the correct order. Although this view has been put forward some time ago, it has not been quantitatively proven yet. Bifurcation analysis of a model for the budding yeast cell cycle has identified only two different steady states (one for G1 and one for mitosis) using cell mass as a bifurcation parameter. By analyzing the same model, using different methods of dynamical systems theory, we provide evidence for transitions among several different steady states during the budding yeast cell cycle. By calculating the eigenvalues of the Jacobian of kinetic differential equations we have determined the stability of the cell cycle trajectories of the Chen model. Based on the sign of the real part of the eigenvalues, the cell cycle can be divided into excitation and relaxation periods. During an excitation period, the cell cycle control system leaves a formerly stable steady state and, accordingly, excitation periods can be associated with irreversible cell cycle transitions like START, entry into mitosis and exit from mitosis. During relaxation periods, the control system asymptotically approaches the new steady state. We also show that the dynamical dimension of the Chen’s model fluctuates by increasing during excitation periods followed by decrease during relaxation periods. In each relaxation period the dynamical dimension of the model drops to one, indicating a period where kinetic processes are in steady state and all concentration changes are driven by the increase of cytoplasmic growth.We apply two numerical methods, which have not been used to analyze biological control systems. These methods are more sensitive than the bifurcation analysis used before because they identify those transitions between steady states that are not controlled by a bifurcation parameter (e.g. cell mass). Therefore by applying these tools for a cell cycle control model, we provide a deeper understanding of the dynamical transitions in the underlying molecular network

Optimization of a hydrogen combustion mechanism using both direct and indirect measurements

Journal articleThe Keromnes et al. (2013) mechanism for hydrogen combustion has been optimized using a large set of indirect experimental data, consisting of ignition measurements in shock tubes (566 datapoints in 43 datasets) and rapid compression machines (219/19), and flame velocity measurements (364/59), covering wide ranges of temperature (800 K-2300 K), pressure (0.1 bar-65 bar) and equivalence ratio (phi = 0.2-5.0). According to the sensitivity analysis carried out at each experimental datapoint, 30 Arrhenius parameters and 3 third body collision efficiency parameters of 11 elementary reactions could be optimized using these experimental data. 1749 directly measured rate coefficient values in 56 datasets belonging to the 11 reaction steps were also utilized. Prior uncertainty ranges of the rate coefficients were determined from literature data. Mechanism optimization has led to a new hydrogen combustion mechanism, a set of newly recommended rate parameters with their covariance matrix, and temperature-dependent posterior uncertainty ranges of the rate coefficients. The optimized mechanism generated here was tested together with 13 recent hydrogen combustion mechanisms and proved to be the best one.OTKA (Hungarian Science Research Fund) grants #K84054 and #NN10052