Simple, Fast and Accurate Implementation of the Diffusion Approximation Algorithm for Stochastic Ion Channels with Multiple States

The phenomena that emerge from the interaction of the stochastic opening and closing of ion channels (channel noise) with the non-linear neural dynamics are essential to our understanding of the operation of the nervous system. The effects that channel noise can have on neural dynamics are generally studied using numerical simulations of stochastic models. Algorithms based on discrete Markov Chains (MC) seem to be the most reliable and trustworthy, but even optimized algorithms come with a non-negligible computational cost. Diffusion Approximation (DA) methods use Stochastic Differential Equations (SDE) to approximate the behavior of a number of MCs, considerably speeding up simulation times. However, model comparisons have suggested that DA methods did not lead to the same results as in MC modeling in terms of channel noise statistics and effects on excitability. Recently, it was shown that the difference arose because MCs were modeled with coupled activation subunits, while the DA was modeled using uncoupled activation subunits. Implementations of DA with coupled subunits, in the context of a specific kinetic scheme, yielded similar results to MC. However, it remained unclear how to generalize these implementations to different kinetic schemes, or whether they were faster than MC algorithms. Additionally, a steady state approximation was used for the stochastic terms, which, as we show here, can introduce significant inaccuracies. We derived the SDE explicitly for any given ion channel kinetic scheme. The resulting generic equations were surprisingly simple and interpretable - allowing an easy and efficient DA implementation. The algorithm was tested in a voltage clamp simulation and in two different current clamp simulations, yielding the same results as MC modeling. Also, the simulation efficiency of this DA method demonstrated considerable superiority over MC methods.Comment: 32 text pages, 10 figures, 1 supplementary text + figur

Engineering modular and orthogonal genetic logic gates for robust digital-like synthetic biology

Modular and orthogonal genetic logic gates are essential for building robust biologically based digital devices to customize cell signalling in synthetic biology. Here we constructed an orthogonal AND gate in Escherichia coli using a novel hetero-regulation module from Pseudomonas syringae. The device comprises two co-activating genes hrpR and hrpS controlled by separate promoter inputs, and a σ54-dependent hrpL promoter driving the output. The hrpL promoter is activated only when both genes are expressed, generating digital-like AND integration behaviour. The AND gate is demonstrated to be modular by applying new regulated promoters to the inputs, and connecting the output to a NOT gate module to produce a combinatorial NAND gate. The circuits were assembled using a parts-based engineering approach of quantitative characterization, modelling, followed by construction and testing. The results show that new genetic logic devices can be engineered predictably from novel native orthogonal biological control elements using quantitatively in-context characterized parts

Prediction by Promoter Logic in Bacterial Quorum Sensing

Quorum-sensing systems mediate chemical communication between bacterial cells, coordinating cell-density-dependent processes like biofilm formation and virulence-factor expression. In the proteobacterial LuxI/LuxR quorum sensing paradigm, a signaling molecule generated by an enzyme (LuxI) diffuses between cells and allosterically stimulates a transcriptional regulator (LuxR) to activate its cognate promoter (pR). By expressing either LuxI or LuxR in positive feedback from pR, these versatile systems can generate smooth (monostable) or abrupt (bistable) density-dependent responses to suit the ecological context. Here we combine theory and experiment to demonstrate that the promoter logic of pR – its measured activity as a function of LuxI and LuxR levels – contains all the biochemical information required to quantitatively predict the responses of such feedback loops. The interplay of promoter logic with feedback topology underlies the versatility of the LuxI/LuxR paradigm: LuxR and LuxI positive-feedback systems show dramatically different responses, while a dual positive/negative-feedback system displays synchronized oscillations. These results highlight the dual utility of promoter logic: to probe microscopic parameters and predict macroscopic phenotype

Principles of genetic circuit design

Cells navigate environments, communicate and build complex patterns by initiating gene expression in response to specific signals. Engineers seek to harness this capability to program cells to perform tasks or create chemicals and materials that match the complexity seen in nature. This Review describes new tools that aid the construction of genetic circuits. Circuit dynamics can be influenced by the choice of regulators and changed with expression 'tuning knobs'. We collate the failure modes encountered when assembling circuits, quantify their impact on performance and review mitigation efforts. Finally, we discuss the constraints that arise from circuits having to operate within a living cell. Collectively, better tools, well-characterized parts and a comprehensive understanding of how to compose circuits are leading to a breakthrough in the ability to program living cells for advanced applications, from living therapeutics to the atomic manufacturing of functional materials.National Institute of General Medical Sciences (U.S.) (Grant P50 GM098792)National Institute of General Medical Sciences (U.S.) (Grant R01 GM095765)National Science Foundation (U.S.). Synthetic Biology Engineering Research Center (EEC0540879)Life Technologies, Inc. (A114510)National Science Foundation (U.S.). Graduate Research FellowshipUnited States. Office of Naval Research. Multidisciplinary University Research Initiative (Grant 4500000552