A novel measure to analyze protein structures: Aspect ratio in protein alpha shapes.

Proteins' three-dimensional (3D) structures are analyzed traditionally using geometric descriptors such as torsional angles and inter-atomic distances. In this study a measure that is borrowed from computational geometry, aspect ratio of each tetrahedron in alpha shapes of proteins, is utilized. This geometric descriptor differentiates alpha and beta structural classes of proteins when combined with principal components analysis. The method converts the structures of individual proteins, 3D coordinates of the atoms, to points on a plane. It has a high degree of accuracy in differentiating R and T structures of hemoglobin. Therefore, it is anticipated that the geometric measure can be used successfully in a method that is extended to solve classification problems in machine learning.

A quantitative model of the effect of unreplicated DNA on cell cycle progression in frog egg extracts.

A critical goal in cell biology is to develop a systems-level perspective of eukaryotic cell cycle controls. Among these controls, a complex signaling network (called 'checkpoints') arrests progression through the cell cycle when there is a threat to genomic integrity such as unreplicated or damaged DNA. Understanding the regulatory principles of cell cycle checkpoints is important because loss of checkpoint regulation may be a requisite step on the roadway to cancer. Mathematical modeling has proved to be a useful guide to cell cycle regulation by revealing the importance of bistability, hysteresis and time lags in governing cell cycle transitions and checkpoint mechanisms. In this report, we propose a mathematical model of the frog egg cell cycle including effects of unreplicated DNA on progression into mitosis. By a stepwise approach utilizing parameter estimation tools, we build a model that is grounded in fundamental behaviors of the cell cycle engine (hysteresis and time lags), includes new elements in the signaling network (Myt1 and Chk1 kinases), and fits a large and diverse body of data from the experimental literature. The model provides a validated framework upon which to build additional aspects of the cell cycle checkpoint signaling network, including those control signals in the mammalian cell cycle that are commonly mutated in cancer.

Computational insights on the competing effects of nitric oxide in regulating apoptosis.

Despite the establishment of the important role of nitric oxide (NO) on apoptosis, a molecular-level understanding of the origin of its dichotomous pro- and anti-apoptotic effects has been elusive. We propose a new mathematical model for simulating the effects of nitric oxide (NO) on apoptosis. The new model integrates mitochondria-dependent apoptotic pathways with NO-related reactions, to gain insights into the regulatory effect of the reactive NO species N(2)O(3), non-heme iron nitrosyl species (FeL(n)NO), and peroxynitrite (ONOO(-)). The biochemical pathways of apoptosis coupled with NO-related reactions are described by ordinary differential equations using mass-action kinetics. In the absence of NO, the model predicts either cell survival or apoptosis (a bistable behavior) with shifts in the onset time of apoptotic response depending on the strength of extracellular stimuli. Computations demonstrate that the relative concentrations of anti- and pro-apoptotic reactive NO species, and their interplay with glutathione, determine the net anti- or pro-apoptotic effects at long time points. Interestingly, transient effects on apoptosis are also observed in these simulations, the duration of which may reach up to hours, despite the eventual convergence to an anti-apoptotic state. Our computations point to the importance of precise timing of NO production and external stimulation in determining the eventual pro- or anti-apoptotic role of NO.