Computational Methods in Systems Biology

Database of Dynamic Signatures Generated 307

each type of node has to be precomputed using Cylindrical Algebraic Decom-
position (CAD). The current set of computed input-output logic files can be
found at /usr/local/share/DSGRN/logic/ in the local installation of DSGRN.
The interpretation of the logic files are given in the Documentation linked from
the DSGRN website [ 22 ]. The second limitation is the size of the parameter
graph. This size is a product of parameter graphs of all the nodes and grows fast
with the type of the node, as well as number of nodes. The command line tool
dsgrncan compute the size of the parameter graph based on the network struc-
ture, so that the user can check its size (see Documentation, section High-Level
API) before committing to the calculation.

Acknowledgment.The work of T. G. was partially supported by NSF grants DMS-
1226213 DMS-1361240 and DARPA D12AP200025. B. C. was supported by DARPA
D12AP200025. The work of S. H. and K. M. was partially supported by grants NSF-
DMS-1125174, 1248071, 1521771 and a DARPA contract HR0011-16-2-0033.

References

1. Goncalves, E., et al.: Bridging the layers: towards integration of signal transduction,
   regulation and metabolism into mathematical models. Mol. BioSyst. 9 (7), 1576–
   1583 (2013)


2. Heatha, A., Kavria, L.: Computational challenges in Systems Biology. Comput.
   Sci. Rev. 3 , 1–17 (2009)


3. Karlebach, G., Shamir, R.: Modelling and analysis of gene regulatory networks.
   Nature 9 , 770–780 (2008)


4. Bornholt, S.: Boolean network models of cellular regulation: prospects and limita-
   tions. J. R. Soc. Interface 5 , 134–150 (2008)


5. Saadatpour, A., Reka, A.: Boolean modeling of biological regulatory networks: A
   methodology tutorial. Methods 62 , 3–12 (2013)


6. Thomas, R.: Regulatory networks seen as asynchronous automata: a logical descrip-
   tion.J.Theor.Biol. 153 , 1–23 (1991)


7. Tyson, J.J., Novak, B.: In: Dekker, A.M.W.V. (ed.) Handbook of Systems Biology.
   Academic Press, San Diego (2013)


8. Chen, K., et al.: Integrative analysis of cell cycle control in budding yeast. Mol.
   Biol. Cell 15 , 3841–3862 (2004)


9. Conley, C.: Isolated Invariant Sets and the Morse Index. American Mathematical
   Society, Providence (1978). ISBN: 9780821888834


10. Mischaikow, K., Mrozek, M.: Handbook of dynamical systems, vol. 2, pp.
    393–460. North-Holland, Amsterdam (2002). doi:10.1016/S1874-575X(02)80030-3.
    http://dx.doi.org.proxy.libraries.rutgers.edu/10.1016/S1874-575X(02)80030-3


11. Kalies, W.D., Mischaikow, K., VanderVorst, R.C.A.M.: An algorithmic approach
    to chain recurrence. Found. Comput. Math. 5 , 409–449 (2005). ISSN: 1615–3375


12. Gedeon, T., Harker, S., Kokubu, H., Mischaikow, K., Oka, H.: Global dynamics
    for steep sigmoidal nonlinearities in two dimensions. Physica D 339 , 18–38 (2017)


13. Streck, A., Lorenz, T., Siebert, H.: Minimization and equivalence in multi-valued
    logical models of regulatory networks. Natural Comput. 14 , 555–566 (2015). ISSN:
    1572–9796


14. Batt, G., Belta, C., Weiss, R.: Temporal logic analysis of gene networks under
    parameter uncertainty. IEEE Trans. Autom. Control 53 , 215–229 (2008)