Evolution of robustness to noise and mutation in gene expression dynamics

DRMY1 promotes robust morphogenesis in Arabidopsis by sustaining the translation of cytokinin-signaling inhibitor proteins

Robustness is the invariant development of phenotype despite environmental changes and genetic perturbations. In the Arabidopsis flower bud, four sepals robustly initiate and grow to a constant size to enclose and protect the inner floral organs. We previously characterized the mutant development-related myb-like 1 (drmy1), where 3-5 sepals initiate variably and grow to different sizes, compromising their protective function. The molecular mechanism underlying this loss of robustness was unclear. Here, we show that drmy1 has reduced TARGET OF RAPAMYCIN (TOR) activity, ribosomal content, and translation. Translation reduction decreases the protein level of ARABIDOPSIS RESPONSE REGULATOR7 (ARR7) and ARABIDOPSIS HISTIDINE PHOSPHOTRANSFER PROTEIN 6 (AHP6), two cytokinin-signaling inhibitors that are normally rapidly produced before sepal initiation. The resultant upregulation of cytokinin signaling disrupts robust auxin patterning and sepal initiation. Our work shows that the homeostasis of translation, a ubiquitous cellular process, is crucial for the robust spatiotemporal patterning of organogenesis.

DRMY1 promotes robust morphogenesis by sustaining the translation of cytokinin signaling inhibitor proteins

Robustness is the invariant development of phenotype despite environmental changes and genetic perturbations. In the Arabidopsis flower bud, four sepals robustly initiate and grow to constant size to enclose and protect the inner floral organs. We previously characterized the mutant development related myb-like1 ( drmy1 ), where 3-5 sepals initiate variably and grow to different sizes, compromising their protective function. The molecular mechanism underlying this loss of robustness was unclear. Here, we show that drmy1 has reduced TARGET OF RAPAMYCIN (TOR) activity, ribosomal content, and translation. Translation reduction decreases the protein level of ARABIDOPSIS RESPONSE REGULATOR7 (ARR7) and ARABIDOPSIS HISTIDINE PHOSPHOTRANSFER PROTEIN 6 (AHP6), two cytokinin signaling inhibitors that are normally rapidly produced before sepal initiation. The resultant upregulation of cytokinin signaling disrupts robust auxin patterning and sepal initiation. Our work shows that the homeostasis of translation, a ubiquitous cellular process, is crucial for the robust spatiotemporal patterning of organogenesis.

Developmental hourglass: Verification by numerical evolution and elucidation by dynamical-systems theory

Determining the general laws between evolution and development is a fundamental biological challenge. Developmental hourglasses have attracted increased attention as candidates for such laws, but the necessity of their emergence remains elusive. We conducted evolutionary simulations of developmental processes to confirm the emergence of the developmental hourglass and unveiled its establishment. We considered organisms consisting of cells containing identical gene networks that control morphogenesis and evolved them under selection pressure to induce more cell types. By computing the similarity between the spatial patterns of gene expression of two species that evolved from a common ancestor, a developmental hourglass was observed, that is, there was a correlation peak in the intermediate stage of development. The fraction of pleiotropic genes increased, whereas the variance in individuals decreased, consistent with previous experimental reports. Reduction of the unavoidable variance by initial or developmental noise, essential for survival, was achieved up to the hourglass bottleneck stage, followed by diversification in developmental processes, whose timing is controlled by the slow expression dynamics conserved among organisms sharing the hourglass. This study suggests why developmental hourglasses are observed within a certain phylogenetic range of species.

Developing the genotype-to-phenotype relationship in evolutionary theory: A primer of developmental features

For decades, there have been repeated calls for more integration across evolutionary and developmental biology. However, critiques in the literature and recent funding initiatives suggest this integration remains incomplete. We suggest one way forward is to consider how we elaborate the most basic concept of development, the relationship between genotype and phenotype, in traditional models of evolutionary processes. For some questions, when more complex features of development are accounted for, predictions of evolutionary processes shift. We present a primer on concepts of development to clarify confusion in the literature and fuel new questions and approaches. The basic features of development involve expanding a base model of genotype-to-phenotype to include the genome, space, and time. A layer of complexity is added by incorporating developmental systems, including signal-response systems and networks of interactions. The developmental emergence of function, which captures developmental feedbacks and phenotypic performance, offers further model elaborations that explicitly link fitness with developmental systems. Finally, developmental features such as plasticity and developmental niche construction conceptualize the link between a developing phenotype and the external environment, allowing for a fuller inclusion of ecology in evolutionary models. Incorporating aspects of developmental complexity into evolutionary models also accommodates a more pluralistic focus on the causal importance of developmental systems, individual organisms, or agents in generating evolutionary patterns. Thus, by laying out existing concepts of development, and considering how they are used across different fields, we can gain clarity in existing debates around the extended evolutionary synthesis and pursue new directions in evolutionary developmental biology. Finally, we consider how nesting developmental features in traditional models of evolution can highlight areas of evolutionary biology that need more theoretical attention.

A linear reciprocal relationship between robustness and plasticity in homeostatic biological networks

In physics of living systems, a search for relationships of a few macroscopic variables that emerge from many microscopic elements is a central issue. We evolved gene regulatory networks so that the expression of core genes (partial system) is insensitive to environmental changes. Then, we found the expression levels of the remaining genes autonomously increase to provide a plastic (sensitive) response. A feedforward structure from the non-core to core genes evolved autonomously. Negative proportionality was observed between the average changes in core and non-core genes, reflecting reciprocity between the macroscopic robustness of homeostatic genes and plasticity of regulator genes. The proportion coefficient between those genes is represented by their number ratio, as in the "lever principle", whereas the decrease in the ratio results in a transition from perfect to partial adaptation, in which only a portion of the core genes exhibits robustness against environmental changes. This reciprocity between robustness and plasticity was satisfied throughout the evolutionary course, imposing an evolutionary constraint. This result suggests a simple macroscopic law for the adaptation characteristic in evolved complex biological networks.

An Approach for Systems-Level Understanding of Prostate Cancer from High-Throughput Data Integration to Pathway Modeling and Simulation

To understand complex diseases, high-throughput data are generated at large and multiple levels. However, extracting meaningful information from large datasets for comprehensive understanding of cell phenotypes and disease pathophysiology remains a major challenge. Despite tremendous advances in understanding molecular mechanisms of cancer and its progression, current knowledge appears discrete and fragmented. In order to render this wealth of data more integrated and thus informative, we have developed a GECIP toolbox to investigate the crosstalk and the responsible genes'/proteins' connectivity of enriched pathways from gene expression data. To implement this toolbox, we used mainly gene expression datasets of prostate cancer, and the three datasets were GSE17951, GSE8218, and GSE1431. The raw samples were processed for normalization, prediction of differentially expressed genes, and the prediction of enriched pathways for the differentially expressed genes. The enriched pathways have been processed for crosstalk degree calculations for which number connections per gene, the frequency of genes in the pathways, sharing frequency, and the connectivity have been used. For network prediction, protein-protein interaction network database FunCoup2.0 was used, and cytoscape software was used for the network visualization. In our results, we found that there were enriched pathways 27, 45, and 22 for GSE17951, GSE8218, and GSE1431, respectively, and 11 pathways in common between all of them. From the crosstalk results, we observe that focal adhesion and PI3K pathways, both experimentally proven central for cellular output upon perturbation of numerous individual/distinct signaling pathways, displayed highest crosstalk degree. Moreover, we also observe that there were more critical pathways which appear to be highly significant, and these pathways are HIF1a, hippo, AMPK, and Ras. In terms of the pathways' components, GSK3B, YWHAE, HIF1A, ATP1A3, and PRKCA are shared between the aforementioned pathways and have higher connectivity with the pathways and the other pathway components. Finally, we conclude that the focal adhesion and PI3K pathways are the most critical pathways, and since for many other pathways, high-rank enrichment did not translate to high crosstalk degree, the global impact of one pathway on others appears distinct from enrichment.

Adaptive evolvability through direct selection instead of indirect, second-order selection

Can evolvability itself be the product of adaptive evolution? To answer this question is challenging, because any DNA mutation that alters only evolvability is subject to indirect, "second order" selection on the future effects of this mutation. Such indirect selection is weaker than "first-order" selection on mutations that alter fitness, in the sense that it can operate only under restrictive conditions. Here I discuss a route to adaptive evolvability that overcomes this challenge. Specifically, a recent evolution experiment showed that some mutations can enhance both fitness and evolvability through a combination of direct and indirect selection. Unrelated evidence from gene duplication and the evolution of gene regulation suggests that mutations with such dual effects may not be rare. Through such mutations, evolvability may increase at least in part because it provides an adaptive advantage. These observations suggest a research program on the adaptive evolution of evolvability, which aims to identify such mutations and to disentangle their direct fitness effects from their indirect effects on evolvability. If evolvability is itself adaptive, Darwinian evolution may have created more than life's diversity. It may also have helped create the very conditions that made the success of Darwinian evolution possible.

Heterosis of fitness and phenotypic variance in the evolution of a diploid gene regulatory network

Heterosis describes the phenomenon, whereby a hybrid population has higher fitness than an inbred population, which has previously been explained by either Mendelian dominance or overdominance under the general assumption of a simple genotype-phenotype relationship. However, recent studies have demonstrated that genes interact through a complex gene regulatory network (GRN). Furthermore, phenotypic variance is reportedly lower for heterozygotes, and the origin of such variance-related heterosis remains elusive. Therefore, a theoretical analysis linking heterosis to GRN evolution and stochastic gene expression dynamics is required. Here, we investigated heterosis related to fitness and phenotypic variance in a system with interacting genes by numerically evolving diploid GRNs. According to the results, the heterozygote population exhibited higher fitness than the homozygote population, indicating fitness-related heterosis resulting from evolution. In addition, the heterozygote population exhibited lower noise-related phenotypic variance in expression levels than the homozygous population, implying that the heterozygote population is more robust to noise. Furthermore, the distribution of the ratio of heterozygote phenotypic variance to homozygote phenotypic variance exhibited quantitative similarity with previous experimental results. By applying dominance and differential gene expression rather than only a single gene expression model, we confirmed the correlation between heterosis and differential gene expression. We explain our results by proposing that the convex high-fitness region is evolutionarily shaped in the genetic space to gain noise robustness under genetic mixing through sexual reproduction. These results provide new insights into the effects of GRNs on variance-related heterosis and differential gene expression.

Evolutionary dynamics, evolutionary forces, and robustness: A nonequilibrium statistical mechanics perspective

Evolution through natural selection is an overwhelmingly complex process, and it is not surprising that theoretical approaches are strongly simplifying it. For instance, population genetics considers mainly dynamics of gene allele frequencies. Here, we develop a complementary approach to evolutionary dynamics based on three elements—organism reproduction, variations, and selection—that are essential for any evolutionary theory. By considering such general dynamics as a stochastic thermodynamic process, we clarify the nature and action of the evolutionary forces. We show that some of the forces cannot be described solely in terms of fitness landscapes. We also find that one force contribution can make organism reproduction insensitive (robust) to variations.

Any realistic evolutionary theory has to consider 1) the dynamics of organisms that reproduce and possess heritable traits, 2) the appearance of stochastic variations in these traits, and 3) the selection of those organisms that better survive and reproduce. These elements shape the “evolutionary forces” that characterize the evolutionary dynamics. Here, we introduce a general model of reproduction–variation–selection dynamics. By treating these dynamics as a nonequilibrium thermodynamic process, we make precise the notion of the forces that characterize evolution. One of these forces, in particular, can be associated with the robustness of reproduction to variations. Some of the detailed predictions of our model can be tested by quantitative laboratory experiments, similar to those performed in the past on evolving populations of proteins or viruses.

A Framework for Investigating Rules of Life by Establishing Zones of Influence

The incredible complexity of biological processes across temporal and spatial scales hampers defining common underlying mechanisms driving the patterns of life. However, recent advances in sequencing, big data analysis, machine learning, and molecular dynamics simulation have renewed the hope and urgency of finding potential hidden rules of life. There currently exists no framework to develop such synoptic investigations. Some efforts aim to identify unifying rules of life across hierarchical levels of time, space, and biological organization, but not all phenomena occur across all the levels of these hierarchies. Instead of identifying the same parameters and rules across levels, we posit that each level of a temporal and spatial scale and each level of biological organization has unique parameters and rules that may or may not predict outcomes in neighboring levels. We define this neighborhood, or the set of levels, across which a rule functions as the zone of influence. Here, we introduce the zone of influence framework and explain using three examples: (a) randomness in biology, where we use a Poisson process to describe processes from protein dynamics to DNA mutations to gene expressions, (b) island biogeography, and (c) animal coloration. The zone of influence framework may enable researchers to identify which levels are worth investigating for a particular phenomenon and reframe the narrative of searching for a unifying rule of life to the investigation of how, when, and where various rules of life operate.

Evolution enhances mutational robustness and suppresses the emergence of a new phenotype: A new computational approach for studying evolution

The aim of this paper is two-fold. First, we propose a new computational method to investigate the particularities of evolution. Second, we apply this method to a model of gene regulatory networks (GRNs) and explore the evolution of mutational robustness and bistability. Living systems have developed their functions through evolutionary processes. To understand the particularities of this process theoretically, evolutionary simulation (ES) alone is insufficient because the outcomes of ES depend on evolutionary pathways. We need a reference system for comparison. An appropriate reference system for this purpose is an ensemble of the randomly sampled genotypes. However, generating high-fitness genotypes by simple random sampling is difficult because such genotypes are rare. In this study, we used the multicanonical Monte Carlo method developed in statistical physics to construct a reference ensemble of GRNs and compared it with the outcomes of ES. We obtained the following results. First, mutational robustness was significantly higher in ES than in the reference ensemble at the same fitness level. Second, the emergence of a new phenotype, bistability, was delayed in evolution. Third, the bistable group of GRNs contains many mutationally fragile GRNs compared with those in the non-bistable group. This suggests that the delayed emergence of bistability is a consequence of the mutation-selection mechanism.

Living systems are products of evolution, and their present forms reflect their evolutionary history. Thus, to investigate the particularity of the evolutionary process by computer simulations, an appropriate reference system is needed for comparison with the outcomes of evolutionary simulations. In this study, we considered a model of gene regulatory networks (GRNs). Our idea was to construct a reference ensemble comprising randomly generated GRNs. To produce GRNs with high fitness values, which are rare, we employed a “rare event sampling” method developed in statistical physics. In particular, we focused on the evolution of mutational robustness. Living systems do not lose viability readily, even when some genes are mutated. This trait, called mutational robustness, has developed throughout evolution, along with functionality. Using the abovementioned method, we found that mutational robustness resulting from evolution exceeded that of the reference set. Therefore, mutational robustness is enhanced by evolution. We also found that the emergence of a new phenotype was significantly delayed in evolution. Our results suggest that this delay is a consequence of the fact that mutationally robust GRNs are favored by evolution.

Dynamical systems approach to evolution-development congruence: Revisiting Haeckel's recapitulation theory

It is acknowledged that embryonic development has a tendency to proceed from common toward specific. Ernst Haeckel raised the question of why that tendency prevailed through evolution, and the question remains unsolved. Here, we revisit Haeckel's recapitulation theory, that is, the parallelism between evolution and development through numerical evolution and dynamical systems theory. By using intracellular gene expression dynamics with cell-to-cell interaction over spatially aligned cells to represent the developmental process, gene regulation networks (GRN) that govern these dynamics evolve under the selection pressure to achieve a prescribed spatial gene expression pattern. For most numerical evolutionary experiments, the evolutionary pattern changes over generations, as well as the developmental pattern changes governed by the evolved GRN exhibit remarkable similarity. Changes in both patterns consisted of several epochs where stripes are formed in a short time, whereas for other temporal regimes, the pattern hardly changes. In evolution, these quasi-stationary generations are needed to achieve relevant mutations, whereas, in development, they are due to some gene expressions that vary slowly and control the pattern change. These successive epochal changes in development and evolution are represented as common bifurcations in dynamical systems theory, regulating working network structure from feedforward subnetwork to those containing feedback loops. The congruence is the correspondence between successive acquisitions of subnetworks through evolution and changes in working subnetworks in development. Consistency of the theory with the segmentation gene-expression dynamics is discussed. Novel outlook on recapitulation and heterochrony are provided, testable experimentally by the transcriptome and network analysis.

Evolution of phenotypic fluctuation under host-parasite interactions

Robustness and plasticity are essential features that allow biological systems to cope with complex and variable environments. In a constant environment, robustness, i.e., insensitivity of phenotypes, is expected to increase, whereas plasticity, i.e., the changeability of phenotypes, tends to diminish. Under a variable environment, existence of plasticity will be relevant. The robustness and plasticity, on the other hand, are related to phenotypic variances. As phenotypic variances decrease with the increase in robustness to perturbations, they are expected to decrease through the evolution. However, in nature, phenotypic fluctuation is preserved to a certain degree. One possible cause for this is environmental variation, where one of the most important “environmental” factors will be inter-species interactions. As a first step toward investigating phenotypic fluctuation in response to an inter-species interaction, we present the study of a simple two-species system that comprises hosts and parasites. Hosts are expected to evolve to achieve a phenotype that optimizes fitness. Then, the robustness of the corresponding phenotype will be increased by reducing phenotypic fluctuations. Conversely, plasticity tends to evolve to avoid certain phenotypes that are attacked by parasites. By using a dynamic model of gene expression for the host, we investigate the evolution of the genotype-phenotype map and of phenotypic variances. If the host–parasite interaction is weak, the fittest phenotype of the host evolves to reduce phenotypic variances. In contrast, if there exists a sufficient degree of interaction, the phenotypic variances of hosts increase to escape parasite attacks. For the latter case, we found two strategies: if the noise in the stochastic gene expression is below a certain threshold, the phenotypic variance increases via genetic diversification, whereas above this threshold, it is increased mediated by noise-induced phenotypic fluctuation. We examine how the increase in the phenotypic variances caused by parasite interactions influences the growth rate of a single host, and observed a trade-off between the two. Our results help elucidate the roles played by noise and genetic mutations in the evolution of phenotypic fluctuation and robustness in response to host–parasite interactions.

Plasticity and phenotypic variability induced by internal or external perturbations are common features of biological systems. However, under evolution for given environmental conditions, phenotypic variability is not advantageous, because it leads to the deviation from the fittest state. This has been demonstrated by previous laboratory and computer experiments. As a possible origin for the remnant phenotypic variance, we investigated the role of host–parasite interactions such as those between bacteria and phages. Different parasite-types attack hosts of certain phenotypes. Through numerical simulations of the evolution of the host genotype–phenotype mapping, we found that hosts increase phenotypic variation by increasing phenotypic fluctuations if the interaction is sufficiently strong. Depending on the degree of noise in gene expression dynamics, there are two distinct strategies for increasing phenotypic variances: stochasticity in gene expression or genetic variances. The former strategy, which can work over a faster time scale, leads to a decline in fitness, whereas the latter reduces the robustness of the fitted state. Our results provide insights into how phenotypic variances are preserved and how hosts can escape being attacked by parasites whose genes mutate to adapt to changes in parasites. These two host strategies, which depend on internal and external conditions, can be verified experimentally via the transcriptome analysis of microorganisms.

Dynamics-Evolution Correspondence in Protein Structures

The genotype-phenotype mapping of proteins is a fundamental question in structural biology. In this Letter, with the analysis of a large dataset of proteins from hundreds of protein families, we quantitatively demonstrate the correlations between the noise-induced protein dynamics and mutation-induced variations of native structures, indicating the dynamics-evolution correspondence of proteins. Based on the investigations of the linear responses of native proteins, the origin of such a correspondence is elucidated. It is essential that the noise- and mutation-induced deformations of the proteins are restricted on a common low-dimensional subspace, as confirmed from the data. These results suggest an evolutionary mechanism of the proteins gaining both dynamical flexibility and evolutionary structural variability.

Towards an engineering theory of evolution

Biological technologies are fundamentally unlike any other because biology evolves. Bioengineering therefore requires novel design methodologies with evolution at their core. Knowledge about evolution is currently applied to the design of biosystems ad hoc. Unless we have an engineering theory of evolution, we will neither be able to meet evolution's potential as an engineering tool, nor understand or limit its unintended consequences for our biological designs. Here, we propose the evotype as a helpful concept for engineering the evolutionary potential of biosystems, or other self-adaptive technologies, potentially beyond the realm of biology.

Evolution of dominance in gene expression pattern associated with phenotypic robustness

Background

Mendelian inheritance is a fundamental law of genetics. When we consider two genomes in a diploid cell, a heterozygote’s phenotype is dominated by a particular homozygote according to the law of dominance. Classical Mendelian dominance is concerned with which proteins are dominant, and is usually based on simple genotype–phenotype relationship in which one gene regulates one phenotype. However, in reality, some interactions between genes can exist, resulting in deviations from Mendelian dominance. Whether and how Mendelian dominance is generalized to the phenotypes of gene expression determined by gene regulatory networks (GRNs) remains elusive.

Results

Here, by using the numerical evolution of diploid GRNs, we discuss whether the dominance of phenotype evolves beyond the classical Mendelian case of one-to-one genotype–phenotype relationship. We examine whether complex genotype–phenotype relationship can achieve Mendelian dominance at the expression level by a pair of haplotypes through the evolution of the GRN with interacting genes. This dominance is defined via a pair of haplotypes that differ from each other but have a common phenotype given by the expression of target genes. We numerically evolve the GRN model for a diploid case, in which two GRN matrices are added to give gene expression dynamics and simulate evolution with meiosis and recombination. Our results reveal that group Mendelian dominance evolves even under complex genotype–phenotype relationship. Calculating the degree of dominance shows that it increases through the evolution, correlating closely with the decrease in phenotypic fluctuations and the increase in robustness to initial noise. We also demonstrate that the dominance of gene expression patterns evolves concurrently. This evolution of group Mendelian dominance and pattern dominance is associated with phenotypic robustness against meiosis-induced genome mixing, whereas sexual recombination arising from the mixing of genomes from the parents further enhances dominance and robustness. Due to this dominance, the robustness to genetic differences increases, while optimal fitness is sustained to a significant difference between the two genomes.

Conclusion

Group Mendelian dominance and gene-expression pattern dominance are achieved associated with the increase in phenotypic robustness to noise.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12862-021-01841-6.

Single-Cell RNA-Sequencing Reveals the Breadth of Osteoblast Heterogeneity

The current paradigm of osteoblast fate is that the majority undergo apoptosis, while some further differentiate into osteocytes and others flatten and cover bone surfaces as bone lining cells. Osteoblasts have been described to exhibit heterogeneous expression of a variety of osteoblast markers at both transcriptional and protein levels. To explore further this heterogeneity and its biological significance, Venus‐positive (Venus⁺) cells expressing the fluorescent protein Venus under the control of the 2.3‐kb Col1a1 promoter were isolated from newborn mouse calvariae and subjected to single‐cell RNA sequencing. Functional annotation of the genes expressed in 272 Venus⁺ single cells indicated that Venus⁺ cells are osteoblasts that can be categorized into four clusters. Of these, three clusters (clusters 1 to 3) exhibited similarities in their expression of osteoblast markers, while one (cluster 4) was distinctly different. We identified a total of 1920 cluster‐specific genes and pseudotime ordering analyses based on established concepts and known markers showed that clusters 1 to 3 captured osteoblasts at different maturational stages. Analysis of gene co‐expression networks showed that genes involved in protein synthesis and protein trafficking between endoplasmic reticulum (ER) and Golgi are active in these clusters. However, the cells in these clusters were also defined by extensive heterogeneity of gene expression, independently of maturational stage. Cells of cluster 4 expressed Cd34 and Cxcl12 with relatively lower levels of osteoblast markers, suggesting that this cell type differs from actively bone‐forming osteoblasts and retain or reacquire progenitor properties. Based on expression and machine learning analyses of the transcriptomes of individual osteoblasts, we also identified genes that may be useful as new markers of osteoblast maturational stages. Taken together, our data show much more extensive heterogeneity of osteoblasts than previously documented, with gene profiles supporting diversity of osteoblast functional activities and developmental fates. © 2021 The Authors. JBMR Plus published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research.

Phenotypes to remember: Evolutionary developmental memory capacity and robustness

There is increased awareness of the possibility of developmental memories resulting from evolutionary learning. Genetic regulatory and neural networks can be modelled by analogous formalism raising the important question of productive analogies in principles, processes and performance. We investigate the formation and persistence of various developmental memories of past phenotypes asking how the number of remembered past phenotypes scales with network size, to what extent memories stored form by Hebbian-like rules, and how robust these developmental "devo-engrams" are against networks perturbations (graceful degradation). The analogy between neural and genetic regulatory networks is not superficial in that it allows knowledge transfer between fields that used to be developed separately from each other. Known examples of spectacular phenotypic radiations could partly be accounted for in such terms.

Toward understanding of evolutionary constraints: experimental and theoretical approaches

Although organisms have diversified remarkably through evolution, they do not exhibit unlimited variability. During evolution, the phenotypic changes do not occur at random; instead, they are directional and restricted by the constraints imposed on them. Despite the perceived importance of characterizing the unevenness of these changes, studies on evolutionary constraints have been primarily qualitative in nature. In this review, we focus on the recent studies of evolutionary constraints, which are based on the quantification of high-dimensional phenotypic and genotypic data. Furthermore, we present a theoretical analysis that enables us to predict evolutionary constraints on the basis of phenotypic fluctuation, modeled on the fluctuation-response relationship in statistical physics. The review lays emphasis on the tight interactions between experimental and theoretical analyses in evolutionary biology that will contribute to a better understanding of evolutionary constraints.

Emergence of cooperative bistability and robustness of gene regulatory networks

Gene regulatory networks (GRNs) are complex systems in which many genes regulate mutually to adapt the cell state to environmental conditions. In addition to function, the GRNs possess several kinds of robustness. This robustness means that systems do not lose their functionality when exposed to disturbances such as mutations or noise, and is widely observed at many levels in living systems. Both function and robustness have been acquired through evolution. In this respect, GRNs utilized in living systems are rare among all possible GRNs. In this study, we explored the fitness landscape of GRNs and investigated how robustness emerged in highly-fit GRNs. We considered a toy model of GRNs with one input gene and one output gene. The difference in the expression level of the output gene between two input states, "on" and "off", was considered as fitness. Thus, the determination of the fitness of a GRN was based on how sensitively it responded to the input. We employed the multicanonical Monte Carlo method, which can sample GRNs randomly in a wide range of fitness levels, and classified the GRNs according to their fitness. As a result, the following properties were found: (1) Highly-fit GRNs exhibited bistability for intermediate input between "on" and "off". This means that such GRNs responded to two input states by using different fixed points of dynamics. This bistability emerges necessarily as fitness increases. (2) These highly-fit GRNs were robust against noise because of their bistability. In other words, noise robustness is a byproduct of high fitness. (3) GRNs that were robust against mutations were not extremely rare among the highly-fit GRNs. This implies that mutational robustness is readily acquired through the evolutionary process. These properties are universal irrespective of the evolutionary pathway, because the results do not rely on evolutionary simulation.

Dimensional Reduction in Evolving Spin-Glass Model: Correlation of Phenotypic Responses to Environmental and Mutational Changes

The evolution of high-dimensional phenotypes is investigated using a statistical physics model consisting of interacting spins, in which phenotypes, genotypes, and environments are represented by spin configurations, interaction matrices, and external fields, respectively. We found that phenotypic changes upon diverse environmental change and genetic variation are highly correlated across all spins, consistent with recent experimental observations of biological systems. The dimension reduction in phenotypic changes is shown to be a result of the evolution of the robustness to thermal noise, achieved at the replica symmetric phase.

How to fit in: The learning principles of cell differentiation

Cell differentiation in multicellular organisms requires cells to respond to complex combinations of extracellular cues, such as morphogen concentrations. Some models of phenotypic plasticity conceptualise the response as a relatively simple function of a single environmental cues (e.g. a linear function of one cue), which facilitates rigorous analysis. Conversely, more mechanistic models such those implementing GRNs allows for a more general class of response functions but makes analysis more difficult. Therefore, a general theory describing how cells integrate multi-dimensional signals is lacking. In this work, we propose a theoretical framework for understanding the relationships between environmental cues (inputs) and phenotypic responses (outputs) underlying cell plasticity. We describe the relationship between environment and cell phenotype using logical functions, making the evolution of cell plasticity equivalent to a simple categorisation learning task. This abstraction allows us to apply principles derived from learning theory to understand the evolution of multi-dimensional plasticity. Our results show that natural selection is capable of discovering adaptive forms of cell plasticity associated with complex logical functions. However, developmental dynamics cause simpler functions to evolve more readily than complex ones. By using conceptual tools derived from learning theory we show that this developmental bias can be interpreted as a learning bias in the acquisition of plasticity functions. Because of that bias, the evolution of plasticity enables cells, under some circumstances, to display appropriate plastic responses to environmental conditions that they have not experienced in their evolutionary past. This is possible when the selective environment mirrors the bias of the developmental dynamics favouring the acquisition of simple plasticity functions–an example of the necessary conditions for generalisation in learning systems. These results illustrate the functional parallelisms between learning in neural networks and the action of natural selection on environmentally sensitive gene regulatory networks. This offers a theoretical framework for the evolution of plastic responses that integrate information from multiple cues, a phenomenon that underpins the evolution of multicellularity and developmental robustness.

In organisms composed of many cell types, the differentiation of cells relies on their ability to respond to complex extracellular cues, such as morphogen concentrations, a phenomenon known as cell plasticity. Although cell plasticity plays a crucial role in development and evolution, it is not clear how, and if, cell plasticity can enhance adaptation to a novel environment and/or facilitate robust developmental processes. In some models, the relationships between the environmental cues (inputs) and the phenotypic responses (outputs) are conceptualised as one-to-one (i.e. simple ‘reaction norms’); whereas the phenotype of plastic cells commonly depends on several simultaneous inputs (i.e. many-to-one, multi-dimensional reaction norms). One alternative is the use of a gene-regulatory network (GRN) models that allow for much more general responses; but this can make analysis difficult. In this work we use a theoretical framework based on logical functions and learning theory to characterize such multi-dimensional reaction norms produced by GRNs. This allows us to reveal a strong and previously unnoticed bias towards the acquisition of simple forms of cell plasticity, which increases their ability to adapt to novel environments. Recognising this bias helps us to understand when the evolution of cell plasticity will increase the ability of plastic cells to adapt to novel environments, to respond appropriately to complex extracellular cues and to enhance developmental robustness. Since this set of properties are required for the evolution of multicellularity, our approach can also contribute to our understanding of this evolutionary transition.

Nonlinear gene expression-phenotype relationships contribute to variation and clefting in the A/WySn mouse

BACKGROUND

Cleft lip and palate is one of the most common human birth defects, but the underlying etiology is poorly understood. The A/WySn mouse is a spontaneously occurring model of multigenic clefting in which 20% to 30% of individuals develop an orofacial cleft. Recent work has shown altered methylation at a specific retrotransposon insertion downstream of the Wnt9b locus in clefting animals, which results in decreased Wnt9b expression.

RESULTS

Using a newly developed protocol that allows us to measure morphology, gene expression, and DNA methylation in the same embryo, we relate gene expression in an individual embryo directly to its three-dimensional morphology for the first time. We find that methylation at the retrotransposon relates to Wnt9b expression and morphology. IAP methylation relates to shape of the nasal process in a manner consistent with clefting. Embryos with low IAP methylation exhibit increased among-individual variance in facial shape.

CONCLUSIONS

Methylation and gene expression relate nonlinearly to nasal process morphology. Individuals at one end of a continuum of phenotypic states display a clinical phenotype and increased phenotypic variation. Variable penetrance and expressivity in this model is likely determined both by among-individual variation in methylation and changes in phenotypic robustness along the underlying liability distribution for orofacial clefting.

DnaJ chaperones contribute to canalization

Canalization, an intrinsic robustness of development to external (environmental) or internal (genetic) perturbations, was first proposed over half a century ago. However, whether the robustness to environmental stress (environmental canalization [EC]) and to genetic variation (genetic canalization) are underpinned by the same molecular basis remains elusive. The recent discovery of the involvement of two endoplasmic reticulum (ER)-associated DnaJ genes in developmental buffering, orthologues of which are conserved across Metazoa, indicates that the role of ER-associated DnaJ genes might be conserved across the animal kingdom. To test this, we surveyed the ER-associated DnaJ chaperones in the nematode Caenorhabditis elegans. We then quantified the phenotype, in the form of variance and mean of seam cell counts, from RNA interference knockdown of DnaJs under three different temperatures. We find that seven out of eight ER-associated DnaJs are involved in either EC or microenvironmental canalization. Moreover, we also found two DnaJ genes not specifically associated with ER (DNAJC2/dnj-11 and DNAJA2/dnj-19) were involved in canalization. Protein expression pattern showed that these DnaJs are upregulated by heat stress, yet not all of them are expressed in the seam cells. Moreover, we found that most of the buffering DnaJs also control lifespan. We therefore concluded that a number of DnaJ chaperones, not limited to those associated with the ER, are involved in canalization as a part of the complex system that underlies development.

Formation of dominant mode by evolution in biological systems

A reduction in high-dimensional phenotypic states to a few degrees of freedom is essential to understand biological systems. Here, we show evolutionary robustness causes such reduction which restricts possible phenotypic changes in response to a variety of environmental conditions. First, global protein expression changes in Escherichia coli after various environmental perturbations were shown to be proportional across components, across different types of environmental conditions. To examine if such dimension reduction is a result of evolution, we analyzed a cell model-with a huge number of components, that reproduces itself via a catalytic reaction network-and confirmed that common proportionality in the concentrations of all components is shaped through evolutionary processes. We found that the changes in concentration across all components in response to environmental and evolutionary changes are constrained to the changes along a one-dimensional major axis, within a huge-dimensional state space. On the basis of these observations, we propose a theory in which such constraints in phenotypic changes are achieved both by evolutionary robustness and plasticity and formulate this proposition in terms of dynamical systems. Accordingly, broad experimental and numerical results on phenotypic changes caused by evolution and adaptation are coherently explained.

Chaperones, Canalization, and Evolution of Animal Forms

Over half a century ago, British developmental biologist Conrad Hal Waddington proposed the idea of canalization, that is, homeostasis in development. Since the breakthrough that was made by Rutherford and Lindquist (1998), who proposed a role of Hsp90 in developmental buffering, chaperones have gained much attention in the study of canalization. However, recent studies have revealed that a number of other molecules are also potentially involved in canalization. Here, I introduce the emerging role of DnaJ chaperones in canalization. I also discuss how the expression levels of such buffering molecules can be altered, thereby altering organismal development. Since developmental robustness is maternally inherited in various organisms, I propose that dynamic bet hedging, an increase in within-clutch variation in offspring phenotypes that is caused by unpredictable environmental challenges to the mothers, plays a key role in altering the expression levels of buffering molecules. Investigating dynamic bet hedging at the molecular level and how it impacts upon morphological phenotypes will help our understanding of the molecular mechanisms of canalization and evolutionary processes.

Macroscopic Theory for Evolving Biological Systems Akin to Thermodynamics

We present a macroscopic theory to characterize the plasticity, robustness, and evolvability of biological responses and their fluctuations. First, linear approximation in intracellular reaction dynamics is used to demonstrate proportional changes in the expression of all cellular components in response to a given environmental stress, with the proportion coefficient determined by the change in growth rate as a consequence of the steady growth of cells. We further demonstrate that this relationship is supported through adaptation experiments of bacteria, perhaps too well as this proportionality is held even across cultures of different types of conditions. On the basis of simulations of cell models, we further show that this global proportionality is a consequence of evolution in which expression changes in response to environmental or genetic perturbations are constrained along a unique one-dimensional curve, which is a result of evolutionary robustness. It then follows that the expression changes induced by environmental changes are proportionally reduced across different components of a cell by evolution, which is akin to the Le Chatelier thermodynamics principle. Finally, with the aid of a fluctuation-response relationship, this proportionality is shown to hold between fluctuations caused by genetic changes and those caused by noise. Overall, these results and support from the theoretical and experimental literature suggest a formulation of cellular systems akin to thermodynamics, in which a macroscopic potential is given by the growth rate (or fitness) represented as a function of environmental and evolutionary changes.

Complexity: the organizing principle at the interface of biological (dis)order

The term complexity means several things to biologists.When qualifying morphological phenotype, on the one hand, it is used to signify the sheer complicatedness of living systems, especially as a result of the multicomponent aspect of biological form. On the other hand, it has been used to represent the intricate nature of the connections between constituents that make up form: a more process-based explanation. In the context of evolutionary arguments, complexity has been defined, in a quantifiable fashion, as the amount of information, an informatic template such as a sequence of nucleotides or amino acids stores about its environment. In this perspective, we begin with a brief review of the history of complexity theory. We then introduce a developmental and an evolutionary understanding of what it means for biological systems to be complex.We propose that the complexity of living systems can be understood through two interdependent structural properties: multiscalarity of interconstituent mechanisms and excitability of the biological materials. The answer to whether a system becomes more or less complex over time depends on the potential for its constituents to interact in novel ways and combinations to give rise to new structures and functions, as well as on the evolution of excitable properties that would facilitate the exploration of interconstituent organization in the context of their microenvironments and macroenvironments.

Investigation on changes of modularity and robustness by edge-removal mutations in signaling networks

Background

Biological networks consisting of molecular components and interactions are represented by a graph model. There have been some studies based on that model to analyze a relationship between structural characteristics and dynamical behaviors in signaling network. However, little attention has been paid to changes of modularity and robustness in mutant networks.

Results

In this paper, we investigated the changes of modularity and robustness by edge-removal mutations in three signaling networks. We first observed that both the modularity and robustness increased on average in the mutant network by the edge-removal mutations. However, the modularity change was negatively correlated with the robustness change. This implies that it is unlikely that both the modularity and the robustness values simultaneously increase by the edge-removal mutations. Another interesting finding is that the modularity change was positively correlated with the degree, the number of feedback loops, and the edge betweenness of the removed edges whereas the robustness change was negatively correlated with them. We note that these results were consistently observed in randomly structure networks. Additionally, we identified two groups of genes which are incident to the highly-modularity-increasing and the highly-robustness-decreasing edges with respect to the edge-removal mutations, respectively, and observed that they are likely to be central by forming a connected component of a considerably large size. The gene-ontology enrichment of each of these gene groups was significantly different from the rest of genes. Finally, we showed that the highly-robustness-decreasing edges can be promising edgetic drug-targets, which validates the usefulness of our analysis.

Conclusions

Taken together, the analysis of changes of robustness and modularity against edge-removal mutations can be useful to unravel novel dynamical characteristics underlying in signaling networks.

Electronic supplementary material

The online version of this article (10.1186/s12918-017-0505-2) contains supplementary material, which is available to authorized users.

Dynamics robustness of cascading systems

A most important property of biochemical systems is robustness. Static robustness, e.g., homeostasis, is the insensitivity of a state against perturbations, whereas dynamics robustness, e.g., homeorhesis, is the insensitivity of a dynamic process. In contrast to the extensively studied static robustness, dynamics robustness, i.e., how a system creates an invariant temporal profile against perturbations, is little explored despite transient dynamics being crucial for cellular fates and are reported to be robust experimentally. For example, the duration of a stimulus elicits different phenotypic responses, and signaling networks process and encode temporal information. Hence, robustness in time courses will be necessary for functional biochemical networks. Based on dynamical systems theory, we uncovered a general mechanism to achieve dynamics robustness. Using a three-stage linear signaling cascade as an example, we found that the temporal profiles and response duration post-stimulus is robust to perturbations against certain parameters. Then analyzing the linearized model, we elucidated the criteria of when signaling cascades will display dynamics robustness. We found that changes in the upstream modules are masked in the cascade, and that the response duration is mainly controlled by the rate-limiting module and organization of the cascade’s kinetics. Specifically, we found two necessary conditions for dynamics robustness in signaling cascades: 1) Constraint on the rate-limiting process: The phosphatase activity in the perturbed module is not the slowest. 2) Constraints on the initial conditions: The kinase activity needs to be fast enough such that each module is saturated even with fast phosphatase activity and upstream changes are attenuated. We discussed the relevance of such robustness to several biological examples and the validity of the above conditions therein. Given the applicability of dynamics robustness to a variety of systems, it will provide a general basis for how biological systems function dynamically.

Cells use signaling pathways to transmit information received on its membrane to DNA, and many important cellular processes are tied to signaling networks. Past experiments have shown that cells’ internal signaling networks are sophisticated enough to process and encode temporal information such as the length of time a ligand is bound to a receptor. However, little research has been done to verify whether information encoded onto temporal profiles can be made robust. We examined mathematical models of linear signaling networks and found that the relaxation of the response to a transient stimuli can be made robust to certain parameter fluctuations. Robustness is a key concept in biological systems—it would be disastrous if a cell could not operate if there was a slight change in its environment or physiology. Our research shows that such dynamics robustness is a property of linear signaling cascades, and we outline the design principles needed to generate such robustness. We discovered that two conditions regarding the speed of the internal chemical reactions and concentration levels are needed to generate dynamics robustness.

Coherent organization in gene regulation: a study on six networks

Structural and dynamical fingerprints of evolutionary optimization in biological networks are still unclear. Here we analyze the dynamics of genetic regulatory networks responsible for the regulation of cell cycle and cell differentiation in three organisms or cell types each, and show that they follow a version of Hebb's rule which we have termed coherence. More precisely, we find that simultaneously expressed genes with a common target are less likely to act antagonistically at the attractors of the regulatory dynamics. We then investigate the dependence of coherence on structural parameters, such as the mean number of inputs per node and the activatory/repressory interaction ratio, as well as on dynamically determined quantities, such as the basin size and the number of expressed genes.

Global relationships in fluctuation and response in adaptive evolution

Cells change their internal state to adapt to environmental changes, and evolve in response to the new conditions. The phenotype changes first via adaptation in response to environmental changes, and then through mutational changes in the genomic sequence, followed by selection in evolution. Here, we analysed simulated adaptive evolution using a simple cell model consisting of thousands of intracellular components, and found that the changes in their concentrations by adaptation are proportional to those by evolution across all the components, where the proportion coefficient between the two agreed well with the change in the growth rate of a cell. Furthermore, we demonstrate that the phenotypic variance in concentrations of cellular components due to (non-genetic) noise and to genomic alternations is proportional across all components. This implies that the specific phenotypes that are highly evolvable were already given by non-genetic fluctuations. These global relationships in cellular states were also supported by phenomenological theory based on steady reproduction and transcriptome analysis of laboratory evolution in Escherichia coli. These findings demonstrate that a possible evolutionary change in phenotypic state is highly restricted. Our results provide a basis for the development of a quantitative theory of plasticity and robustness in phenotypic evolution.

Evolution-development congruence in pattern formation dynamics: Bifurcations in gene expression and regulation of networks structures

Search for possible relationships between phylogeny and ontogeny is important in evolutionary-developmental biology. Here we uncover such relationships by numerical evolution and unveil their origin in terms of dynamical systems theory. By representing developmental dynamics of spatially located cells with gene expression dynamics with cell-to-cell interaction under external morphogen gradient, gene regulation networks are evolved under mutation and selection with the fitness to approach a prescribed spatial pattern of expressed genes. For most numerical evolution experiments, evolution of pattern over generations and development of pattern by an evolved network exhibit remarkable congruence. Both in the evolution and development pattern changes consist of several epochs where stripes are formed in a short time, while for other temporal regimes, pattern hardly changes. In evolution, these quasi-stationary regimes are generations needed to hit relevant mutations, while in development, they are due to some gene expression that varies slowly and controls the pattern change. The morphogenesis is regulated by combinations of feedback or feedforward regulations, where the upstream feedforward network reads the external morphogen gradient, and generates a pattern used as a boundary condition for the later patterns. The ordering from up to downstream is common in evolution and development, while the successive epochal changes in development and evolution are represented as common bifurcations in dynamical-systems theory, which lead to the evolution-development congruence. Mechanism of exceptional violation of the congruence is also unveiled. Our results provide a new look on developmental stages, punctuated equilibrium, developmental bottlenecks, and evolutionary acquisition of novelty in morphogenesis.

From globally coupled maps to complex-systems biology

Studies of globally coupled maps, introduced as a network of chaotic dynamics, are briefly reviewed with an emphasis on novel concepts therein, which are universal in high-dimensional dynamical systems. They include clustering of synchronized oscillations, hierarchical clustering, chimera of synchronization and desynchronization, partition complexity, prevalence of Milnor attractors, chaotic itinerancy, and collective chaos. The degrees of freedom necessary for high dimensionality are proposed to equal the number in which the combinatorial exceeds the exponential. Future analysis of high-dimensional dynamical systems with regard to complex-systems biology is briefly discussed.

Robustness to noise in gene expression evolves despite epistatic constraints in a model of gene networks

Stochastic noise in gene expression causes variation in the development of phenotypes, making such noise a potential target of stabilizing selection. Here, we develop a new simulation model of gene networks to study the adaptive landscape underlying the evolution of robustness to noise. We find that epistatic interactions between the determinants of the expression of a gene and its downstream effect impose significant constraints on evolution, but these interactions do allow the gradual evolution of increased robustness. Despite strong sign epistasis, adaptation rarely proceeds via deleterious intermediate steps, but instead occurs primarily through small beneficial mutations. A simple mathematical model captures the relevant features of the single-gene fitness landscape and explains counterintuitive patterns, such as a correlation between the mean and standard deviation of phenotypes. In more complex networks, mutations in regulatory regions provide evolutionary pathways to increased robustness. These results chart the constraints and possibilities of adaptation to reduce expression noise and demonstrate the potential of a novel modeling framework for gene networks.

Effect and evolution of gene expression noise on the fitness landscape

Gene expression is a stochastic process that affects cellular and population fitness. Noise in gene expression can enhance fitness by increasing cell to cell variability as well as the time cells spend in favorable expression states. Using a stochastic model of gene expression together with a fitness function that incorporates the costs and benefits of gene expression in a stressful environment, we show that the fitness landscape is shaped by gene expression noise in more complex ways than previously anticipated. We find that mutations modulating the properties of expression noise enable cell populations to optimize their position on the fitness landscape. Additionally, we find that low levels of expression noise evolve under conditions where the fitness benefits of expression exceed the fitness costs, and that high levels of expression noise evolve when the expression costs exceed the fitness benefits. The results presented in this study expand our understanding of the interplay between stochastic gene expression and fitness in selective environments.

Coherent regulation in yeast's cell-cycle network

We define a measure of coherent activity for gene regulatory networks, a property that reflects the unity of purpose between the regulatory agents with a common target. We propose that such harmonious regulatory action is desirable under a demand for energy efficiency and may be selected for under evolutionary pressures. We consider two recent models of the cell-cycle regulatory network of the yeast, Saccharomyces cerevisiae as a case study and calculate their degree of coherence. A comparison with random networks of similar size and composition reveals that the yeast's cell-cycle regulation is wired to yield an exceptionally high level of coherent regulatory activity. We also investigate the mean degree of coherence as a function of the network size, connectivity and the fraction of repressory/activatory interactions.

Phenotype accessibility and noise in random threshold gene regulatory networks

Evolution requires phenotypic variation in a population of organisms for selection to function. Gene regulatory processes involved in organismal development affect the phenotypic diversity of organisms. Since only a fraction of all possible phenotypes are predicted to be accessed by the end of development, organisms may evolve strategies to use environmental cues and noise-like fluctuations to produce additional phenotypic diversity, and hence to enhance the speed of adaptation. We used a generic model of organismal development --gene regulatory networks-- to investigate how different levels of noise on gene expression states (i.e. phenotypes) may affect access to new, unique phenotypes, thereby affecting phenotypic diversity. We studied additional strategies that organisms might adopt to attain larger phenotypic diversity: either by augmenting their genome or the number of gene expression states. This was done for different types of gene regulatory networks that allow for distinct levels of regulatory influence on gene expression or are more likely to give rise to stable phenotypes. We found that if gene expression is binary, increasing noise levels generally decreases phenotype accessibility for all network types studied. If more gene expression states are considered, noise can moderately enhance the speed of discovery if three or four gene expression states are allowed, and if there are enough distinct regulatory networks in the population. These results were independent of the network types analyzed, and were robust to different implementations of noise. Hence, for noise to increase the number of accessible phenotypes in gene regulatory networks, very specific conditions need to be satisfied. If the number of distinct regulatory networks involved in organismal development is large enough, and the acquisition of more genes or fine tuning of their expression states proves costly to the organism, noise can be useful in allowing access to more unique phenotypes.

Origin and consequences of the relationship between protein mean and variance

Cell-to-cell variance in protein levels (noise) is a ubiquitous phenomenon that can increase fitness by generating phenotypic differences within clonal populations of cells. An important challenge is to identify the specific molecular events that control noise. This task is complicated by the strong dependence of a protein's cell-to-cell variance on its mean expression level through a power-law like relationship (σ²∝μ^1.69). Here, we dissect the nature of this relationship using a stochastic model parameterized with experimentally measured values. This framework naturally recapitulates the power-law like relationship (σ²∝μ^1.6) and accurately predicts protein variance across the yeast proteome (r² = 0.935). Using this model we identified two distinct mechanisms by which protein variance can be increased. Variables that affect promoter activation, such as nucleosome positioning, increase protein variance by changing the exponent of the power-law relationship. In contrast, variables that affect processes downstream of promoter activation, such as mRNA and protein synthesis, increase protein variance in a mean-dependent manner following the power-law. We verified our findings experimentally using an inducible gene expression system in yeast. We conclude that the power-law-like relationship between noise and protein mean is due to the kinetics of promoter activation. Our results provide a framework for understanding how molecular processes shape stochastic variation across the genome.

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

Interpreting a morphogen gradient into a single stripe of gene-expression is a fundamental unit of patterning in early embryogenesis. From both experimental data and computational studies the feed-forward motifs stand out as minimal networks capable of this patterning function. Positive feedback within gene networks has been hypothesised to enhance the sharpness and precision of gene-expression borders, however a systematic analysis has not yet been reported. Here we set out to assess this hypothesis, and find an unexpected result. The addition of positive-feedback can have different effects on two different designs of feed-forward motif– it increases the parametric robustness of one design, while being neutral or detrimental to the other. These results shed light on the abundance of the former motif and especially of mutual-inhibition positive feedback in developmental networks.

Modular network evolution under selection for robustness to noise

Real networks often exhibit modularity, which is defined as the degree to which a network can be decomposed into several subnetworks. The question of how a modular network arises is still open to discussion. The leading hypothesis is that high modularity evolves under multiple goals, which are decomposable to subproblems, as well as under the evolutionary constraint that selection prefers sparse links in a network. In the present study, we investigate an alternative evolutionary constraint entailing increased robustness to noise. To examine this, we present noise-interfused network models involving an analytically solvable linear system and biologically inspired nonlinear systems. The models demonstrate that it is possible to evolve a modular network under both modularly changing goal orientations and enhancing robustness to noise, thereby reducing sensitivity to noise. By performing theoretical analyses of linear systems, it is shown that the evolutionary constraint enforces the establishment of well-balanced noise sensitivities of multiple noise sources and leads to a modular network underlying a modular structure in goals. Moreover, computer simulations confirm that the presented mechanisms of modular network evolution are robust to variations of nonlinearity in network functions. Our findings suggest a positive role for the presence of noise in network evolution.

A network characteristic that correlates environmental and genetic robustness

As scientific advances in perturbing biological systems and technological advances in data acquisition allow the large-scale quantitative analysis of biological function, the robustness of organisms to both transient environmental stresses and inter-generational genetic changes is a fundamental impediment to the identifiability of mathematical models of these functions. An approach to overcoming this impediment is to reduce the space of possible models to take into account both types of robustness. However, the relationship between the two is still controversial. This work uncovers a network characteristic, transient responsiveness, for a specific function that correlates environmental imperturbability and genetic robustness. We test this characteristic extensively for dynamic networks of ordinary differential equations ranging up to 30 interacting nodes and find that there is a power-law relating environmental imperturbability and genetic robustness that tends to linearity as the number of nodes increases. Using our methods, we refine the classification of known 3-node motifs in terms of their environmental and genetic robustness. We demonstrate our approach by applying it to the chemotaxis signaling network. In particular, we investigate plausible models for the role of CheV protein in biochemical adaptation via a phosphorylation pathway, testing modifications that could improve the robustness of the system to environmental and/or genetic perturbation.

Advances in the ways that living systems can be perturbed in order to study how they function and sharp reductions in the cost of computer resources have allowed the collection of large amounts of data. The aim of biological system modeling is to analyze this data in order to pin down the precise interactions of molecules that underlie the observed functions. This is made difficult due to two features of biological systems: (1) Living things do not show an appreciable loss of function across large ranges of environmental factors. (2) Their function is inherited from parent to child more or less unchanged in spite of random mutations in genetic sequences. We find that these two features are more correlated in a specific subset of networks and show how to use this observation to find networks in which these two features appear together. Working within this smaller space of networks may make it easier to find suitable underlying models from data.

Negative interactions and feedback regulations are required for transient cellular response

Signal transduction is a process required to conduct information from a receptor to the nucleus. This process is vital for the control of cellular function and fate. The dynamics of signaling activation and inhibition determine processes such as apoptosis, proliferation, and differentiation. Thus, it is important to understand the factors modulating transient and sustained response. To address this question, by applying mathematical approach we have studied the factors which can alter the activation nature of downstream signaling molecules. The factors which we have investigated are loops (feed forward and feedback loops), cross-talk of signal transduction pathways, and the change in the concentration of the signaling molecules. Based on our results we conclude that among these factors feedback loop and the cross-talks which directly inhibit the target protein dominantly controls the transient cellular response.

Challenges for complex microbial ecosystems: combination of experimental approaches with mathematical modeling

In the past couple of decades, molecular ecological techniques have been developed to elucidate microbial diversity and distribution in microbial ecosystems. Currently, modern techniques, represented by meta-omics and single cell observations, are revealing the incredible complexity of microbial ecosystems and the large degree of phenotypic variation. These studies propound that microbiological techniques are insufficient to untangle the complex microbial network. This minireview introduces the application of advanced mathematical approaches in combination with microbiological experiments to microbial ecological studies. These combinational approaches have successfully elucidated novel microbial behaviors that had not been recognized previously. Furthermore, the theoretical perspective also provides an understanding of the plasticity, robustness and stability of complex microbial ecosystems in nature.

Developmental instability is genetically correlated with phenotypic plasticity, constraining heritability, and fitness

Although adaptive plasticity would seem always to be favored by selection, it occurs less often than expected. This lack of ubiquity suggests that there must be trade-offs, costs, or limitations associated with plasticity. Yet, few costs have been found. We explore one type of limitation, a correlation between plasticity and developmental instability, and use quantitative genetic theory to show why one should expect a genetic correlation. We test that hypothesis using the Landsberg erecta × Cape Verde Islands recombinant inbred lines (RILs) of Arabidopsis thaliana. RILs were grown at four different nitrogen (N) supply levels that span the range of N availabilities previously documented in North American field populations. We found a significant multivariate relationship between the cross-environment trait plasticity and the within-environment, within-RIL developmental instability across 13 traits. This genetic covariation between plasticity and developmental instability has two costs. First, theory predicts diminished fitness for highly plastic lines under stabilizing selection, because their developmental instability and variance around the optimum phenotype will be greater compared to nonplastic genotypes. Second, empirically the most plastic traits exhibited heritabilities reduced by 57% on average compared to nonplastic traits. This demonstration of potential costs in inclusive fitness and heritability provoke a rethinking of the evolutionary role of plasticity.

Using evolutionary computations to understand the design and evolution of gene and cell regulatory networks

This paper surveys modeling approaches for studying the evolution of gene regulatory networks (GRNs). Modeling of the design or 'wiring' of GRNs has become increasingly common in developmental and medical biology, as a means of quantifying gene-gene interactions, the response to perturbations, and the overall dynamic motifs of networks. Drawing from developments in GRN 'design' modeling, a number of groups are now using simulations to study how GRNs evolve, both for comparative genomics and to uncover general principles of evolutionary processes. Such work can generally be termed evolution in silico. Complementary to these biologically-focused approaches, a now well-established field of computer science is Evolutionary Computations (ECs), in which highly efficient optimization techniques are inspired from evolutionary principles. In surveying biological simulation approaches, we discuss the considerations that must be taken with respect to: (a) the precision and completeness of the data (e.g. are the simulations for very close matches to anatomical data, or are they for more general exploration of evolutionary principles); (b) the level of detail to model (we proceed from 'coarse-grained' evolution of simple gene-gene interactions to 'fine-grained' evolution at the DNA sequence level); (c) to what degree is it important to include the genome's cellular context; and (d) the efficiency of computation. With respect to the latter, we argue that developments in computer science EC offer the means to perform more complete simulation searches, and will lead to more comprehensive biological predictions.