Simplified mechanistic models of gene regulation for analysis and design

Simplified mechanistic models of gene regulation are fundamental to systems biology and essential for synthetic biology. However, conventional simplified models typically have outputs that are not directly measurable and are based on assumptions that do not often hold under experimental conditions. To resolve these issues, we propose a ‘model reduction’ methodology and simplified kinetic models of total mRNA and total protein concentration, which link measurements, models and biochemical mechanisms. The proposed approach is based on assumptions that hold generally and include typical cases in systems and synthetic biology where conventional models do not hold. We use novel assumptions regarding the ‘speed of reactions’, which are required for the methodology to be consistent with experimental data. We also apply the methodology to propose simplified models of gene regulation in the presence of multiple protein binding sites, providing both biological insights and an illustration of the generality of the methodology. Lastly, we show that modelling total protein concentration allows us to address key questions on gene regulation, such as efficiency, burden, competition and modularity.     

Switchable genetic oscillator operating in quasi-stable mode

Ring topologies of repressing genes have qualitatively different long-term dynamics if the number of genes is odd (they oscillate) or even (they exhibit bistability). However, these attractors may not fully explain the observed behaviour in transient and stochastic environments such as the cell. We show here that even repressilators possess quasi-stable, travelling wave periodic solutions that are reachable, long-lived and robust to parameter changes. These solutions underlie the sustained oscillations observed in even rings in the stochastic regime, even if these circuits are expected to behave as switches. The existence of such solutions can also be exploited for control purposes: operation of the system around the quasi-stable orbit allows us to turn on and off the oscillations reliably and on demand. We illustrate these ideas with a simple protocol based on optical interference that can induce oscillations robustly both in the stochastic and deterministic regimes.     

Modelling emergence of oscillations in communicating bacteria: a structured approach from one to many cells

Population-level measurements of phenotypic behaviour in biological systems may not necessarily reflect individual cell behaviour. To assess qualitative changes in the behaviour of a single cell, when alone and when part of a community, we developed an agent-based model describing the metabolic states of a population of quorum-coupled cells. The modelling is motivated by published experimental work of a synthetic genetic regulatory network (GRN) used in Escherichia coli cells that exhibit oscillatory behaviour across the population. To decipher the mechanisms underlying oscillations in the system, we investigate the behaviour of the model via numerical simulation and bifurcation analysis. In particular, we study the effect of an increase in population size as well as the spatio-temporal behaviour of the model. Our results demonstrate that oscillations are possible only in the presence of a high concentration of the coupling chemical and are due to a time scale separation in key regulatory components of the system. The model suggests that the population establishes oscillatory behaviour as the system''s preferred stable state. This is achieved via an effective increase in coupling across the population. We conclude that population effects in GRN design need to be taken into consideration and be part of the design process. This is important in planning intervention strategies or designing specific cell behaviours.     

Meta-DNA: synthetic biology via DNA nanostructures and hybridization reactions

Can a wide range of complex biochemical behaviour arise from repeated applications of a highly reduced class of interactions? In particular, can the range of DNA manipulations achieved by protein enzymes be simulated via simple DNA hybridization chemistry? In this work, we develop a biochemical system which we call meta-DNA (abbreviated as mDNA), based on strands of DNA as the only component molecules. Various enzymatic manipulations of these mDNA molecules are simulated via toehold-mediated DNA strand displacement reactions. We provide a formal model to describe the required properties and operations of our mDNA, and show that our proposed DNA nanostructures and hybridization reactions provide these properties and functionality. Our meta-nucleotides are designed to form flexible linear assemblies (single-stranded mDNA (ssmDNA)) analogous to single-stranded DNA. We describe various isothermal hybridization reactions that manipulate our mDNA in powerful ways analogous to DNA–DNA reactions and the action of various enzymes on DNA. These operations on mDNA include (i) hybridization of ssmDNA into a double-stranded mDNA (dsmDNA) and heat denaturation of a dsmDNA into its component ssmDNA, (ii) strand displacement of one ssmDNA by another, (iii) restriction cuts on the backbones of ssmDNA and dsmDNA, (iv) polymerization reactions that extend ssmDNA on a template to form a complete dsmDNA, (v) synthesis of mDNA sequences via mDNA polymerase chain reaction, (vi) isothermal denaturation of a dsmDNA into its component ssmDNA, and (vii) an isothermal replicator reaction that exponentially amplifies ssmDNA strands and may be modified to allow for mutations.     

Modelling co-translational dimerization for programmable nonlinearity in synthetic biology

Nonlinearity plays a fundamental role in the performance of both natural and synthetic biological networks. Key functional motifs in living microbial systems, such as the emergence of bistability or oscillations, rely on nonlinear molecular dynamics. Despite its core importance, the rational design of nonlinearity remains an unmet challenge. This is largely due to a lack of mathematical modelling that accounts for the mechanistic basis of nonlinearity. We introduce a model for gene regulatory circuits that explicitly simulates protein dimerization—a well-known source of nonlinear dynamics. Specifically, our approach focuses on modelling co-translational dimerization: the formation of protein dimers during—and not after—translation. This is in contrast to the prevailing assumption that dimer generation is only viable between freely diffusing monomers (i.e. post-translational dimerization). We provide a method for fine-tuning nonlinearity on demand by balancing the impact of co- versus post-translational dimerization. Furthermore, we suggest design rules, such as protein length or physical separation between genes, that may be used to adjust dimerization dynamics in vivo. The design, build and test of genetic circuits with on-demand nonlinear dynamics will greatly improve the programmability of synthetic biological systems.     

Tensor methods for parameter estimation and bifurcation analysis of stochastic reaction networks

Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge of stochastic models is to calibrate a large number of model parameters against the experimental data. Another difficulty is to study how the behaviour of a stochastic model depends on its parameters, i.e. whether a change in model parameters can lead to a significant qualitative change in model behaviour (bifurcation). In this paper, tensor-structured parametric analysis (TPA) is developed to address these computational challenges. It is based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. This approach enables simultaneous computation of the model properties for all parameter values within a parameter space. The TPA is illustrated by studying the parameter estimation, robustness, sensitivity and bifurcation structure in stochastic models of biochemical networks. A Matlab implementation of the TPA is available at http://www.stobifan.org.     

A simplified analysis for the evaluation of stochastic response of elasto-plastic oscillators

The paper deals with dynamic hysteretic oscillators without post-yielding hardening, called ideal elasto-plastic oscillators, subjected to white noise. They are characterized by the fact that they do not reach stationarity even though excited by stationary stochastic processes. A simplified solution procedure to capture this behaviour is presented in this paper. It is based on modelling the accumulated plastic deformations as a homogeneous compound Poisson process. In particular, two aspects are addressed in the paper: (1) evaluation of the probabilistic parameters of the accumulated plastic deformation process; and (2) evaluation of the second-order cumulants of the response by means of closed form expressions. Although the presented results are not rigorous and rely on an empirical basis, the aim is a very handy and sufficiently accurate procedure to obtain the evaluation of the second-order probabilistic parameters of elasto-plastic oscillators. Moreover, by testing this procedure against Monte Carlo simulations, a parametric study has been conducted in order to assess the range of validity of the homogeneous compound Poisson process model. The presented procedure can be easily extended to the case of non-normal delta correlated input processes.     

Delayed self-regulation and time-dependent chemical drive leads to novel states in epigenetic landscapes

The epigenetic pathway of a cell as it differentiates from a stem cell state to a mature lineage-committed one has been historically understood in terms of Waddington''s landscape, consisting of hills and valleys. The smooth top and valley-strewn bottom of the hill represent their undifferentiated and differentiated states, respectively. Although mathematical ideas rooted in nonlinear dynamics and bifurcation theory have been used to quantify this picture, the importance of time delays arising from multistep chemical reactions or cellular shape transformations have been ignored so far. We argue that this feature is crucial in understanding cell differentiation and explore the role of time delay in a model of a single-gene regulatory circuit. We show that the interplay of time-dependent drive and delay introduces a new regime where the system shows sustained oscillations between the two admissible steady states. We interpret these results in the light of recent perplexing experiments on inducing the pluripotent state in mouse somatic cells. We also comment on how such an oscillatory state can provide a framework for understanding more general feedback circuits in cell development.     

压电驱动合成喷的设计及分析

介绍了合成喷的基本原理,并分析了压电驱动合成喷设计的基本思路和关键点。对喷的两个重要部件：压电驱动器和腔体的尺寸设计作了分析和说明。讨论了合成喷的电输入参数,选择并实验研究了驱动器的相关特性。分析认为：压电驱动合成喷的尺寸设计应使Rc/Rm,h,m和腔体体积V较小,而电输入则应选择为较高电压,频率为驱动器谐频的方法输入。     

Biology by design: reduction and synthesis of cellular components and behaviour.

Biological research is experiencing an increasing focus on the application of knowledge rather than on its generation. Thanks to the increased understanding of cellular systems and technological advances, biologists are more frequently asking not only ‘how can I understand the structure and behaviour of this biological system?’, but also ‘how can I apply that knowledge to generate novel functions in different biological systems or in other contexts?’ Active pursuit of the latter has nurtured the emergence of synthetic biology. Here, we discuss the motivation behind, and foundational technologies enabling, the development of this nascent field. We examine some early successes and applications while highlighting the challenges involved. Finally, we consider future directions and mention non-scientific considerations that can influence the field''s growth.     

The diminishing role of hubs in dynamical processes on complex networks

It is notoriously difficult to predict the behaviour of a complex self-organizing system, where the interactions among dynamical units form a heterogeneous topology. Even if the dynamics of each microscopic unit is known, a real understanding of their contributions to the macroscopic system behaviour is still lacking. Here, we develop information-theoretical methods to distinguish the contribution of each individual unit to the collective out-of-equilibrium dynamics. We show that for a system of units connected by a network of interaction potentials with an arbitrary degree distribution, highly connected units have less impact on the system dynamics when compared with intermediately connected units. In an equilibrium setting, the hubs are often found to dictate the long-term behaviour. However, we find both analytically and experimentally that the instantaneous states of these units have a short-lasting effect on the state trajectory of the entire system. We present qualitative evidence of this phenomenon from empirical findings about a social network of product recommendations, a protein–protein interaction network and a neural network, suggesting that it might indeed be a widespread property in nature.     

A synthetic aperture telescope based on a pair of gratings

A synthetic aperture is an effective approach to enhancement of the resolution of telescopes. In this paper, a new method to improve the resolution by using a pair of gratings is proposed. It allows collection of parts of the light diffracted from the object which could not previously reach the imaging device. This method improves the resolution and light energy utilization ratio of telescopes without introducing new chromatic aberration. An experiment for resolution testing was carried out and the feasibility and availability of the method were verified.     

Towards synthetic biological approaches to resource utilization on space missions

This paper demonstrates the significant utility of deploying non-traditional biological techniques to harness available volatiles and waste resources on manned missions to explore the Moon and Mars. Compared with anticipated non-biological approaches, it is determined that for 916 day Martian missions: 205 days of high-quality methane and oxygen Mars bioproduction with Methanobacterium thermoautotrophicum can reduce the mass of a Martian fuel-manufacture plant by 56%; 496 days of biomass generation with Arthrospira platensis and Arthrospira maxima on Mars can decrease the shipped wet-food mixed-menu mass for a Mars stay and a one-way voyage by 38%; 202 days of Mars polyhydroxybutyrate synthesis with Cupriavidus necator can lower the shipped mass to three-dimensional print a 120 m³ six-person habitat by 85% and a few days of acetaminophen production with engineered Synechocystis sp. PCC 6803 can completely replenish expired or irradiated stocks of the pharmaceutical, thereby providing independence from unmanned resupply spacecraft that take up to 210 days to arrive. Analogous outcomes are included for lunar missions. Because of the benign assumptions involved, the results provide a glimpse of the intriguing potential of ‘space synthetic biology’, and help focus related efforts for immediate, near-term impact.     

合成孔径成像中掩埋目标的深度误差分析

在掩埋目标三维成像过程中,沉积层底质的不同与掩埋深度的变化,会使成像结果中目标深度与真实深度出现偏差。针对这一问题,可以利用下视的面阵合成孔径三维成像算法,通过构建水下分层模型与声速剖面模型,对掩埋点目标进行三维成像仿真。通过改变沉积层底质与掩埋深度,从理论分析与仿真结果研究深度误差的变化。研究表明,深度误差随沉积层声速和掩埋深度的增加而不断变大。     

A family of weak stochastic Newmark methods for simplified and efficient Monte Carlo simulations of oscillators

Engineers are often more concerned with the computation of statistical moments (or mathematical expectations) of the response of stochastically driven dynamical systems than with the determination of path‐wise response histories. With this in perspective, weak stochastic solutions of dynamical systems, modelled as n degrees‐of‐freedom (DOF) mechanical oscillators and driven by additive and/or multiplicative white noise (or, filtered white noise) processes, are considered in this study. While weak stochastic solutions are simpler and quicker to compute than strong (sample path‐wise) solutions, it must be emphasized that sample realizations of weak solutions have no path‐wise similarity with strong solutions. However, the statistical moment of any continuous and sufficiently differentiable deterministic function of the weak stochastic response is ‘close’ to that of the true response (if it exists) within a certain order of a given time step size. Computation of weak response therefore assumes great significance in the context of simulations of stochastically driven dynamical systems (oscillators) of engineering interest. To efficiently generate such weak responses, a novel class of weak stochastic Newmark methods (WSNMs), based on implicit Ito–Taylor expansions of displacement and velocity fields, is proposed. The resulting multiple stochastic integrals (MSIs) in these expansions are replaced by a set of random variables with considerably simpler and discrete probability densities. In fact, yet another simplifying feature of the present strategy is that there is no need to model and compute some of the higher‐level MSIs. Estimates of error orders of these methods in terms of a given time step size are derived and a proof of global convergence provided. Numerical illustrations are provided and compared with exact solutions whenever available to demonstrate the accuracy, simplicity and higher computational speed of WSNMs vis‐à‐vis a few other popularly used stochastic integration schemes as well as the path‐wise versions of the stochastic Newmark scheme. Copyright © 2006 John Wiley & Sons, Ltd.     

Co-culture systems and technologies: taking synthetic biology to the next level

Co-culture techniques find myriad applications in biology for studying natural or synthetic interactions between cell populations. Such techniques are of great importance in synthetic biology, as multi-species cell consortia and other natural or synthetic ecology systems are widely seen to hold enormous potential for foundational research as well as novel industrial, medical and environmental applications with many proof-of-principle studies in recent years. What is needed for co-cultures to fulfil their potential? Cell–cell interactions in co-cultures are strongly influenced by the extracellular environment, which is determined by the experimental set-up, which therefore needs to be given careful consideration. An overview of existing experimental and theoretical co-culture set-ups in synthetic biology and adjacent fields is given here, and challenges and opportunities involved in such experiments are discussed. Greater focus on foundational technology developments for co-cultures is needed for many synthetic biology systems to realize their potential in both applications and answering biological questions.     

Quasi-robust control of biochemical reaction networks via stochastic morphing

One of the main objectives of synthetic biology is the development of molecular controllers that can manipulate the dynamics of a given biochemical network that is at most partially known. When integrated into smaller compartments, such as living or synthetic cells, controllers have to be calibrated to factor in the intrinsic noise. In this context, biochemical controllers put forward in the literature have focused on manipulating the mean (first moment) and reducing the variance (second moment) of the target molecular species. However, many critical biochemical processes are realized via higher-order moments, particularly the number and configuration of the probability distribution modes (maxima). To bridge the gap, we put forward the stochastic morpher controller that can, under suitable timescale separations, morph the probability distribution of the target molecular species into a predefined form. The morphing can be performed at a lower-resolution, allowing one to achieve desired multi-modality/multi-stability, and at a higher-resolution, allowing one to achieve arbitrary probability distributions. Properties of the controller, such as robustness and convergence, are rigorously established, and demonstrated on various examples. Also proposed is a blueprint for an experimental implementation of stochastic morpher.