Design principles of stripe-forming motifs: the role of positive feedback

Robustness and innovation in synthetic genotype networks

Genotype networks are sets of genotypes connected by small mutational changes that share the same phenotype. They facilitate evolutionary innovation by enabling the exploration of different neighborhoods in genotype space. Genotype networks, first suggested by theoretical models, have been empirically confirmed for proteins and RNAs. Comparative studies also support their existence for gene regulatory networks (GRNs), but direct experimental evidence is lacking. Here, we report the construction of three interconnected genotype networks of synthetic GRNs producing three distinct phenotypes in Escherichia coli. Our synthetic GRNs contain three nodes regulating each other by CRISPR interference and governing the expression of fluorescent reporters. The genotype networks, composed of over twenty different synthetic GRNs, provide robustness in face of mutations while enabling transitions to innovative phenotypes. Through realistic mathematical modeling, we quantify robustness and evolvability for the complete genotype-phenotype map and link these features mechanistically to GRN motifs. Our work thereby exemplifies how GRN evolution along genotype networks might be driving evolutionary innovation.

Cooperative stability renders protein complex formation more robust and controllable

Protein complexes are the fundamental units of many biological functions. Despite their many advantages, one major adverse impact of protein complexes is accumulations of unassembled subunits that may disrupt other processes or exert cytotoxic effects. Synthesis of excess subunits can be inhibited via negative feedback control or they can be degraded more efficiently than assembled subunits, with this latter being termed cooperative stability. Whereas controlled synthesis of complex subunits has been investigated extensively, how cooperative stability acts in complex formation remains largely unexplored. To fill this knowledge gap, we have built quantitative models of heteromeric complexes with or without cooperative stability and compared their behaviours in the presence of synthesis rate variations. A system displaying cooperative stability is robust against synthesis rate variations as it retains high dimer/monomer ratios across a broad range of parameter configurations. Moreover, cooperative stability can alleviate the constraint of limited supply of a given subunit and makes complex abundance more responsive to unilateral upregulation of another subunit. We also conducted an in silico experiment to comprehensively characterize and compare four types of circuits that incorporate combinations of negative feedback control and cooperative stability in terms of eight systems characteristics pertaining to optimality, robustness and controllability. Intriguingly, though individual circuits prevailed for distinct characteristics, the system with cooperative stability alone achieved the most balanced performance across all characteristics. Our study provides theoretical justification for the contribution of cooperative stability to natural biological systems and represents a guideline for designing synthetic complex formation systems with desirable characteristics.

Patterning, From Conifers to Consciousness: Turing’s Theory and Order From Fluctuations

This is a brief account of Turing’s ideas on biological pattern and the events that led to their wider acceptance by biologists as a valid way to investigate developmental pattern, and of the value of theory more generally in biology. Periodic patterns have played a key role in this process, especially 2D arrays of oriented stripes, which proved a disappointment in theoretical terms in the case of Drosophila segmentation, but a boost to theory as applied to skin patterns in fish and model chemical reactions. The concept of “order from fluctuations” is a key component of Turing’s theory, wherein pattern arises by selective amplification of spatial components concealed in the random disorder of molecular and/or cellular processes. For biological examples, a crucial point from an analytical standpoint is knowing the nature of the fluctuations, where the amplifier resides, and the timescale over which selective amplification occurs. The answer clarifies the difference between “inelegant” examples such as Drosophila segmentation, which is perhaps better understood as a programmatic assembly process, and “elegant” ones expressible in equations like Turing’s: that the fluctuations and selection process occur predominantly in evolutionary time for the former, but in real time for the latter, and likewise for error suppression, which for Drosophila is historical, in being lodged firmly in past evolutionary events. The prospects for a further extension of Turing’s ideas to the complexities of brain development and consciousness is discussed, where a case can be made that it could well be in neuroscience that his ideas find their most important application.

Fixed Point Attractor Theory Bridges Structure and Function in C. elegans Neuronal Network

Understanding the structure–function relationship in a neuronal network is one of the major challenges in neuroscience research. Despite increasing researches at circuit connectivity and neural network structure, their structure-based biological interpretability remains unclear. Based on the attractor theory, here we develop an analytical framework that links neural circuit structures and their functions together through fixed point attractor in Caenorhabditis elegans. In this framework, we successfully established the structural condition for the emergence of multiple fixed points in C. elegans connectome. Then we construct a finite state machine to explain how functions related to bistable phenomena at the neural activity and behavioral levels are encoded. By applying the proposed framework to the command circuit in C. elegans, we provide a circuit level interpretation for the forward-reverse switching behaviors. Interestingly, network properties of the command circuit and first layer amphid interneuron circuit can also be inferred from their functions in this framework. Our research indicates the reliability of the fixed point attractor bridging circuit structure and functions, suggesting its potential applicability to more complex neuronal circuits in other species.

Elucidating multi-input processing 3-node gene regulatory network topologies capable of generating striped gene expression patterns

A central problem in developmental and synthetic biology is understanding the mechanisms by which cells in a tissue or a Petri dish process external cues and transform such information into a coherent response, e.g., a terminal differentiation state. It was long believed that this type of positional information could be entirely attributed to a gradient of concentration of a specific signaling molecule (i.e., a morphogen). However, advances in experimental methodologies and computer modeling have demonstrated the crucial role of the dynamics of a cell’s gene regulatory network (GRN) in decoding the information carried by the morphogen, which is eventually translated into a spatial pattern. This morphogen interpretation mechanism has gained much attention in systems biology as a tractable system to investigate the emergent properties of complex genotype-phenotype maps. In this study, we apply a Markov chain Monte Carlo (MCMC)-like algorithm to probe the design space of three-node GRNs with the ability to generate a band-like expression pattern (target phenotype) in the middle of an arrangement of 30 cells, which resemble a simple (1-D) morphogenetic field in a developing embryo. Unlike most modeling studies published so far, here we explore the space of GRN topologies with nodes having the potential to perceive the same input signal differently. This allows for a lot more flexibility during the search space process, and thus enables us to identify a larger set of potentially interesting and realizable morphogen interpretation mechanisms. Out of 2061 GRNs selected using the search space algorithm, we found 714 classes of network topologies that could correctly interpret the morphogen. Notably, the main network motif that generated the target phenotype in response to the input signal was the type 3 Incoherent Feed-Forward Loop (I3-FFL), which agrees with previous theoretical expectations and experimental observations. Particularly, compared to a previously reported pattern forming GRN topologies, we have uncovered a great variety of novel network designs, some of which might be worth inquiring through synthetic biology methodologies to test for the ability of network design with minimal regulatory complexity to interpret a developmental cue robustly.

Systems biology is a fast growing field largely powered by advances in high-performance computing and sophisticated mathematical modeling of biological systems. Based on these advances, we are now in a position to mechanistically understand and accurately predict the behavior of complex biological processes, including cell differentiation and spatial pattern formation during embryogenesis. In this article, we use an in silico approach to probe the design space of multi-input, three-node Gene Regulatory Networks (GRNs) capable of generating a striped gene expression pattern in the context of a simplified 1-D morphogenetic field.

Precise determination of input-output mapping for multimodal gene circuits using data from transient transfection

The mapping of molecular inputs to their molecular outputs (input/output, I/O mapping) is an important characteristic of gene circuits, both natural and synthetic. Experimental determination of such mappings for synthetic circuits is best performed using stably integrated genetic constructs. In mammalian cells, stable integration of complex circuits is a time-consuming process that hampers rapid characterization of multiple circuit variants. On the other hand, transient transfection is quick. However, it is an extremely noisy process and it is unclear whether the obtained data have any relevance to the input/output mapping of a circuit obtained in the case of a stable integration. Here we describe a data processing workflow, Peakfinder algorithm for flow cytometry data (PFAFF), that allows extracting precise input/output mapping from single-cell protein expression data gathered by flow cytometry after a transient transfection. The workflow builds on the numerically-proven observation that the multivariate modes of input and output expression of multi-channel flow cytometry datasets, pre-binned by the expression level of an independent transfection reporter gene, harbor cells with circuit gene copy numbers distributions that depend deterministically on the properties of a bin. We validate our method by simulating flow cytometry data for seven multi-node circuit architectures, including a complex bi-modal circuit, under stable integration and transient transfection scenarios. The workflow applied to the simulated transient transfection data results in similar conclusions to those reached with simulated stable integration data. This indicates that the input/output mapping derived from transient transfection data using our method is an excellent approximation of the ground truth. Thus, the method allows to determine input/output mapping of complex gene network using noisy transient transfection data.

One of the key features of a gene circuit is its input/output behavior. A few earlier publications attempted to develop methods to extract this behavior using transient transfection of circuit components in mammalian cells. However, the hitherto developed methods are only suitable for circuit with monomodal output distribution. Moreover, the relationship between the extracted I/O mapping and the "ground truth" that would have obtained with stably-integrated circuits, has not been addressed. Here we explore cell populations easily identifiable in flow cytometry data, namely, the peaks of fluorescent readout distribution in cells binned by the common expression value of the transfection reporter, or marker, gene. Using numerical simulations, we find that the distribution of circuit copy number in these cells deterministically depends on marker fluorescence in the noise-dependent manner. Moreover, we find that this is true also in the case of bi-modal output distribution. Using the peaks of input and output distributions, we are able to reconstruct the I/O mapping of the circuit and relate it to the I/O mapping of the stably-integrated circuit. The reconstruction is enabled by a new computational method we call PFAFF. The method is extensively validated with forward-simulated flow cytometry data from stable and transient transfections, with up to seven different circuits. The results show excellent correlation between the I/O behavior extracted by PFAFF from simulated transient transfection data, and the data simulated for stably integrated circuit.

Spatiotemporal control of gene expression boundaries using a feedforward loop

BACKGROUND

A feedforward loop (FFL) is commonly observed in several biological networks. The FFL network motif has been mostly studied with respect to variation of the input signal in time, with only a few studies of FFL activity in a spatially distributed system such as morphogen-mediated tissue patterning. However, most morphogen gradients also evolve in time.

RESULTS

We studied the spatiotemporal behavior of a coherent FFL in two contexts: (a) a generic, oscillating morphogen gradient and (b) the dorsal-ventral patterning of the early Drosophila embryo by a gradient of the NF-κB homolog dorsal with its early target Twist. In both models, we found features in the dynamics of the intermediate node-phase difference and noise filtering-that were largely independent of the parameterization of the models, and thus were functions of the structure of the FFL itself. In the dorsal gradient model, we also found that proper target gene expression was not possible without including the effect of maternal pioneer factor Zelda.

CONCLUSIONS

An FFL buffers fluctuation to changes in the morphogen signal ensuring stable gene expression boundaries.

Synthetic circuits reveal how mechanisms of gene regulatory networks constrain evolution

Phenotypic variation is the raw material of adaptive Darwinian evolution. The phenotypic variation found in organismal development is biased towards certain phenotypes, but the molecular mechanisms behind such biases are still poorly understood. Gene regulatory networks have been proposed as one cause of constrained phenotypic variation. However, most pertinent evidence is theoretical rather than experimental. Here, we study evolutionary biases in two synthetic gene regulatory circuits expressed in Escherichia coli that produce a gene expression stripe-a pivotal pattern in embryonic development. The two parental circuits produce the same phenotype, but create it through different regulatory mechanisms. We show that mutations cause distinct novel phenotypes in the two networks and use a combination of experimental measurements, mathematical modelling and DNA sequencing to understand why mutations bring forth only some but not other novel gene expression phenotypes. Our results reveal that the regulatory mechanisms of networks restrict the possible phenotypic variation upon mutation. Consequently, seemingly equivalent networks can indeed be distinct in how they constrain the outcome of further evolution.

Endocytosis as a stabilizing mechanism for tissue homeostasis

Cells in tissues communicate by secreted growth factors (GF) and other signals. An important function of cell circuits is tissue homeostasis: maintaining proper balance between the amounts of different cell types. Homeostasis requires negative feedback on the GFs, to avoid a runaway situation in which cells stimulate each other and grow without control. Feedback can be obtained in at least two ways: endocytosis in which a cell removes its cognate GF by internalization and cross-inhibition in which a GF down-regulates the production of another GF. Here we ask whether there are design principles for cell circuits to achieve tissue homeostasis. We develop an analytically solvable framework for circuits with multiple cell types and find that feedback by endocytosis is far more robust to parameter variation and has faster responses than cross-inhibition. Endocytosis, which is found ubiquitously across tissues, can even provide homeostasis to three and four communicating cell types. These design principles form a conceptual basis for how tissues maintain a healthy balance of cell types and how balance may be disrupted in diseases such as degeneration and fibrosis.

A strategy for effective latent HIV reactivation using subtherapeutic drug doses

Cell state switches underlie a plethora of biological phenomena and disease treatment strategies. Hence the ability to efficiently switch states in a chosen direction is of central importance in a number of scenarios. Increasing the concentration of an effector that results in a given switch is often limited by side effects. Approaches are thus increasingly sought to bypass these constraints, increasing the frequency of state switching without increasing the frequency of the side effect. Here, we employ dynamical systems theory to uncover a simple strategy as to how to maximize the probability of reactivating latent Human immunodeficiency virus (HIV) whilst maintaining minimal side effects. We demonstrate that continuous supply of an effector is significantly more likely to result in a switch with minimal side effects than the same effector supplied in temporally discrete doses. Importantly this continual dosage is likely to occur far below the Minimum effective dose at a concentration that has classically been thought subtherapeutic. We therefore suggest that in many interventional settings there exists potential to reduce drug dose much further than has previously been thought possible yet still maintaining efficacy.

Automated Design Framework for Synthetic Biology Exploiting Pareto Optimality

In this work we consider Pareto optimality for automated design in synthetic biology. We present a generalized framework based on a mixed-integer dynamic optimization formulation that, given design specifications, allows the computation of Pareto optimal sets of designs, that is, the set of best trade-offs for the metrics of interest. We show how this framework can be used for (i) forward design, that is, finding the Pareto optimal set of synthetic designs for implementation, and (ii) reverse design, that is, analyzing and inferring motifs and/or design principles of gene regulatory networks from the Pareto set of optimal circuits. Finally, we illustrate the capabilities and performance of this framework considering four case studies. In the first problem we consider the forward design of an oscillator. In the remaining problems, we illustrate how to apply the reverse design approach to find motifs for stripe formation, rapid adaption, and fold-change detection, respectively.

Design Principles of Biological Oscillators through Optimization: Forward and Reverse Analysis

From cyanobacteria to human, sustained oscillations coordinate important biological functions. Although much has been learned concerning the sophisticated molecular mechanisms underlying biological oscillators, design principles linking structure and functional behavior are not yet fully understood. Here we explore design principles of biological oscillators from a multiobjective optimization perspective, taking into account the trade-offs between conflicting performance goals or demands. We develop a comprehensive tool for automated design of oscillators, based on multicriteria global optimization that allows two modes: (i) the automatic design (forward problem) and (ii) the inference of design principles (reverse analysis problem). From the perspective of synthetic biology, the forward mode allows the solution of design problems that mimic some of the desirable properties appearing in natural oscillators. The reverse analysis mode facilitates a systematic exploration of the design space based on Pareto optimality concepts. The method is illustrated with two case studies: the automatic design of synthetic oscillators from a library of biological parts, and the exploration of design principles in 3-gene oscillatory systems.

Wiring for independence: positive feedback motifs facilitate individuation of traits in development and evolution

Independent selection response of a trait is contingent on the availability of genetic variation that is not entangled with other traits. Mechanistically, such variational individuation in spite of shared genome results from gene regulation. Changes that increase individuation of traits are likely caused by gene regulatory changes. Yet the effect of regulatory evolution on population variation is understudied. Trait individuation also occurs during development. Developmental differentiation involves two stages-induction of differentiation and the maintenance of differentiated fate. The corresponding gene regulatory transition involves the feed-forward and the regulated feedback motifs. Here we consider analogous transition pattern at the evolutionary scale, establishing an autonomous regulatory sub-network involved in the independent trait variation. A population genetic simulation of regulated feedback loop dynamics under small perturbations shows a decoupling of variation in gene expression between the upstream gene and the responding downstream gene. We furthermore observe that the ranges of dynamics that can be generated by feedback and feed-forward networks overlap. Such phenotypic overlap enables genetic accessibility of network-specific expression dynamics. We suggest that feedback topology may eventually confer selective advantage leading from a gradual process to threshold individuation, i.e., the emergence of a novel trait.

Dynamics of gene circuits shapes evolvability

To what extent does the dynamical mechanism producing a specific biological phenotype bias the ability to evolve into novel phenotypes? We use the interpretation of a morphogen gradient into a single stripe of gene expression as a model phenotype. Although there are thousands of three-gene circuit topologies that can robustly develop a stripe of gene expression, the vast majority of these circuits use one of just six fundamentally different dynamical mechanisms. Here we explore the potential for gene circuits that use each of these six mechanisms to evolve novel phenotypes such as multiple stripes, inverted stripes, and gradients of gene expression. Through a comprehensive and systematic analysis, we find that circuits that use alternative mechanisms differ in the likelihood of reaching novel phenotypes through mutation. We characterize the phenotypic transitions and identify key ingredients of the evolutionary potential, such as sensitive interactions and phenotypic hubs. Finally, we provide an intuitive understanding on how the modular design of a particular mechanism favors the access to novel phenotypes. Our work illustrates how the dynamical mechanism by which an organism develops constrains how it can evolve. It is striking that these dynamical mechanisms and their impact on evolvability can be observed even for such an apparently simple patterning task, performed by just three-node circuits.

A unified design space of synthetic stripe-forming networks

Synthetic biology is a promising tool to study the function and properties of gene regulatory networks. Gene circuits with predefined behaviours have been successfully built and modelled, but largely on a case-by-case basis. Here we go beyond individual networks and explore both computationally and synthetically the design space of possible dynamical mechanisms for 3-node stripe-forming networks. First, we computationally test every possible 3-node network for stripe formation in a morphogen gradient. We discover four different dynamical mechanisms to form a stripe and identify the minimal network of each group. Next, with the help of newly established engineering criteria we build these four networks synthetically and show that they indeed operate with four fundamentally distinct mechanisms. Finally, this close match between theory and experiment allows us to infer and subsequently build a 2-node network that represents the archetype of the explored design space.