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Richard M. Murray

Publications and source records attributed to Richard M. Murray.

3 recordsLinked to original sources

Synthesizing Combination Therapies for Evolutionary Dynamics of Disease for Nonlinear Pharmacodynamics

Our previous results proposed an iterative scalable algorithm for the systematic design of sparse, small gain feedback strategies that stabilize the evolutionary dynamics of a generic disease model with linear pharmacodynamics. In this manuscript, we use piecewise linear approximations to model nonlinear drug effects. We leverage results from optimal controller synthesis for positive systems to formulate the feedback synthesis problem as an optimization problem that sequentially explores piecewise linear subsystems corresponding to higher and higher treatment dosages.

Evolutionary Biology

Resource usage and gene circuit performance characterization in a cell-free ?breadboard?

The many successes of synthetic biology have come in a manner largely different from those in other engineering disciplines; in particular, without well-characterized and simplified prototyping environments to play a role analogous to wind-tunnels in aerodynamics and breadboards in electrical engineering. However, as the complexity of synthetic circuits increases, the benefits--in cost savings and design cycle time--of a more traditional engineering approach can be significant. We have recently developed an in vitro breadboard prototyping platform based on E. coli cell extract that allows biocircuits to operate in an environment considerably simpler than but functionally similar to in vivo. The simplicity of this system makes it a promising tool for rapid biocircuit design and testing, as well as for probing fundamental aspects of gene circuit operation normally masked by cellular complexity. In this work we characterize the cell-free breadboard using real-time and simultaneous measurements of transcriptional and translational activities of a small set of reporter genes and a transcriptional activation cascade. We determine the effects of promoter strength, gene concentration, and nucleoside triphosphate concentration on biocircuit properties, and we isolate the specific contributions of essential biomolecular resources--core RNA polymerase and ribosomes--to overall performance. Importantly, we show how limits on resources, particularly those involved in translation, are manifested as reduced expression in the presence of orthogonal genes that serve as additional loads on the system.

Synthetic Biology

Designing Robustness to Temperature in a Feedforward Loop Circuit

Incoherent feedforward loops represent important biomolecular circuit elements capable of a rich set of dynamic behavior including adaptation and pulsed responses. Temperature can modulate some of these properties through its effect on the underlying reaction rate parameters. It is generally unclear how to design such a circuit where the properties are robust to variations in temperature. Here, we address this issue using a combination of tools from control and dynamical systems theory as well as preliminary experimental measurements towards such a design. We formalize temperature as an uncertainty acting on system dynamics, exploring both structured and unstructured uncertainty representations. Next, we analyze a standard incoherent feedforward loop circuit, noting mechanisms that intrinsically confer temperature robustness to some of its properties. Further, we explore different negative feedback configurations that can enhance the robustness to temperature. Finally, we find that the response of an incoherent feedforward loop circuit in cells can change with temperature. These results present groundwork for the design of a temperature-robust incoherent feedforward loop circuit.

Synthetic Biology