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

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

Fluorescent Calcium Imaging and Subsequent In Situ Hybridization for Neuronal Precursor Characterization in Xenopus laevis

Spontaneous intracellular calcium activity can be observed in a variety of cell types and is proposed to play critical roles in a variety of physiological processes. In particular, appropriate regulation of calcium activity patterns during embryogenesis is necessary for many aspects of vertebrate neural development, including proper neural tube closure, synaptogenesis, and neurotransmitter phenotype specification. While the observation that calcium activity patterns can differ in both frequency and amplitude suggests a compelling mechanism by which these fluxes might transmit encoded signals to downstream effectors and regulate gene expression, existing population-level approaches have lacked the precision necessary to further explore this possibility. Furthermore, these approaches limit studies of the role of cell-cell interactions by precluding the ability to assay the state of neuronal determination in the absence of cell-cell contact. Therefore, we have established an experimental workflow that pairs time-lapse calcium imaging of dissociated neuronal explants with a fluorescence in situ hybridization assay, allowing the unambiguous correlation of calcium activity pattern with molecular phenotype on a single-cell level. We were successfully able to use this approach to distinguish and characterize specific calcium activity patterns associated with differentiating neural cells and neural progenitor cells, respectively; beyond this, however, the experimental framework described in this article could be readily adapted to investigate correlations between any time-series activity profile and expression of a gene or genes of interest

Addressable, "Packet-Based" Intercellular Communication through Plasmid Conjugation

We develop a system for implementing "packet-based" intercellular communication in an engineered bacterial population via conjugation. Our system uses gRNA-based identification markers that allow messages to be addressed to specific strains via Cas9-mediated cleavage of messages sent to the wrong recipient, which we show reduces plasmid transfer by four orders of magnitude. Integrase-mediated editing of the address on the message plasmid allows cells to dynamically update the message's recipients in vivo. As a proof-of-concept demonstration of our system, we propose a linear path scheme that would propagate a message sequentially through the strains of a population in a defined order

Effective electroosmotic transport of water in an intrinsically microporous polyamine (PIM-EA-TB)

Tertiary-amine-based Polymers of Intrinsic Microporosity (PIMs) provide a class of highly porous molecularly rigid materials for the electrochemical transport of both ionic and neutral species. Here, the transport of water molecules together with chloride anions (i.e. the electroosmotic drag coefficient) is studied for the intrinsically microporous polyamine PIM-EA-TB immersed in aqueous 0.01 M NaCl (i) when protonated for pH  4. Preliminary data suggest that in both cases a high electroosmotic drag coefficient is observed based on direct H2O transport into a D2O-filled compartment (quantified by 1H-NMR). For PIM-EA-TB there is a strong pH dependence with a higher electroosmotic drag coefficient in less acidic solutions (going from approx. 400 H2O per anion at pH 3 to approx. 4000 H2O per anion at pH 7), although the underlying absolute rate of water transport at a fixed voltage of −1 V appears to be essentially pH independent. Water transport through the PIM-EA-TB microchannels is rationalised based on the relative populations of chloride anions and of water in the micropores (essentially a ‘piston’ mechanism)

Fluorescent Calcium Imaging and Subsequent In Situ Hybridization for Neuronal Precursor Characterization in Xenopus laevis

Spontaneous intracellular calcium activity can be observed in a variety of cell types and is proposed to play critical roles in a variety of physiological processes. In particular, appropriate regulation of calcium activity patterns during embryogenesis is necessary for many aspects of vertebrate neural development, including proper neural tube closure, synaptogenesis, and neurotransmitter phenotype specification. While the observation that calcium activity patterns can differ in both frequency and amplitude suggests a compelling mechanism by which these fluxes might transmit encoded signals to downstream effectors and regulate gene expression, existing population-level approaches have lacked the precision necessary to further explore this possibility. Furthermore, these approaches limit studies of the role of cell-cell interactions by precluding the ability to assay the state of neuronal determination in the absence of cell-cell contact. Therefore, we have established an experimental workflow that pairs time-lapse calcium imaging of dissociated neuronal explants with a fluorescence in situ hybridization assay, allowing the unambiguous correlation of calcium activity pattern with molecular phenotype on a single-cell level. We were successfully able to use this approach to distinguish and characterize specific calcium activity patterns associated with differentiating neural cells and neural progenitor cells, respectively; beyond this, however, the experimental framework described in this article could be readily adapted to investigate correlations between any time-series activity profile and expression of a gene or genes of interest

A Markovian Entropy Measure for the Analysis of Calcium Activity Time Series

Methods to analyze the dynamics of calcium activity often rely on visually distinguishable features in time series data such as spikes, waves, or oscillations. However, systems such as the developing nervous system display a complex, irregular type of calcium activity which makes the use of such methods less appropriate. Instead, for such systems there exists a class of methods (including information theoretic, power spectral, and fractal analysis approaches) which use more fundamental properties of the time series to analyze the observed calcium dynamics. We present a new analysis method in this class, the Markovian Entropy measure, which is an easily implementable calcium time series analysis method which represents the observed calcium activity as a realization of a Markov Process and describes its dynamics in terms of the level of predictability underlying the transitions between the states of the process. We applied our and other commonly used calcium analysis methods on a dataset from Xenopus laevis neural progenitors which displays irregular calcium activity and a dataset from murine synaptic neurons which displays activity time series that are well-described by visually-distinguishable features. We find that the Markovian Entropy measure is able to distinguish between biologically distinct populations in both datasets, and that it can separate biologically distinct populations to a greater extent than other methods in the dataset exhibiting irregular calcium activity. These results support the benefit of using the Markovian Entropy measure to analyze calcium dynamics, particularly for studies using time series data which do not exhibit easily distinguishable features

The genetic insulator RiboJ increases expression of insulated genes

A primary objective of synthetic biology is the construction of genetic circuits with behaviors that can be predicted based on the properties of the constituent genetic parts from which they are built. However a significant issue in the construction of synthetic genetic circuits is a phenomenon known as context dependence in which the behavior of a given part changes depending on the choice of adjacent or nearby parts. Interactions between parts compromise the modularity of the circuit, impeding the implementation of predictable genetic constructs. To address this issue, investigators have devised genetic insulators that prevent these unintended context-dependent interactions between neighboring parts. One of the most commonly used insulators in bacterial systems is the self-cleaving ribozyme RiboJ. Despite its utility as an insulator, there has been no systematic quantitative assessment of the effect of RiboJ on the expression level of downstream genetic parts. Here, we characterized the impact of insulation with RiboJ on expression of a reporter gene driven by a promoter from a library of 24 frequently employed constitutive promoters in an Escherichia coli model system. We show that, depending on the strength of the promoter, insulation with RiboJ increased protein abundance between twofold and tenfold and increased transcript abundance by an average of twofold. This result demonstrates that genetic insulators in E. coli can impact the expression of downstream genes, information that is essential for the design of predictable genetic circuits and constructs

The genetic insulator RiboJ increases expression of insulated genes

A primary objective of synthetic biology is the construction of genetic circuits with behaviors that can be predicted based on the properties of the constituent genetic parts from which they are built. However a significant issue in the construction of synthetic genetic circuits is a phenomenon known as context dependence in which the behavior of a given part changes depending on the choice of adjacent or nearby parts. Interactions between parts compromise the modularity of the circuit, impeding the implementation of predictable genetic constructs. To address this issue, investigators have devised genetic insulators that prevent these unintended context-dependent interactions between neighboring parts. One of the most commonly used insulators in bacterial systems is the self-cleaving ribozyme RiboJ. Despite its utility as an insulator, there has been no systematic quantitative assessment of the effect of RiboJ on the expression level of downstream genetic parts. Here, we characterized the impact of insulation with RiboJ on expression of a reporter gene driven by a promoter from a library of 24 frequently employed constitutive promoters in an Escherichia coli model system. We show that, depending on the strength of the promoter, insulation with RiboJ increased protein abundance between twofold and tenfold and increased transcript abundance by an average of twofold. This result demonstrates that genetic insulators in E. coli can impact the expression of downstream genes, information that is essential for the design of predictable genetic circuits and constructs