Cell-Free Prototyping of AND-Logic Gates Based on Heterogeneous RNA Activators.

RNA-based devices controlling gene expression bear great promise for synthetic biology, as they offer many advantages such as short response times and light metabolic burden compared to protein-circuits. However, little work has been done regarding their integration to multilevel regulated circuits. In this work, we combined a variety of small transcriptional activator RNAs (STARs) and toehold switches to build highly effective AND-gates. To characterize the components and their dynamic range, we used an Escherichia coli (E. coli) cell-free transcription-translation (TX-TL) system dispensed via nanoliter droplets. We analyzed a prototype gate in vitro as well as in silico, employing parametrized ordinary differential equations (ODEs), for which parameters were inferred via parallel tempering, a Markov chain Monte Carlo (MCMC) method. On the basis of this analysis, we created nine additional AND-gates and tested them in vitro. The functionality of the gates was found to be highly dependent on the concentration of the activating RNA for either the STAR or the toehold switch. All gates were successfully implemented in vivo, offering a dynamic range comparable to the level of protein circuits. This study shows the potential of a rapid prototyping approach for RNA circuit design, using cell-free systems in combination with a model prediction.

Marginal process framework: A model reduction tool for Markov jump processes.

Markov jump process models have many applications across science. Often these models are defined on a state space of product form and only one of the components of the process is of direct interest. In this paper we extend the marginal process framework, which provides a marginal description of the component of interest, to the case of fully coupled processes. We use entropic matching to obtain a finite-dimensional approximation of the filtering equation, which governs the transition rates of the marginal process. The resulting equations can be seen as a combination of two projection operations applied to the full master equation so that we obtain a principled model reduction framework. We demonstrate the resulting reduced description on the totally asymmetric exclusion process. An important class of Markov jump processes are stochastic reaction networks, which have applications in chemical and biomolecular kinetics, ecological models, and models of social networks. We obtain a particularly simple instantiation of the marginal process framework for mass-action systems by using product Poisson distributions for the approximate solution of the filtering equation. We investigate the resulting approximate marginal process analytically and numerically.

Reconstructing dynamic molecular states from single-cell time series.

The notion of state for a system is prevalent in the quantitative sciences and refers to the minimal system summary sufficient to describe the time evolution of the system in a self-consistent manner. This is a prerequisite for a principled understanding of the inner workings of a system. Owing to the complexity of intracellular processes, experimental techniques that can retrieve a sufficient summary are beyond our reach. For the case of stochastic biomolecular reaction networks, we show how to convert the partial state information accessible by experimental techniques into a full system state using mathematical analysis together with a computational model. This is intimately related to the notion of conditional Markov processes and we introduce the posterior master equation and derive novel approximations to the corresponding infinite-dimensional posterior moment dynamics. We exemplify this state reconstruction approach using both in silico data and single-cell data from two gene expression systems in Saccharomyces cerevisiae, where we reconstruct the dynamic promoter and mRNA states from noisy protein abundance measurements.

Inferring causal molecular networks: empirical assessment through a community-based effort.

It remains unclear whether causal, rather than merely correlational, relationships in molecular networks can be inferred in complex biological settings. Here we describe the HPN-DREAM network inference challenge, which focused on learning causal influences in signaling networks. We used phosphoprotein data from cancer cell lines as well as in silico data from a nonlinear dynamical model. Using the phosphoprotein data, we scored more than 2,000 networks submitted by challenge participants. The networks spanned 32 biological contexts and were scored in terms of causal validity with respect to unseen interventional data. A number of approaches were effective, and incorporating known biology was generally advantageous. Additional sub-challenges considered time-course prediction and visualization. Our results suggest that learning causal relationships may be feasible in complex settings such as disease states. Furthermore, our scoring approach provides a practical way to empirically assess inferred molecular networks in a causal sense.

Scalable inference of heterogeneous reaction kinetics from pooled single-cell recordings.

Mathematical methods combined with measurements of single-cell dynamics provide a means to reconstruct intracellular processes that are only partly or indirectly accessible experimentally. To obtain reliable reconstructions, the pooling of measurements from several cells of a clonal population is mandatory. However, cell-to-cell variability originating from diverse sources poses computational challenges for such process reconstruction. We introduce a scalable Bayesian inference framework that properly accounts for population heterogeneity. The method allows inference of inaccessible molecular states and kinetic parameters; computation of Bayes factors for model selection; and dissection of intrinsic, extrinsic and technical noise. We show how additional single-cell readouts such as morphological features can be included in the analysis. We use the method to reconstruct the expression dynamics of a gene under an inducible promoter in yeast from time-lapse microscopy data.

Markov chain aggregation and its applications to combinatorial reaction networks.

We consider a continuous-time Markov chain (CTMC) whose state space is partitioned into aggregates, and each aggregate is assigned a probability measure. A sufficient condition for defining a CTMC over the aggregates is presented as a variant of weak lumpability, which also characterizes that the measure over the original process can be recovered from that of the aggregated one. We show how the applicability of de-aggregation depends on the initial distribution. The application section is devoted to illustrate how the developed theory aids in reducing CTMC models of biochemical systems particularly in connection to protein-protein interactions. We assume that the model is written by a biologist in form of site-graph-rewrite rules. Site-graph-rewrite rules compactly express that, often, only a local context of a protein (instead of a full molecular species) needs to be in a certain configuration in order to trigger a reaction event. This observation leads to suitable aggregate Markov chains with smaller state spaces, thereby providing sufficient reduction in computational complexity. This is further exemplified in two case studies: simple unbounded polymerization and early EGFR/insulin crosstalk.

Mapping behavioral specifications to model parameters in synthetic biology.

With recent improvements of protocols for the assembly of transcriptional parts, synthetic biological devices can now more reliably be assembled according to a given design. The standardization of parts open up the way for in silico design tools that improve the construct and optimize devices with respect to given formal design specifications. The simplest such optimization is the selection of kinetic parameters and protein abundances such that the specified design constraints are robustly satisfied. In this work we address the problem of determining parameter values that fulfill specifications expressed in terms of a functional on the trajectories of a dynamical model. We solve this inverse problem by linearizing the forward operator that maps parameter sets to specifications, and then inverting it locally. This approach has two advantages over brute-force random sampling. First, the linearization approach allows us to map back intervals instead of points and second, every obtained value in the parameter region is satisfying the specifications by construction. The method is general and can hence be incorporated in a pipeline for the rational forward design of arbitrary devices in synthetic biology.