A mathematical model of the phosphoinositide pathway

Phosphoinositides are signalling lipids that constitute a complex network regulating many cellular processes. We propose a computational model that accounts for all species of phosphoinositides in the plasma membrane of mammalian cells. The model replicates the steady-state of the pathway and most known dynamic phenomena. Sensitivity analysis demonstrates model robustness to alterations in the parameters. Model analysis suggest that the greatest contributor to phosphatidylinositol 4,5-biphosphate (PI(4,5)P2) production is a flux representing the direct transformation of PI into PI(4,5) P2, also responsible for the maintenance of this pool when phosphatidylinositol 4-phosphate (PI(4) P) is decreased. PI(5)P is also shown to be a significant source for PI(4,5)P2 production. The model was validated with siRNA screens that knocked down the expression of enzymes in the pathway. The screen monitored the activity of the epithelium sodium channel (ENaC), which is activated by PI(4,5)P2. While the model may deepen our understanding of other physiological processes involving phosphoinositides, we highlight therapeutic effects of ENaC modulation in Cystic Fibrosis (CF). The model suggests control strategies where the activities of the enzyme phosphoinositide 4-phosphate 5-kinase I (PIP5KI) or the PI4K + PIP5KI + DVL protein complex are decreased and cause an efficacious reduction in PI(4,5)P2 levels while avoiding undesirable alterations in other phosphoinositide pools

A mathematical model of the phosphoinositide pathway

Phosphoinositides are signalling lipids that constitute a complex network regulating many cellular processes. We propose a computational model that accounts for all species of phosphoinositides in the plasma membrane of mammalian cells. The model replicates the steady-state of the pathway and most known dynamic phenomena. Sensitivity analysis demonstrates model robustness to alterations in the parameters. Model analysis suggest that the greatest contributor to phosphatidylinositol 4,5-biphosphate (PI(4,5)P2) production is a flux representing the direct transformation of PI into PI(4,5) P2, also responsible for the maintenance of this pool when phosphatidylinositol 4-phosphate (PI(4) P) is decreased. PI(5)P is also shown to be a significant source for PI(4,5)P2 production. The model was validated with siRNA screens that knocked down the expression of enzymes in the pathway. The screen monitored the activity of the epithelium sodium channel (ENaC), which is activated by PI(4,5)P2. While the model may deepen our understanding of other physiological processes involving phosphoinositides, we highlight therapeutic effects of ENaC modulation in Cystic Fibrosis (CF). The model suggests control strategies where the activities of the enzyme phosphoinositide 4-phosphate 5-kinase I (PIP5KI) or the PI4K + PIP5KI + DVL protein complex are decreased and cause an efficacious reduction in PI(4,5)P2 levels while avoiding undesirable alterations in other phosphoinositide pools

Modelling shock heating in cluster mergers - I. Moving beyond the spherical accretion model

The thermal history of the intracluster medium (ICM) is complex. Heat input from cluster mergers, from active galactic nuclei (AGN) and from winds in galaxies offsets and may even prevent the cooling of the ICM. Consequently, the processes that set the temperature and density structure of the ICM play a key role in determining how galaxies form. In this paper, we focus on the heating of the ICM during cluster mergers, with the eventual aim of incorporating this mechanism into semi-analytic models for galaxy formation. We generate and examine a suite of non-radiative hydrodynamic simulations of mergers in which the initial temperature and density structure of the systems are set using realistic scaling laws. Our collisions cover a range of mass ratios and impact parameters, and consider both systems composed entirely of gas (these reduce the physical processes involved), and systems comprising a realistic mixture of gas and dark matter. We find that the heating of the ICM can be understood relatively simply by considering evolution of the gas entropy during the mergers. The increase in this quantity in our simulations closely corresponds to that predicted from scaling relations based on the increase in cluster mass. We examine the physical processes that succeed in generating the entropy in order to understand why previous analytical approaches failed. We find the following. (i) The energy that is thermalized during the collision greatly exceeds the kinetic energy available when the systems first touch. The smaller system penetrates deep into the gravitational potential before it is disrupted. (ii) For systems with a large mass ratio, most of the energy is thermalized in the massive component. The heating of the smaller system is minor and its gas sinks to the centre of the final system. This contrasts with spherically symmetric analytical models in which accreted material is simply added to the outer radius of the system. (iii) The bulk of the entropy generation occurs in two distinct episodes. The first episode occurs following the collision of the cores, when a large shock wave is generated that propagates outwards from the centre. This causes the combined system to expand rapidly and overshoot hydrostatic equilibrium. The second entropy generation episode occurs as this material is shock heated as it recollapses. Both heating processes play an important role, contributing approximately equally to the final entropy. This revised model for entropy generation improves our physical understanding of cosmological gas simulations