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.     

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。     

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.     

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.     

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.     

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.     

合成孔径声呐Chirp Scaling成像算法

在合成孔径声呐领域中经典的成像处理方法是距离-多普勒算法。距离-多普勒算法的主要缺点是在进行方位处理时需要进行距离二次脉压和在进行距离徙动校正时需要进行插值处理,这样将导致运算量迅速增加,并且降低了成像精度。而ChirpScaling算法是在二维频域中精确实现距离门徙动校正和二次距离压缩,避免了插值运算,用该算法处理了仿真点目标的回波数据,结果表明该算法既能够实现更加精确的成像又能够避免插值运算而提高运算效能。     

Maximizing protein translation rate in the non-homogeneous ribosome flow model: a convex optimization approach

Translation is an important stage in gene expression. During this stage, macro-molecules called ribosomes travel along the mRNA strand linking amino acids together in a specific order to create a functioning protein. An important question, related to many biomedical disciplines, is how to maximize protein production. Indeed, translation is known to be one of the most energy-consuming processes in the cell, and it is natural to assume that evolution shaped this process so that it maximizes the protein production rate. If this is indeed so then one can estimate various parameters of the translation machinery by solving an appropriate mathematical optimization problem. The same problem also arises in the context of synthetic biology, namely, re-engineer heterologous genes in order to maximize their translation rate in a host organism. We consider the problem of maximizing the protein production rate using a computational model for translation–elongation called the ribosome flow model (RFM). This model describes the flow of the ribosomes along an mRNA chain of length n using a set of n first-order nonlinear ordinary differential equations. It also includes n + 1 positive parameters: the ribosomal initiation rate into the mRNA chain, and n elongation rates along the chain sites. We show that the steady-state translation rate in the RFM is a strictly concave function of its parameters. This means that the problem of maximizing the translation rate under a suitable constraint always admits a unique solution, and that this solution can be determined using highly efficient algorithms for solving convex optimization problems even for large values of n. Furthermore, our analysis shows that the optimal translation rate can be computed based only on the optimal initiation rate and the elongation rate of the codons near the beginning of the ORF. We discuss some applications of the theoretical results to synthetic biology, molecular evolution, and functional genomics.     

A comparative analysis of hotspot identification methods

The identification of crash hotspots is the first step of the highway safety management process. Errors in hotspot identification may result in the inefficient use of resources for safety improvements and may reduce the global effectiveness of the safety management process. Despite the importance of using effective hotspot identification (HSID) methods, only a few researchers have compared the performance of various methods. In this research, seven commonly applied HSID methods were compared against four robust and informative quantitative evaluation criteria. The following HSID methods were compared: crash frequency (CF), equivalent property damage only (EPDO) crash frequency, crash rate (CR), proportion method (P), empirical Bayes estimate of total-crash frequency (EB), empirical Bayes estimate of severe-crash frequency (EBs), and potential for improvement (PFI). The HSID methods were compared using the site consistency test, the method consistency test, the total rank differences test, and the total score test. These tests evaluate each HSID method's performance in a variety of areas, such as efficiency in identifying sites that show consistently poor safety performance, reliability in identifying the same hotspots in subsequent time periods, and ranking consistency. To evaluate the HSID methods, five years of crash data from the Italian motorway A16 were used.The quantitative evaluation tests showed that the EB method performs better than the other HSID methods. Test results highlight that the EB method is the most consistent and reliable method for identifying priority investigation locations. The EB expected frequency of total-crashes (EB) performed better than the EB expected frequency of severe-crashes (EBs), although the results differed only slightly when the number of identified hotspots increased. The CF method performed better than other HSID methods with more appealing theoretical arguments. In particular, the CF method performed better than the CR method. This result is quite alarming, since many agencies use the CR method. The PFI and EPDO methods were largely inconsistent. The proportion method performed worst in all of the tests. Overall, these results are consistent with the results of previous studies.The identification of engineering countermeasures that may reduce crashes was successful in all of the hotspots identified with the EB method; this finding shows that the identified hotspots can also be corrected.The advantages associated with the EB method were based on crash data from one Italian motorway, and the relative performances of HSID methods may change when using other crash data. However, the study results are very significant and are consistent with earlier findings. To further clarify the benefits of the EB method, this study should be replicated in other countries. Nevertheless, the study results, combined with previous research results, strongly suggest that the EB method should be the standard in the identification of hotspots.