CNETML: maximum likelihood inference of phylogeny from copy number profiles of multiple samples

Phylogenetic trees based on copy number profiles from multiple samples of a patient are helpful to understand cancer evolution. Here, we develop a new maximum likelihood method, CNETML, to infer phylogenies from such data. CNETML is the first program to jointly infer the tree topology, node ages, and mutation rates from total copy numbers of longitudinal samples. Our extensive simulations suggest CNETML performs well on copy numbers relative to ploidy and under slight violation of model assumptions. The application of CNETML to real data generates results consistent with previous discoveries and provides novel early copy number events for further investigation.

Automated design of gene circuits with optimal mushroom-bifurcation behavior

Recent advances in synthetic biology are enabling exciting technologies, including the next generation of biosensors, the rational design of cell memory, modulated synthetic cell differentiation, and generic multifunctional biocircuits. These novel applications require the design of gene circuits leading to sophisticated behaviors and functionalities. At the same time, designs need to be kept minimal to avoid compromising cell viability. Bifurcation theory addresses such challenges by associating circuit dynamical properties with molecular details of its design. Nevertheless, incorporating bifurcation analysis into automated design processes has not been accomplished yet. This work presents an optimization-based method for the automated design of synthetic gene circuits with specified bifurcation diagrams that employ minimal network topologies. Using this approach, we designed circuits exhibiting the mushroom bifurcation, distilled the most robust topologies, and explored its multifunctional behavior. We then outline potential applications in biosensors, memory devices, and synthetic cell differentiation.

Deterministic evolution and stringent selection during preneoplasia

The earliest events during human tumour initiation, although poorly characterized, may hold clues to malignancy detection and prevention1. Here we model occult preneoplasia by biallelic inactivation of TP53, a common early event in gastric cancer, in human gastric organoids. Causal relationships between this initiating genetic lesion and resulting phenotypes were established using experimental evolution in multiple clonally derived cultures over 2 years. TP53 loss elicited progressive aneuploidy, including copy number alterations and structural variants prevalent in gastric cancers, with evident preferred orders. Longitudinal single-cell sequencing of TP53-deficient gastric organoids similarly indicates progression towards malignant transcriptional programmes. Moreover, high-throughput lineage tracing with expressed cellular barcodes demonstrates reproducible dynamics whereby initially rare subclones with shared transcriptional programmes repeatedly attain clonal dominance. This powerful platform for experimental evolution exposes stringent selection, clonal interference and a marked degree of phenotypic convergence in premalignant epithelial organoids. These data imply predictability in the earliest stages of tumorigenesis and show evolutionary constraints and barriers to malignant transformation, with implications for earlier detection and interception of aggressive, genome-instable tumours.

Deep reinforcement learning for optimal experimental design in biology

The field of optimal experimental design uses mathematical techniques to determine experiments that are maximally informative from a given experimental setup. Here we apply a technique from artificial intelligence-reinforcement learning-to the optimal experimental design task of maximizing confidence in estimates of model parameter values. We show that a reinforcement learning approach performs favourably in comparison with a one-step ahead optimisation algorithm and a model predictive controller for the inference of bacterial growth parameters in a simulated chemostat. Further, we demonstrate the ability of reinforcement learning to train over a distribution of parameters, indicating that this approach is robust to parametric uncertainty.

Phenotypic plasticity and genetic control in colorectal cancer evolution

Genetic and epigenetic variation, together with transcriptional plasticity, contribute to intratumour heterogeneity1. The interplay of these biological processes and their respective contributions to tumour evolution remain unknown. Here we show that intratumour genetic ancestry only infrequently affects gene expression traits and subclonal evolution in colorectal cancer (CRC). Using spatially resolved paired whole-genome and transcriptome sequencing, we find that the majority of intratumour variation in gene expression is not strongly heritable but rather 'plastic'. Somatic expression quantitative trait loci analysis identified a number of putative genetic controls of expression by cis-acting coding and non-coding mutations, the majority of which were clonal within a tumour, alongside frequent structural alterations. Consistently, computational inference on the spatial patterning of tumour phylogenies finds that a considerable proportion of CRCs did not show evidence of subclonal selection, with only a subset of putative genetic drivers associated with subclone expansions. Spatial intermixing of clones is common, with some tumours growing exponentially and others only at the periphery. Together, our data suggest that most genetic intratumour variation in CRC has no major phenotypic consequence and that transcriptional plasticity is, instead, widespread within a tumour.

Fluctuating methylation clocks for cell lineage tracing at high temporal resolution in human tissues

Molecular clocks that record cell ancestry mutate too slowly to measure the short-timescale dynamics of cell renewal in adult tissues. Here, we show that fluctuating DNA methylation marks can be used as clocks in cells where ongoing methylation and demethylation cause repeated 'flip-flops' between methylated and unmethylated states. We identify endogenous fluctuating CpG (fCpG) sites using standard methylation arrays and develop a mathematical model to quantitatively measure human adult stem cell dynamics from these data. Small intestinal crypts were inferred to contain slightly more stem cells than the colon, with slower stem cell replacement in the small intestine. Germline APC mutation increased the number of replacements per crypt. In blood, we measured rapid expansion of acute leukemia and slower growth of chronic disease. Thus, the patterns of human somatic cell birth and death are measurable with fluctuating methylation clocks (FMCs).

Reconstructing single-cell karyotype alterations in colorectal cancer identifies punctuated and gradual diversification patterns

Central to tumor evolution is the generation of genetic diversity. However, the extent and patterns by which de novo karyotype alterations emerge and propagate within human tumors are not well understood, especially at single-cell resolution. Here, we present 3D Live-Seq-a protocol that integrates live-cell imaging of tumor organoid outgrowth and whole-genome sequencing of each imaged cell to reconstruct evolving tumor cell karyotypes across consecutive cell generations. Using patient-derived colorectal cancer organoids and fresh tumor biopsies, we demonstrate that karyotype alterations of varying complexity are prevalent and can arise within a few cell generations. Sub-chromosomal acentric fragments were prone to replication and collective missegregation across consecutive cell divisions. In contrast, gross genome-wide karyotype alterations were generated in a single erroneous cell division, providing support that aneuploid tumor genomes can evolve via punctuated evolution. Mapping the temporal dynamics and patterns of karyotype diversification in cancer enables reconstructions of evolutionary paths to malignant fitness.

Engineered acetoacetate-inducible whole-cell biosensors based on the AtoSC two-component system

Whole-cell biosensors hold potential in a variety of industrial, medical, and environmental applications. These biosensors can be constructed through the repurposing of bacterial sensing mechanisms, including the common two-component system (TCS). Here we report on the construction of a range of novel biosensors that are sensitive to acetoacetate, a molecule that plays a number of roles in human health and biology. These biosensors are based on the AtoSC TCS. An ordinary differential equation model to describe the action of the AtoSC TCS was developed and sensitivity analysis of this model used to help inform biosensor design. The final collection of biosensors constructed displayed a range of switching behaviours at physiologically relevant acetoacetate concentrations and can operate in several Escherichia coli host strains. It is envisaged that these biosensor strains will offer an alternative to currently available commercial strip tests and, in future, may be adopted for more complex in vivo or industrial monitoring applications.

Single strain control of microbial consortia

The scope of bioengineering is expanding from the creation of single strains to the design of microbial communities, allowing for division-of-labour, specialised sub-populations and interaction with “wild” microbiomes. However, in the absence of stabilising interactions, competition between microbes inevitably leads to the removal of less fit community members over time. Here, we leverage amensalism and competitive exclusion to stabilise a two-strain community by engineering a strain of Escherichia coli which secretes a toxin in response to competition. We show experimentally and mathematically that such a system can produce stable populations with a composition that is tunable by easily controllable parameters. This system creates a tunable, stable two-strain consortia while only requiring the engineering of a single strain.

Engineered microbial communities can divide labour between their members and interface with natural microbiomes. Here the authors demonstrate how a single toxin producing engineered strain can tune the composition of a two-strain community.

Automated design of synthetic microbial communities

Microbial species rarely exist in isolation. In naturally occurring microbial systems there is strong evidence for a positive relationship between species diversity and productivity of communities. The pervasiveness of these communities in nature highlights possible advantages for genetically engineered strains to exist in cocultures as well. Building synthetic microbial communities allows us to create distributed systems that mitigate issues often found in engineering a monoculture, especially as functional complexity increases. Here, we demonstrate a methodology for designing robust synthetic communities that include competition for nutrients, and use quorum sensing to control amensal bacteriocin interactions in a chemostat environment. We computationally explore all two- and three- strain systems, using Bayesian methods to perform model selection, and identify the most robust candidates for producing stable steady state communities. Our findings highlight important interaction motifs that provide stability, and identify requirements for selecting genetic parts and further tuning the community composition.

Evolutionary dynamics of neoantigens in growing tumors

Cancers accumulate mutations that lead to neoantigens, novel peptides that elicit an immune response, and consequently undergo evolutionary selection. Here we establish how negative selection shapes the clonality of neoantigens in a growing cancer by constructing a mathematical model of neoantigen evolution. The model predicts that, without immune escape, tumor neoantigens are either clonal or at low frequency; hypermutated tumors can only establish after the evolution of immune escape. Moreover, the site frequency spectrum of somatic variants under negative selection appears more neutral as the strength of negative selection increases, which is consistent with classical neutral theory. These predictions are corroborated by the analysis of neoantigen frequencies and immune escape in exome and RNA sequencing data from 879 colon, stomach and endometrial cancers.

FlopR: An Open Source Software Package for Calibration and Normalization of Plate Reader and Flow Cytometry Data

The measurement of gene expression using fluorescence markers has been a cornerstone of synthetic biology for the past two decades. However, the use of arbitrary units has limited the usefulness of these data for many quantitative purposes. Calibration of fluorescence measurements from flow cytometry and plate reader spectrophotometry has been implemented previously, but the tools are disjointed. Here we pull together, and in some cases improve, extant methods into a single software tool, written as a package in the R statistical framework. The workflow is validated using Escherichia coli engineered to express green fluorescent protein (GFP) from a set of commonly used constitutive promoters. We then demonstrate the package's power by identifying the time evolution of distinct subpopulations of bacteria from bulk plate reader data, a task previously reliant on laborious flow cytometry or colony counting experiments. Along with standardized parts and experimental methods, the development and dissemination of usable tools for quantitative measurement and data analysis will benefit the synthetic biology community by improving interoperability.

Subclonal reconstruction of tumors by using machine learning and population genetics

Most cancer genomic data are generated from bulk samples composed of mixtures of cancer subpopulations, as well as normal cells. Subclonal reconstruction methods based on machine learning aim to separate those subpopulations in a sample and infer their evolutionary history. However, current approaches are entirely data driven and agnostic to evolutionary theory. We demonstrate that systematic errors occur in the analysis if evolution is not accounted for, and this is exacerbated with multi-sampling of the same tumor. We present a novel approach for model-based tumor subclonal reconstruction, called MOBSTER, which combines machine learning with theoretical population genetics. Using public whole-genome sequencing data from 2,606 samples from different cohorts, new data and synthetic validation, we show that this method is more robust and accurate than current techniques in single-sample, multiregion and longitudinal data. This approach minimizes the confounding factors of nonevolutionary methods, thus leading to more accurate recovery of the evolutionary history of human cancers.

From Microbial Communities to Distributed Computing Systems

A distributed biological system can be defined as a system whose components are located in different subpopulations, which communicate and coordinate their actions through interpopulation messages and interactions. We see that distributed systems are pervasive in nature, performing computation across all scales, from microbial communities to a flock of birds. We often observe that information processing within communities exhibits a complexity far greater than any single organism. Synthetic biology is an area of research which aims to design and build synthetic biological machines from biological parts to perform a defined function, in a manner similar to the engineering disciplines. However, the field has reached a bottleneck in the complexity of the genetic networks that we can implement using monocultures, facing constraints from metabolic burden and genetic interference. This makes building distributed biological systems an attractive prospect for synthetic biology that would alleviate these constraints and allow us to expand the applications of our systems into areas including complex biosensing and diagnostic tools, bioprocess control and the monitoring of industrial processes. In this review we will discuss the fundamental limitations we face when engineering functionality with a monoculture, and the key areas where distributed systems can provide an advantage. We cite evidence from natural systems that support arguments in favor of distributed systems to overcome the limitations of monocultures. Following this we conduct a comprehensive overview of the synthetic communities that have been built to date, and the components that have been used. The potential computational capabilities of communities are discussed, along with some of the applications that these will be useful for. We discuss some of the challenges with building co-cultures, including the problem of competitive exclusion and maintenance of desired community composition. Finally, we assess computational frameworks currently available to aide in the design of microbial communities and identify areas where we lack the necessary tools.

Deep reinforcement learning for the control of microbial co-cultures in bioreactors

Multi-species microbial communities are widespread in natural ecosystems. When employed for biomanufacturing, engineered synthetic communities have shown increased productivity in comparison with monocultures and allow for the reduction of metabolic load by compartmentalising bioprocesses between multiple sub-populations. Despite these benefits, co-cultures are rarely used in practice because control over the constituent species of an assembled community has proven challenging. Here we demonstrate, in silico, the efficacy of an approach from artificial intelligence-reinforcement learning-for the control of co-cultures within continuous bioreactors. We confirm that feedback via a trained reinforcement learning agent can be used to maintain populations at target levels, and that model-free performance with bang-bang control can outperform a traditional proportional integral controller with continuous control, when faced with infrequent sampling. Further, we demonstrate that a satisfactory control policy can be learned in one twenty-four hour experiment by running five bioreactors in parallel. Finally, we show that reinforcement learning can directly optimise the output of a co-culture bioprocess. Overall, reinforcement learning is a promising technique for the control of microbial communities.

Measuring the distribution of fitness effects in somatic evolution by combining clonal dynamics with dN/dS ratios

The distribution of fitness effects (DFE) defines how new mutations spread through an evolving population. The ratio of non-synonymous to synonymous mutations (dN/dS) has become a popular method to detect selection in somatic cells. However the link, in somatic evolution, between dN/dS values and fitness coefficients is missing. Here we present a quantitative model of somatic evolutionary dynamics that determines the selective coefficients of individual driver mutations from dN/dS estimates. We then measure the DFE for somatic mutant clones in ostensibly normal oesophagus and skin. We reveal a broad distribution of fitness effects, with the largest fitness increases found for TP53 and NOTCH1 mutants (proliferative bias 1-5%). This study provides the theoretical link between dN/dS values and selective coefficients in somatic evolution, and measures the DFE of mutations in human tissues.

Measuring single cell divisions in human tissues from multi-region sequencing data

Both normal tissue development and cancer growth are driven by a branching process of cell division and mutation accumulation that leads to intra-tissue genetic heterogeneity. However, quantifying somatic evolution in humans remains challenging. Here, we show that multi-sample genomic data from a single time point of normal and cancer tissues contains information on single-cell divisions. We present a new theoretical framework that, applied to whole-genome sequencing data of healthy tissue and cancer, allows inferring the mutation rate and the cell survival/death rate per division. On average, we found that cells accumulate 1.14 mutations per cell division in healthy haematopoiesis and 1.37 mutations per division in brain development. In both tissues, cell survival was maximal during early development. Analysis of 131 biopsies from 16 tumours showed 4 to 100 times increased mutation rates compared to healthy development and substantial inter-patient variation of cell survival/death rates.

Detecting Changes in the Caenorhabditis elegans Intestinal Environment Using an Engineered Bacterial Biosensor

Caenorhabditis elegans has become a key model organism within biology. In particular, the transparent gut, rapid growing time, and ability to create a defined gut microbiota make it an ideal candidate organism for understanding and engineering the host microbiota. Here we present the development of an experimental model that can be used to characterize whole-cell bacterial biosensors in vivo. A dual-plasmid sensor system responding to isopropyl β-d-1-thiogalactopyranoside was developed and fully characterized in vitro. Subsequently, we show that the sensor was capable of detecting and reporting on changes in the intestinal environment of C. elegans after introducing an exogenous inducer into the environment. The protocols presented here may be used to aid the rational design of engineered bacterial circuits, primarily for diagnostic applications. In addition, the model system may serve to reduce the use of current animal models and aid in the exploration of complex questions within general nematode and host-microbe biology.

Crypt fusion as a homeostatic mechanism in the human colon

OBJECTIVE

The crypt population in the human intestine is dynamic: crypts can divide to produce two new daughter crypts through a process termed crypt fission, but whether this is balanced by a second process to remove crypts, as recently shown in mouse models, is uncertain. We examined whether crypt fusion (the process of two neighbouring crypts fusing into a single daughter crypt) occurs in the human colon.

DESIGN

We used somatic alterations in the gene cytochrome c oxidase (CCO) as lineage tracing markers to assess the clonality of bifurcating colon crypts (n=309 bifurcating crypts from 13 patients). Mathematical modelling was used to determine whether the existence of crypt fusion can explain the experimental data, and how the process of fusion influences the rate of crypt fission.

RESULTS

In 55% (21/38) of bifurcating crypts in which clonality could be assessed, we observed perfect segregation of clonal lineages to the respective crypt arms. Mathematical modelling showed that this frequency of perfect segregation could not be explained by fission alone (p<10-20). With the rates of fission and fusion taken to be approximately equal, we then used the distribution of CCO-deficient patch size to estimate the rate of crypt fission, finding a value of around 0.011 divisions/crypt/year.

CONCLUSIONS

We have provided the evidence that human colonic crypts undergo fusion, a potential homeostatic process to regulate total crypt number. The existence of crypt fusion in the human colon adds a new facet to our understanding of the highly dynamic and plastic phenotype of the colonic epithelium.

Modelling microbiome recovery after antibiotics using a stability landscape framework

Treatment with antibiotics is one of the most extreme perturbations to the human microbiome. Even standard courses of antibiotics dramatically reduce the microbiome's diversity and can cause transitions to dysbiotic states. Conceptually, this is often described as a 'stability landscape': the microbiome sits in a landscape with multiple stable equilibria, and sufficiently strong perturbations can shift the microbiome from its normal equilibrium to another state. However, this picture is only qualitative and has not been incorporated in previous mathematical models of the effects of antibiotics. Here, we outline a simple quantitative model based on the stability landscape concept and demonstrate its success on real data. Our analytical impulse-response model has minimal assumptions with three parameters. We fit this model in a Bayesian framework to data from a previous study of the year-long effects of short courses of four common antibiotics on the gut and oral microbiomes, allowing us to compare parameters between antibiotics and microbiomes, and further validate our model using data from another study looking at the impact of a combination of last-resort antibiotics on the gut microbiome. Using Bayesian model selection we find support for a long-term transition to an alternative microbiome state after courses of certain antibiotics in both the gut and oral microbiomes. Quantitative stability landscape frameworks are an exciting avenue for future microbiome modelling.

Two New Plasmid Post-segregational Killing Mechanisms for the Implementation of Synthetic Gene Networks in Escherichia coli

Plasmids are the workhorse of both industrial biotechnology and synthetic biology, but ensuring they remain in bacterial cells is a challenge. Antibiotic selection cannot be used to stabilize plasmids in most real-world applications, and inserting dynamical gene networks into the genome remains challenging. Plasmids have evolved several mechanisms for stability, one of which, post-segregational killing (PSK), ensures that plasmid-free cells do not survive. Here we demonstrate the plasmid-stabilizing capabilities of the axe/txe toxin-antitoxin system and the microcin-V bacteriocin system in the probiotic bacteria Escherichia coli Nissle 1917 and show that they can outperform the commonly used hok/sok. Using plasmid stability assays, automated flow cytometry analysis, mathematical models, and Bayesian statistics we quantified plasmid stability in vitro. Furthermore, we used an in vivo mouse cancer model to demonstrate plasmid stability in a real-world therapeutic setting. These new PSK systems, plus the developed Bayesian methodology, will have wide applicability in clinical and industrial biotechnology.

Towards an Aspect-Oriented Design and Modelling Framework for Synthetic Biology

Work on synthetic biology has largely used a component-based metaphor for system construction. While this paradigm has been successful for the construction of numerous systems, the incorporation of contextual design issues—either compositional, host or environmental—will be key to realising more complex applications. Here, we present a design framework that radically steps away from a purely parts-based paradigm by using aspect-oriented software engineering concepts. We believe that the notion of concerns is a powerful and biologically credible way of thinking about system synthesis. By adopting this approach, we can separate core concerns, which represent modular aims of the design, from cross-cutting concerns, which represent system-wide attributes. The explicit handling of cross-cutting concerns allows for contextual information to enter the design process in a modular way. As a proof-of-principle, we implemented the aspect-oriented approach in the Python tool, SynBioWeaver, which enables the combination, or weaving, of core and cross-cutting concerns. The power and flexibility of this framework is demonstrated through a number of examples covering the inclusion of part context, combining circuit designs in a context dependent manner, and the generation of rule, logic and reaction models from synthetic circuit designs.

Author Correction: Quantification of subclonal selection in cancer from bulk sequencing data

In the version of this article originally published, in the "Theoretical framework of subclonal selection" section of the main text, ref. 11 instead of ref. 19 should have been cited at the end of the phrase "Our previously presented frequentist approach to detect subclonal selection from bulk sequencing data involves an R2 test statistic." The error has been corrected in the HTML and PDF versions of the article.

Computing with biological switches and clocks

The complex dynamics of biological systems is primarily driven by molecular interactions that underpin the regulatory networks of cells. These networks typically contain positive and negative feedback loops, which are responsible for switch-like and oscillatory dynamics, respectively. Many computing systems rely on switches and clocks as computational modules. While the combination of such modules in biological systems leads to a variety of dynamical behaviours, it is also driving development of new computing algorithms. Here we present a historical perspective on computation by biological systems, with a focus on switches and clocks, and discuss parallels between biology and computing. We also outline our vision for the future of biological computing.

Quantification of subclonal selection in cancer from bulk sequencing data

Subclonal architectures are prevalent across cancer types. However, the temporal evolutionary dynamics that produce tumor subclones remain unknown. Here we measure clone dynamics in human cancers by using computational modeling of subclonal selection and theoretical population genetics applied to high-throughput sequencing data. Our method determined the detectable subclonal architecture of tumor samples and simultaneously measured the selective advantage and time of appearance of each subclone. We demonstrate the accuracy of our approach and the extent to which evolutionary dynamics are recorded in the genome. Application of our method to high-depth sequencing data from breast, gastric, blood, colon and lung cancer samples, as well as metastatic deposits, showed that detectable subclones under selection, when present, consistently emerged early during tumor growth and had a large fitness advantage (>20%). Our quantitative framework provides new insight into the evolutionary trajectories of human cancers and facilitates predictive measurements in individual tumors from widely available sequencing data.

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.

Catch my drift? Making sense of genomic intra-tumour heterogeneity

The cancer genome is shaped by three components of the evolutionary process: mutation, selection and drift. While many studies have focused on the first two components, the role of drift in cancer evolution has received little attention. Drift occurs when all individuals in the population have the same likelihood of producing surviving offspring, and so by definition a drifting population is one that is evolving neutrally. Here we focus on how neutral evolution is manifested in the cancer genome. We discuss how neutral passenger mutations provide a magnifying glass that reveals the evolutionary dynamics underpinning cancer development, and outline how statistical inference can be used to quantify these dynamics from sequencing data. We argue that only after we understand the impact of neutral drift on the genome can we begin to make full sense of clonal selection. This article is part of a Special Issue entitled: Evolutionary principles - heterogeneity in cancer? Edited by Dr. Robert A. Gatenby.

A computational method for the investigation of multistable systems and its application to genetic switches

Background

Genetic switches exhibit multistability, form the basis of epigenetic memory, and are found in natural decision making systems, such as cell fate determination in developmental pathways. Synthetic genetic switches can be used for recording the presence of different environmental signals, for changing phenotype using synthetic inputs and as building blocks for higher-level sequential logic circuits. Understanding how multistable switches can be constructed and how they function within larger biological systems is therefore key to synthetic biology.

Results

Here we present a new computational tool, called StabilityFinder, that takes advantage of sequential Monte Carlo methods to identify regions of parameter space capable of producing multistable behaviour, while handling uncertainty in biochemical rate constants and initial conditions. The algorithm works by clustering trajectories in phase space, and iteratively minimizing a distance metric. Here we examine a collection of models of genetic switches, ranging from the deterministic Gardner toggle switch to stochastic models containing different positive feedback connections. We uncover the design principles behind making bistable, tristable and quadristable switches, and find that rate of gene expression is a key parameter. We demonstrate the ability of the framework to examine more complex systems and examine the design principles of a three gene switch. Our framework allows us to relax the assumptions that are often used in genetic switch models and we show that more complex abstractions are still capable of multistable behaviour.

Conclusions

Our results suggest many ways in which genetic switches can be enhanced and offer designs for the construction of novel switches. Our analysis also highlights subtle changes in correlation of experimentally tunable parameters that can lead to bifurcations in deterministic and stochastic systems. Overall we demonstrate that StabilityFinder will be a valuable tool in the future design and construction of novel gene networks.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0375-z) contains supplementary material, which is available to authorized users.

Mechanistic Modelling and Bayesian Inference Elucidates the Variable Dynamics of Double-Strand Break Repair

DNA double-strand breaks are lesions that form during metabolism, DNA replication and exposure to mutagens. When a double-strand break occurs one of a number of repair mechanisms is recruited, all of which have differing propensities for mutational events. Despite DNA repair being of crucial importance, the relative contribution of these mechanisms and their regulatory interactions remain to be fully elucidated. Understanding these mutational processes will have a profound impact on our knowledge of genomic instability, with implications across health, disease and evolution. Here we present a new method to model the combined activation of non-homologous end joining, single strand annealing and alternative end joining, following exposure to ionising radiation. We use Bayesian statistics to integrate eight biological data sets of double-strand break repair curves under varying genetic knockouts and confirm that our model is predictive by re-simulating and comparing to additional data. Analysis of the model suggests that there are at least three disjoint modes of repair, which we assign as fast, slow and intermediate. Our results show that when multiple data sets are combined, the rate for intermediate repair is variable amongst genetic knockouts. Further analysis suggests that the ratio between slow and intermediate repair depends on the presence or absence of DNA-PKcs and Ku70, which implies that non-homologous end joining and alternative end joining are not independent. Finally, we consider the proportion of double-strand breaks within each mechanism as a time series and predict activity as a function of repair rate. We outline how our insights can be directly tested using imaging and sequencing techniques and conclude that there is evidence of variable dynamics in alternative repair pathways. Our approach is an important step towards providing a unifying theoretical framework for the dynamics of DNA repair processes.

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.

Robustness of MEK-ERK Dynamics and Origins of Cell-to-Cell Variability in MAPK Signaling

Cellular signaling processes can exhibit pronounced cell-to-cell variability in genetically identical cells. This affects how individual cells respond differentially to the same environmental stimulus. However, the origins of cell-to-cell variability in cellular signaling systems remain poorly understood. Here, we measure the dynamics of phosphorylated MEK and ERK across cell populations and quantify the levels of population heterogeneity over time using high-throughput image cytometry. We use a statistical modeling framework to show that extrinsic noise, particularly that from upstream MEK, is the dominant factor causing cell-to-cell variability in ERK phosphorylation, rather than stochasticity in the phosphorylation/dephosphorylation of ERK. We furthermore show that without extrinsic noise in the core module, variable (including noisy) signals would be faithfully reproduced downstream, but the within-module extrinsic variability distorts these signals and leads to a drastic reduction in the mutual information between incoming signal and ERK activity.

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Active MEK and ERK levels differ profoundly among genetically identical cells

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A statistical framework is developed to identify the causes of this variability

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Analysis shows that extrinsic noise upstream MEK-ERK module causes cell variability

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Within-module extrinsic variability distorts signals

Identification of neutral tumor evolution across cancer types

Despite extraordinary efforts to profile cancer genomes, interpreting the vast amount of genomic data in the light of cancer evolution remains challenging. Here we demonstrate that neutral tumor evolution results in a power-law distribution of the mutant allele frequencies reported by next-generation sequencing of tumor bulk samples. We find that the neutral power law fits with high precision 323 of 904 cancers from 14 types and from different cohorts. In malignancies identified as evolving neutrally, all clonal selection seemingly occurred before the onset of cancer growth and not in later-arising subclones, resulting in numerous passenger mutations that are responsible for intratumoral heterogeneity. Reanalyzing cancer sequencing data within the neutral framework allowed the measurement, in each patient, of both the in vivo mutation rate and the order and timing of mutations. This result provides a new way to interpret existing cancer genomic data and to discriminate between functional and non-functional intratumoral heterogeneity.

Ptch1 and Gli regulate Shh signalling dynamics via multiple mechanisms

In the vertebrate neural tube, the morphogen Sonic Hedgehog (Shh) establishes a characteristic pattern of gene expression. Here we quantify the Shh gradient in the developing mouse neural tube and show that while the amplitude of the gradient increases over time, the activity of the pathway transcriptional effectors, Gli proteins, initially increases but later decreases. Computational analysis of the pathway suggests three mechanisms that could contribute to this adaptation: transcriptional upregulation of the inhibitory receptor Ptch1, transcriptional downregulation of Gli and the differential stability of active and inactive Gli isoforms. Consistent with this, Gli2 protein expression is downregulated during neural tube patterning and adaptation continues when the pathway is stimulated downstream of Ptch1. Moreover, the Shh-induced upregulation of Gli2 transcription prevents Gli activity levels from adapting in a different cell type, NIH3T3 fibroblasts, despite the upregulation of Ptch1. Multiple mechanisms therefore contribute to the intracellular dynamics of Shh signalling, resulting in different signalling dynamics in different cell types.

A theoretical framework for the regulation of Shh morphogen-controlled gene expression

How morphogen gradients govern the pattern of gene expression in developing tissues is not well understood. Here, we describe a statistical thermodynamic model of gene regulation that combines the activity of a morphogen with the transcriptional network it controls. Using Sonic hedgehog (Shh) patterning of the ventral neural tube as an example, we show that the framework can be used together with the principled parameter selection technique of approximate Bayesian computation to obtain a dynamical model that accurately predicts tissue patterning. The analysis indicates that, for each target gene regulated by Gli, which is the transcriptional effector of Shh signalling, there is a neutral point in the gradient, either side of which altering the Gli binding affinity has opposite effects on gene expression. This explains recent counterintuitive experimental observations. The approach is broadly applicable and provides a unifying framework to explain the temporospatial pattern of morphogen-regulated gene expression.

Model selection in systems biology depends on experimental design

Experimental design attempts to maximise the information available for modelling tasks. An optimal experiment allows the inferred models or parameters to be chosen with the highest expected degree of confidence. If the true system is faithfully reproduced by one of the models, the merit of this approach is clear - we simply wish to identify it and the true parameters with the most certainty. However, in the more realistic situation where all models are incorrect or incomplete, the interpretation of model selection outcomes and the role of experimental design needs to be examined more carefully. Using a novel experimental design and model selection framework for stochastic state-space models, we perform high-throughput in-silico analyses on families of gene regulatory cascade models, to show that the selected model can depend on the experiment performed. We observe that experimental design thus makes confidence a criterion for model choice, but that this does not necessarily correlate with a model's predictive power or correctness. Finally, in the special case of linear ordinary differential equation (ODE) models, we explore how wrong a model has to be before it influences the conclusions of a model selection analysis.

Different models of the same process represent distinct hypotheses about reality. These can be decided between within the framework of model selection, where the evidence for each is given by their ability to reproduce a set of experimental data. Even if one of the models is correct, the chances of identifying it can be hindered by the quality of the data, both in terms of its signal to measurement error ratio and the intrinsic discriminatory potential of the experiment undertaken. This potential can be predicted in various ways, and maximising it is one aim of experimental design. In this work we present a computationally efficient method of experimental design for model selection. We exploit the efficiency to consider the implications of the realistic case where all models are more or less incorrect, showing that experiments can be chosen that, considered individually, lead to unequivocal support for opposed hypotheses.

A framework for parameter estimation and model selection from experimental data in systems biology using approximate Bayesian computation

As modeling becomes a more widespread practice in the life sciences and biomedical sciences, researchers need reliable tools to calibrate models against ever more complex and detailed data. Here we present an approximate Bayesian computation (ABC) framework and software environment, ABC-SysBio, which is a Python package that runs on Linux and Mac OS X systems and that enables parameter estimation and model selection in the Bayesian formalism by using sequential Monte Carlo (SMC) approaches. We outline the underlying rationale, discuss the computational and practical issues and provide detailed guidance as to how the important tasks of parameter inference and model selection can be performed in practice. Unlike other available packages, ABC-SysBio is highly suited for investigating, in particular, the challenging problem of fitting stochastic models to data. In order to demonstrate the use of ABC-SysBio, in this protocol we postulate the existence of an imaginary reaction network composed of seven interrelated biological reactions (involving a specific mRNA, the protein it encodes and a post-translationally modified version of the protein), a network that is defined by two files containing 'observed' data that we provide as supplementary information. In the first part of the PROCEDURE, ABC-SysBio is used to infer the parameters of this system, whereas in the second part we use ABC-SysBio's relevant functionality to discriminate between two different reaction network models, one of them being the 'true' one. Although computationally expensive, the additional insights gained in the Bayesian formalism more than make up for this cost, especially in complex problems.

Reduced burden of very large and rare CNVs in bipolar affective disorder

OBJECTIVES

Large, rare chromosomal copy number variants (CNVs) have been shown to increase the risk for schizophrenia and other neuropsychiatric disorders including autism, attention-deficit hyperactivity disorder, learning difficulties, and epilepsy. Their role in bipolar disorder (BD) is less clear. There are no reports of an increase in large, rare CNVs in BD in general, but some have reported an increase in early-onset cases. We previously found that the rate of such CNVs in individuals with BD was not increased, even in early-onset cases. Our aim here was to examine the rate of large rare CNVs in BD in comparison with a new large independent reference sample from the same country.

METHODS

We studied the CNVs in a case-control sample consisting of 1,650 BD cases (reported previously) and 10,259 reference individuals without a known psychiatric disorder who took part in the original Wellcome Trust Case Control Consortium (WTCCC) study. The 10,259 reference individuals were affected with six non-psychiatric disorders (coronary artery disease, types 1 and 2 diabetes, hypertension, Crohn's disease, and rheumatoid arthritis). Affymetrix 500K array genotyping data were used to call the CNVs.

RESULTS

The rate of CNVs > 100 kb was not statistically different between cases and controls. The rate of very large (defined as > 1 Mb) and rare (< 1%) CNVs was significantly lower in patients with BD compared with the reference group. CNV loci associated with schizophrenia were not enriched in BD and, in fact, cases of BD had the lowest number of such CNVs compared with any of the WTCCC cohorts; this finding held even for the early-onset BD cases.

CONCLUSIONS

Schizophrenia and BD differ with respect to CNV burden and association with specific CNVs. Our findings support the hypothesis that BD is etiologically distinct from schizophrenia with respect to large, rare CNVs and the accompanying associated neurodevelopmental abnormalities.

On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo

Approximate Bayesian computation (ABC) has gained popularity over the past few years for the analysis of complex models arising in population genetics, epidemiology and system biology. Sequential Monte Carlo (SMC) approaches have become work-horses in ABC. Here we discuss how to construct the perturbation kernels that are required in ABC SMC approaches, in order to construct a sequence of distributions that start out from a suitably defined prior and converge towards the unknown posterior. We derive optimality criteria for different kernels, which are based on the Kullback-Leibler divergence between a distribution and the distribution of the perturbed particles. We will show that for many complicated posterior distributions, locally adapted kernels tend to show the best performance. We find that the added moderate cost of adapting kernel functions is easily regained in terms of the higher acceptance rate. We demonstrate the computational efficiency gains in a range of toy examples which illustrate some of the challenges faced in real-world applications of ABC, before turning to two demanding parameter inference problems in molecular biology, which highlight the huge increases in efficiency that can be gained from choice of optimal kernels. We conclude with a general discussion of the rational choice of perturbation kernels in ABC SMC settings.

Independent estimation of the frequency of rare CNVs in the UK population confirms their role in schizophrenia

BACKGROUND

Several large, rare chromosomal copy number variants (CNVs) have recently been shown to increase risk for schizophrenia and other neuropsychiatric disorders including autism, ADHD, learning difficulties and epilepsy.

AIMS

We wanted to examine the frequencies of these schizophrenia-associated variants in a large sample of individuals with non-psychiatric illnesses to better understand the robustness and specificity of the association with schizophrenia.

METHODS

We used Affymetrix 500K microarray data from 10,259 individuals from the UK Wellcome Trust Case Control Consortium (WTCCC) who are affected with six non-psychiatric disorders (coronary artery disease, Crohn's disease, hypertension, rheumatoid arthritis, types 1 and 2 diabetes) to establish the frequencies of nine CNV loci strongly implicated in schizophrenia, and compared them with the previous findings.

RESULTS

Deletions at 1q21.1, 3q29, 15q11.2, 15q13.1 and 22q11.2 (VCFS region), and duplications at 16p11.2 were found significantly more often in schizophrenia cases, compared with the WTCCC reference set. Deletions at 17p12 and 17q12, were also more common in schizophrenia cases but not significantly so, while duplications at 16p13.1 were found at nearly the same rate as in previous schizophrenia samples. The frequencies of CNVs in the WTCCC non-psychiatric controls at three of the loci (15q11.2, 16p13.1 and 17p12) were significantly higher than those reported in previous control populations.

CONCLUSIONS

The evidence for association with schizophrenia is compelling for six rare CNV loci, while the remaining three require further replication in large studies. Risk at these loci extends to other neurodevelopmental disorders but their involvement in common non-psychiatric disorders should also be investigated.

Calibrating spatio-temporal models of leukocyte dynamics against in vivo live-imaging data using approximate Bayesian computation

In vivo studies allow us to investigate biological processes at the level of the organism. But not all aspects of in vivo systems are amenable to direct experimental measurements. In order to make the most of such data we therefore require statistical tools that allow us to obtain reliable estimates for e.g. kinetic in vivo parameters. Here we show how we can use approximate Bayesian computation approaches in order to analyse leukocyte migration in zebrafish embryos in response to injuries. We track individual leukocytes using live imaging following surgical injury to the embryos' tail-fins. The signalling gradient that leukocytes follow towards the site of the injury cannot be directly measured but we can estimate its shape and how it changes with time from the directly observed patterns of leukocyte migration. By coupling simple models of immune signalling and leukocyte migration with the unknown gradient shape into a single statistical framework we can gain detailed insights into the tissue-wide processes that are involved in the innate immune response to wound injury. In particular we find conclusive evidence for a temporally and spatially changing signalling gradient that modulates the changing activity of the leukocyte population in the embryos. We conclude with a robustness analysis which highlights the most important factors determining the leukocyte dynamics. Our approach relies only on the ability to simulate numerically the process under investigation and is therefore also applicable in other in vivo contexts and studies.

SMN1 gene duplications are associated with sporadic ALS

OBJECTIVE

To investigate the role of SMN1 and SMN2 copy number variation and point mutations in amyotrophic lateral sclerosis (ALS) pathogenesis in a large population.

METHODS

We conducted a genetic association study including 847 patients with ALS and 984 controls. We used multiplexed ligation-dependent probe amplification (MLPA) assays to determine SMN1 and SMN2 copy numbers and examined effects on disease susceptibility and disease course. Furthermore, we sequenced SMN genes to determine if SMN mutations were more prevalent in patients with ALS. A meta-analysis was performed with results from previous studies.

RESULTS

SMN1 duplications were associated with ALS susceptibility (odds ratio [OR] 2.07, 95% confidence interval [CI] 1.34-3.20, p = 0.001). A meta-analysis with previous data including 3,469 individuals showed a similar effect: OR 1.85, 95% CI 1.18-2.90, p = 0.008). SMN1 deletions and SMN2 copy number status were not associated with ALS. SMN1 or SMN2 copy number variants had no effect on survival or the age at onset of the disease. We found no enrichment of SMN point mutations in patients with ALS.

CONCLUSIONS

Our data provide firm evidence for a role of common SMN1 duplications in ALS, and raise new questions regarding the disease mechanisms involved.

Bayesian design strategies for synthetic biology

We discuss how statistical inference techniques can be applied in the context of designing novel biological systems. Bayesian techniques have found widespread application and acceptance in the systems biology community, where they are used for both parameter estimation and model selection. Here we show that the same approaches can also be used in order to engineer synthetic biological systems by inferring the structure and parameters that are most likely to give rise to the dynamics that we require a system to exhibit. Problems that are shared between applications in systems and synthetic biology include the vast potential spaces that need to be searched for suitable models and model parameters; the complex forms of likelihood functions; and the interplay between noise at the molecular level and nonlinearity in the dynamics owing to often complex feedback structures. In order to meet these challenges, we have to develop suitable inferential tools and here, in particular, we illustrate the use of approximate Bayesian computation and unscented Kalman filtering-based approaches. These partly complementary methods allow us to tackle a number of recurring problems in the design of biological systems. After a brief exposition of these two methodologies, we focus on their application to oscillatory systems.