J. Math. Biol. DOI 10.1007/s00285-010-0375-3 Mathematical Biology Design of regulation and dynamics in simple biochemical pathways Ram Rup Sarkar · R. Maithreye · Somdatta Sinha Received: 16 March 2010 / Revised: 22 July 2010 © Springer-Verlag 2010 Abstract Complex regulation of biochemical pathways in a cell is brought about by the interaction of simpler regulatory structures. Among the basic regulatory designs, feedback inhibition of gene expression is the most common motif in gene regulation and a ubiquitous control structure found in nature. In this work, we have studied a common structural feature (delayed feedback) in gene organisation and shown, both theoretically and experimentally, its subtle but important functional role in gene expres- sion kinetics in a negatively auto-regulated system. Using simple deterministic and stochastic models with varying levels of realism, we present detailed theoretical repre- sentations of negatively auto-regulated transcriptional circuits with increasing delays in the establishment of feedback of repression. The models of the circuits with and without delay are studied analytically as well as numerically for variation of parame- ters and delay lengths. The positive invariance, boundedness of the solutions, local and global asymptotic stability of both the systems around the unique positive steady state are studied analytically. Existence of transient temporal dynamics is shown mathe- matically. Comparison of the two types of model circuits shows that even though the long-term dynamics is stable and not affected by delays in repression, there is interesting variation in the transient dynamical features with increasing delays. The- oretical predictions are validated through experimentally constructed gene circuits of similar designs. This combined theoretical and experimental study helps delineate the opposing effects of delay-induced instability, and the stability-enhancing property of negative feedback in the pathway behaviour, and gives rationale for the abundance of similar designs in real biochemical pathways. R. R. Sarkar · R. Maithreye · S. Sinha (B ) Mathematical and Computational Biology Group, Centre for Cellular and Molecular Biology (CSIR), Uppal Road, Hyderabad 500007, India e-mail: sinha@ccmb.res.in 123