Biomolecular mechanisms for signal differentiation

Abstract

Summary Cells can sense temporal changes of molecular signals, allowing them to predict environmental variations and modulate their behavior. This paper elucidates biomolecular mechanisms of time derivative computation, facilitating the design of reliable synthetic differentiator devices for a variety of applications, ultimately expanding our understanding of cell behavior. In particular, we describe and analyze three alternative biomolecular topologies that are able to work as signal differentiators to input signals around their nominal operation. We propose strategies to preserve their performance even in the presence of high-frequency input signal components which are detrimental to the performance of most differentiators. We find that the core of the proposed topologies appears in natural regulatory networks and we further discuss their biological relevance. The simple structure of our designs makes them promising tools for realizing derivative control action in synthetic biology.

A Hidden Proportional Feedback Mechanism Underlies Enhanced Dynamic Performance and Noise Rejection in Sensor-Based Antithetic Integral Control

“…where, for convenience and with a slight abuse of notation, σ x is absorbed in the dynamics of the process and so ũ does not involve x1 . Taking the Laplace transforms on both sides of the equalities in (28) and recalling that the transfer matrix of the controller is…”

“…Since the introduction of the AIF controller, efforts have been directed towards enhancing its performance either by tuning and exploring the dynamic trade-offs [21][22][23], or by adding extra circuitry [24][25][26][27][28][29][30] including molecular buffering, which was inspired by [31], and realizations of Proportional-Integral (PI) and Proportional-Integral-Derivative (PID) controllers. The need for such advanced biomolecular controllers arises from the limitations of standalone integral controllers.…”

Multicellular PD Control in Microbial Consortia

“…3) Derivative controller cells: Biomolecular topologies allowing cells to sense temporal changes of molecules signals [17], [18] can be employed to realize a derivative control action. As shown in Appendix A, an approximation of the time derivative of the control error e(t) can be obtained by embedding in the controller population the biomolecular circuit represented in Figure 1, whose dynamics can be described as follows:…”

“…Specifically, the dynamics of the concentration of Q u in the Proportional controllers is given by: where γ p is the dilution rate of the quorum sensing molecules into the Proportional cells, μ and θ are positive control parameters, and β P is a tunable parameter which plays the role of a proportional gain. It has been shown in [9] that the first term in (4) realizes a control action that is a function of the control error: Derivative controller cells: Biomolecular topologies allowing cells to sense temporal changes of molecules signals [17], [18] can be employed to realize a derivative control action. As shown in Appendix A, an approximation of the time derivative of the control error e ( t ) can be obtained by embedding in the controller population the biomolecular circuit represented in Figure 1, whose dynamics can be described as follows: where γ d is the dilution rate of A due to cell growth and division, and β a and β m are activation rates of species A and M , respectively, which in turns are actively degraded by Q x and A , respectively, through enzymatic reactions modeled here with Michaelis-Menten functions with constants γ α , k a , γ m , k m .…”

“…Derivative controller cells: Biomolecular topologies allowing cells to sense temporal changes of molecules signals [17], [18] can be employed to realize a derivative control action. As shown in Appendix A, an approximation of the time derivative of the control error e ( t ) can be obtained by embedding in the controller population the biomolecular circuit represented in Figure 1, whose dynamics can be described as follows: where γ d is the dilution rate of A due to cell growth and division, and β a and β m are activation rates of species A and M , respectively, which in turns are actively degraded by Q x and A , respectively, through enzymatic reactions modeled here with Michaelis-Menten functions with constants γ α , k a , γ m , k m .…”