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One of the most common modes of secretion of toxins in gram-negative bacteria is via the type three secretion system (TTSS), which enables the toxins to be specifically exported into the host cell. The hilA gene product is a key regulator of the expression of the TTSS located on the pathogenicity island (SPI-1) of Salmonella enterica serovar Typhimurium. It has been proposed earlier that the regulation of HilA expression is via a complex feedforward loop involving the transactivators HilD, HilC and RtsA. In this paper, we have constructed a mathematical model of regulation of hilA-promoter by all the three activators using two feedforward loops. We have modified the model to include additional complexities in regulation such as the proposed positive feedback and cross regulations of the three transactivators. Results of the various models indicate that the basic model involving two Type I coherent feedforward loops with an OR gate is sufficient to explain the published experimental observations. We also discuss two scenarios where the regulation can occur via monomers or heterodimers of the transactivators and propose experiments that can be performed to distinguish the two modes of regulator function.
Pubmed ID: 19003447
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XPPAUT is a tool for solving differential equations, difference equations, delay equations, functional equations, boundary value problems, and stochastic equations. It evolved from a chapter written by John Rinzel and me on the qualitative theory of nerve membranes and eventually became a commercial product for MSDOS computers called PHASEPLANE. It is now available as a program running under X11 and Windows. The code brings together a number of useful algorithms and is extremely portable. All the graphics and interface are written completely in Xlib which explains the somewhat idiosyncratic and primitive widgets interface. XPP contains the code for the popular bifurcation program, AUTO . Thus, you can switch back and forth between XPP and AUTO, using the values of one program in the other and vice-versa. I have put a ``friendly'' face on AUTO as well. You do not need to know much about it to play around with it. XPP has the capabilities for handling up to 590 differential equations. There are over a dozen solvers including several for stiff systems, a solver for integral equations and a symplectic solver. Up to 10 graphics windows can be visible at once and a variety of color combinations is supported. PostScript output is supported as well as GIF and animator GIF movies Post processing is easy and includes the ability to make histograms, FFTs and applying functions to columns of your data. Equilibria and linear stability as well as one-dimensional invariant sets can be computed. Nullclines and flow fields aid in the qualitative understanding of two-dimensional models. Poincare maps and equations on cylinders and tori are also supported. Some useful averaging theory tricks and various methods for dealing with coupled oscillators are included primarily because that is what I do for a living. Equations with Dirac delta functions are allowable. I have added an animation package that allows you to create animated versions of your simulations, such as a little pendulum moving back and forth or lamprey swimming. See toys! for examples. There is a curve-fitter based on the Marquardt-Levenberg algorithm which lets you fit data points to the solutions to dynamical systems. It is possible to automatically generate "movies'' of three-dimensional views of attractors or parametric changes in the attractor as some parameters vary. Dynamically link to external subroutines XPP has been successfully compiled on a SPARC II under OpenLook, a SPARC 1.5 running generic X, a NeXT running X11R4, a DEC 5000, a PC using Linux or Windows, and SGI and an HP 730. It also runs under Win95/NT/98 if you have an X-Server. I cannot vouch for other platforms but it has been compiled on the IBM RS6000. Building XPP requires only the standard C compiler, and Xlib. Look at the any README files that come with the distribution for solutions to common compilation problems.
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