We focus on developing and applying the mathematical methods of control & dynamical systems. Applications are to complex systems in engineering and nature, especially for design of biomolecular circuits. Our approach uses both theoretical models and laboratory experiments.


  • Patel A, Murray RM, Sen S, “Assessment of Robustness to Temperature in a Negative Feedback Loop and a Feedforward Loop”, bioRxiv preprint server, 10.1101/774042, 2019.

  • Patel A, Sen S, “Experimental Evidence for Constraints in Amplitude-Timescale Co-variation of a Biomolecular Pulse Generating Circuit Design ”, bioRxiv preprint server, 10.1101/756049, 2019.

  • Banerjee S, Sen S, “Robustness of a Biomolecular Oscillator to Pulse Perturbations”, IET Systems Biology, 10.1049/iet-syb.2019.0029, 2020.

  • Dey A, Bokka V, Sen S, “Dependence of Bacterial Growth Rate on Dynamic Temperature Changes”, IET Systems Biology, 10.1049/iet-syb.2018.5125, 2019.

  • Dey A, Chakrabarti K, Gola KK, Sen S, “A Kalman Filter Approach for Biomolecular Systems with Noise Covariance Updating”, Sixth Indian Control Conference (accepted), 2019. arXiv preprint server: 1712.02150 q-bio.QM.

  • Relan R, Dey A, Sen S, “The Best Linear Approximation of Biomolecular Systems”, Fifth Indian Control Conference, IIT Delhi, 2019.

  • Patel A, Sen S, “Non-normality Can Facilitate Pulsing in Biomolecular Circuits”, IET Systems Biology, 12(5), Pages 199-204, 10.1049/iet-syb.2018.0008, 2018.

  • Bokka V, Dey A, Sen S, “Period-Amplitude Co-variation in Biomolecular Oscillators”, IET Systems Biology, 12(4), Pages 190-198, 10.1049/iet-syb.2018.0015, 2018.

  • Agarwal A, Dey A, Relan R, Sen S, “Nonparametric Analysis of Nonlinear Distortions for Biomolecular Systems”, Third IFAC International Conference on Advances in Control and Optimization of Dynamical Systems, Hyderabad, 2018.

  • Banerjee S, Bokka V, Sen S, “Attentuation of Pulse Disturbances in Biomolecular Oscillators”, Third IFAC International Conference on Advances in Control and Optimization of Dynamical Systems, Hyderabad, 2018.

  • Patel A, Sen S, “On Amplitude-Timescale Constraints in a Pulse Generating Biomolecular Circuit”, Indian Control Conference, IIT Kanpur, 2018.

  • Dey A, Sen S, “Describing function-based Approximations of Biomolecular Systems”, IET Systems Biology, 12(3), Pages 93-100, 10.1049/iet-syb.2017.0026, 2017.

  • Sen S, Apurva D, Satija R, Siegal D, Murray RM, “Design of a Toolbox of RNA Thermometers”, ACS Synthetic Biology, 6(8), 1461-1470, 10.1021/acssynbio.6b00301, 2017. Synthetic Biology: Engineering, Evolution & Design Conference, 2015, oral presentation; biorxiv preprint server, 10.1101/017369, 2015. Updated version - bioRxiv preprint server, 10.1101/017269, 2016.

  • Joshi SK, Sen S, Kar IN, “Synchronization of Ring Coupled Four Oscillators”, Indian Control Conference, IIT Guwahati, 2017.

  • Joshi SK, Sen S, Kar IN, “Synchronization of Coupled Oscillator Dynamics”, 4th International Conference on Advances in Control and Optimization of Dynamical Systems, 2016.

  • Sen S, “Transient Response Characteristics in a Biomolecular Integral Controller”, IET Systems Biology, 10(2), Pages 57-63, 10.1049/iet-syb.2015.0004, 2016.

  • Dey A, Sen S, “Describing Function-based Approximations of Biomolecular Signalling Systems”, European Control Conference, Pages 2292-2297, 10.1109/ECC.2015.7330880, 2015.

  • Sen S, Murray RM, “Negative Feedback Facilitates Temperature Robustness in Biomolecular Circuit Dynamics”, bioRxiv preprint server, 10.1101/007385, 2014.

  • Sen S, Kim J, Murray RM, “Designing Robustness to Temperature in a Feedforward Loop Circuit”, 53rd IEEE Conference on Decision and Control, Pages 4629-4634, 10.1109/CDC.2014.7040112, 2014.

  • Kim J, Khetarpal I, Sen S, Murray RM, “Synthetic Circuit for Exact Adaptation and Fold-Change Detection”, Nucleic Acids Research, 42(9), Pages 6078-6089, 10.1093/nar/gku233, 2014.

  • Bokka V, Sen S, “Sensitivity Analysis of Oscillatory Circuits”, 3rd International Conference on Advances in Control and Optimization of Dynamical Systems, 10.3182/20140313-3-IN-3024.00220, 2014.

  • Sen S, “Characterization of Tradeoffs in Biomolecular Signaling”, BioSystems, 114(3), Pages 261-268, 10.1016/j.biosystems.2013.09.006, 2013.

  • Sen S, Murray RM, “Temperature Dependence of Biomolecular Circuit Designs”, 52nd IEEE Conference on Decision and Control, Pages 1398-1403, 10.1109/CDC.2013.6760078, 2013.

  • Sen S, Murray RM, “Performance Metrics for a Biomolecular Step Response”, 51st IEEE Conference on Decision and Control, Pages 5536-5541, 10.1109/CDC.2012.6425892, 2012.

  • Sen S, “Tradeoffs in Simple Biomolecular Signaling Systems”, Systems & Control Letters, 61(8), Pages 834-838, 10.1016/j.sysconle.2012.04.011, 2012.

  • Sen S, GarcĂ­a-Ojalvo J, Elowitz MB, “Dynamical Consequences of Bandpass Feedback Loops in a Bacterial Phosphorelay”, PLoS ONE 6(9): e25102, doi:10.1371/journal.pone.0025102, 2011.

  • Sen S, “Regulatory Consequences of Bandpass Feedback in a Bacterial Phosphorelay”, Ph.D. Dissertation, California Institute of Technology.


Sustainable development relies on research into understanding how natural systems behave and how this behaviour can be harnessed for engineering design. Using a combination of the mathematical methods of control & dynamical systems, and experimental measurements, we investigate how biological systems behave and how these insights can be transferred for design of biological and engineering processes. Ongoing research includes,

  • Biomolecular circuit design. Characterizing and ensuring robustness in the performance of designed biomolecular circuits in different environmental conditions is a major challenge (see, for example, CAGEN). We are particularly interested in the role of temperature, a key environmental parameter that can universally affect biomolecular circuit reactions. Our approach combines simple mathematical models with fluorescent reporter-based experimental measurements of circuit performance in cells growing in temperature-controlled environments.

  • Dynamics of genetic circuits. Some of the most fascinating dynamics arises in how interactions between genes and proteins inside cells, called genetic circuits, control cellular behaviour. These appear to combine multiple rhythmic cycles and decision-making transitions, making this subject of investigation both mathematically challenging as well as of fundamental biological importance. We plan to study these phenomena using both dynamical system models and single-cell time-lapse microscopy experiments.

  • Simplified representations of complex models. Mathematical models are extremely important to capture the complex nature of modern engineering systems. Simplified representations of these models are essential both for understanding the relative importance of different underlying interactions and especially for ease in the design process. We aim to apply and develop model reduction tools such as balanced truncation and averaging.

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