Enoch Yeung

Linear DNA for Rapid Prototyping of Synthetic Biological Circuits in an Escherichia coli Based TX-TL Cell-Free System

Accelerating the pace of synthetic biology experiments requires new approaches for rapid prototyping of circuits from individual DNA regulatory elements. However, current testing standards require days to weeks due to cloning and in vivo transformation. In this work, we first characterized methods to protect linear DNA strands from exonuclease degradation in an Escherichia coli based transcription-translation cell-free system (TX-TL), as well as mechanisms of degradation. This enabled the use of linear DNA PCR products in TX-TL. We then compared expression levels and binding dynamics of different promoters on linear DNA and plasmid DNA. We also demonstrated assembly technology to rapidly build circuits entirely in vitro from separate parts. Using this strategy, we prototyped a four component genetic switch in under 8 h entirely in vitro. Rapid in vitro assembly has future applications for prototyping multiple component circuits if combined with predictive computational models.

Rapid cell-free forward engineering of novel genetic ring oscillators

While complex dynamic biological networks control gene expression in all living organisms, the forward engineering of comparable synthetic networks remains challenging. The current paradigm of characterizing synthetic networks in cells results in lengthy design-build-test cycles, minimal data collection, and poor quantitative characterization. Cell-free systems are appealing alternative environments, but it remains questionable whether biological networks behave similarly in cell-free systems and in cells. We characterized in a cell-free system the ‘repressilator’, a three-node synthetic oscillator. We then engineered novel three, four, and five-gene ring architectures, from characterization of circuit components to rapid analysis of complete networks. When implemented in cells, our novel 3-node networks produced population-wide oscillations and 95% of 5-node oscillator cells oscillated for up to 72 hr. Oscillation periods in cells matched the cell-free system results for all networks tested. An alternate forward engineering paradigm using cell-free systems can thus accurately capture cellular behavior. DOI: http://dx.doi.org/10.7554/eLife.09771.001

Representing structure in linear interconnected dynamical systems

Interconnected dynamical systems are a pervasive component in our modern worlds infrastructure. One of the fundamental steps to understanding the complex behavior and dynamics of these systems is determining how to appropriately represent their structure. In this work, we discuss different ways of representing a systems structure. We define and present, in particular, four representations of system structure-complete computational, subsystem, signal, and zero pattern structure-and discuss some of their fundamental properties. We illustrate their application with a numerical example and show how radically different representations of structure can be consistent with a single LTI input-output system.

Initial-Condition Estimation in Network Synchronization Processes: Algebraic and Graphical Characterizations of the Estimator

A graph-theoretic analysis of state inference for a class of network synchronization (or diffusive) processes is pursued. Precisely, estimation is studied for a nonrandom initial condition of a canonical synchronization dynamic defined on a graph, from noisy observations at a single network node. By characterizing the maximum-likelihood estimation of the initial condition and the associated Cramer–Rao bound, graph properties are identified (e.g., symmetries, interconnection strengths, spectral measures) that determine (1) whether or not estimation is possible and (2) the quality of the estimate.

Dynamical structure function identifiability conditions enabling signal structure reconstruction

Networks of controlled dynamical systems exhibit a variety of interconnection patterns that could be interpreted as the structure of the system. One such interpretation of system structure is a systems signal structure, characterized as the open-loop causal dependencies among manifest variables and represented by its dynamical structure function. Although this notion of structure is among the weakest available, previous work has shown that if no a priori structural information is known about the system, not even the Boolean structure of the dynamical structure function is identifiable. Consequently, one method previously suggested for obtaining the necessary a priori structural information is to leverage knowledge about target specificity of the controlled inputs. This work extends these results to demonstrate precisely the a priori structural information that is both necessary and sufficient to reconstruct the network from input-output data. This extension is important because it significantly broadens the applicability of the identifiability conditions, enabling the design of network reconstruction experiments that were previously impossible due to practical constraints on the types of actuation mechanisms available to the engineer or scientist. The work is motivated by the proteomics problem of reconstructing the Per-Arnt-Sim Kinase pathway used in the metabolism of sugars.

Mathematical relationships between representations of structure in linear interconnected dynamical systems

A dynamical system can exhibit structure on multiple levels. Different system representations can capture different elements of a dynamical systems structure. We consider LTI input-output dynamical systems and present four representations of structure: complete computational structure, subsystem structure, signal structure, and input output sparsity structure. We then explore some of the mathematical relation ships that relate these different representations of structure. In particular, we show that signal and subsystem structure are fundamentally different ways of representing system structure. A signal structure does not always specify a unique subsystem structure nor does subsystem structure always specify a unique signal structure. We illustrate these concepts with a numerical example.

Network structure preserving model reduction with weak a priori structural information

This paper extends a state projection method for structure preserving model reduction to situations where only a weaker notion of system structure is available. This weaker notion of structure, identifying the causal relationship between manifest variables of the system, is especially relevant is settings such as systems biology, where a clear partition of state variables into distinct subsystems may be unknown, or not even exist. The resulting technique, like similar approaches, does not provide theoretical performance guarantees, so an extensive computational study is conducted, and it is observed to work fairly well in practice. Moreover, conditions characterizing structurally minimal realizations and sufficient conditions characterizing edge loss resulting from the reduction process, are presented.

Quantifying crosstalk in biochemical systems

Recent work has introduced biocircuit architectures that exhibit robust oscillatory behavior in organisms ranging from cyanobacteria to mammals. Complementary research in synthetic biology has introduced oscillators in vivo and in vitro suggesting that robust oscillation can be recapitulated using a small number of biochemical components. In this work, we introduce signaling crosstalk in biocircuits as a consequence of enzyme-mediated biochemical reactions. As a motivating example, we consider an in vitro oscillator with two types of crosstalk: crosstalk in production and degradation of RNA signals. We then propose a framework for quantifying crosstalk and use it to derive several dynamical constraints and suggest design techniques for ameliorating crosstalk in vitro biochemical systems. We demonstrate that the effects of crosstalk can be attenuated through the effective tuning of two key parameters in order to recover desired system dynamics. As an example, we show that by changing the balance between production and degradation crosstalk, we can tune a system to be stable or exhibit oscillatory behavior.

Resource competition as a source of non-minimum phase behavior in transcription-translation systems

In this paper, we explore how resource limitations can lead to coupling interactions between orthogonal components in a transcription-translation system and the effect those interactions have on its dynamical behavior. To illustrate these ideas, we present a motivating example featuring a classical network motif: the signal cascade. We show that through coupling interactions arising from competition for limited resources, the system exhibits a non-minimum phase step response. These observations lead us to identify a key network motif with the potential to introduce right half plane zeros into the system transfer function. We characterize the parametric conditions under which the network motif produces a right half plane zero. Finally, we illustrate these results with two examples, showing how resource limitations can 1) introduce the network motif through these coupling interactions, 2) satisfy our parametric conditions to produce a right half plane zero.

A Minimal Realization Technique for the Dynamical Structure Function of a Class of LTI Systems

The dynamical structure function of a linear time invariant (LTI) system reveals causal dependencies among manifest variables without specifying any particular relationships among the unmeasured states of the system. As such, it is a useful representation for complex networks where a coarse description of global system structure is desired without detailing the intricacies of a full state realization. In this paper, we consider the problem of finding a minimal state realization for a given dynamical structure function. Interestingly, some dynamical structure functions require uncontrollable modes in their state realizations to deliver the desired input-output behavior while respecting a specified system structure. As a result, the minimal order necessary to realize a particular dynamical structure function may be greater than that necessary to realize its associated transfer function. Although finding a minimal realization for a given dynamical structure function is difficult in general, we present a straightforward procedure here that works for a simplified class of systems.