Network motifs: structure does not determine function

QOMIC: quantum optimization for motif identification

Motivation

Network motif identification (MI) problem aims to find topological patterns in biological networks. Identifying disjoint motifs is a computationally challenging problem using classical computers. Quantum computers enable solving high complexity problems which do not scale using classical computers. In this article, we develop the first quantum solution, called QOMIC (Quantum Optimization for Motif IdentifiCation), to the MI problem. QOMIC transforms the MI problem using a integer model, which serves as the foundation to develop our quantum solution. We develop and implement the quantum circuit to find motif locations in the given network using this model.

Results

Our experiments demonstrate that QOMIC outperforms the existing solutions developed for the classical computer, in term of motif counts. We also observe that QOMIC can efficiently find motifs in human regulatory networks associated with five neurodegenerative diseases: Alzheimer's, Parkinson's, Huntington's, Amyotrophic Lateral Sclerosis, and Motor Neurone Disease.

Availability and implementation

Our implementation can be found in https://github.com/ngominhhoang/Quantum-Motif-Identification.git.

Hypergraph animals

Here we introduce simple structures for the analysis of complex hypergraphs, hypergraph animals. These structures are designed to describe the local node neighborhoods of nodes in hypergraphs. We establish their relationships to lattice animals and network motifs, and we develop their combinatorial properties for sparse and uncorrelated hypergraphs. We make use of the tight link of hypergraph animals to partition numbers, which opens up a vast mathematical framework for the analysis of hypergraph animals. We then study their abundances in random hypergraphs. Two transferable insights result from this analysis: (i) it establishes the importance of high-cardinality edges in ensembles of random hypergraphs that are inspired by the classical Erdös-Renyí random graphs; and (ii) there is a close connection between degree and hyperedge cardinality in random hypergraphs that shapes animal abundances and spectra profoundly. Both findings imply that hypergraph animals can have the potential to affect information flow and processing in complex systems. Our analysis also suggests that we need to spend more effort on investigating and developing suitable conditional ensembles of random hypergraphs that can capture real-world structures and their complex dependency structures.

Dynamics and bifurcations in genetic circuits with fibration symmetries

Circuit building blocks of gene regulatory networks (GRN) have been identified through the fibration symmetries of the underlying biological graph. Here, we analyse analytically six of these circuits that occur as functional and synchronous building blocks in these networks. Of these, the lock-on, toggle switch, Smolen oscillator, feed-forward fibre and Fibonacci fibre circuits occur in living organisms, notably Escherichia coli; the sixth, the repressilator, is a synthetic GRN. We consider synchronous steady states determined by a fibration symmetry (or balanced colouring) and determine analytic conditions for local bifurcation from such states, which can in principle be either steady-state or Hopf bifurcations. We identify conditions that characterize the first bifurcation, the only one that can be stable near the bifurcation point. We model the state of each gene in terms of two variables: mRNA and protein concentration. We consider all possible 'admissible' models-those compatible with the network structure-and then specialize these general results to simple models based on Hill functions and linear degradation. The results systematically classify using graph symmetries the complexity and dynamics of these circuits, which are relevant to understand the functionality of natural and synthetic cells.

Competition and evolutionary selection among core regulatory motifs in gene expression control

Gene products that are beneficial in one environment may become burdensome in another, prompting the emergence of diverse regulatory schemes that carry their own bioenergetic cost. By ensuring that regulators are only expressed when needed, we demonstrate that autoregulation generally offers an advantage in an environment combining mutation and time-varying selection. Whether positive or negative feedback emerges as dominant depends primarily on the demand for the target gene product, typically to ensure that the detrimental impact of inevitable mutations is minimized. While self-repression of the regulator curbs the spread of these loss-of-function mutations, self-activation instead facilitates their propagation. By analyzing the transcription network of multiple model organisms, we reveal that reduced bioenergetic cost may contribute to the preferential selection of autoregulation among transcription factors. Our results not only uncover how seemingly equivalent regulatory motifs have fundamentally different impact on population structure, growth dynamics, and evolutionary outcomes, but they can also be leveraged to promote the design of evolutionarily robust synthetic gene circuits.

A group theoretic approach to model comparison with simplicial representations

The complexity of biological systems, and the increasingly large amount of associated experimental data, necessitates that we develop mathematical models to further our understanding of these systems. Because biological systems are generally not well understood, most mathematical models of these systems are based on experimental data, resulting in a seemingly heterogeneous collection of models that ostensibly represent the same system. To understand the system we therefore need to understand how the different models are related to each other, with a view to obtaining a unified mathematical description. This goal is complicated by the fact that a number of distinct mathematical formalisms may be employed to represent the same system, making direct comparison of the models very difficult. A methodology for comparing mathematical models based on their underlying conceptual structure is therefore required. In previous work we developed an appropriate framework for model comparison where we represent models, specifically the conceptual structure of the models, as labelled simplicial complexes and compare them with the two general methodologies of comparison by distance and comparison by equivalence. In this article we continue the development of our model comparison methodology in two directions. First, we present a rigorous and automatable methodology for the core process of comparison by equivalence, namely determining the vertices in a simplicial representation, corresponding to model components, that are conceptually related and the identification of these vertices via simplicial operations. Our methodology is based on considerations of vertex symmetry in the simplicial representation, for which we develop the required mathematical theory of group actions on simplicial complexes. This methodology greatly simplifies and expedites the process of determining model equivalence. Second, we provide an alternative mathematical framework for our model-comparison methodology by representing models as groups, which allows for the direct application of group-theoretic techniques within our model-comparison methodology.

A synthetic synthesis to explore animal evolution and development

Identifying the general principles by which genotypes are converted into phenotypes remains a challenge in the post-genomic era. We still lack a predictive understanding of how genes shape interactions among cells and tissues in response to signalling and environmental cues, and hence how regulatory networks generate the phenotypic variation required for adaptive evolution. Here, we discuss how techniques borrowed from synthetic biology may facilitate a systematic exploration of evolvability across biological scales. Synthetic approaches permit controlled manipulation of both endogenous and fully engineered systems, providing a flexible platform for investigating causal mechanisms in vivo. Combining synthetic approaches with multi-level phenotyping (phenomics) will supply a detailed, quantitative characterization of how internal and external stimuli shape the morphology and behaviour of living organisms. We advocate integrating high-throughput experimental data with mathematical and computational techniques from a variety of disciplines in order to pursue a comprehensive theory of evolution.

This article is part of the theme issue ‘Genetic basis of adaptation and speciation: from loci to causative mutations’.

Turing pattern design principles and their robustness

Turing patterns have morphed from mathematical curiosities into highly desirable targets for synthetic biology. For a long time, their biological significance was sometimes disputed but there is now ample evidence for their involvement in processes ranging from skin pigmentation to digit and limb formation. While their role in developmental biology is now firmly established, their synthetic design has so far proved challenging. Here, we review recent large-scale mathematical analyses that have attempted to narrow down potential design principles. We consider different aspects of robustness of these models and outline why this perspective will be helpful in the search for synthetic Turing-patterning systems. We conclude by considering robustness in the context of developmental modelling more generally. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

Testing biological network motif significance with exponential random graph models

Analysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks, related to their biological functions. However, there is disagreement as to the statistical significance of these motifs, and there are potential problems with standard methods for estimating this significance. Exponential random graph models (ERGMs) are a class of statistical model that can overcome some of the shortcomings of commonly used methods for testing the statistical significance of motifs. ERGMs were first introduced into the bioinformatics literature over 10 years ago but have had limited application to biological networks, possibly due to the practical difficulty of estimating model parameters. Advances in estimation algorithms now afford analysis of much larger networks in practical time. We illustrate the application of ERGM to both an undirected protein-protein interaction (PPI) network and directed gene regulatory networks. ERGM models indicate over-representation of triangles in the PPI network, and confirm results from previous research as to over-representation of transitive triangles (feed-forward loop) in an E. coli and a yeast regulatory network. We also confirm, using ERGMs, previous research showing that under-representation of the cyclic triangle (feedback loop) can be explained as a consequence of other topological features.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s41109-021-00434-y.

Integrated omics networks reveal the temporal signaling events of brassinosteroid response in Arabidopsis

Brassinosteroids (BRs) are plant steroid hormones that regulate cell division and stress response. Here we use a systems biology approach to integrate multi-omic datasets and unravel the molecular signaling events of BR response in Arabidopsis. We profile the levels of 26,669 transcripts, 9,533 protein groups, and 26,617 phosphorylation sites from Arabidopsis seedlings treated with brassinolide (BL) for six different lengths of time. We then construct a network inference pipeline called Spatiotemporal Clustering and Inference of Omics Networks (SC-ION) to integrate these data. We use our network predictions to identify putative phosphorylation sites on BES1 and experimentally validate their importance. Additionally, we identify BRONTOSAURUS (BRON) as a transcription factor that regulates cell division, and we show that BRON expression is modulated by BR-responsive kinases and transcription factors. This work demonstrates the power of integrative network analysis applied to multi-omic data and provides fundamental insights into the molecular signaling events occurring during BR response.

Model comparison via simplicial complexes and persistent homology

In many scientific and technological contexts, we have only a poor understanding of the structure and details of appropriate mathematical models. We often, therefore, need to compare different models. With available data we can use formal statistical model selection to compare and contrast the ability of different mathematical models to describe such data. There is, however, a lack of rigorous methods to compare different models a priori. Here, we develop and illustrate two such approaches that allow us to compare model structures in a systematic way by representing models as simplicial complexes. Using well-developed concepts from simplicial algebraic topology, we define a distance between models based on their simplicial representations. Employing persistent homology with a flat filtration provides for alternative representations of the models as persistence intervals, which represent model structure, from which the model distances are also obtained. We then expand on this measure of model distance to study the concept of model equivalence to determine the conceptual similarity of models. We apply our methodology for model comparison to demonstrate an equivalence between a positional-information model and a Turing-pattern model from developmental biology, constituting a novel observation for two classes of models that were previously regarded as unrelated.

A KMT2A-AFF1 gene regulatory network highlights the role of core transcription factors and reveals the regulatory logic of key downstream target genes

Regulatory interactions mediated by transcription factors (TFs) make up complex networks that control cellular behavior. Fully understanding these gene regulatory networks (GRNs) offers greater insight into the consequences of disease-causing perturbations than can be achieved by studying single TF binding events in isolation. Chromosomal translocations of the lysine methyltransferase 2A (KMT2A) gene produce KMT2A fusion proteins such as KMT2A-AFF1 (previously MLL-AF4), causing poor prognosis acute lymphoblastic leukemias (ALLs) that sometimes relapse as acute myeloid leukemias (AMLs). KMT2A-AFF1 drives leukemogenesis through direct binding and inducing the aberrant overexpression of key genes, such as the anti-apoptotic factor BCL2 and the proto-oncogene MYC However, studying direct binding alone does not incorporate possible network-generated regulatory outputs, including the indirect induction of gene repression. To better understand the KMT2A-AFF1-driven regulatory landscape, we integrated ChIP-seq, patient RNA-seq, and CRISPR essentiality screens to generate a model GRN. This GRN identified several key transcription factors such as RUNX1 that regulate target genes downstream of KMT2A-AFF1 using feed-forward loop (FFL) and cascade motifs. A core set of nodes are present in both ALL and AML, and CRISPR screening revealed several factors that help mediate response to the drug venetoclax. Using our GRN, we then identified a KMT2A-AFF1:RUNX1 cascade that represses CASP9, as well as KMT2A-AFF1-driven FFLs that regulate BCL2 and MYC through combinatorial TF activity. This illustrates how our GRN can be used to better connect KMT2A-AFF1 behavior to downstream pathways that contribute to leukemogenesis, and potentially predict shifts in gene expression that mediate drug response.

Network motif-based analysis of regulatory patterns in paralogous gene pairs

Current high-throughput experimental techniques make it feasible to infer gene regulatory interactions at the whole-genome level with reasonably good accuracy. Such experimentally inferred regulatory networks have become available for a number of simpler model organisms such as S. cerevisiae, and others. The availability of such networks provides an opportunity to compare gene regulatory processes at the whole genome level, and in particular, to assess similarity of regulatory interactions for homologous gene pairs either from the same or from different species. We present here a new technique for analyzing the regulatory interaction neighborhoods of paralogous gene pairs. Our central focus is the analysis of S. cerevisiae gene interaction graphs, which are of particular interest due to the ancestral whole-genome duplication (WGD) that allows to distinguish between paralogous transcription factors that are traceable to this duplication event and other paralogues. Similar analysis is also applied to E. coli and C. elegans networks. We compare paralogous gene pairs according to the presence and size of bi-fan arrays, classically associated in the literature with gene duplication, within other network motifs. We further extend this framework beyond transcription factor comparison to obtain topology-based similarity metrics based on the overlap of interaction neighborhoods applicable to most genes in a given organism. We observe that our network divergence metrics show considerably larger similarity between paralogues, especially those traceable to WGD. This is the case for both yeast and C. elegans, but not for E. coli regulatory network. While there is no obvious cross-species link between metrics, different classes of paralogues show notable differences in interaction overlap, with traceable duplications tending toward higher overlap compared to genes with shared protein families. Our findings indicate that divergence in paralogous interaction networks reflects a shared genetic origin, and that our approach may be useful for investigating structural similarity in the interaction networks of paralogous genes.

Dynamical modules in metabolism, cell and developmental biology

Modularity is an essential feature of any adaptive complex system. Phenotypic traits are modules in the sense that they have a distinguishable structure or function, which can vary (quasi-)independently from its context. Since all phenotypic traits are the product of some underlying regulatory dynamics, the generative processes that constitute the genotype-phenotype map must also be functionally modular. Traditionally, modular processes have been identified as structural modules in regulatory networks. However, structure only constrains, but does not determine, the dynamics of a process. Here, we propose an alternative approach that decomposes the behaviour of a complex regulatory system into elementary activity-functions. Modular activities can occur in networks that show no structural modularity, making dynamical modularity more widely applicable than structural decomposition. Furthermore, the behaviour of a regulatory system closely mirrors its functional contribution to the outcome of a process, which makes dynamical modularity particularly suited for functional decomposition. We illustrate our approach with numerous examples from the study of metabolism, cellular processes, as well as development and pattern formation. We argue that dynamical modules provide a shared conceptual foundation for developmental and evolutionary biology, and serve as the foundation for a new account of process homology, which is presented in a separate contribution by DiFrisco and Jaeger to this focus issue.

Self-selection of evolutionary strategies: adaptive versus non-adaptive forces

The evolution of complex genetic networks is shaped over the course of many generations through multiple mechanisms. These mechanisms can be broken into two predominant categories: adaptive forces, such as natural selection, and non-adaptive forces, such as recombination, genetic drift, and random mutation. Adaptive forces are influenced by the environment, where individuals better suited for their ecological niche are more likely to reproduce. This adaptive force results in a selective pressure which creates a bias in the reproduction of individuals with beneficial traits. Non-adaptive forces, in contrast, are not influenced by the environment: Random mutations occur in offspring regardless of whether they improve the fitness of the offspring. Both adaptive and non-adaptive forces play critical roles in the development of a species over time, and both forces are intrinsically linked to one another. We hypothesize that even under a simple sexual reproduction model, selective pressure will result in changes in the mutation rate and genome size. We tested this hypothesis by evolving Boolean networks using a modified genetic algorithm. Our results demonstrate that changes in environmental signals can result in selective pressure which affects mutation rate.

Extrinsic noise of the target gene governs abundance pattern of feed-forward loop motifs

Feed-forward loop (FFL) is found to be a recurrent structure in bacterial and yeast gene transcription regulatory networks. In a generic FFL, transcription factor (TF) S regulates production of another TF X while both of these TFs regulate production of final gene-product Y. Depending upon the regulatory programs (activation or repression), FFLs are grouped into two broad classes: coherent (C) and incoherent (I), each class containing four distinct types (C1-C4 and I1-I4). These FFL types are experimentally observed to occur with varied frequencies, C1 and I1 being the abundant ones. Here we present a stochastic framework singling out the absolute value of the normalized covariance of X and Y to be the determining factor behind the abundance of FFLs while considering differential promoter activities of X and Y. Our theoretical construct employs two possible signal integration mechanisms (additive and multiplicative) to synthesize Y while steady-state population level of S remains fixed or becomes tunable reflecting two possible environmental signaling scenarios. Our model categorically points out that abundant FFLs exhibit higher amount of the designated metric which has a biophysical connotation of extrinsic noise for the target gene Y. Our predictions emanating from an overarching analytical expression utilizing biologically plausible parametric conditions are substantiated by stochastic simulation.

Likelihood-free nested sampling for parameter inference of biochemical reaction networks

The development of mechanistic models of biological systems is a central part of Systems Biology. One major challenge in developing these models is the accurate inference of model parameters. In recent years, nested sampling methods have gained increased attention in the Systems Biology community due to the fact that they are parallelizable and provide error estimates with no additional computations. One drawback that severely limits the usability of these methods, however, is that they require the likelihood function to be available, and thus cannot be applied to systems with intractable likelihoods, such as stochastic models. Here we present a likelihood-free nested sampling method for parameter inference which overcomes these drawbacks. This method gives an unbiased estimator of the Bayesian evidence as well as samples from the posterior. We derive a lower bound on the estimators variance which we use to formulate a novel termination criterion for nested sampling. The presented method enables not only the reliable inference of the posterior of parameters for stochastic systems of a size and complexity that is challenging for traditional methods, but it also provides an estimate of the obtained variance. We illustrate our approach by applying it to several realistically sized models with simulated data as well as recently published biological data. We also compare our developed method with the two most popular other likeliood-free approaches: pMCMC and ABC-SMC. The C++ code of the proposed methods, together with test data, is available at the github web page https://github.com/Mijan/LFNS_paper.

The behaviour of mathematical models of biochemical reactions is governed by model parameters encoding for various reaction rates, molecule concentrations and other biochemical quantities. As the general purpose of these models is to reproduce and predict the true biological response to different stimuli, the inference of these parameters, given experimental observations, is a crucial part of Systems Biology. While plenty of methods have been published for the inference of model parameters, most of them require the availability of the likelihood function and thus cannot be applied to models that do not allow for the computation of the likelihood. Further, most established methods do not provide an estimate of the variance of the obtained estimator. In this paper, we present a novel inference method that accurately approximates the posterior distribution of parameters and does not require the evaluation of the likelihood function. Our method is based on the nested sampling algorithm and approximates the likelihood with a particle filter. We show that the resulting posterior estimates are unbiased and provide a way to estimate not just the posterior distribution, but also an error estimate of the final estimator. We illustrate our method on several stochastic models with simulated data as well as one model of transcription with real biological data.

Circuits with broken fibration symmetries perform core logic computations in biological networks

We show that logic computational circuits in gene regulatory networks arise from a fibration symmetry breaking in the network structure. From this idea we implement a constructive procedure that reveals a hierarchy of genetic circuits, ubiquitous across species, that are surprising analogues to the emblematic circuits of solid-state electronics: starting from the transistor and progressing to ring oscillators, current-mirror circuits to toggle switches and flip-flops. These canonical variants serve fundamental operations of synchronization and clocks (in their symmetric states) and memory storage (in their broken symmetry states). These conclusions introduce a theoretically principled strategy to search for computational building blocks in biological networks, and present a systematic route to design synthetic biological circuits.

We show that the core functional logic of genetic circuits arises from a fundamental symmetry breaking of the interactions of the biological network. The idea can be put into a hierarchy of symmetric genetic circuits that reveals their logical functions. We do so through a constructive procedure that naturally reveals a series of building blocks, widely present across species. This hierarchy maps to a progression of fundamental units of electronics, starting with the transistor, progressing to ring oscillators and current-mirror circuits and then to synchronized clocks, switches and finally to memory devices such as latches and flip-flops.

Integrated multi-omics framework of the plant response to jasmonic acid

Understanding the systems-level actions of transcriptional responses to hormones provides insight into how the genome is reprogrammed in response to environmental stimuli. Here, we investigated the signalling pathway of the hormone jasmonic acid (JA), which controls a plethora of critically important processes in plants and is orchestrated by the transcription factor MYC2 and its closest relatives in Arabidopsis thaliana. We generated an integrated framework of the response to JA, which spans from the activity of master and secondary regulatory transcription factors, through gene expression outputs and alternative splicing, to protein abundance changes, protein phosphorylation and chromatin remodelling. We integrated time-series transcriptome analysis with (phospho)proteomic data to reconstruct gene regulatory network models. These enabled us to predict previously unknown points of crosstalk of JA to other signalling pathways and to identify new components of the JA regulatory mechanism, which we validated through targeted mutant analysis. These results provide a comprehensive understanding of how a plant hormone remodels cellular functions and plant behaviour, the general principles of which provide a framework for analyses of cross-regulation between other hormone and stress signalling pathways.

Integrated multi-omics framework of the plant response to jasmonic acid

Understanding the systems-level actions of transcriptional responses to hormones provides insight into how the genome is reprogrammed in response to environmental stimuli. Here, we investigated the signalling pathway of the hormone jasmonic acid (JA), which controls a plethora of critically important processes in plants and is orchestrated by the transcription factor MYC2 and its closest relatives in Arabidopsis thaliana. We generated an integrated framework of the response to JA, which spans from the activity of master and secondary regulatory transcription factors, through gene expression outputs and alternative splicing, to protein abundance changes, protein phosphorylation and chromatin remodelling. We integrated time-series transcriptome analysis with (phospho)proteomic data to reconstruct gene regulatory network models. These enabled us to predict previously unknown points of crosstalk of JA to other signalling pathways and to identify new components of the JA regulatory mechanism, which we validated through targeted mutant analysis. These results provide a comprehensive understanding of how a plant hormone remodels cellular functions and plant behaviour, the general principles of which provide a framework for analyses of cross-regulation between other hormone and stress signalling pathways.

Stem-cell-ubiquitous genes spatiotemporally coordinate division through regulation of stem-cell-specific gene networks

Stem cells are responsible for generating all of the differentiated cells, tissues, and organs in a multicellular organism and, thus, play a crucial role in cell renewal, regeneration, and organization. A number of stem cell type-specific genes have a known role in stem cell maintenance, identity, and/or division. Yet, how genes expressed across different stem cell types, referred to here as stem-cell-ubiquitous genes, contribute to stem cell regulation is less understood. Here, we find that, in the Arabidopsis root, a stem-cell-ubiquitous gene, TESMIN-LIKE CXC2 (TCX2), controls stem cell division by regulating stem cell-type specific networks. Development of a mathematical model of TCX2 expression allows us to show that TCX2 orchestrates the coordinated division of different stem cell types. Our results highlight that genes expressed across different stem cell types ensure cross-communication among cells, allowing them to divide and develop harmonically together.

Stem-cell-ubiquitous genes spatiotemporally coordinate division through regulation of stem-cell-specific gene networks

Stem cells are responsible for generating all of the differentiated cells, tissues, and organs in a multicellular organism and, thus, play a crucial role in cell renewal, regeneration, and organization. A number of stem cell type-specific genes have a known role in stem cell maintenance, identity, and/or division. Yet, how genes expressed across different stem cell types, referred to here as stem-cell-ubiquitous genes, contribute to stem cell regulation is less understood. Here, we find that, in the Arabidopsis root, a stem-cell-ubiquitous gene, TESMIN-LIKE CXC2 (TCX2), controls stem cell division by regulating stem cell-type specific networks. Development of a mathematical model of TCX2 expression allows us to show that TCX2 orchestrates the coordinated division of different stem cell types. Our results highlight that genes expressed across different stem cell types ensure cross-communication among cells, allowing them to divide and develop harmonically together.

Gene Regulatory Network Inference from Single-Cell Data Using Multivariate Information Measures

While single-cell gene expression experiments present new challenges for data processing, the cell-to-cell variability observed also reveals statistical relationships that can be used by information theory. Here, we use multivariate information theory to explore the statistical dependencies between triplets of genes in single-cell gene expression datasets. We develop PIDC, a fast, efficient algorithm that uses partial information decomposition (PID) to identify regulatory relationships between genes. We thoroughly evaluate the performance of our algorithm and demonstrate that the higher-order information captured by PIDC allows it to outperform pairwise mutual information-based algorithms when recovering true relationships present in simulated data. We also infer gene regulatory networks from three experimental single-cell datasets and illustrate how network context, choices made during analysis, and sources of variability affect network inference. PIDC tutorials and open-source software for estimating PID are available. PIDC should facilitate the identification of putative functional relationships and mechanistic hypotheses from single-cell transcriptomic data.

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PIDC infers gene regulatory networks from single-cell transcriptomic data

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Multivariate information measures and context in PIDC improve network inference

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Heterogeneity in single-cell data carries information about gene-gene interactions

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Fast, efficient, open-source software is made freely available

Modularity, criticality, and evolvability of a developmental gene regulatory network

The existence of discrete phenotypic traits suggests that the complex regulatory processes which produce them are functionally modular. These processes are usually represented by networks. Only modular networks can be partitioned into intelligible subcircuits able to evolve relatively independently. Traditionally, functional modularity is approximated by detection of modularity in network structure. However, the correlation between structure and function is loose. Many regulatory networks exhibit modular behaviour without structural modularity. Here we partition an experimentally tractable regulatory network-the gap gene system of dipteran insects-using an alternative approach. We show that this system, although not structurally modular, is composed of dynamical modules driving different aspects of whole-network behaviour. All these subcircuits share the same regulatory structure, but differ in components and sensitivity to regulatory interactions. Some subcircuits are in a state of criticality, while others are not, which explains the observed differential evolvability of the various expression features in the system.

Feed-forward regulation adaptively evolves via dynamics rather than topology when there is intrinsic noise

In transcriptional regulatory networks (TRNs), a canonical 3-node feed-forward loop (FFL) is hypothesized to evolve to filter out short spurious signals. We test this adaptive hypothesis against a novel null evolutionary model. Our mutational model captures the intrinsically high prevalence of weak affinity transcription factor binding sites. We also capture stochasticity and delays in gene expression that distort external signals and intrinsically generate noise. Functional FFLs evolve readily under selection for the hypothesized function but not in negative controls. Interestingly, a 4-node “diamond” motif also emerges as a short spurious signal filter. The diamond uses expression dynamics rather than path length to provide fast and slow pathways. When there is no idealized external spurious signal to filter out, but only internally generated noise, only the diamond and not the FFL evolves. While our results support the adaptive hypothesis, we also show that non-adaptive factors, including the intrinsic expression dynamics, matter.

Feed‐forward loops (FFLs) can filter out noise, but whether their overrepresentation in GRNs reflects adaptive evolution for this function is debated. Here, the authors develop a null model of regulatory evolution and find that FFLs evolve readily under selection for the noise filtering function.

An enriched network motif family regulates multistep cell fate transitions with restricted reversibility

Multistep cell fate transitions with stepwise changes of transcriptional profiles are common to many developmental, regenerative and pathological processes. The multiple intermediate cell lineage states can serve as differentiation checkpoints or branching points for channeling cells to more than one lineages. However, mechanisms underlying these transitions remain elusive. Here, we explored gene regulatory circuits that can generate multiple intermediate cellular states with stepwise modulations of transcription factors. With unbiased searching in the network topology space, we found a motif family containing a large set of networks can give rise to four attractors with the stepwise regulations of transcription factors, which limit the reversibility of three consecutive steps of the lineage transition. We found that there is an enrichment of these motifs in a transcriptional network controlling the early T cell development, and a mathematical model based on this network recapitulates multistep transitions in the early T cell lineage commitment. By calculating the energy landscape and minimum action paths for the T cell model, we quantified the stochastic dynamics of the critical factors in response to the differentiation signal with fluctuations. These results are in good agreement with experimental observations and they suggest the stable characteristics of the intermediate states in the T cell differentiation. These dynamical features may help to direct the cells to correct lineages during development. Our findings provide general design principles for multistep cell linage transitions and new insights into the early T cell development. The network motifs containing a large family of topologies can be useful for analyzing diverse biological systems with multistep transitions.

The functions of cells are dynamically controlled in many biological processes including development, regeneration and disease progression. Cell fate transition, or the switch of cellular functions, often involves multiple steps. The intermediate stages of the transition provide the biological systems with the opportunities to regulate the transitions in a precise manner. These transitions are controlled by key regulatory genes of which the expression shows stepwise patterns, but how the interactions of these genes can determine the multistep processes was unclear. Here, we present a comprehensive analysis on the design principles of gene circuits that govern multistep cell fate transition. We found a large network family with common structural features that can generate systems with the ability to control three consecutive steps of the transition. We found that this type of networks is enriched in a gene circuit controlling the development of T lymphocyte, a crucial type of immune cells. We performed mathematical modeling using this gene circuit and we recapitulated the stepwise and irreversible loss of stem cell properties of the developing T lymphocytes. Our findings can be useful to analyze a wide range of gene regulatory networks controlling multistep cell fate transitions.

Comparison of Combinatorial Signatures of Global Network Dynamics Generated by Two Classes of ODE Models

Modeling the dynamics of biological networks introduces many challenges, among them the lack of first principle models, the size of the networks, and difficulties with parameterization. Discrete time Boolean networks and related continuous time switching systems provide a computationally accessible way to translate the structure of the network to predictions about the dynamics. Recent work has shown that the parameterized dynamics of switching systems can be captured by a combinatorial object, called a Dynamic Signatures Generated by Regulatory Networks (DSGRN) database, that consists of a parameter graph characterizing a finite parameter space decomposition, whose nodes are assigned a Morse graph that captures global dynamics for all corresponding parameters. We show that for a given network there is a way to associate the same type of object by considering a continuous time ODE system with a continuous right-hand side, which we call an L-system. The main goal of this paper is to compare the two DSGRN databases for the same network. Since the L-systems can be thought of as perturbations (not necessarily small) of the switching systems, our results address the correspondence between global parameterized dynamics of switching systems and their perturbations. We show that, at corresponding parameters, there is an order preserving map from the Morse graph of the switching system to that of the L-system that is surjective on the set of attractors and bijective on the set of fixed-point attractors. We provide important examples showing why this correspondence cannot be strengthened.

Global optimization using Gaussian processes to estimate biological parameters from image data

Parameter estimation is a major challenge in computational modeling of biological processes. This is especially the case in image-based modeling where the inherently quantitative output of the model is measured against image data, which is typically noisy and non-quantitative. In addition, these models can have a high computational cost, limiting the number of feasible simulations, and therefore rendering most traditional parameter estimation methods unsuitable. In this paper, we present a pipeline that uses Gaussian process learning to estimate biological parameters from noisy, non-quantitative image data when the model has a high computational cost. This approach is first successfully tested on a parametric function with the goal of retrieving the original parameters. We then apply it to estimating parameters in a biological setting by fitting artificial in-situ hybridization (ISH) data of the developing murine limb bud. We expect that this method will be of use in a variety of modeling scenarios where quantitative data is missing and the use of standard parameter estimation approaches in biological modeling is prohibited by the computational cost of the model.

Assessing Escherichia coli metabolism models and simulation approaches in phenotype predictions: Validation against experimental data

Over the last years, several genome-scale metabolic models (GEMs) and kinetic models of Escherichia coli were published. Their predictive performance varies according to the evaluation metric considered, the computational simulation methods used, and the type/quality of experimental data available. However, the GEM approach is often not compared with the kinetic modeling framework. Also, the different genome-scale reconstruction versions and simulation methods of mutant phenotypes are usually not validated to predict intracellular fluxes using large experimental datasets. Here, we intended to (i) systematically evaluate the prediction performance of three E. coli GEMs (iJR904, iAF1260, and iJO1366) available in the literature according to predictive growth metrics (intracellular flux distribution); (ii) assess the reliability of a E. coli GEM in the prediction of gene knockout phenotypes when different simulation methods (parsimonious flux balance analysis, Minimization of Metabolic Adjustment, linear version of MoMA, Regulatory on/off minimization, and Minimization of Metabolites Balance) are used; and finally (iii) investigate the flux distribution predictive power of the constrained-based modeling approach (selected stoichiometric GEM) and compare it with the kinetic modeling approach (two published kinetic models) for E. coli central metabolism, in order to assess their accuracy. Results show that the phenotype predictions were not significantly sensitive to the metabolic models, although the GEM iAF1260 was more accurate in the prediction of central carbon fluxes at low dilution rates. Furthermore, we observed that the choice of the appropriate simulation method of mutant phenotypes depends on the biological question to be addressed. In terms of the two modeling approaches, none outperformed the other for all the tested scenarios. © 2018 American Institute of Chemical Engineers Biotechnol. Prog., 34:1344-1354, 2018.

Contributions of regulated transcription and mRNA decay to the dynamics of gene expression

Organisms have acquired sophisticated regulatory networks that control gene expression in response to cellular perturbations. Understanding of the mechanisms underlying the coordinated changes in gene expression in response to external and internal stimuli is a fundamental issue in biology. Recent advances in high-throughput technologies have enabled the measurement of diverse biological information, including gene expression levels, kinetics of gene expression, and interactions among gene expression regulatory molecules. By coupling these technologies with quantitative modeling, we can now uncover the biological roles and mechanisms of gene regulation at the system level. This review consists of two parts. First, we focus on the methods using uridine analogs that measure synthesis and decay rates of RNAs, which demonstrate how cells dynamically change the regulation of gene expression in response to both internal and external cues. Second, we discuss the underlying mechanisms of these changes in kinetics, including the functions of transcription factors and RNA-binding proteins. Overall, this review will help to clarify a system-level view of gene expression programs in cells. This article is categorized under: Regulatory RNAs/RNAi/Riboswitches > Regulatory RNAs RNA Turnover and Surveillance > Regulation of RNA Stability RNA Methods > RNA Analyses in vitro and In Silico.

Detection of network motifs using three-way ANOVA

Motivation

Gene regulatory networks (GRN) can be determined via various experimental techniques, and also by computational methods, which infer networks from gene expression data. However, these techniques treat interactions separately such that interdependencies of interactions forming meaningful subnetworks are typically not considered.

Methods

For the investigation of network properties and for the classification of different (sub-)networks based on gene expression data, we consider biological network motifs consisting of three genes and up to three interactions, e.g. the cascade chain (CSC), feed-forward loop (FFL), and dense-overlapping regulon (DOR). We examine several conventional methods for the inference of network motifs, which typically consider each interaction individually. In addition, we propose a new method based on three-way ANOVA (ANalysis Of VAriance) (3WA) that analyzes entire subnetworks at once. To demonstrate the advantages of such a more holistic perspective, we compare the ability of 3WA and other methods to detect and categorize network motifs on large real and artificial datasets.

Results

We find that conventional methods perform much better on artificial data (AUC up to 80%), than on real E. coli expression datasets (AUC 50% corresponding to random guessing). To explain this observation, we examine several important properties that differ between datasets and analyze predicted motifs in detail. We find that in case of real networks our new 3WA method outperforms (AUC 70% in E. coli) previous methods by exploiting the interdependencies in the full motif structure. Because of important differences between current artificial datasets and real measurements, the construction and testing of motif detection methods should focus on real data.

Identifying robust hysteresis in networks

We present a new modeling and computational tool that computes rigorous summaries of network dynamics over large sets of parameter values. These summaries, organized in a database, can be searched for observed dynamics, e.g., bistability and hysteresis, to discover parameter regimes over which they are supported. We illustrate our approach on several networks underlying the restriction point of the cell cycle in humans and yeast. We rank networks by how robustly they support hysteresis, which is the observed phenotype. We find that the best 6-node human network and the yeast network share similar topology and robustness of hysteresis, in spite of having no homology between the corresponding nodes of the network. Our approach provides a new tool linking network structure and dynamics.

To summarize our understanding of how genes, their products and other cellular actors interact with each other, we often employ networks to describe their interactions. However, networks do not fully specify how the underlying biological system behaves in different conditions, nor how such response evolves in time. We present a new modeling and computational approach that allows us to compute and collect summaries of network dynamics for large sets of parameter values. We can then search these summaries for all observed behavior. We illustrate our approach on networks that govern entry to the cell cycle in humans and yeast. We rank networks based on how robustly they exhibit the experimentally observed behavior of hysteresis. We find similarities in network structure of the best ranked networks in yeast and humans, which are not explained by a common ancestry. Our approach provides a tool linking network structure and the behavior of the underlying system.

Combining a Toggle Switch and a Repressilator within the AC-DC Circuit Generates Distinct Dynamical Behaviors

Although the structure of a genetically encoded regulatory circuit is an important determinant of its function, the relationship between circuit topology and the dynamical behaviors it can exhibit is not well understood. Here, we explore the range of behaviors available to the AC-DC circuit. This circuit consists of three genes connected as a combination of a toggle switch and a repressilator. Using dynamical systems theory, we show that the AC-DC circuit exhibits both oscillations and bistability within the same region of parameter space; this generates emergent behaviors not available to either the toggle switch or the repressilator alone. The AC-DC circuit can switch on oscillations via two distinct mechanisms, one of which induces coherence into ensembles of oscillators. In addition, we show that in the presence of noise, the AC-DC circuit can behave as an excitable system capable of spatial signal propagation or coherence resonance. Together, these results demonstrate how combinations of simple motifs can exhibit multiple complex behaviors.

Organization of feed-forward loop motifs reveals architectural principles in natural and engineered networks

Network motifs are significantly overrepresented subgraphs that have been proposed as building blocks for natural and engineered networks. Detailed functional analysis has been performed for many types of motif in isolation, but less is known about how motifs work together to perform complex tasks. To address this issue, we measure the aggregation of network motifs via methods that extract precisely how these structures are connected. Applying this approach to a broad spectrum of networked systems and focusing on the widespread feed-forward loop motif, we uncover striking differences in motif organization. The types of connection are often highly constrained, differ between domains, and clearly capture architectural principles. We show how this information can be used to effectively predict functionally important nodes in the metabolic network of Escherichia coli. Our findings have implications for understanding how networked systems are constructed from motif parts and elucidate constraints that guide their evolution.

Decoding Signal Processing at the Single-Cell Level

The feedforward circuitry regulating ERK-dependent early response genes acts as a signal integrator rather than a signal persistence detector.

Linear Integration of ERK Activity Predominates over Persistence Detection in Fra-1 Regulation

ERK signaling regulates the expression of target genes, but it is unclear how ERK activity dynamics are interpreted. Here, we investigate this question using simultaneous, live, single-cell imaging of two ERK activity reporters and expression of Fra-1, a target gene controlling epithelial cell identity. We find that Fra-1 is expressed in proportion to the amplitude and duration of ERK activity. In contrast to previous "persistence detector" and "selective filter" models in which Fra-1 expression only occurs when ERK activity persists beyond a threshold duration, our observations demonstrate that the network regulating Fra-1 expression integrates total ERK activity and responds to it linearly. However, exploration of a generalized mathematical model of the Fra-1 coherent feedforward loop demonstrates that it can perform either linear integration or persistence detection, depending on the basal mRNA production rate and protein production delays. Our data indicate that significant basal expression and short delays cause Fra-1 to respond linearly to integrated ERK activity.

'Molecular habituation' as a potential mechanism of gradual homeostatic loss with age

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Constitutive signals indicate homeostatic dysregulation but their effect on signal transduction remains largely unexplored.

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A theoretical approach is undertaken to examine how oxidative stress may affect redox signal transduction.

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Constitutive signals can result in a ‘molecular habituation’ effect that interferes with information transmission.

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The robustness of such a theoretical observation to the underlying methodology hints at the generality of this principle.

The ability of reactive oxygen species (ROS) to cause molecular damage has meant that chronic oxidative stress has been mostly studied from the point of view of being a source of toxicity to the cell. However, the known duality of ROS molecules as both damaging agents and cellular redox signals implies another perspective in the study of sustained oxidative stress. This is a perspective of studying oxidative stress as a constitutive signal within the cell. In this work, we adopt a theoretical perspective as an exploratory and explanatory approach to examine how chronic oxidative stress can interfere with signal processing by redox signalling pathways in the cell. We report that constitutive signals can give rise to a ‘molecular habituation’ effect that can prime for a gradual loss of biological function. This is because a constitutive signal in the environment has the potential to reduce the responsiveness of a signalling pathway through the prolonged activation of negative regulators. Additionally, we demonstrate how this phenomenon is likely to occur in different signalling pathways exposed to persistent signals and furthermore at different levels of biological organisation.

Form and function in gene regulatory networks: the structure of network motifs determines fundamental properties of their dynamical state space

Network motifs have been studied extensively over the past decade, and certain motifs, such as the feed-forward loop, play an important role in regulatory networks. Recent studies have used Boolean network motifs to explore the link between form and function in gene regulatory networks and have found that the structure of a motif does not strongly determine its function, if this is defined in terms of the gene expression patterns the motif can produce. Here, we offer a different, higher-level definition of the ‘function’ of a motif, in terms of two fundamental properties of its dynamical state space as a Boolean network. One is the basin entropy, which is a complexity measure of the dynamics of Boolean networks. The other is the diversity of cyclic attractor lengths that a given motif can produce. Using these two measures, we examine all 104 topologically distinct three-node motifs and show that the structural properties of a motif, such as the presence of feedback loops and feed-forward loops, predict fundamental characteristics of its dynamical state space, which in turn determine aspects of its functional versatility. We also show that these higher-level properties have a direct bearing on real regulatory networks, as both basin entropy and cycle length diversity show a close correspondence with the prevalence, in neural and genetic regulatory networks, of the 13 connected motifs without self-interactions that have been studied extensively in the literature.

A spectrum of modularity in multi-functional gene circuits

A major challenge in systems biology is to understand the relationship between a circuit's structure and its function, but how is this relationship affected if the circuit must perform multiple distinct functions within the same organism? In particular, to what extent do multi‐functional circuits contain modules which reflect the different functions? Here, we computationally survey a range of bi‐functional circuits which show no simple structural modularity: They can switch between two qualitatively distinct functions, while both functions depend on all genes of the circuit. Our analysis reveals two distinct classes: hybrid circuits which overlay two simpler mono‐functional sub‐circuits within their circuitry, and emergent circuits, which do not. In this second class, the bi‐functionality emerges from more complex designs which are not fully decomposable into distinct modules and are consequently less intuitive to predict or understand. These non‐intuitive emergent circuits are just as robust as their hybrid counterparts, and we therefore suggest that the common bias toward studying modular systems may hinder our understanding of real biological circuits.

The combination of the functionalities of feedback circuits is determinant for the attractors' number and size in pathway-like Boolean networks

Molecular regulation was initially assumed to follow both a unidirectional and a hierarchical organization forming pathways. Regulatory processes, however, form highly interlinked networks with non-hierarchical and non-unidirectional structures that contain statistically overrepresented circuits or motifs. Here, we analyze the behavior of pathways containing non-unidirectional (i.e. bidirectional) and non-hierarchical interactions that create motifs. In comparison with unidirectional and hierarchical pathways, our pathways have a high diversity of behaviors, characterized by the size and number of attractors. Motifs have been studied individually showing that feedback circuit motifs regulate the number and size of attractors. It is less clear what happens in molecular networks that usually contain multiple feedbacks. Here, we find that the way feedback circuits couple to each other (i.e., the combination of the functionalities of feedback circuits) regulate both the number and size of the attractors. We show that the different expected results of epistasis analysis (a method to infer regulatory interactions) are produced by many non-hierarchical and non-unidirectional structures. Thus, these structures cannot be correctly inferred by epistasis analysis. Finally, we show that the combinations of functionalities, combined with other network properties, allow for a better characterization of regulatory structures.

Functional architecture and global properties of the Corynebacterium glutamicum regulatory network: Novel insights from a dataset with a high genomic coverage

Corynebacterium glutamicum is a Gram-positive, anaerobic, rod-shaped soil bacterium able to grow on a diversity of carbon sources like sugars and organic acids. It is a biotechnological relevant organism because of its highly efficient ability to biosynthesize amino acids, such as l-glutamic acid and l-lysine. Here, we reconstructed the most complete C. glutamicum regulatory network to date and comprehensively analyzed its global organizational properties, systems-level features and functional architecture. Our analyses show the tremendous power of Abasy Atlas to study the functional organization of regulatory networks. We created two models of the C. glutamicum regulatory network: all-evidences (containing both weak and strong supported interactions, genomic coverage=73%) and strongly-supported (only accounting for strongly supported evidences, genomic coverage=71%). Using state-of-the-art methodologies, we prove that power-law behaviors truly govern the connectivity and clustering coefficient distributions. We found a non-previously reported circuit motif that we named complex feed-forward motif. We highlighted the importance of feedback loops for the functional architecture, beyond whether they are statistically over-represented or not in the network. We show that the previously reported top-down approach is inadequate to infer the hierarchy governing a regulatory network because feedback bridges different hierarchical layers, and the top-down approach disregards the presence of intermodular genes shaping the integration layer. Our findings all together further support a diamond-shaped, three-layered hierarchy exhibiting some feedback between processing and coordination layers, which is shaped by four classes of systems-level elements: global regulators, locally autonomous modules, basal machinery and intermodular genes.

Estimation of delays in generalized asynchronous Boolean networks

A new generalized asynchronous Boolean network (GABN) model has been proposed in this paper. This continuous-time discrete-state model captures the biological reality of cellular dynamics without compromising the computational efficiency of the Boolean framework. The GABN synthesis procedure is based on the prior knowledge of the logical structure of the regulatory network, and the experimental transcriptional parameters. The novelty of the proposed methodology lies in considering different delays associated with the activation and deactivation of a particular protein (especially the transcription factors). A few illustrative examples of some well-studied network motifs have been provided to explore the scope of using the GABN model for larger networks. The GABN model of the p53-signaling pathway in response to γ-irradiation has also been simulated in the current paper to provide an indirect validation of the proposed schema.

Linear models of activation cascades: analytical solutions and coarse-graining of delayed signal transduction

Cellular signal transduction usually involves activation cascades, the sequential activation of a series of proteins following the reception of an input signal. Here, we study the classic model of weakly activated cascades and obtain analytical solutions for a variety of inputs. We show that in the special but important case of optimal gain cascades (i.e. when the deactivation rates are identical) the downstream output of the cascade can be represented exactly as a lumped nonlinear module containing an incomplete gamma function with real parameters that depend on the rates and length of the cascade, as well as parameters of the input signal. The expressions obtained can be applied to the non-identical case when the deactivation rates are random to capture the variability in the cascade outputs. We also show that cascades can be rearranged so that blocks with similar rates can be lumped and represented through our nonlinear modules. Our results can be used both to represent cascades in computational models of differential equations and to fit data efficiently, by reducing the number of equations and parameters involved. In particular, the length of the cascade appears as a real-valued parameter and can thus be fitted in the same manner as Hill coefficients. Finally, we show how the obtained nonlinear modules can be used instead of delay differential equations to model delays in signal transduction.

Temporal phases of long-term potentiation (LTP): myth or fact?

Long-term potentiation (LTP) remains the most widely accepted model for learning and memory. In accordance with this belief, the temporal differentiation of LTP into early and late phases is accepted as reflecting the differentiation of short-term and long-term memory. Moreover, during the past 30 years, protein synthesis inhibitors have been used to separate the early, protein synthesis-independent (E-LTP) phase and the late, protein synthesis-dependent (L-LTP) phase. However, the role of these proteins has not been formally identified. Additionally, several reports failed to show an effect of protein synthesis inhibitors on LTP. In this review, a detailed analysis of extensive behavioral and electrophysiological data reveals that the presumed correspondence of LTP temporal phases to memory phases is neither experimentally nor theoretically consistent. Moreover, an overview of the time courses of E-LTP in hippocampal slices reveals a wide variability ranging from <1 h to more than 5 h. The existence of all these conflictual findings should lead to a new vision of LTP. We believe that the E-LTP vs. L-LTP distinction, established with protein synthesis inhibitor studies, reflects a false dichotomy. We suggest that the duration of LTP and its dependency on protein synthesis are related to the availability of a set of proteins at synapses and not to the de novo synthesis of plasticity-related proteins. This availability is determined by protein turnover kinetics, which is regulated by previous and ongoing electrical activities and by energy store availability.

A Statistical Approach Reveals Designs for the Most Robust Stochastic Gene Oscillators

The engineering of transcriptional networks presents many challenges due to the inherent uncertainty in the system structure, changing cellular context, and stochasticity in the governing dynamics. One approach to address these problems is to design and build systems that can function across a range of conditions; that is they are robust to uncertainty in their constituent components. Here we examine the parametric robustness landscape of transcriptional oscillators, which underlie many important processes such as circadian rhythms and the cell cycle, plus also serve as a model for the engineering of complex and emergent phenomena. The central questions that we address are: Can we build genetic oscillators that are more robust than those already constructed? Can we make genetic oscillators arbitrarily robust? These questions are technically challenging due to the large model and parameter spaces that must be efficiently explored. Here we use a measure of robustness that coincides with the Bayesian model evidence, combined with an efficient Monte Carlo method to traverse model space and concentrate on regions of high robustness, which enables the accurate evaluation of the relative robustness of gene network models governed by stochastic dynamics. We report the most robust two and three gene oscillator systems, plus examine how the number of interactions, the presence of autoregulation, and degradation of mRNA and protein affects the frequency, amplitude, and robustness of transcriptional oscillators. We also find that there is a limit to parametric robustness, beyond which there is nothing to be gained by adding additional feedback. Importantly, we provide predictions on new oscillator systems that can be constructed to verify the theory and advance design and modeling approaches to systems and synthetic biology.

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.

Making sense of transcription networks

When transcription regulatory networks are compared among distantly related eukaryotes, a number of striking similarities are observed: a larger-than-expected number of genes, extensive overlapping connections, and an apparently high degree of functional redundancy. It is often assumed that the complexity of these networks represents optimized solutions, precisely sculpted by natural selection; their common features are often asserted to be adaptive. Here, we discuss support for an alternative hypothesis: the common structural features of transcription networks arise from evolutionary trajectories of "least resistance"--that is, the relative ease with which certain types of network structures are formed during their evolution.

Control of complex networks requires both structure and dynamics

The study of network structure has uncovered signatures of the organization of complex systems. However, there is also a need to understand how to control them; for example, identifying strategies to revert a diseased cell to a healthy state, or a mature cell to a pluripotent state. Two recent methodologies suggest that the controllability of complex systems can be predicted solely from the graph of interactions between variables, without considering their dynamics: structural controllability and minimum dominating sets. We demonstrate that such structure-only methods fail to characterize controllability when dynamics are introduced. We study Boolean network ensembles of network motifs as well as three models of biochemical regulation: the segment polarity network in Drosophila melanogaster, the cell cycle of budding yeast Saccharomyces cerevisiae, and the floral organ arrangement in Arabidopsis thaliana. We demonstrate that structure-only methods both undershoot and overshoot the number and which sets of critical variables best control the dynamics of these models, highlighting the importance of the actual system dynamics in determining control. Our analysis further shows that the logic of automata transition functions, namely how canalizing they are, plays an important role in the extent to which structure predicts dynamics.