The PSF Model is a transformation of a dynamical protein signaling model to matrix operations (1).

Part I: ODE Model

It consists of a network of interactions between molecular species, initial species concentrations, kinetic rates and signaling inputs. It computes trajectories from initial conditions by ordinary differential equations. Many such models are available in a public repository (2).

Part II: Matrix Model

Subsequently, for any input, PSF computes the equilibrium concentration of all cellular species, and the time required to reach equilibrium, and stores the results in a matrix. If transients appear, they can also be characterized by amplitude and time. For this the model must have the properties of a balanced system (3).


The result are protein signaling functions which operate like generalized Hill functions. For any molecular species in the network the concentration of all other species under any input can be computed by matrix operations.



(1) Scheler G. Transfer functions for protein signal transduction: application to a model of striatal neural plasticity. PLoS One. 2013;8(2):e55762. doi: 10.1371/journal.pone.0055762. Epub 2013 Feb 6.

(2) Nick Juty, Raza Ali, Mihai Glont, Sarah Keating, Nicolas Rodriguez, Maciej J. Swat, Sarala M. Wimalaratne, Henning Hermjakob, Nicolas Le Novère, Camille Laibe and Vijayalakshmi Chelliah BioModels: Content, Features, Functionality and Use. CPT: Pharmacometrics & Systems Pharmacology 2015

(3) Deng J, Feinberg M, Jones C, Nachman A (2011) On the steady states of weakly reversible chemical reaction networks. Arxiv preprint: arXiv 11112386v2 1–20.

(4) Scheler, G. Timing in cells: invariance and nonsynchronicity. 5th Conference on Systems Biology of Mammalian Cells (SBMC) 2014.

(5) Scheler G. Self-organization of signal transduction. F1000Research 2013 Apr 23;2:116. doi: 10.12688/f1000research.2-116.v1.

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