Property:Abstract
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S
Biological signaling systems not only detect the absolute levels of the signals, but are also able to sense the fold-changes of the signals. The ability to detect fold-changes provides a powerful tool for biological organisms to adapt to the changes in environment. Here we present the first novel syn- thetic fold-change detector (FCD) circuit built from ground up in vivo. We systematically designed the FCD circuit in silico, prototyped it in cell-free transcription-translation platform (TX-TL), and eventually implemented it in E. coli cells. We were able to show that the FCD circuit can not only generate pulse-like behavior in response to input, but also produce the same pulse response with inputs of the same fold-change, despite of di�erent absolute signal levels. +
A
An analytical approach to bistable biological circuit discrimination using real algebraic geometry +
Biomolecular circuits with two distinct and stable steady states have been identified as essential components in a wide range of biological networks, with a variety of mechanisms and topologies giving rise to their important bistable property. Understanding the differences between circuit implementations is an important question, particularly for the synthetic biologist faced with determining which bistable circuit design out of many is best for their specific application. In this work we explore the applicability of Sturm's theorem—a tool from nineteenth-century real algebraic geometry—to comparing ‘functionally equivalent’ bistable circuits without the need for numerical simulation. We first consider two genetic toggle variants and two different positive feedback circuits, and show how specific topological properties present in each type of circuit can serve to increase the size of the regions of parameter space in which they function as switches. We then demonstrate that a single competitive monomeric activator added to a purely monomeric (and otherwise monostable) mutual repressor circuit is sufficient for bistability. Finally, we compare our approach with the Routh–Hurwitz method and derive consistent, yet more powerful, parametric conditions. The predictive power and ease of use of Sturm's theorem demonstrated in this work suggest that algebraic geometric techniques may be underused in biomolecular circuit analysis. +
V
Borrowing a concept from hydrodynamic analysis, this paper presents stream functions which satisfy Laplace's equation as a local-minima free method for producing potential-field based navigation functions in two dimensions. These functions generate smoother paths (i.e. more suited to aircraft-like vehicles) than previous methods. A method is developed for constructing analytic stream functions to produce arbitrary vehicle behaviors while avoiding obstacles, and an exact solution for the case of a single uniformly moving obstacle is presented. The effects of introducing multiple obstacles are discussed and current work in this direction is detailed. Experimental results generated on the Cornell RoboFlag testbed are presented and discussed. +
U
Caltech's ducted fan experiment is used
as a case study to investigate the properties of
an algorithm for uniting local and global controllers
proposed in (Teel and Kapoor, 1997)
To simplify the control design process and to illustrate robustness,
the ducted fan is
modeled as a linear system with input rate limits.
The local controller is an (fairly aggressive) LQR state feedback while
the (semi-)global controller is a much less aggressive
LQR state feedback. Closed-loop simulation results
are provided
using a fully nonlinear model of the ducted fan derived
from wind tunnel data. Experimental results are also
provided using the actual Caltech ducted fan. +
A
Cell-free expression systems provide a method for rapid DNA circuit prototyping and functional protein synthesis. While crude extracts remain a black box with many components carrying out unknown reactions, the PURE system contains only the required transcription and translation components for protein production. All proteins and small molecules are at known concentrations, opening up the possibility of detailed modeling for reliable computational predictions. However, there is little to no experimental data supporting the expression of target proteins for detailed protein models PURE models. In this work, we build a chemical reaction network transcription model for PURE protein synthesis. We compare the transcription models using DNA encoding for the malachite-green aptamer (MGapt) to measure mRNA production. Furthermore, we expand the PURE detailed translation model for an arbitrary set of amino acids and length. Lastly, we combine the transcription and the expanded translation models to create a PURE protein synthesis model built purely from mass-action reactions. We use the combined model to capture the translation of a plasmid encoding MGapt and deGFP under a T7-promoter and a strong RBS. The model accurately predicts the MGapt mRNA production for the first two hours, the dynamics of deGFP expression, and the total protein production with an accuracy within 10%. +
M
Metabolic perturbations to an E. coli-based cell-free system reveal a trade-off between transcription and translation +
Cell-free transcription-translation (TX-TL) systems have been used for diverse applications, from prototyping gene circuits to providing a platform for the development of synthetic life, but their performance is limited by issues such as batch-to-batch variability, poor predictability, and limited lifetime. These issues stem largely from the fact that cell lysate contains an active and complex metabolism whose effect on TX-TL has remained largely uncharacterized.
Motivated by a minimal model of cell-free metabolism, this work explored the effects of energy molecules, which power TX-TL, and fuel molecules, which regenerate energy by harnessing core metabolism, on an E. coli -based TX-TL system. This work reports a compensatory interaction between TX-TL components Mg2+ and 3-phosphoglyceric acid (3-PGA, used to regenerate ATP), where if one component’s concentration is increased, the other’s must likewise be increased to maintain optimal translation. Furthermore, maximum mRNA and protein production occur in opposite concentration regimes of Mg+2 and 3-PGA, suggesting a TX-TL trade-off. To explore the observed phenomenon, transcription and translation were decoupled. Under translation inhibition, transcriptional output was uniform across Mg2+ and 3-PGA concentrations, but in a translation-only system, maximum protein production occurred in the previously found optimal regime of Mg2+ and 3-PGA. Using alternative fuels to regenerate energy, this work found that the trade-off is universal across the different fuel sources, and that a system’s position along the trade-off is determined strongly by Mg2+. The location and slope of the trade-off curve are determined strongly by DNA concentration, cell lysate batch, and the fraction of cell lysate in a reaction. Finally, in systems where additional energy is supplied and where a fuel source is absent, the trade-off is absent.
Overall, these results suggest the trade-off arises from limitations in translation regulation and efficient energy regeneration. This work represents a significant advancement in understanding the effects of fuel and energy metabolism on TX-TL in cell-free systems and lays the foundation for improving TX-TL performance, lifetime, standardization, and prediction.
P
Cells must detect and respond to molecular events such as the presence or absence of specific small molecules. To accomplish this, cells have evolved methods to measure the presence and concentration of these small molecules in their environment and enact changes in gene expression or behavior. However, cells don’t usually change their DNA in response to outside stimuli. In this work, we have engineered a genetic circuit that can enact specific and controlled genetic changes in response to small molecule stimuli. Known DNA sequences can be repeatedly integrated in a genomic array such that their identity and order encodes information about past small molecule concentrations that the cell has experienced. To accomplish this, we use catalytically inactive CRISPR-Cas9 (dCas9) to bind to and block attachment sites for the integrase Bxb1. Therefore, through the co-expression of dCas9 and guide RNA, Bxb1 can be directed to integrate one of two engineered plasmids, which correspond to two orthogonal small molecule inducers that can be recorded with this system. We identified the optimal location of guide RNA binding to the Bxb1 attP integrase attachment site, and characterized the detection limits of the system by measuring the minimal small molecule concentration and shortest induction time necessary to produce measurable differences in array composition as read out by Oxford Nanopore sequencing technology. +
F
Classification of stabilizability is obtained for multi-input nonlinear systems
possessing a simple steady-state or Hopf bifurcation with the critical mode being linearly
uncontrollable. Stabilizability is defined as the existence of a sufficiently smooth state
feedback such that the bifurcation for the closed loop system is supercritical, and in the
meantime, the linearly controllable modes are locally asymptotically stable. Necessary and
sufficient conditions of stabilizability are derived under certain nondegeneracy
conditions. Explicit construction of stabilizing feedbacks is obtained for the cases when
the system is stabilizable. +
M
Consensus protocols in coordinated multi-agent systems are
distributed algorithms. Just using local information
available to each single agent, all agents converge to an
identical consensus state and the convergence speed is
determined by the algebraic connectivity of the
communication network. In order to achieve a faster
consensus seeking, we propose multi-hop relay protocols
based on the current ``nearest neighbor rules'' consensus
protocols. By employing multiple-hop paths in the network,
more information is passed around and each agent enlarges
its "available" neighborhood. We demonstrate that these
relay protocols can increase the algebraic connectivity
without physically adding or changing any communication
links. Moreover, time delay sensitivity of relay protocols
are discussed in detail. We point out that a trade off
exists between convergence performance and time delay
robustness. Simulation results are also provided to verify
the efficiency of relay protocols. +
P
Contract-based design is a method to facilitate modular system design. While there has been substantial progress on the theory of contracts, there has been less progress on scalable algorithms for the algebraic operations in this theory. In this paper, we present: 1) principles to implement a contract-based design tool at scale and 2) Pacti, a tool that can efficiently compute these operations. We then illustrate the use of Pacti in a variety of case studies. +
G
Control of vehicle formations has emerged as a topic of significant interest to the controls
community. In this paper, we merge tools from graph theory and control theory to derive
stability criteria for formation stabilization. The interconnection between vehicles (i.e., which
vehicles are sensed by other vehicles) is modeled as a graph, and the eigenvalues of the Laplacian
matrix of the graph are used in stating a Nyquist-like stability criterion for vehicle formations.
The location of the Laplacian eigenvalues can be correlated to the graph structure, and therefore
used to identify desirable and undesirable formation interconnection topologies. +
O
Control of vehicle formations has emerged as a topic of significant
interest to the controls community. In applications such as microsatellites
and underwater vehicles, formations have the potential for greater functionality
and versatility than individual vehicles. In this thesis, we investigate two
topics relevant to control of vehicle formations: optimal vehicle control and
cooperative control. +
A
An Experimental Comparison of Tradeoffs in Using Compliant Manipulators for Robotic Grasping Tasks +
Controllers developed for control of flexible-link robots in hybrid
force-position control tasks by a new singular perturbation analysis
of flexible manipulators are implemented on an experimental two-robot
grasping setup. Various performance criteria are set up and
experimental results are discussed within that setting to show
tradeoffs in using flexible link robots for grasping. We conclude that
large flexibility can be controlled without too much additional
effort, has performance comparable to rigid robots and possesses
enhancing properties which make it attractive for use in certain types
of applications. +
R
Conventional simultaneous localization and map- ping (SLAM) algorithms rely on geometric measurements and require loop-closure detections to correct for drift accumulated over a vehicle trajectory. Semantic measurements can add measurement redundancy and an alternative form of loop closure. We propose two different estimation algorithms that incorporate semantic measurements provided by vision-based object classifiers. An a priori map of regions where the objects can be detected is assumed. The first estimation framework is posed as a maximum-likelihood problem, where the likelihood function for semantic measurements is derived from the con- fusion matrices of the object classifiers. The second estimation framework is comprised of two parts: 1) a continuous-state estimation formulation that includes semantic measurements as a form of state constraints and 2) a discrete-state estimation formulation used to compute the certainty of object detection measurements using a Hidden Markov Model (HMM). The advantages of incorporating semantic measurements in these frameworks are demonstrated in numerical simulations. In particular, the proposed estimation algorithms improve upon the robustness and accuracy of conventional SLAM algorithms. Also, the certainty metric of object detection measurements derived from the HMM in our simulation are greater than the certainty levels provided by the confusion matrix in object classification algorithms. +
C
Convergence properties of distributed consensus protocols on networks of dynamical agents have been analyzed by combinations of algebraic graph theory and control theory tools under certain assumptions, such as strong connectivity. Strong connectivity can be regarded as the requirement that the information of each agent propagates to all the others, possibly with intermediate steps and manipulations. However, because of network failures or malicious attacks, it is possible that this assumption no longer holds, so that some agents are
only receiving or only transmitting information from other subsets of agents. In this case, strong connectivity is replaced by weak connectivity. We analyze the convergence properties of distributed consensus on directed graphs with weakly connected components. We show conditions for which the agreement is reached, and, for the cases in which such conditions do not
hold, we provide bounds on the residual disagreement.
in terms of the number of agents that must fail for the +
V
Correct-by-construction synthesis of high-level re- active control relies on the use of formal methods to generate controllers with provable guarantees on their behavior. While this approach has been successfully applied to a wide range of systems and environments, it scales poorly with the increasing size of the environment. A receding horizon framework was recently proposed to mitigate this computational blowup, by decomposing the global control problem into several tractable subproblems. The existence of a global controller is ensured through symbolic checks of the specification, and local controllers are synthesized when needed, using the current state of the environment as the initial condition. This reduces the size of the synthesized strategy, but does not provide much improvement for problems with large dynamic environments, because the large number of possible global environment strategies. Ad hoc methods to locally restrict the environment have previously been used, at the risk of losing correctness. This paper presents a method of reducing specifications by eliminating locally redundant variables, while maintaining the correctness of controllers. We demonstrate the method using an autonomous car example, on problem sizes that were previously unsolvable due to the number of variables in the environment. We also demonstrate how the reduced specifications can be used to identify opportunities for reusing the synthesized local controllers. +
Q
Crosstalk is defined as the set of unwanted interactions among the different entities of a network. Crosstalk is present in various degrees in every system where information is transmitted through a means that is accessible by all the individual units of the network. Using concepts from graph theory, we introduce a quantifiable measure for sensitivity to crosstalk, and analytically derive the structure of the networks in which it is minimized. It is shown that networks with an inhomogeneous degree distribution are more robust to crosstalk than corresponding homogeneous networks. We provide a method to construct the graph with the minimum possible sensitivity to crosstalk, given its order and size. Finally, for networks with a fixed degree sequence, we present an algorithm to find the optimal interconnection structure among their vertices. +
D
Current bacterial synthetic circuits rely on the fast dilution and high protein expression that occurs during exponential phase. However, constant exponential phase is both difficult to ensure in a lab environment and almost certainly impractical in any natural setting. Here, we characterize the performance of 13 E. coli native 38 promoters, as well as a previously identified 38 consensus promoter. We then make tetO combinatorial versions of the three strongest promoters to allow for inducible delayed expression. The design of these combinatorial promoters allows for design of circuits with inducible stationary phase activity that can be used for phase-dependent delays in dynamic circuits or spatial partitioning of biofilms. +
S
Current methods for assembling biosynthetic pathways in microorganisms require a process of repeated trial and error and have long design-build-test cycles. We describe the use of a cell-free transcription-translation (TX-TL) system as a biomolecular breadboard for the rapid engineering of the 1,4-butanediol (BDO) pathway. We demonstrate the reliability of TX-TL as a platform for engineering biological systems by undertaking a careful characterization of its transcription and translation capabilities and provide a detailed analysis of its metabolic output. Using TX-TL to survey the design space of the BDO pathway enables rapid tuning of pathway enzyme expression levels for improved product yield. Leveraging TX-TL to screen enzyme variants for improved catalytic activity accelerates design iterations that can be directly applied to in vivo strain development. +
P
Prototyping 1,4-butanediol (BDO) biosynthesis pathway in a cell-free transcription-translation (TX-TL) system +
Current methods for assembling metabolic pathways require a process of repeated trial and error and have a long design-build-test cycle. Further, it remains a challenge to precisely tune enzyme expression levels for maximizing target metabolite production. Recently it was shown that a cell-free transcriptional-translation system (TX-TL) can be used to rapidly prototype novel complex biocircuits as well as metabolic pathways. TX-TL systems allow protein expression from multiple DNA pieces, opening up the possibility of modulating concentrations of DNA encoding individual pathway enzymes and testing the related effect on metabolite production. In this work, we demonstrate TX-TL as a platform for exploring the design space of metabolic pathways using a 1,4-BDO biosynthesis pathway as an example. Using TX-TL, we verified enzyme expression and enzyme activity and identified the conversion of 4-hydroxybutyrate to downstream metabolites as a limiting step of the 1,4-BDO pathway. We further tested combinations of various enzyme expression levels and found increasing downstream enzyme expression levels improved 1,4-BDO production. +
