A geometric and structural approach to the analysis and design of biological circuit dynamics: a theory tailored for synthetic biology

Much of the progress in developing our ability to successfully design genetic circuits with predictable dynamics has followed the strategy of molding biological systems to fit into conceptual frameworks used in other disciplines, most notably the engineering sciences. Because biological systems have fundamental differences from systems in these other disciplines, this approach is challenging and the insights obtained from such analyses are often not framed in a biologically-intuitive way. Here, we present a new theoretical framework for analyzing the dynamics of genetic circuits that is tailored towards the unique properties associated with biological systems and experiments. Our framework approximates a complex circuit as a set of simpler circuits, which the system can transition between by saturating its various internal components. These approximations are connected to the intrinsic structure of the system, so this representation allows the analysis of dynamics which emerge solely from the system's structure. Using our framework, we analyze the presence of structural bistability in a leaky autoactivation motif and the presence of structural oscillations in the Repressilator

Robust Perfect Adaptation in Biomolecular Reaction Networks

For control in biomolecular systems, the most basic objective of maintaining a small error in a target variable, say the expression level of some protein, is often difficult due to the presence of both large uncertainty of every type and intrinsic limitations on the controller's implementation. This paper explores the limits of biochemically plausible controller design for the problem of robust perfect adaptation (RPA), biologists' term for robust steady state tracking. It is well-known that for a large class of nonlinear systems, a system has RPA iff it has integral feedback control (IFC), which has been used extensively in real control systems to achieve RPA. However, we show that due to intrinsic physical limitations on the dynamics of chemical reaction networks (CRNs), cells cannot implement IFC directly in the concentration of a chemical species. This contrasts with electronic implementations, particularly digital, where it is trivial to implement IFC directly in a single state. Therefore, biomolecular systems have to achieve RPA by encoding the integral control variable into the network architecture of a CRN. We describe a general framework to implement RPA in CRNs and show that well-known network motifs that achieve RPA, such as (negative) integral feedback (IFB) and incoherent feedforward (IFF), are examples of such implementations. We also develop methods to designing integral feedback variables for unknown plants. This standard control notion is surprisingly nontrivial and relatively unstudied in biomolecular control. The methods developed here connect different existing fields and approaches on the problem of biomolecular control, and hold promise for systematic chemical reaction controller synthesis as well as analysis

Fast On-line Statistical Learning on a GPGPU

On-line Machine Learning using Stochastic Gradient Descent is an inherently sequential computation. This makes it difficult to improve performance by simply employing parallel architectures. Langford et al. made a modification to the standard stochastic gradient descent approach which opens up the possibility of parallel computation. They also proved that there is no significant loss in accuracy in their approach. They did empirically demonstrate the performance gain in speed for the case of a pipelined architecture with a few processing units. In this paper we report on applying the Langford et al. approach on a General Purpose Graphics Processing Unit (GPGPU) with a large number of processing units. We accelerate the learning speed by approximately 4.5 times compared to a standard single threaded approach with comparable accuracy. We also evaluate the GPU performance for the sequential variant of the algorithm, which has not previously been reported. Finally, we investigate how changes in the number of threads, number of blocks, and amount of delay, effects the overall performance and accuracy

Stability and Control of Biomolecular Circuits through Structure

Due to omnipresent uncertainties and environmental disturbances, natural and engineered biological organisms face the challenging control problem of achieving robust performance using unreliable parts. The key to overcoming this challenge rests in identifying structures of biomolecular circuits that are largely invariant despite uncertainties, and building feedback control through such structures. In this work, we develop the tool of log derivatives to capture structures in how the production and degradation rates of molecules depend on concentrations of reactants. We show that log derivatives could establish stability of fixed points based on structure, despite large variations in rates and functional forms of models. Furthermore, we demonstrate how control objectives, such as robust perfect adaptation (i.e. step disturbance rejection), could be implemented through the structures captured. Due to the method's simplicity, structural properties for analysis and design of biomolecular circuits can often be determined by a glance at the equations

A geometric and structural approach to the analysis and design of biological circuit dynamics: a theory tailored for synthetic biology

Much of the progress in developing our ability to successfully design genetic circuits with predictable dynamics has followed the strategy of molding biological systems to fit into conceptual frameworks used in other disciplines, most notably the engineering sciences. Because biological systems have fundamental differences from systems in these other disciplines, this approach is challenging and the insights obtained from such analyses are often not framed in a biologically-intuitive way. Here, we present a new theoretical framework for analyzing the dynamics of genetic circuits that is tailored towards the unique properties associated with biological systems and experiments. Our framework approximates a complex circuit as a set of simpler circuits, which the system can transition between by saturating its various internal components. These approximations are connected to the intrinsic structure of the system, so this representation allows the analysis of dynamics which emerge solely from the system's structure. Using our framework, we analyze the presence of structural bistability in a leaky autoactivation motif and the presence of structural oscillations in the Repressilator

Coupled Reaction Networks for Noise Suppression

Noise is intrinsic to many important regulatory processes in living cells, and often forms obstacles to be overcome for reliable biological functions. However, due to stochastic birth and death events of all components in biomolecular systems, suppression of noise of one component by another is fundamentally hard and costly. Quantitatively, a widely-cited severe lower bound on noise suppression in biomolecular systems was established by Lestas et. al. in 2010, assuming that the plant and the controller have separate birth and death reactions. This makes the precision observed in several biological phenomena, e.g., cell fate decision making and cell cycle time ordering, seem impossible. We demonstrate that coupling, a mechanism widely observed in biology, could suppress noise lower than the bound of Lestas et. al. with moderate energy cost. Furthermore, we systematically investigate the coupling mechanism in all two-node reaction networks, showing that negative feedback suppresses noise better than incoherent feedforward achitectures, coupled systems have less noise than their decoupled version for a large class of networks, and coupling has its own fundamental limitations in noise suppression. Results in this work have implications for noise suppression in biological control and provide insight for a new efficient mechanism of noise suppression in biology

Robust Perfect Adaptation in Biomolecular Reaction Networks

For control in biomolecular systems, the most basic objective of maintaining a small error in a target variable, say the expression level of some protein, is often difficult due to the presence of both large uncertainty of every type and intrinsic limitations on the controller's implementation. This paper explores the limits of biochemically plausible controller design for the problem of robust perfect adaptation (RPA), biologists' term for robust steady state tracking. It is well-known that for a large class of nonlinear systems, a system has RPA iff it has integral feedback control (IFC), which has been used extensively in real control systems to achieve RPA. However, we show that due to intrinsic physical limitations on the dynamics of chemical reaction networks (CRNs), cells cannot implement IFC directly in the concentration of a chemical species. This contrasts with electronic implementations, particularly digital, where it is trivial to implement IFC directly in a single state. Therefore, biomolecular systems have to achieve RPA by encoding the integral control variable into the network architecture of a CRN. We describe a general framework to implement RPA in CRNs and show that well-known network motifs that achieve RPA, such as (negative) integral feedback (IFB) and incoherent feedforward (IFF), are examples of such implementations. We also develop methods to designing integral feedback variables for unknown plants. This standard control notion is surprisingly nontrivial and relatively unstudied in biomolecular control. The methods developed here connect different existing fields and approaches on the problem of biomolecular control, and hold promise for systematic chemical reaction controller synthesis as well as analysis