Evolution of biological cooperation: an algorithmic approach.

This manuscript presents an algorithmic approach to cooperation in biological systems, drawing on fundamental ideas from statistical mechanics and probability theory. Fisher's geometric model of adaptation suggests that the evolution of organisms well adapted to multiple constraints comes at a significant complexity cost. By utilizing combinatorial models of fitness, we demonstrate that the probability of adapting to all constraints decreases exponentially with the number of constraints, thereby generalizing Fisher's result. Our main focus is understanding how cooperation can overcome this adaptivity barrier. Through these combinatorial models, we demonstrate that when an organism needs to adapt to a multitude of environmental variables, division of labor emerges as the only viable evolutionary strategy.

Global repression by tailless during segmentation.

The orphan nuclear receptor Tailless (Tll) exhibits conserved roles in brain formation and maintenance that are shared, for example, with vertebrate orthologous forms (Tlx). However, the early expression of tll in two gap domains in the segmentation cascade of Drosophila is unusual even for most other insects. Here we investigate tll regulation on pair-rule stripes. With ectopic misexpression of tll we detected unexpected repression of almost all pair-rule stripes of hairy (h), even-skipped (eve), runt (run), and fushi-tarazu (ftz). Examining Tll embryonic ChIP-chip data with regions mapped as Cis-Regulatory Modules (CRMs) of pair-rule stripes we verified Tll interactions to these regions. With the ChIP-chip data we also verified Tll interactions to the CRMs of gap domains and in the misexpression assay, Tll-mediated repression on Kruppel (Kr), kni (kni) and giant (gt) according to their differential sensitivity to Tll. These results with gap genes confirmed previous data from the literature and argue against indirect repression roles of Tll in the striped pattern. Moreover, the prediction of Tll binding sites in the CRMs of eve stripes and the mathematical modeling of their removal using an experimentally validated theoretical framework shows effects on eve stripes compatible with the absence of a repressor binding to the CRMs. In addition, modeling increased tll levels in the embryo results in the differential repression of eve stripes, agreeing well with the results of the misexpression assay. In genetic assays we investigated eve 5, that is strongly repressed by the ectopic domain and representative of more central stripes not previously implied to be under direct regulation of tll. While this stripe is little affected in tll-, its posterior border is expanded in gt- but detected with even greater expansion in gt-;tll-. We end up by discussing tll with key roles in combinatorial repression mechanisms to contain the expression of medial patterns of the segmentation cascade in the extremities of the embryo.

The effect of mutational robustness on the evolvability of multicellular organisms and eukaryotic cells.

Canalization involves mutational robustness, the lack of phenotypic change as a result of genetic mutations. Given the large divergence in phenotype across species, understanding the relationship between high robustness and evolvability has been of interest to both theorists and experimentalists. Although canalization was originally proposed in the context of multicellular organisms, the effect of multicellularity and other classes of hierarchical organization on evolvability has not been considered by theoreticians. We address this issue using a Boolean population model with explicit representation of an environment in which individuals with explicit genotype and a hierarchical phenotype representing multicellularity evolve. Robustness is described by a single real number between zero and one which emerges from the genotype-phenotype map. We find that high robustness is favoured in constant environments, and lower robustness is favoured after environmental change. Multicellularity and hierarchical organization severely constrain robustness: peak evolvability occurs at an absolute level of robustness of about 0.99 compared with values of about 0.5 in a classical neutral network model. These constraints result in a sharp peak of evolvability in which the maximum is set by the fact that the fixation of adaptive mutations becomes more improbable as robustness decreases. When robustness is put under genetic control, robustness levels leading to maximum evolvability are selected for, but maximal relative fitness appears to require recombination.

Fully interpretable deep learning model of transcriptional control.

MOTIVATION: The universal expressibility assumption of Deep Neural Networks (DNNs) is the key motivation behind recent worksin the systems biology community to employDNNs to solve important problems in functional genomics and moleculargenetics. Typically, such investigations have taken a 'black box' approach in which the internal structure of themodel used is set purely by machine learning considerations with little consideration of representing the internalstructure of the biological system by the mathematical structure of the DNN. DNNs have not yet been applied to thedetailed modeling of transcriptional control in which mRNA production is controlled by the binding of specific transcriptionfactors to DNA, in part because such models are in part formulated in terms of specific chemical equationsthat appear different in form from those used in neural networks. RESULTS: In this paper, we give an example of a DNN whichcan model the detailed control of transcription in a precise and predictive manner. Its internal structure is fully interpretableand is faithful to underlying chemistry of transcription factor binding to DNA. We derive our DNN from asystems biology model that was not previously recognized as having a DNN structure. Although we apply our DNNto data from the early embryo of the fruit fly Drosophila, this system serves as a test bed for analysis of much larger datasets obtained by systems biology studies on a genomic scale. . AVAILABILITY AND IMPLEMENTATION: The implementation and data for the models used in this paper are in a zip file in the supplementary material. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

An in silico analysis of robust but fragile gene regulation links enhancer length to robustness.

Organisms must ensure that expression of genes is directed to the appropriate tissues at the correct times, while simultaneously ensuring that these gene regulatory systems are robust to perturbation. This idea is captured by a mathematical concept called r-robustness, which says that a system is robust to a perturbation in up to r - 1 randomly chosen parameters. r-robustness implies that the biological system has a small number of sensitive parameters and that this number can be used as a robustness measure. In this work we use this idea to investigate the robustness of gene regulation using a sequence level model of the Drosophila melanogaster gene even-skipped. We consider robustness with respect to mutations of the enhancer sequence and with respect to changes of the transcription factor concentrations. We find that gene regulation is r-robust with respect to mutations in the enhancer sequence and identify a number of sensitive nucleotides. In both natural and in silico predicted enhancers, the number of nucleotides that are sensitive to mutation correlates negatively with the length of the sequence, meaning that longer sequences are more robust. The exact degree of robustness obtained is dependent not only on DNA sequence, but also on the local concentration of regulatory factors. We find that gene regulation can be remarkably sensitive to changes in transcription factor concentrations at the boundaries of expression features, while it is robust to perturbation elsewhere.

Adaptation, fitness landscape learning and fast evolution.

We consider evolution of a large population, where fitness of each organism is defined by many phenotypical traits. These traits result from expression of many genes. Under some assumptions on  fitness we prove that such model organisms  are capable, to some extent, to recognize the fitness landscape. That fitness landscape learning sharply reduces the number of mutations needed for adaptation. Moreover, this learning increases phenotype robustness with respect to mutations, i.e., canalizes the phenotype.  We show that learning and canalization work only when evolution is gradual. Organisms can be adapted to  many constraints associated with a hard environment, if that environment becomes harder step by step. Our results explain why evolution can involve genetic changes of a relatively large effect and why the total number of changes are surprisingly small.

Physical implications of so(2, 1) symmetry in exact solutions for a self-repressing gene.

We chemically characterize the symmetries underlying the exact solutions of a stochastic negatively self-regulating gene. The breaking of symmetry at a low molecular number causes three effects. Two branches of the solution exist, having high and low switching rates, such that the low switching rate branch approaches deterministic behavior and the high switching rate branch exhibits sub-Fano behavior. The average protein number differs from the deterministically expected value. Bimodal probability distributions appear as the protein number becomes a readout of the ON/OFF state of the gene.

Correction: A sequence level model of an intact locus predicts the location and function of nonadditive enhancers.

[This corrects the article DOI: 10.1371/journal.pone.0180861.].

Synthetic enhancer design by in silico compensatory evolution reveals flexibility and constraint in cis-regulation.

BACKGROUND: Models that incorporate specific chemical mechanisms have been successful in describing the activity of Drosophila developmental enhancers as a function of underlying transcription factor binding motifs. Despite this, the minimum set of mechanisms required to reconstruct an enhancer from its constituent parts is not known. Synthetic biology offers the potential to test the sufficiency of known mechanisms to describe the activity of enhancers, as well as to uncover constraints on the number, order, and spacing of motifs. RESULTS: Using a functional model and in silico compensatory evolution, we generated putative synthetic even-skipped stripe 2 enhancers with varying degrees of similarity to the natural enhancer. These elements represent the evolutionary trajectories of the natural stripe 2 enhancer towards two synthetic enhancers designed ab initio. In the first trajectory, spatially regulated expression was maintained, even after more than a third of binding sites were lost. In the second, sequences with high similarity to the natural element did not drive expression, but a highly diverged sequence about half the length of the minimal stripe 2 enhancer drove ten times greater expression. Additionally, homotypic clusters of Zelda or Stat92E motifs, but not Bicoid, drove expression in developing embryos. CONCLUSIONS: Here, we present a functional model of gene regulation to test the degree to which the known transcription factors and their interactions explain the activity of the Drosophila even-skipped stripe 2 enhancer. Initial success in the first trajectory showed that the gene regulation model explains much of the function of the stripe 2 enhancer. Cases where expression deviated from prediction indicates that undescribed factors likely act to modulate expression. We also showed that activation driven Bicoid and Hunchback is highly sensitive to spatial organization of binding motifs. In contrast, Zelda and Stat92E drive expression from simple homotypic clusters, suggesting that activation driven by these factors is less constrained. Collectively, the 40 sequences generated in this work provides a powerful training set for building future models of gene regulation.

A sequence level model of an intact locus predicts the location and function of nonadditive enhancers.

Metazoan gene expression is controlled through the action of long stretches of noncoding DNA that contain enhancers-shorter sequences responsible for controlling a single aspect of a gene's expression pattern. Models built on thermodynamics have shown how enhancers interpret protein concentration in order to determine specific levels of gene expression, but the emergent regulatory logic of a complete regulatory locus shows qualitative and quantitative differences from isolated enhancers. Such differences may arise from steric competition limiting the quantity of DNA that can simultaneously influence the transcription machinery. We incorporated this competition into a mechanistic model of gene regulation, generated efficient algorithms for this computation, and applied it to the regulation of Drosophila even-skipped (eve). This model finds the location of enhancers and identifies which factors control the boundaries of eve expression. This model predicts a new enhancer that, when assayed in vivo, drives expression in a non-eve pattern. Incorporation of chromatin accessibility eliminates this inconsistency.

DNA Occupancy of Polymerizing Transcription Factors: A Chemical Model of the ETS Family Factor Yan.

Transcription factors use both protein-DNA and protein-protein interactions to assemble appropriate complexes to regulate gene expression. Although most transcription factors operate as monomers or dimers, a few, including the E26 transformation-specific family repressors Drosophila melanogaster Yan and its human homolog TEL/ETV6, can polymerize. Although polymerization is required for both the normal and oncogenic function of Yan and TEL/ETV6, the mechanisms by which it influences the recruitment, organization, and stability of transcriptional complexes remain poorly understood. Further, a quantitative description of the DNA occupancy of a polymerizing transcription factor is lacking, and such a description would have broader applications to the conceptually related area of polymerizing chromatin regulators. To expand the theoretical basis for understanding how the oligomeric state of a transcriptional regulator influences its chromatin occupancy and function, we leveraged the extensive biochemical characterization of E26 transformation-specific factors to develop a mathematical model of Yan occupancy at chemical equilibrium. We find that spreading condensation from a specific binding site can take place in a path-independent manner given reasonable values of the free energies of specific and non-specific DNA binding and protein-protein cooperativity. Our calculations show that polymerization confers upon a transcription factor the unique ability to extend occupancy across DNA regions far from specific binding sites. In contrast, dimerization promotes recruitment to clustered binding sites and maximizes discrimination between specific and non-specific sites. We speculate that the association with non-specific DNA afforded by polymerization may enable regulatory behaviors that are well-suited to transcriptional repressors but perhaps incompatible with precise activation.

Parallel Simulated Annealing Using an Adaptive Resampling Interval.

This paper presents a parallel simulated annealing algorithm that is able to achieve 90% parallel efficiency in iteration on up to 192 processors and up to 40% parallel efficiency in time when applied to a 5000-dimension Rastrigin function. Our algorithm breaks scalability barriers in the method of Chu et al. (1999) by abandoning adaptive cooling based on variance. The resulting gains in parallel efficiency are much larger than the loss of serial efficiency from lack of adaptive cooling. Our algorithm resamples the states across processors periodically. The resampling interval is tuned according to the success rate for each specific number of processors. We further present an adaptive method to determine the resampling interval based on the adoption rate. This adaptive method is able to achieve nearly identical parallel efficiency but higher success rates compared to the fixed interval one using the best interval found.

The analysis of novel distal Cebpa enhancers and silencers using a transcriptional model reveals the complex regulatory logic of hematopoietic lineage specification.

C/EBPα plays an instructive role in the macrophage-neutrophil cell-fate decision and its expression is necessary for neutrophil development. How Cebpa itself is regulated in the myeloid lineage is not known. We decoded the cis-regulatory logic of Cebpa, and two other myeloid transcription factors, Egr1 and Egr2, using a combined experimental-computational approach. With a reporter design capable of detecting both distal enhancers and silencers, we analyzed 46 putative cis-regulatory modules (CRMs) in cells representing myeloid progenitors, and derived early macrophages or neutrophils. In addition to novel enhancers, this analysis revealed a surprisingly large number of silencers. We determined the regulatory roles of 15 potential transcriptional regulators by testing 32,768 alternative sequence-based transcriptional models against CRM activity data. This comprehensive analysis allowed us to infer the cis-regulatory logic for most of the CRMs. Silencer-mediated repression of Cebpa was found to be effected mainly by TFs expressed in non-myeloid lineages, highlighting a previously unappreciated contribution of long-distance silencing to hematopoietic lineage resolution. The repression of Cebpa by multiple factors expressed in alternative lineages suggests that hematopoietic genes are organized into densely interconnected repressive networks instead of hierarchies of mutually repressive pairs of pivotal TFs. More generally, our results demonstrate that de novo cis-regulatory dissection is feasible on a large scale with the aid of transcriptional modeling. Current address: Department of Biology, University of North Dakota, 10 Cornell Street, Stop 9019, Grand Forks, ND 58202-9019, USA.

Natural variation of the expression pattern of the segmentation gene even-skipped in melanogaster.

The evolution of canalized traits is a central question in evolutionary biology. Natural variation in highly conserved traits can provide clues about their evolutionary potential. Here we investigate natural variation in a conserved trait-even-skipped (eve) expression at the cellular blastoderm stage of embryonic development in Drosophila melanogaster. Expression of the pair-rule gene eve was quantitatively measured in three inbred lines derived from a natural population of D. melanogaster. One line showed marked differences in the spacing, amplitude and timing of formation of the characteristic seven-striped pattern over a 50-min period prior to the onset of gastrulation. Stripe 5 amplitude and the width of the interstripe between stripes 4 and 5 were both reduced in this line, while the interstripe distance between stripes 3 and 4 was increased. Engrailed expression in stage 10 embryos revealed a statistically significant increase in the length of parasegment 6 and a decrease in the length of parasegments 8 and 9. These changes are larger than those previously reported between D. melanogaster and D. pseudoobscura, two species that are thought to have diverged from a common ancestor over 25 million years ago. This line harbors a rare 448 bp deletion in the first intron of knirps (kni). This finding suggested that reduced Kni levels caused the deviant eve expression, and indeed we observed lower levels of Kni protein at early cycle 14A in L2 compared to the other two lines. A second of the three lines displayed an approximately 20% greater level of expression for all seven eve stripes. The three lines are each viable and fertile, and none display a segmentation defect as adults, suggesting that early-acting variation in eve expression is ameliorated by developmental buffering mechanisms acting later in development. Canalization of the segmentation pathway may reduce the fitness consequences of genetic variation, thus allowing the persistence of mutations with unexpectedly strong gene expression phenotypes.

Noise-Driven Phenotypic Heterogeneity with Finite Correlation Time in Clonal Populations.

There has been increasing awareness in the wider biological community of the role of clonal phenotypic heterogeneity in playing key roles in phenomena such as cellular bet-hedging and decision making, as in the case of the phage-λ lysis/lysogeny and B. Subtilis competence/vegetative pathways. Here, we report on the effect of stochasticity in growth rate, cellular memory/intermittency, and its relation to phenotypic heterogeneity. We first present a linear stochastic differential model with finite auto-correlation time, where a randomly fluctuating growth rate with a negative average is shown to result in exponential growth for sufficiently large fluctuations in growth rate. We then present a non-linear stochastic self-regulation model where the loss of coherent self-regulation and an increase in noise can induce a shift from bounded to unbounded growth. An important consequence of these models is that while the average change in phenotype may not differ for various parameter sets, the variance of the resulting distributions may considerably change. This demonstrates the necessity of understanding the influence of variance and heterogeneity within seemingly identical clonal populations, while providing a mechanism for varying functional consequences of such heterogeneity. Our results highlight the importance of a paradigm shift from a deterministic to a probabilistic view of clonality in understanding selection as an optimization problem on noise-driven processes, resulting in a wide range of biological implications, from robustness to environmental stress to the development of drug resistance.

Gene regulation and noise reduction by coupling of stochastic processes.

Here we characterize the low-noise regime of a stochastic model for a negative self-regulating binary gene. The model has two stochastic variables, the protein number and the state of the gene. Each state of the gene behaves as a protein source governed by a Poisson process. The coupling between the two gene states depends on protein number. This fact has a very important implication: There exist protein production regimes characterized by sub-Poissonian noise because of negative covariance between the two stochastic variables of the model. Hence the protein numbers obey a probability distribution that has a peak that is sharper than those of the two coupled Poisson processes that are combined to produce it. Biochemically, the noise reduction in protein number occurs when the switching of the genetic state is more rapid than protein synthesis or degradation. We consider the chemical reaction rates necessary for Poisson and sub-Poisson processes in prokaryotes and eucaryotes. Our results suggest that the coupling of multiple stochastic processes in a negative covariance regime might be a widespread mechanism for noise reduction.

Ancestral resurrection of the Drosophila S2E enhancer reveals accessible evolutionary paths through compensatory change.

Upstream regulatory sequences that control gene expression evolve rapidly, yet the expression patterns and functions of most genes are typically conserved. To address this paradox, we have reconstructed computationally and resurrected in vivo the cis-regulatory regions of the ancestral Drosophila eve stripe 2 element and evaluated its evolution using a mathematical model of promoter function. Our feed-forward transcriptional model predicts gene expression patterns directly from enhancer sequence. We used this functional model along with phylogenetics to generate a set of possible ancestral eve stripe 2 sequences for the common ancestors of 1) D. simulans and D. sechellia; 2) D. melanogaster, D. simulans, and D. sechellia; and 3) D. erecta and D. yakuba. These ancestral sequences were synthesized and resurrected in vivo. Using a combination of quantitative and computational analysis, we find clear support for functional compensation between the binding sites for Bicoid, Giant, and Krüppel over the course of 40-60 My of Drosophila evolution. We show that this compensation is driven by a coupling interaction between Bicoid activation and repression at the anterior and posterior border necessary for proper placement of the anterior stripe 2 border. A multiplicity of mechanisms for binding site turnover exemplified by Bicoid, Giant, and Krüppel sites, explains how rapid sequence change may occur while maintaining the function of the cis-regulatory element.

A prognostic gene signature for metastasis-free survival of triple negative breast cancer patients.

Although triple negative breast cancers (TNBC) are the most aggressive subtype of breast cancer, they currently lack targeted therapies. Because this classification still includes a heterogeneous collection of tumors, new tools to classify TNBCs are urgently required in order to improve our prognostic capability for high risk patients and predict response to therapy. We previously defined a gene expression signature, RKIP Pathway Metastasis Signature (RPMS), based upon a metastasis-suppressive signaling pathway initiated by Raf Kinase Inhibitory Protein (RKIP). We have now generated a new BACH1 Pathway Metastasis gene signature (BPMS) that utilizes targets of the metastasis regulator BACH1. Specifically, we substituted experimentally validated target genes to generate a new BACH1 metagene, developed an approach to optimize patient tumor stratification, and reduced the number of signature genes to 30. The BPMS significantly and selectively stratified metastasis-free survival in basal-like and, in particular, TNBC patients. In addition, the BPMS further stratified patients identified as having a good or poor prognosis by other signatures including the Mammaprint® and Oncotype® clinical tests. The BPMS is thus complementary to existing signatures and is a prognostic tool for high risk ER-HER2- patients. We also demonstrate the potential clinical applicability of the BPMS as a single sample predictor. Together, these results reveal the potential of this pathway-based BPMS gene signature to identify high risk TNBC patients that can respond effectively to targeted therapy, and highlight BPMS genes as novel drug targets for therapeutic development.

Preparation of Drosophila embryos for quantitative imaging of gene expression.

Quantitative measurements derived using sophisticated microscopy techniques are essential for understanding the basic principles that control the behavior of biological systems. We have developed a five-step data pipeline to extract quantitative data on segmentation gene expression from confocal images of gene expression patterns in Drosophila. This protocol describes the preparation of Drosophila embryos for imaging by confocal microscopy. Embryos are collected at the appropriate developmental stage and fixed. They are then stained with both primary antibodies and secondary antibodies conjugated with fluorophores to reveal the segmentation gene expression patterns.

Quantitative imaging of gene expression in Drosophila embryos.

Quantitative measurements derived using sophisticated microscopy techniques are essential for understanding the basic principles that control the behavior of biological systems. Here we describe a data pipeline developed to extract quantitative data on segmentation gene expression from confocal images of gene expression patterns in Drosophila. The pipeline consists of image segmentation, background removal, temporal characterization of an embryo, data registration, and data averaging. This pipeline has been successfully applied to obtain quantitative gene expression data at cellular resolution in space and at 6.5-min resolution in time. It has also enabled the construction of a spatiotemporal atlas of segmentation gene expression. We describe the software used to construct a workflow for extracting quantitative data on segmentation gene expression and the BREReA package, which implements the methods for background removal and registration of segmentation gene expression patterns.