A Case Study on the Parametric Occurrence of Multiple Steady States

We consider the problem of determining multiple steady states for positive real values in models of biological networks. Investigating the potential for these in models of the mitogen-activated protein kinases (MAPK) network has consumed considerable effort using special insights into the structure of corresponding models. Here we apply combinations of symbolic computation methods for mixed equality/inequality systems, specifically virtual substitution, lazy real triangularization and cylindrical algebraic decomposition. We determine multistationarity of an 11-dimensional MAPK network when numeric values are known for all but potentially one parameter. More precisely, our considered model has 11 equations in 11 variables and 19 parameters, 3 of which are of interest for symbolic treatment, and furthermore positivity conditions on all variables and parameters.Comment: Accepted into ISSAC 2017. This version has additional page showing all 11 CAD trees discussed in Section 2.1.

Identifying the parametric occurrence of multiple steady states for some biological networks

We consider a problem from biological network analysis of determining regions in a parameter space over which there are multiple steady states for positive real values of variables and parameters. We describe multiple approaches to address the problem using tools from Symbolic Computation. We describe how progress was made to achieve semi-algebraic descriptions of the multistationarity regions of parameter space, and compare symbolic results to numerical methods. The biological networks studied are models of the mitogen-activated protein kinases (MAPK) network which has already consumed considerable effort using special insights into its structure of corresponding models. Our main example is a model with 11 equations in 11 variables and 19 parameters, 3 of which are of interest for symbolic treatment. The model also imposes positivity conditions on all variables and parameters. We apply combinations of symbolic computation methods designed for mixed equality/inequality systems, specifically virtual substitution, lazy real triangularization and cylindrical algebraic decomposition, as well as a simplification technique adapted from Gaussian elimination and graph theory. We are able to determine multistationarity of our main example over a 2-dimensional parameter space. We also study a second MAPK model and a symbolic grid sampling technique which can locate such regions in 3-dimensional parameter space.Comment: 60 pages - author preprint. Accepted in the Journal of Symbolic Computatio

Impaired IL-23-dependent induction of IFN-gamma underlies mycobacterial disease in patients with inherited TYK2 deficiency

Human cells homozygous for rare loss-of-expression (LOE) TYK2 alleles have impaired, but not abolished, cellular responses to IFN-alpha/beta (underlying viral diseases in the patients) and to IL-12 and IL-23 (underlying mycobacterial diseases). Cells homozygous for the common P1104A TYK2 allele have selectively impaired responses to IL-23 (underlying isolated mycobacterial disease). We report three new forms of TYK2 deficiency in six patients from five families homozygous for rare TYK2 alleles (R864C, G996R, G634E, or G1010D) or compound heterozygous for P1104A and a rare allele (A928V). All these missense alleles encode detectable proteins. The R864C and G1010D alleles are hypomorphic and loss-of-function (LOF), respectively, across signaling pathways. By contrast, hypomorphic G996R, G634E, and A928V mutations selectively impair responses to IL-23, like P1104A. Impairment of the IL-23-dependent induction of IFN-gamma is the only mechanism of mycobacterial disease common to patients with complete TYK2 deficiency with or without TYK2 expression, partial TYK2 deficiency across signaling pathways, or rare or common partial TYK2 deficiency specific for IL-23 signaling.ANRS Nord-Sud ; CIBSS ; CODI ; Comité para el Desarrollo de la Investigación ; Fulbright Future Scholarshi

Semi-algebraic methods for symbolic analysis of complex reaction networks

Deutsche Forschungsgemeinschaft (DFG), SPP 1489 program

Dataset supporting the paper: Symbolic Versus Numerical Computation and Visualization of Parameter Regions for Multistationarity of Biological Networks

<p>Dataset supporting the paper:</p> <p>Matthew England, Hassan Errami, Dima Grigoriev, Ovidiu Radulescu, Thomas Sturm, and Andreas Weber. Symbolic Versus Numerical Computation and Visualization of Parameter Regions for Multistationarity of Biological Networks.  In Proceedings of CASC ’17, Beijing, China, September 18-22 2017, 15 pages. Springer, 2017.</p> <p>The files whose name starts with "SamplePoints" are text files containing the data that produced the plots in the paper.</p> <p>The files whose name starts with "Sys" show the Maple computations used to produce the data.  The mw files are to be run with the Maple Computer Algebra System (https://www.maplesoft.com/products/maple/).  Pdf printouts of these have also been included for those who do not have access to Maple.</p> <p> </p