Hila Sheftel

Evolutionary Trade-Offs, Pareto Optimality, and the Geometry of Phenotype Space

Managing Trade-Offs Most organisms experience selection on a host of traits to determine their likelihood to succeed evolutionarily. However, specific traits may experience trade-offs in determining an organisms optimal phenotype. Shoval et al. (p. 1157; see the Perspective by Noor and Milo) relate physical traits to the task that they are optimizing using a Pareto curve, a power law probability distribution, to show that a single set of trait values optimizes performance at a given task and that performance decreases as an organisms phenotype moves away from this set of trait values. The results suggest how selection makes the best trade-offs for an arbitrary number of tasks and traits and may explain examples of evolutionary variation. The fitness of an organism can be modeled graphically to determine how phenotypic trade-offs are maximized. Biological systems that perform multiple tasks face a fundamental trade-off: A given phenotype cannot be optimal at all tasks. Here we ask how trade-offs affect the range of phenotypes found in nature. Using the Pareto front concept from economics and engineering, we find that best–trade-off phenotypes are weighted averages of archetypes—phenotypes specialized for single tasks. For two tasks, phenotypes fall on the line connecting the two archetypes, which could explain linear trait correlations, allometric relationships, as well as bacterial gene-expression patterns. For three tasks, phenotypes fall within a triangle in phenotype space, whose vertices are the archetypes, as evident in morphological studies, including on Darwin’s finches. Tasks can be inferred from measured phenotypes based on the behavior of organisms nearest the archetypes.

A cellular and regulatory map of the cholinergic nervous system of C. elegans

Nervous system maps are of critical importance for understanding how nervous systems develop and function. We systematically map here all cholinergic neuron types in the male and hermaphrodite C. elegans nervous system. We find that acetylcholine (ACh) is the most broadly used neurotransmitter and we analyze its usage relative to other neurotransmitters within the context of the entire connectome and within specific network motifs embedded in the connectome. We reveal several dynamic aspects of cholinergic neurotransmitter identity, including a sexually dimorphic glutamatergic to cholinergic neurotransmitter switch in a sex-shared interneuron. An expression pattern analysis of ACh-gated anion channels furthermore suggests that ACh may also operate very broadly as an inhibitory neurotransmitter. As a first application of this comprehensive neurotransmitter map, we identify transcriptional regulatory mechanisms that control cholinergic neurotransmitter identity and cholinergic circuit assembly. DOI: http://dx.doi.org/10.7554/eLife.12432.001

Automated imaging with ScanLag reveals previously undetectable bacterial growth phenotypes

We developed an automated system, ScanLag, that measures in parallel the delay in growth (lag time) and growth rate of thousands of cells. Using ScanLag, we detected small subpopulations of bacteria with dramatically increased lag time upon starvation. By screening a library of Escherichia coli deletion mutants, we achieved two-dimensional mapping of growth characteristics, which showed that ScanLag enables multidimensional screens for quantitative characterization and identification of rare phenotypic variants.

Inferring biological tasks using Pareto analysis of high-dimensional data

We present the Pareto task inference method (ParTI; http://www.weizmann.ac.il/mcb/UriAlon/download/ParTI) for inferring biological tasks from high-dimensional biological data. Data are described as a polytope, and features maximally enriched closest to the vertices (or archetypes) allow identification of the tasks the vertices represent. We demonstrate that human breast tumors and mouse tissues are well described by tetrahedrons in gene expression space, with specific tumor types and biological functions enriched at each of the vertices, suggesting four key tasks.

Evolutionary Tradeoffs between Economy and Effectiveness in Biological Homeostasis Systems

Biological regulatory systems face a fundamental tradeoff: they must be effective but at the same time also economical. For example, regulatory systems that are designed to repair damage must be effective in reducing damage, but economical in not making too many repair proteins because making excessive proteins carries a fitness cost to the cell, called protein burden. In order to see how biological systems compromise between the two tasks of effectiveness and economy, we applied an approach from economics and engineering called Pareto optimality. This approach allows calculating the best-compromise systems that optimally combine the two tasks. We used a simple and general model for regulation, known as integral feedback, and showed that best-compromise systems have particular combinations of biochemical parameters that control the response rate and basal level. We find that the optimal systems fall on a curve in parameter space. Due to this feature, even if one is able to measure only a small fraction of the systems parameters, one can infer the rest. We applied this approach to estimate parameters in three biological systems: response to heat shock and response to DNA damage in bacteria, and calcium homeostasis in mammals.

The geometry of the Pareto front in biological phenotype space

When organisms perform a single task, selection leads to phenotypes that maximize performance at that task. When organisms need to perform multiple tasks, a trade-off arises because no phenotype can optimize all tasks. Recent work addressed this question, and assumed that the performance at each task decays with distance in trait space from the best phenotype at that task. Under this assumption, the best-fitness solutions (termed the Pareto front) lie on simple low-dimensional shapes in trait space: line segments, triangles and other polygons. The vertices of these polygons are specialists at a single task. Here, we generalize this finding, by considering performance functions of general form, not necessarily functions that decay monotonically with distance from their peak. We find that, except for performance functions with highly eccentric contours, simple shapes in phenotype space are still found, but with mildly curving edges instead of straight ones. In a wide range of systems, complex data on multiple quantitative traits, which might be expected to fill a high-dimensional phenotype space, is predicted instead to collapse onto low-dimensional shapes; phenotypes near the vertices of these shapes are predicted to be specialists, and can thus suggest which tasks may be at play.

Geometry of the Gene Expression Space of Individual Cells

There is a revolution in the ability to analyze gene expression of single cells in a tissue. To understand this data we must comprehend how cells are distributed in a high-dimensional gene expression space. One open question is whether cell types form discrete clusters or whether gene expression forms a continuum of states. If such a continuum exists, what is its geometry? Recent theory on evolutionary trade-offs suggests that cells that need to perform multiple tasks are arranged in a polygon or polyhedron (line, triangle, tetrahedron and so on, generally called polytopes) in gene expression space, whose vertices are the expression profiles optimal for each task. Here, we analyze single-cell data from human and mouse tissues profiled using a variety of single-cell technologies. We fit the data to shapes with different numbers of vertices, compute their statistical significance, and infer their tasks. We find cases in which single cells fill out a continuum of expression states within a polyhedron. This occurs in intestinal progenitor cells, which fill out a tetrahedron in gene expression space. The four vertices of this tetrahedron are each enriched with genes for a specific task related to stemness and early differentiation. A polyhedral continuum of states is also found in spleen dendritic cells, known to perform multiple immune tasks: cells fill out a tetrahedron whose vertices correspond to key tasks related to maturation, pathogen sensing and communication with lymphocytes. A mixture of continuum-like distributions and discrete clusters is found in other cell types, including bone marrow and differentiated intestinal crypt cells. This approach can be used to understand the geometry and biological tasks of a wide range of single-cell datasets. The present results suggest that the concept of cell type may be expanded. In addition to discreet clusters in gene-expression space, we suggest a new possibility: a continuum of states within a polyhedron, in which the vertices represent specialists at key tasks.

Evolutionary trade-offs and the structure of polymorphisms

Populations of organisms show genetic differences called polymorphisms. Understanding the effects of polymorphisms is important for biology and medicine. Here, we ask which polymorphisms occur at high frequency when organisms evolve under trade-offs between multiple tasks. Multiple tasks present a problem, because it is not possible to be optimal at all tasks simultaneously and hence compromises are necessary. Recent work indicates that trade-offs lead to a simple geometry of phenotypes in the space of traits: phenotypes fall on the Pareto front, which is shaped as a polytope: a line, triangle, tetrahedron etc. The vertices of these polytopes are the optimal phenotypes for a single task. Up to now, work on this Pareto approach has not considered its genetic underpinnings. Here, we address this by asking how the polymorphism structure of a population is affected by evolution under trade-offs. We simulate a multi-task selection scenario, in which the population evolves to the Pareto front: the line segment between two archetypes or the triangle between three archetypes. We find that polymorphisms that become prevalent in the population have pleiotropic phenotypic effects that align with the Pareto front. Similarly, epistatic effects between prevalent polymorphisms are parallel to the front. Alignment with the front occurs also for asexual mating. Alignment is reduced when drift or linkage is strong, and is replaced by a more complex structure in which many perpendicular allele effects cancel out. Aligned polymorphism structure allows mating to produce offspring that stand a good chance of being optimal multi-taskers in at least one of the locales available to the species. This article is part of the theme issue ‘Self-organization in cell biology’.

Universal cancer tasks, evolutionary tradeoffs, and the functions of driver mutations

Recent advances have led to an appreciation of the vast molecular diversity of cancer. Detailed data has enabled powerful methods to sort tumors into groups with benefits for prognosis and treatment. We are still missing, however, a general theoretical framework to understand the diversity of tumor gene-expression and mutations. To address this, we present a framework based on multi-task evolution theory, using the fact that tumors evolve in the body, and that tumors are faced with multiple tasks that contribute to their fitness. In accordance with the theory, we find that tradeoff between tasks constrains tumor gene-expression to a continuum bounded by a polyhedron. The vertices of the polyhedron are gene-expression profiles each specializing in one task, allowing the tasks to be identified. We find five universal cancer tasks across tissue-types: cell-division, biomass & energy, lipogenesis, immune-interaction and invasion & tissue remodeling. Tumors whose gene-expression lies close to a vertex are task specialists. We find evidence that such specialists are more sensitive to drugs that interfere with this task. We find that driver mutations, but not passenger mutations, tune gene-expression towards specialization in specific tasks. This approach can integrate additional types of molecular data into a theoretically-based framework for understanding tumor diversity.

Evolutionary tradeoffs and the structure of allelic polymorphisms

Populations of organisms show prevalent genetic differences called polymorphisms. Understanding the effects of polymorphisms is of central importance in biology and medicine. Here, we ask which polymorphisms occur at high frequency when organisms evolve under tradeoffs between multiple tasks. Multiple tasks present a problem, because it is not possible to be optimal at all tasks simultaneously and hence compromises are necessary. Recent work indicates that tradeoffs lead to a simple geometry of phenotypes in the space of traits: phenotypes fall on the Pareto front, which is shaped as a polytope: a line, triangle, tetrahedron etc. The vertices of these polytopes are the optimal phenotypes for a single task. Up to now, work on this Pareto approach has not considered its genetic underpinnings. Here, we address this by asking how the polymorphism structure of a population is affected by evolution under tradeoffs. We simulate a multi-task selection scenario, in which the population evolves to the Pareto front: the line segment between two archetypes or the triangle between three archetypes. We find that polymorphisms that become prevalent in the population have pleiotropic phenotypic effects that align with the Pareto front. Similarly, epistatic effects between prevalent polymorphisms are parallel to the front. Alignment with the front occurs also for asexual mating. Alignment is reduced when drift or linkage is strong, and is replaced by a more complex structure in which many perpendicular allele effects cancel out. Aligned polymorphism structure allows mating to produce offspring that stand a good chance of being optimal multi-taskers in at least one of the locales available to the species.