The yeast pheromone response pathway is a canonical three-step mitogen activated protein kinase (MAPK) cascade which requires a scaffold protein for proper signal transduction. Recent experimental studies into the role the scaffold plays in modulating the character of the transduced signal, show that the presence of the scaffold increases the biphasic nature of the signal response. This runs contrary to prior theoretical investigations into how scaffolds function. We describe a mathematical model of the yeast MAPK cascade specifically designed to capture the experimental conditions and results of these empirical studies. We demonstrate how the system can exhibit either graded or ultrasensitive (biphasic) response dynamics based on the binding kinetics of enzymes to the scaffold. At the basis of our theory is an analytical result that weak interactions make the response biphasic while tight interactions lead to a graded response. We then show via an analysis of the kinetic binding rate constants how the results of experimental manipulations, modeled as changes to certain of these binding constants, lead to predictions of pathway output consistent with experimental observations. We demonstrate how the results of these experimental manipulations are consistent within the framework of our theoretical treatment of this scaffold-dependent MAPK cascades, and how future efforts in this style of systems biology can be used to interpret the results of other signal transduction observations.

Many human diseases are characterized by multiple stages of progression. While the typical sequence of disease progression can be identified, there may be large individual variations among patients. Identifying mean stage durations and their variations is critical for statistical hypothesis testing needed to determine if treatment is having a significant effect on the progression, or if a new therapy is showing a delay of progression through a multistage disease. In this paper we focus on two methods for extracting stage duration statistics from longitudinal datasets: an extension of the linear regression technique, and a counting algorithm. Both are non-iterative, non-parametric and computationally cheap methods, which makes them invaluable tools for studying the epidemiology of diseases, with a goal of identifying different patterns of progression by using bioinformatics methodologies. Here we show that the regression method performs well for calculating the mean stage durations under a wide variety of assumptions, however, its generalization to variance calculations fails under realistic assumptions about the data collection procedure. On the other hand, the counting method yields reliable estimations for both means and variances of stage durations. Applications to Alzheimer disease progression are discussed.

Background: We study the selection dynamics in a heterogeneous spatial colony of cells. We use two spatial generalizations of the Moran process, which include cell divisions, death and migration. In the first model, migration is included explicitly as movement to a proximal location. In the second, migration is implicit, through the varied ability of cell types to place their offspring a distance away, in response to another cell's death. Results: In both models, we find that migration has a direct positive impact on the ability of a single mutant cell to invade a pre-existing colony. Thus, a decrease in the growth potential can be compensated by an increase in cell migration. We further find that the neutral ridges (the set of all types with the invasion probability equal to that of the host cells) remain invariant under the increase of system size (for large system sizes), thus making the invasion probability a universal characteristic of the cells selection status. We find that repeated instances of large scale celldeath, such as might arise during therapeutic intervention or host response, strongly select for the migratory phenotype. Conclusions: These models can help explain the many examples in the biological literature, where genes involved in cell's migratory and invasive machinery are also associated with increased cellular fitness, even though there is no known direct effect of these genes on the cellular reproduction. The models can also help to explain how chemotherapy may provide a selection mechanism for highly invasive phenotypes.