Nonlinear Dyn https://doi.org/10.1007/s11071-018-4215-0 ORIGINAL PAPER Mathematical modelling of nonlinear dynamics generated from modular interconnections in cellular SOS response system Silpa Bhaskaran · Achuthsankar S. Nair Received: 13 June 2017 / Accepted: 17 March 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract Nonlinear dynamics in synthetic biology systems, generated as a consequence of interconnec- tions between biological modules, poses challenges to the objective of engineering biological systems with predictable characteristics. Mathematical models, that often provide accurate descriptions of the biological modules in isolation, fail to capture such nonlineari- ties that arise in the interconnected modules. Without the modelling and quantification of these nonlineari- ties, systems biology models cannot be predictable or reliable. Hence it become a key area of focus of sys- tems and synthetic biologists. To this end, we anal- yse the nonlinearities in the SOS response system, a prime cellular network in bacterial cells that functions to repair the DNA damage. It is shown that the dynam- ics of the modules in the SOS response system differ in isolation and in integration, and substantial variation is observed when more modules are connected. The inter- dependence among major modules is quantified, which imparts whether the integrated dynamics is an attenu- ation or amplification of the isolated dynamics. From a synthetic biology perspective, our study contributes to the effective engineering of biological devices from the integration of biological modules in a bottom-up fashion. Meanwhile, it also complements the investi- gations on the DNA damage repairing mechanism in living cells. S. Bhaskaran (B ) · A. S. Nair Department of Computational Biology and Bioinformatics, University of Kerala, Trivandrum, India e-mail: silpabhaskaran@gmail.com Keywords Biological networks · Modularity · SOS response system · Dynamics · Cascaded layering framework · Functionality · Mutual dynamics · Synthetic biology 1 Introduction Dynamic behaviour of biological networks is a key topic of investigation for systems and synthetic biolo- gists, as it helps in their efforts on engineering a living cell with predictable characteristics. Elucidation of the network dynamics enables them to probe into the basic design principles of living systems. These insights can be applied to the designing of novel biological systems or to the redesigning of existing biological systems for novel applications, with the help of mathematical mod- els and engineering principles. Adopting the modular approach for the engineering of artificial systems, biological systems are also often designed and fabricated in a hierarchical manner. The small and simple modules are redesigned and engi- neered initially which are integrated with each other to form the higher level of systems. With this objec- tive, several biological modules have been modelled and analysed by the systems biologists. These mod- ules, in turn, have been engineered and incorporated into living cells by the synthetic biologists, so that they exhibited the characteristics they have been looking for. The successful engineering of the repressilator by [1] and the toggle switch by [2] is the pioneering work 123