Robust set-point regulation of gene expression using resource competition couplings in mammalian cells

Gene expression depends on the cellular con-text. One major contributor to gene expression variability is competition for limited transcriptional and translational re-sources, which may induce indirect couplings among otherwise independently-regulated genes. Here, we apply control theoretical concepts and tools to design an incoherent feedforward loop (iFFL) biomolecular controller operating in mammalian cells using translational-resource competition couplings. Harnessing a resource-aware mathematical model, we demonstrate analytically and computationally that our resource-aware design can achieve near-constant set-point regulation of gene expression whilst ensuring robustness to plasmid uptake variation. We also provide an analytical condition on the model parameters to guide the design of the resource-aware iFFL controller ensuring robustness and performance in set-point regulation. Our theoretical design based on translational-resource competition couplings represents a promising approach to build more sophisticated resource-aware control circuits operating at the host-cell level

Absolute protein quantification using fluorescence measurements with FPCountR

This paper presents a generalisable method for the calibration of fluorescence readings on microplate readers, in order to convert arbitrary fluorescence units into absolute units. FPCountR relies on the generation of bespoke fluorescent protein (FP) calibrants, assays to determine protein concentration and activity, and a corresponding analytical workflow. We systematically characterise the assay protocols for accuracy, sensitivity and simplicity, and describe an ‘ECmax’ assay that outperforms the others and even enables accurate calibration without requiring the purification of FPs. To obtain cellular protein concentrations, we consider methods for the conversion of optical density to either cell counts or alternatively to cell volumes, as well as examining how cells can interfere with protein counting via fluorescence quenching, which we quantify and correct for the first time. Calibration across different instruments, disparate filter sets and mismatched gains is demonstrated to yield equivalent results. It also reveals that mCherry absorption at 600 nm does not confound cell density measurements unless expressed to over 100,000 proteins per cell. FPCountR is presented as pair of open access tools (protocol and R package) to enable the community to use this method, and ultimately to facilitate the quantitative characterisation of synthetic microbial circuits

Characterization of biologically relevant network structures form time-series data

High-throughput data acquisition in synthetic biology leads to an abundance of data that need to be processed and aggregated into useful biological models. Building dynamical models based on this wealth of data is of paramount importance to understand and optimize designs of synthetic biology constructs. However, building models manually for each data set is inconvenient and might become infeasible for highly complex synthetic systems. In this paper, we present state-of-the-art system identification techniques and combine them with chemical reaction network theory (CRNT) to generate dynamic models automatically. On the system identification side, Sparse Bayesian Learning offers methods to learn from data the sparsest set of dictionary functions necessary to capture the dynamics of the system into ODE models; on the CRNT side, building on such sparse ODE models, all possible network structures within a given parameter uncertainty region can be computed. Additionally, the system identification process can be complemented with constraints on the parameters to, for example, enforce stability or non-negativity---thus offering relevant physical constraints over the possible network structures. In this way, the wealth of data can be translated into biologically relevant network structures, which then steers the data acquisition, thereby providing a vital step for closed-loop system identification

Cell-free prediction of protein expression costs for growing cells

Translating heterologous proteins places significant burden on host cells, consuming expression resources leading to slower cell growth and productivity. Yet predicting the cost of protein production for any given gene is a major challenge, as multiple processes and factors combine to determine translation efficiency. To enable prediction of the cost of gene expression in bacteria, we describe here a standard cell-free lysate assay that provides a relative measure of resource consumption when a protein coding sequence is expressed. These lysate measurements can then be used with a computational model of translation to predict the in vivo burden placed on growing E. coli cells for a variety of proteins of different functions and lengths. Using this approach, we can predict the burden of expressing multigene operons of different designs and differentiate between the fraction of burden related to gene expression compared to action of a metabolic pathway

Systematic computation of non-linear cellular and molecular dynamics with low-power cytomimetic circuits: A simulation study

This paper presents a novel method for the systematic implementation of low-power microelectronic circuits aimed at computing nonlinear cellular and molecular dynamics. The method proposed is based on the Nonlinear Bernoulli Cell Formalism (NBCF), an advanced mathematical framework stemming from the Bernoulli Cell Formalism (BCF) originally exploited for the modular synthesis and analysis of linear, time-invariant, high dynamic range, logarithmic filters. Our approach identifies and exploits the striking similarities existing between the NBCF and coupled nonlinear ordinary differential equations (ODEs) typically appearing in models of naturally encountered biochemical systems. The resulting continuous-time, continuous-value, low-power CytoMimetic electronic circuits succeed in simulating fast and with good accuracy cellular and molecular dynamics. The application of the method is illustrated by synthesising for the first time microelectronic CytoMimetic topologies which simulate successfully: 1) a nonlinear intracellular calcium oscillations model for several Hill coefficient values and 2) a gene-protein regulatory system model. The dynamic behaviours generated by the proposed CytoMimetic circuits are compared and found to be in very good agreement with their biological counterparts. The circuits exploit the exponential law codifying the low-power subthreshold operation regime and have been simulated with realistic parameters from a commercially available CMOS process. They occupy an area of a fraction of a square-millimetre, while consuming between 1 and 12 microwatts of power. Simulations of fabrication-related variability results are also presented

Deep Learning Concepts and Applications for Synthetic Biology.

Synthetic biology has a natural synergy with deep learning. It can be used to generate large data sets to train models, for example by using DNA synthesis, and deep learning models can be used to inform design, such as by generating novel parts or suggesting optimal experiments to conduct. Recently, research at the interface of engineering biology and deep learning has highlighted this potential through successes including the design of novel biological parts, protein structure prediction, automated analysis of microscopy data, optimal experimental design, and biomolecular implementations of artificial neural networks. In this review, we present an overview of synthetic biology-relevant classes of data and deep learning architectures. We also highlight emerging studies in synthetic biology that capitalize on deep learning to enable novel understanding and design, and discuss challenges and future opportunities in this space

An Exact Solution for the Lattice Gas Model in One Dimension

A simple method to obtain a canonical partition function for one dimensional lattice gas model is presented. The simplification is based upon rewriting a sum over all possible configurations to a sum over numbers of clusters in the system.Comment: 6 pages, LaTe

The exit time finite state projection scheme: bounding exit distributions and occupation measures of continuous-time Markov chains

We introduce the exit time finite state projection (ETFSP) scheme, a truncation- based method that yields approximations to the exit distribution and occupation measure associated with the time of exit from a domain (i.e., the time of first passage to the complement of the domain) of time-homogeneous continuous-time Markov chains. We prove that: (i) the computed approximations bound the measures from below; (ii) the total variation distances between the approximations and the measures decrease monotonically as states are added to the truncation; and (iii) the scheme converges, in the sense that, as the truncation tends to the entire state space, the total variation distances tend to zero. Furthermore, we give a computable bound on the total variation distance between the exit distribution and its approximation, and we delineate the cases in which the bound is sharp. We also revisit the related finite state projection scheme and give a comprehensive account of its theoretical properties. We demonstrate the use of the ETFSP scheme by applying it to two biological examples: the computation of the first passage time associated with the expression of a gene, and the fixation times of competing species subject to demographic noise

Stationary distributions of continuous-time Markov chains: a review of theory and truncation-based approximations

Computing the stationary distributions of a continuous-time Markov chain involves solving a set of linear equations. In most cases of interest, the number of equations is infinite or too large, and cannot be solved analytically or numerically. Several approximation schemes overcome this issue by truncating the state space to a manageable size. In this review, we first give a comprehensive theoretical account of the stationary distributions and their relation to the long-term behaviour of the Markov chain, which is readily accessible to non-experts and free of irreducibility assumptions made in standard texts. We then review truncation-based approximation schemes paying particular attention to their convergence and to the errors they introduce, and we illustrate their performance with an example of a stochastic reaction network of relevance in biology and chemistry. We conclude by elaborating on computational trade-offs associated with error control and some open questions

Robust synchronization in networks of cyclic feedback systems

This paper presents a result on the robust synchronization of outputs of statically interconnected non-identical cyclic feedback systems that are used to model, among other processes, gene expression. The result uses incremental versions of the small gain theorem and dissipativity theory to arrive at an upper bound on the norm of the synchronization error between corresponding states, giving a measure of the degree of convergence of the solutions. This error bound is shown to be a function of the difference between the parameters of the interconnected systems, and disappears in the case where the systems are identical, thus retrieving an earlier synchronization result