Avraham E. Mayo

Detailed map of a cis-regulatory input function

Most genes are regulated by multiple transcription factors that bind specific sites in DNA regulatory regions. These cis-regulatory regions perform a computation: the rate of transcription is a function of the active concentrations of each of the input transcription factors. Here, we used accurate gene expression measurements from living cell cultures, bearing GFP reporters, to map in detail the input function of the classic lacZYA operon of Escherichia coli, as a function of about a hundred combinations of its two inducers, cAMP and isopropyl β-d-thiogalactoside (IPTG). We found an unexpectedly intricate function with four plateau levels and four thresholds. This result compares well with a mathematical model of the binding of the regulatory proteins cAMP receptor protein (CRP) and LacI to the lac regulatory region. The model is also used to demonstrate that with few mutations, the same region could encode much purer AND-like or even OR-like functions. This possibility means that the wild-type region is selected to perform an elaborate computation in setting the transcription rate. The present approach can be generally used to map the input functions of other genes.

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.

Plasticity of the cis-regulatory input function of a gene.

The transcription rate of a gene is often controlled by several regulators that bind specific sites in the genes cis-regulatory region. The combined effect of these regulators is described by a cis-regulatory input function. What determines the form of an input function, and how variable is it with respect to mutations? To address this, we employ the well-characterized lac operon of Escherichia coli, which has an elaborate input function, intermediate between Boolean AND-gate and OR-gate logic. We mapped in detail the input function of 12 variants of the lac promoter, each with different point mutations in the regulator binding sites, by means of accurate expression measurements from living cells. We find that even a few mutations can significantly change the input function, resulting in functions that resemble Pure AND gates, OR gates, or single-input switches. Other types of gates were not found. The variant input functions can be described in a unified manner by a mathematical model. The model also lets us predict which functions cannot be reached by point mutations. The input function that we studied thus appears to be plastic, in the sense that many of the mutations do not ruin the regulation completely but rather result in new ways to integrate the inputs.

Individuality and togetherness in joint improvised motion.

Actors, dancers and musicians that improvise together report special moments of togetherness: high performance and synchrony, seemingly without a leader and a follower. Togetherness seems to conflict with individuality- the idiosyncratic character of each persons performance. To understand the relation of individuality and togetherness, we employed the mirror game paradigm in which two players are asked to mirror each other and create interesting synchronized motion, with and without a designated leader. The mirror game enables quantitative characterization of moments of togetherness in which complex motion is generated with high synchrony. We find that each person as a leader does basic strokes of motion with a characteristic signature, in terms of the shape of their velocity profile between two stopping events. In moments of togetherness both players change their signature to a universal stroke shape. This universal velocity profile resembles a half-period of a sine wave, and is therefore symmetric and maximally smooth. Thus, instead of converging to an intermediate motion signature, or having one player dominate, players seem to shift their basic motion signatures to a shape that is altogether different from their individually preferred shapes; the resulting motion may be easier to predict and to agree on. The players then build complex motion by using such smooth elementary strokes.

Robust control of nitrogen assimilation by a bifunctional enzyme in E. coli.

Bacteria regulate the assimilation of multiple nutrients to enable growth. How is balanced utilization achieved, despite fluctuations in the concentrations of the enzymes that make up the regulatory circuitry? Here we address this question by studying the nitrogen system of E. coli. A mechanism based on the avidity of a bifunctional enzyme, adenylyltransferase (AT/AR), to its multimeric substrate, glutamine synthetase, is proposed to maintain a robust ratio between two key metabolites, glutamine and α-ketoglutarate. This ratio is predicted to be insensitive to variations in protein levels of the core circuit and to the rate of nitrogen utilization. We find using mass spectrometry that the metabolite ratio is robust to variations in protein levels and that this robustness depends on the bifunctional enzyme. Moreover, robustness carries through to the bacteria growth rate. Interrupting avidity by adding a monofunctional AT/AR mutant to the native system abolishes robustness, as predicted by the proposed mechanism.

Design principles of cell circuits with paradoxical components

Biological systems display complex networks of interactions both at the level of molecules inside the cell and at the level of interactions between cells. Networks of interacting molecules, such as transcription networks, have been shown to be composed of recurring circuits called network motifs, each with specific dynamical functions. Much less is known about the possibility of such circuit analysis in networks made of communicating cells. Here, we study models of circuits in which a few cell types interact by means of signaling molecules. We consider circuits of cells with architectures that seem to recur in immunology. An intriguing feature of these circuits is their use of signaling molecules with a pleiotropic or paradoxical role, such as cytokines that increase both cell growth and cell death. We find that pleiotropic signaling molecules can provide cell circuits with systems-level functions. These functions include for different circuits maintenance of homeostatic cell concentrations, robust regulation of differentiation processes, and robust pulses of cells or cytokines.

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.

Evolution of Bow-Tie Architectures in Biology

Bow-tie or hourglass structure is a common architectural feature found in many biological systems. A bow-tie in a multi-layered structure occurs when intermediate layers have much fewer components than the input and output layers. Examples include metabolism where a handful of building blocks mediate between multiple input nutrients and multiple output biomass components, and signaling networks where information from numerous receptor types passes through a small set of signaling pathways to regulate multiple output genes. Little is known, however, about how bow-tie architectures evolve. Here, we address the evolution of bow-tie architectures using simulations of multi-layered systems evolving to fulfill a given input-output goal. We find that bow-ties spontaneously evolve when the information in the evolutionary goal can be compressed. Mathematically speaking, bow-ties evolve when the rank of the input-output matrix describing the evolutionary goal is deficient. The maximal compression possible (the rank of the goal) determines the size of the narrowest part of the network—that is the bow-tie. A further requirement is that a process is active to reduce the number of links in the network, such as product-rule mutations, otherwise a non-bow-tie solution is found in the evolutionary simulations. This offers a mechanism to understand a common architectural principle of biological systems, and a way to quantitate the effective rank of the goals under which they evolved.

Paradoxical Signaling by a Secreted Molecule Leads to Homeostasis of Cell Levels

A widespread feature of extracellular signaling in cell circuits is paradoxical pleiotropy: the same secreted signaling molecule can induce opposite effects in the responding cells. For example, the cytokine IL-2 can promote proliferation and death of T cells. The role of such paradoxical signaling remains unclear. To address this, we studied CD4(+) T cell expansion in culture. We found that cells with a 30-fold difference in initial concentrations reached a homeostatic concentration nearly independent of initial cell levels. Below an initial threshold, cell density decayed to extinction (OFF-state). We show that these dynamics relate to the paradoxical effect of IL-2, which increases the proliferation rate cooperatively and the death rate linearly. Mathematical modeling explained the observed cell and cytokine dynamics and predicted conditions that shifted cell fate from homeostasis to the OFF-state. We suggest that paradoxical signaling provides cell circuits with specific dynamical features that are robust to environmental perturbations.

Prediction of multidimensional drug dose responses based on measurements of drug pairs

Significance We present a mechanism-free formula that predicts effects of multiple drugs at all doses based on measurements of drug pairs at a few doses. The formula bypasses the combinatorial explosion problem by greatly reducing the number of measurements needed to design optimal cocktails for cancer and infection. Finding potent multidrug combinations against cancer and infections is a pressing therapeutic challenge; however, screening all combinations is difficult because the number of experiments grows exponentially with the number of drugs and doses. To address this, we present a mathematical model that predicts the effects of three or more antibiotics or anticancer drugs at all doses based only on measurements of drug pairs at a few doses, without need for mechanistic information. The model provides accurate predictions on available data for antibiotic combinations, and on experiments presented here on the response matrix of three cancer drugs at eight doses per drug. This approach offers a way to search for effective multidrug combinations using a small number of experiments.