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.     

Testing the reproducibility and robustness of the cancer biology literature by robot

Scientific results should not just be ‘repeatable’ (replicable in the same laboratory under identical conditions), but also ‘reproducible’ (replicable in other laboratories under similar conditions). Results should also, if possible, be ‘robust’ (replicable under a wide range of conditions). The reproducibility and robustness of only a small fraction of published biomedical results has been tested; furthermore, when reproducibility is tested, it is often not found. This situation is termed ‘the reproducibility crisis'', and it is one the most important issues facing biomedicine. This crisis would be solved if it were possible to automate reproducibility testing. Here, we describe the semi-automated testing for reproducibility and robustness of simple statements (propositions) about cancer cell biology automatically extracted from the literature. From 12 260 papers, we automatically extracted statements predicted to describe experimental results regarding a change of gene expression in response to drug treatment in breast cancer, from these we selected 74 statements of high biomedical interest. To test the reproducibility of these statements, two different teams used the laboratory automation system Eve and two breast cancer cell lines (MCF7 and MDA-MB-231). Statistically significant evidence for repeatability was found for 43 statements, and significant evidence for reproducibility/robustness in 22 statements. In two cases, the automation made serendipitous discoveries. The reproduced/robust knowledge provides significant insight into cancer. We conclude that semi-automated reproducibility testing is currently achievable, that it could be scaled up to generate a substantive source of reliable knowledge and that automation has the potential to mitigate the reproducibility crisis.     

Intelligently deciphering unintelligible designs: algorithmic algebraic model checking in systems biology

Systems biology, as a subject, has captured the imagination of both biologists and systems scientists alike. But what is it? This review provides one researcher''s somewhat idiosyncratic view of the subject, but also aims to persuade young scientists to examine the possible evolution of this subject in a rich historical context. In particular, one may wish to read this review to envision a subject built out of a consilience of many interesting concepts from systems sciences, logic and model theory, and algebra, culminating in novel tools, techniques and theories that can reveal deep principles in biology—seen beyond mere observations. A particular focus in this review is on approaches embedded in an embryonic program, dubbed ‘algorithmic algebraic model checking’, and its powers and limitations.     

The principles of pedestrian route choice

Pedestrian route choice, the process by which individuals decide on their walking path between two locations, is a fundamental problem across disciplines. Because this behaviour is investigated from different conceptual and methodological angles, and because it strongly depends on the environmental context, it is challenging to establish a systematic framework for research. Here, by reviewing previous work, we identify four principles for pedestrian route choice that are relevant across disciplines. First, ‘information perception’ deals with how pedestrians can perceive information selectively and purposely, given the limited available information. Second, ‘information integration’ considers how pedestrians subjectively integrate environmental spatial information into mental representations. Third, ‘responding to information’ is concerned with how pedestrians tend to be attracted and repelled by specific attributes individually and how this can lead to positive or negative feedback loops across many individuals. Fourth ‘decision-making mechanisms'' describe how pedestrians trade off the evidence provided by different attributes. How pedestrians perceive, integrate, respond to, and act upon information is not fixed but varies with the context. We give examples for each principle and explain how these principles shape pedestrian choice behaviours. We hope this contribution provides a systematic overview of the field and helps to spark inspiration among specialists.     

Disordered animal multilayer reflectors and the localization of light

Multilayer optical reflectors constructed from ‘stacks’ of alternating layers of high and low refractive index dielectric materials are present in many animals. For example, stacks of guanine crystals with cytoplasm gaps occur within the skin and scales of fish, and stacks of protein platelets with cytoplasm gaps occur within the iridophores of cephalopods. Common to all these animal multilayer reflectors are different degrees of random variation in the thicknesses of the individual layers in the stack, ranging from highly periodic structures to strongly disordered systems. However, previous discussions of the optical effects of such thickness disorder have been made without quantitative reference to the propagation of light within the reflector. Here, we demonstrate that Anderson localization provides a general theoretical framework to explain the common coherent interference and optical properties of these biological reflectors. Firstly, we illustrate how the localization length enables the spectral properties of the reflections from more weakly disordered ‘coloured’ and more strongly disordered ‘silvery’ reflectors to be explained by the same physical process. Secondly, we show how the polarization properties of reflection can be controlled within guanine–cytoplasm reflectors, with an interplay of birefringence and thickness disorder explaining the origin of broadband polarization-insensitive reflectivity.     

The nanometre-scale physiology of bone: steric modelling and scanning transmission electron microscopy of collagen�Cmineral structure

The nanometre-scale structure of collagen and bioapatite within bone establishes bone''s physical properties, including strength and toughness. However, the nanostructural organization within bone is not well known and is debated. Widely accepted models hypothesize that apatite mineral (‘bioapatite’) is present predominantly inside collagen fibrils: in ‘gap channels’ between abutting collagen molecules, and in ‘intermolecular spaces’ between adjacent collagen molecules. However, recent studies report evidence of substantial extrafibrillar bioapatite, challenging this hypothesis. We studied the nanostructure of bioapatite and collagen in mouse bones by scanning transmission electron microscopy (STEM) using electron energy loss spectroscopy and high-angle annular dark-field imaging. Additionally, we developed a steric model to estimate the packing density of bioapatite within gap channels. Our steric model and STEM results constrain the fraction of total bioapatite in bone that is distributed within fibrils at less than or equal to 0.42 inside gap channels and less than or equal to 0.28 inside intermolecular overlap regions. Therefore, a significant fraction of bone''s bioapatite (greater than or equal to 0.3) must be external to the fibrils. Furthermore, we observe extrafibrillar bioapatite between non-mineralized collagen fibrils, suggesting that initial bioapatite nucleation and growth are not confined to the gap channels as hypothesized in some models. These results have important implications for the mechanics of partially mineralized and developing tissues.     

The feasibility of coherent energy transfer in microtubules

It was once purported that biological systems were far too ‘warm and wet’ to support quantum phenomena mainly owing to thermal effects disrupting quantum coherence. However, recent experimental results and theoretical analyses have shown that thermal energy may assist, rather than disrupt, quantum coherent transport, especially in the ‘dry’ hydrophobic interiors of biomolecules. Specifically, evidence has been accumulating for the necessary involvement of quantum coherent energy transfer between uniquely arranged chromophores in light harvesting photosynthetic complexes. The ‘tubulin’ subunit proteins, which comprise microtubules, also possess a distinct architecture of chromophores, namely aromatic amino acids, including tryptophan. The geometry and dipolar properties of these aromatics are similar to those found in photosynthetic units indicating that tubulin may support coherent energy transfer. Tubulin aggregated into microtubule geometric lattices may support such energy transfer, which could be important for biological signalling and communication essential to living processes. Here, we perform a computational investigation of energy transfer between chromophoric amino acids in tubulin via dipole excitations coupled to the surrounding thermal environment. We present the spatial structure and energetic properties of the tryptophan residues in the microtubule constituent protein tubulin. Plausibility arguments for the conditions favouring a quantum mechanism of signal propagation along a microtubule are provided. Overall, we find that coherent energy transfer in tubulin and microtubules is biologically feasible.     

On the reliability of seasonal climate forecasts

Seasonal climate forecasts are being used increasingly across a range of application sectors. A recent UK governmental report asked: how good are seasonal forecasts on a scale of 1–5 (where 5 is very good), and how good can we expect them to be in 30 years time? Seasonal forecasts are made from ensembles of integrations of numerical models of climate. We argue that ‘goodness’ should be assessed first and foremost in terms of the probabilistic reliability of these ensemble-based forecasts; reliable inputs are essential for any forecast-based decision-making. We propose that a ‘5’ should be reserved for systems that are not only reliable overall, but where, in particular, small ensemble spread is a reliable indicator of low ensemble forecast error. We study the reliability of regional temperature and precipitation forecasts of the current operational seasonal forecast system of the European Centre for Medium-Range Weather Forecasts, universally regarded as one of the world-leading operational institutes producing seasonal climate forecasts. A wide range of ‘goodness’ rankings, depending on region and variable (with summer forecasts of rainfall over Northern Europe performing exceptionally poorly) is found. Finally, we discuss the prospects of reaching ‘5’ across all regions and variables in 30 years time.     

Dichotomous feedback: a signal sequestration-based feedback mechanism for biocontroller design

We introduce a new design framework for implementing negative feedback regulation in synthetic biology, which we term ‘dichotomous feedback’. Our approach is different from current methods, in that it sequesters existing fluxes in the process to be controlled, and in this way takes advantage of the process’s architecture to design the control law. This signal sequestration mechanism appears in many natural biological systems and can potentially be easier to realize than ‘molecular sequestration’ and other comparison motifs that are nowadays common in biomolecular feedback control design. The loop is closed by linking the strength of signal sequestration to the process output. Our feedback regulation mechanism is motivated by two-component signalling systems, where a second response regulator could be competing with the natural response regulator thus sequestering kinase activity. Here, dichotomous feedback is established by increasing the concentration of the second response regulator as the level of the output of the natural process increases. Extensive analysis demonstrates how this type of feedback shapes the signal response, attenuates intrinsic noise while increasing robustness and reducing crosstalk.     

The virtue of innovation: innovation through the lenses of biological evolution

We rehearse the processes of innovation and discovery in general terms, using as our main metaphor the biological concept of an evolutionary fitness landscape. Incremental and disruptive innovations are seen, respectively, as successful searches carried out locally or more widely. They may also be understood as reflecting evolution by mutation (incremental) versus recombination (disruptive). We also bring a platonic view, focusing on virtue and memory. We use ‘virtue’ as a measure of efforts, including the knowledge required to come up with disruptive and incremental innovations, and ‘memory’ as a measure of their lifespan, i.e. how long they are remembered. Fostering innovation, in the evolutionary metaphor, means providing the wherewithal to promote novelty, good objective functions that one is trying to optimize, and means to improve one''s knowledge of, and ability to navigate, the landscape one is searching. Recombination necessarily implies multi- or inter-disciplinarity. These principles are generic to all kinds of creativity, novel ideas formation and the development of new products and technologies.     

The human foot and heel–sole–toe walking strategy: a mechanism enabling an inverted pendular gait with low isometric muscle force?

Mechanically, the most economical gait for slow bipedal locomotion requires walking as an ‘inverted pendulum’, with: I, an impulsive, energy-dissipating leg compression at the beginning of stance; II, a stiff-limbed vault; and III, an impulsive, powering push-off at the end of stance. The characteristic ‘M’-shaped vertical ground reaction forces of walking in humans reflect this impulse–vault–impulse strategy. Humans achieve this gait by dissipating energy during the heel-to-sole transition in early stance, approximately stiff-limbed, flat-footed vaulting over midstance and ankle plantarflexion (powering the toes down) in late stance. Here, we show that the ‘M’-shaped walking ground reaction force profile does not require the plantigrade human foot or heel–sole–toe stance; it is maintained in tip–toe and high-heel walking as well as in ostriches. However, the unusual, stiff, human foot structure—with ground-contacting heel behind ankle and toes in front—enables both mechanically economical inverted pendular walking and physiologically economical muscle loading, by producing extreme changes in mechanical advantage between muscles and ground reaction forces. With a human foot, and heel–sole–toe strategy during stance, the shin muscles that dissipate energy, or calf muscles that power the push-off, need not be loaded at all—largely avoiding the ‘cost of muscle force’—during the passive vaulting phase.     

An analytical approach to bistable biological circuit discrimination using real algebraic geometry

Biomolecular circuits with two distinct and stable steady states have been identified as essential components in a wide range of biological networks, with a variety of mechanisms and topologies giving rise to their important bistable property. Understanding the differences between circuit implementations is an important question, particularly for the synthetic biologist faced with determining which bistable circuit design out of many is best for their specific application. In this work we explore the applicability of Sturm''s theorem—a tool from nineteenth-century real algebraic geometry—to comparing ‘functionally equivalent’ bistable circuits without the need for numerical simulation. We first consider two genetic toggle variants and two different positive feedback circuits, and show how specific topological properties present in each type of circuit can serve to increase the size of the regions of parameter space in which they function as switches. We then demonstrate that a single competitive monomeric activator added to a purely monomeric (and otherwise monostable) mutual repressor circuit is sufficient for bistability. Finally, we compare our approach with the Routh–Hurwitz method and derive consistent, yet more powerful, parametric conditions. The predictive power and ease of use of Sturm''s theorem demonstrated in this work suggest that algebraic geometric techniques may be underused in biomolecular circuit analysis.     

Current-reinforced random walks for constructing transport networks

Biological systems that build transport networks, such as trail-laying ants and the slime mould Physarum, can be described in terms of reinforced random walks. In a reinforced random walk, the route taken by ‘walking’ particles depends on the previous routes of other particles. Here, we present a novel form of random walk in which the flow of particles provides this reinforcement. Starting from an analogy between electrical networks and random walks, we show how to include current reinforcement. We demonstrate that current-reinforcement results in particles converging on the optimal solution of shortest path transport problems, and avoids the self-reinforcing loops seen in standard density-based reinforcement models. We further develop a variant of the model that is biologically realistic, in the sense that the particles can be identified as ants and their measured density corresponds to those observed in maze-solving experiments on Argentine ants. For network formation, we identify the importance of nonlinear current reinforcement in producing networks that optimize both network maintenance and travel times. Other than ant trail formation, these random walks are also closely related to other biological systems, such as blood vessels and neuronal networks, which involve the transport of materials or information. We argue that current reinforcement is likely to be a common mechanism in a range of systems where network construction is observed.     

Next-generation tools for evolutionary invasion analyses

Evolutionary invasion analysis is a powerful technique for modelling in evolutionary biology. The general approach is to derive an expression for the growth rate of a mutant allele encoding some novel phenotype, and then to use this expression to predict long-term evolutionary outcomes. Mathematically, such ‘invasion fitness’ expressions are most often derived using standard linear stability analyses from dynamical systems theory. Interestingly, there is a mathematically equivalent approach to such stability analyses that is often employed in mathematical epidemiology, and that is based on so-called ‘next-generation’ matrices. Although this next-generation matrix approach has sometimes also been used in evolutionary invasion analyses, it is not yet common in this area despite the fact that it can sometimes greatly simplify calculations. The aim of this article is to bring the approach to a wider evolutionary audience in two ways. First, we review the next-generation matrix approach and provide a novel, and easily intuited, interpretation of how this approach relates to more standard techniques. Second, we illustrate next-generation methods in evolutionary invasion analysis through a series of informative examples. Although focusing primarily on evolutionary invasion analysis, we provide several insights that apply to biological modelling in general.     

The evolvability of programmable hardware

In biological systems, individual phenotypes are typically adopted by multiple genotypes. Examples include protein structure phenotypes, where each structure can be adopted by a myriad individual amino acid sequence genotypes. These genotypes form vast connected ‘neutral networks’ in genotype space. The size of such neutral networks endows biological systems not only with robustness to genetic change, but also with the ability to evolve a vast number of novel phenotypes that occur near any one neutral network. Whether technological systems can be designed to have similar properties is poorly understood. Here we ask this question for a class of programmable electronic circuits that compute digital logic functions. The functional flexibility of such circuits is important in many applications, including applications of evolutionary principles to circuit design. The functions they compute are at the heart of all digital computation. We explore a vast space of 10⁴⁵ logic circuits (‘genotypes’) and 10¹⁹ logic functions (‘phenotypes’). We demonstrate that circuits that compute the same logic function are connected in large neutral networks that span circuit space. Their robustness or fault-tolerance varies very widely. The vicinity of each neutral network contains circuits with a broad range of novel functions. Two circuits computing different functions can usually be converted into one another via few changes in their architecture. These observations show that properties important for the evolvability of biological systems exist in a commercially important class of electronic circuitry. They also point to generic ways to generate fault-tolerant, adaptable and evolvable electronic circuitry.     

Modelling biological behaviours with the unified modelling language: an immunological case study and critique

We present a framework to assist the diagrammatic modelling of complex biological systems using the unified modelling language (UML). The framework comprises three levels of modelling, ranging in scope from the dynamics of individual model entities to system-level emergent properties. By way of an immunological case study of the mouse disease experimental autoimmune encephalomyelitis, we show how the framework can be used to produce models that capture and communicate the biological system, detailing how biological entities, interactions and behaviours lead to higher-level emergent properties observed in the real world. We demonstrate how the UML can be successfully applied within our framework, and provide a critique of UML''s ability to capture concepts fundamental to immunology and biology more generally. We show how specialized, well-explained diagrams with less formal semantics can be used where no suitable UML formalism exists. We highlight UML''s lack of expressive ability concerning cyclic feedbacks in cellular networks, and the compounding concurrency arising from huge numbers of stochastic, interacting agents. To compensate for this, we propose several additional relationships for expressing these concepts in UML''s activity diagram. We also demonstrate the ambiguous nature of class diagrams when applied to complex biology, and question their utility in modelling such dynamic systems. Models created through our framework are non-executable, and expressly free of simulation implementation concerns. They are a valuable complement and precursor to simulation specifications and implementations, focusing purely on thoroughly exploring the biology, recording hypotheses and assumptions, and serve as a communication medium detailing exactly how a simulation relates to the real biology.     

震后功能可快速恢复联肢剪力墙研究

震后功能可快速恢复成为地震工程领域的研究前沿。该文基于损伤控制的思想,提出一种震后功能可快速恢复的联肢剪力墙,由低损伤墙肢和可更换连梁组成。在强烈地震作用下,低损伤墙肢无损坏或轻微损坏,可更换连梁耗散地震能量,震后可通过更换连梁中的消能梁段(或阻尼器)而实现快速修复。试验研究表明,钢管-双层钢板-混凝土组合剪力墙的承载力高,压弯破坏时极限变形能力达1/33,远大于钢筋混凝土剪力墙的变形能力;在1/100位移角时,钢管-双层钢板-混凝土组合剪力墙轻微损坏,可作为低损伤墙肢。该文中可更换钢连梁由中部的消能梁段和两端的非消能梁段组成,大尺寸试件的拟静力试验表明,往复剪切作用下连梁的塑性变形和损伤集中在中部的消能梁段,可更换钢连梁的塑性转角可达0.06 rad,滞回曲线饱满、稳定,通过合理设计连接节点可实现强震后方便更换消能梁段。     

Information processing by simple molecular motifs and susceptibility to noise

Biological organisms rely on their ability to sense and respond appropriately to their environment. The molecular mechanisms that facilitate these essential processes are however subject to a range of random effects and stochastic processes, which jointly affect the reliability of information transmission between receptors and, for example, the physiological downstream response. Information is mathematically defined in terms of the entropy; and the extent of information flowing across an information channel or signalling system is typically measured by the ‘mutual information’, or the reduction in the uncertainty about the output once the input signal is known. Here, we quantify how extrinsic and intrinsic noise affects the transmission of simple signals along simple motifs of molecular interaction networks. Even for very simple systems, the effects of the different sources of variability alone and in combination can give rise to bewildering complexity. In particular, extrinsic variability is apt to generate ‘apparent’ information that can, in extreme cases, mask the actual information that for a single system would flow between the different molecular components making up cellular signalling pathways. We show how this artificial inflation in apparent information arises and how the effects of different types of noise alone and in combination can be understood.     

Adhesion energy can regulate vesicle fusion and stabilize partially fused states

Release of neurotransmitters from nerve terminals occurs by fusion of synaptic vesicles with the plasma membrane, and this process is highly regulated. Although major molecular components that control docking and fusion of vesicles to the synaptic membrane have been identified, the detailed mechanics of this process is not yet understood. We have developed a mathematical model that predicts how adhesion forces imposed by docking and fusion molecular machinery would affect the fusion process. We have computed the membrane stress that is produced by adhesion-driven vesicle bending and find that it is compressive. Further, our computations of the membrane curvature predict that strong adhesion can create a metastable state with a partially opened pore that would correspond to the ‘kiss and run’ release mode. Our model predicts that the larger the vesicle size, the more likely the metastable state with a transiently opened pore. These results contribute to understanding the mechanics of the fusion process, including possible clamping of the fusion by increasing molecular adhesion, and a balance between ‘kiss and run’ and full collapse fusion modes.