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4. Describe under what conditions a positively auto-regulated gene circuit can undergo bistability.

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Living cells react to external stimuli by mediating specific responses that are governed by the dynamics of underlying biochemical and genetic networks.

Biochemical networks can exhibit bistable responses such that the network possesses two stable steady states over a range of signal.The possibility of bistability in simple genetic and metabolic networks has been realized for quite some time.

Mechanisms to attain bistability

1 - One of the most widely accepted and studied mechanisms through which bistability can be attained in a genetic circuit is a direct or indirect transcriptional positive feedback characterized by a kinetic order greater than one (cooperativity), so that the dependence of the expression rate on the transcription factor (TF) is superlinear. This mechanism is sufficient to produce bistability for a wide range of parameter values.The existence of bistability depends on the kinetic parameters of the network.

2 - By activating the TF via a post-translational network that is ultrasensitive, in which a sharp transition occurs between inactive and active forms of the TF. For example, ‘zero-order ultrasensitivity’ can be observed in multistep or reversible covalent modification cascades as long as one of the enzymes involved operates near saturation (zero kinetic order).

3 - Another way to achieve ultrasensitivity is via stoichiometric sequestration etc.

So a general, analytic set of conditions for bistability in simple two-element genetic circuits has been derived for monomeric regulation. A simple geometric argument reveals that wide parameter spaces allow monomeric regulation to generate multiple stable states. These results permit to predict the expected scenarios where a reliable switch could be obtained. Current efforts in engineering cellular systems would benefit from our general analysis. In this context, although dimerization seems to be a widespread mechanism in GRNs, the studies indicates that potential scenarios for monomeric regulation could be easily achieved. The current state of the art in synthetic biology allows for a customized engineering of monomeric transcription factors e.g. Zinc finger TFs can be easily designed to bind different DNA sequences . Building these monomeric transcription factors in a properly designed network, the experimental implementation of monomeric bistable circuits seems thus to be feasible.

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