Biological organisms use their sensory systems to detect changes in their environment. The ability of sensory systems to adapt to static inputs allows wide dynamic range as well as sensitivity to input changes including fold-change detection, a response that depends only on fold changes in input, and not on absolute changes. This input scale invariance underlies an important strategy for search that depends solely on the spatial profile of the input. Synthetic efforts to reproduce the architecture and response of cellular circuits provide an important step to foster understanding at the molecular level. We report the bottom-up assembly of biochemical systems that show exact adaptation and fold-change detection. Using a malachite green aptamer as the output, a synthetic transcriptional circuit with the connectivity of an incoherent feed-forward loop motif exhibits pulse generation and exact adaptation. A simple mathematical model was used to assess the amplitude and duration of pulse response as well as the parameter regimes required for fold-change detection. Upon parameter tuning, this synthetic circuit exhibits fold-change detection for four successive rounds of two-fold input changes. The experimental realization of fold-change detection circuit highlights the programmability of transcriptional switches and the ability to obtain predictive dynamical systems in a cell-free environment for technological applications.

Abstract. Biomolecular temperature sensors can be used for efficient control of large-volume bioreactors, for spatiotemporal control and imaging of gene expression, as well as to engineer robustness to temperature in biomolecular circuit design. While RNA-based sensors, called 'thermometers', have been investigated in natural and synthetic contexts, an important challenge is to design different responses to temperature, differing in sensitivities and thresholds. We address this issue using experimental measurements in cells and in cell-free biomolecular 'breadboards' in combination with computations of RNA thermodynamics. We designed a library of RNA thermometers, finding, com-ND 4.0 International license peer-reviewed) is the author/funder. It is made available under aThe copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/017269 doi: bioRxiv preprint first posted online Mar. 30, 2015; putationally, that it could contain a multiplicity of responses to temperature. We constructed this library and found a wide range of responses to temperature, ranging from 3.5-fold to over 10-fold in the temperature range 29 • C -37 • C. These were largely linear responses with over 10-fold difference in slopes. We correlated the measured responses with computational expectations, finding that while there was no strong correlation in the individual values, the overall trends were similar. These results present a toolbox of RNA-based circuit elements with varying temperature sensitivities.

Under conditions of nutrient limitation, Bacillus subtilis cells terminally differentiate into a dormant spore state. Progression to sporulation is controlled by a genetic circuit consisting of a phosphorelay embedded in multiple transcriptional feedback loops, which is used to activate the master regulator Spo0A by phosphorylation. These transcriptional regulatory interactions are “bandpass”-like, in the sense that activation occurs within a limited band of Spo0A∼P concentrations. Additionally, recent results show that the phosphorelay activation occurs in pulses, in a cell-cycle dependent fashion. However, the impact of these pulsed bandpass interactions on the circuit dynamics preceding sporulation remains unclear. In order to address this question, we measured key features of the bandpass interactions at the single-cell level and analyzed them in the context of a simple mathematical model. The model predicted the emergence of a delayed phase shift between the pulsing activity of the different sporulation genes, as well as the existence of a stable state, with elevated Spo0A activity but no sporulation, embedded within the dynamical structure of the system. To test the model, we used time-lapse fluorescence microscopy to measure dynamics of single cells initiating sporulation. We observed the delayed phase shift emerging during the progression to sporulation, while a re-engineering of the sporulation circuit revealed behavior resembling the predicted additional state. These results show that periodically-driven bandpass feedback loops can give rise to complex dynamics in the progression towards sporulation.

Synchronization is most significant phenomena to study the collective behaviour of coupled oscillators. Synchronization is said to occur if phase locking and consensus among corresponding states of coupled dynamical systems is achieved. In general, how to achieve exact conditions for synchronization is unclear. Therefore, it becomes essential to derive conditions on these coupled dynamical systems which lead to synchronization. Here, we aim to derive sufficient conditions for synchronization of selected benchmark oscillators which are linearly coupled. We have used Lyapunov approach to obtain sufficiency condition for synchronization of coupled oscillators. We study synchronization of Van der Pol oscillators and Fitzhugh Nagumo oscillators with all-to-all connectivity, for both uniformly and non-uniformly linearly coupled configurations. These results have been numerically simulated for both the above types of oscillators.Keywords: Van der Pol, Fitzhugh Nagumo(FHN), coupled oscillators, neuronal membrane potential v i and recovery variable w i .

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