Publisher Correction: Creative exploration as a scale-invariant search on a meaning landscape.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Creative exploration as a scale-invariant search on a meaning landscape.

Can knowledge accumulated in systems biology on mechanisms governing cell behavior help us to elucidate cognitive processes, such as human creative search? To address this, we focus on the property of scale invariance, which allows sensory systems to adapt to environmental signals spanning orders of magnitude. For example, bacteria search for nutrients, by responding to relative changes in nutrient concentration rather than absolute levels, via a sensory mechanism termed fold-change detection (FCD). Scale invariance is prevalent in cognition, yet the specific mechanisms are mostly unknown. Here, we screen many possible dynamic equation topologies, to find that an FCD model best describes creative search dynamics. The model further predicts robustness to variations in meaning perception, in agreement with behavioral data. We thus suggest FCD as a specific mechanism for scale invariant search, connecting sensory processes of cells and cognitive processes in human.

Placebo can enhance creativity.

BACKGROUND: The placebo effect is usually studied in clinical settings for decreasing negative symptoms such as pain, depression and anxiety. There is interest in exploring the placebo effect also outside the clinic, for enhancing positive aspects of performance or cognition. Several studies indicate that placebo can enhance cognitive abilities including memory, implicit learning and general knowledge. Here, we ask whether placebo can enhance creativity, an important aspect of human cognition. METHODS: Subjects were randomly assigned to a control group who smelled and rated an odorant (n = 45), and a placebo group who were treated identically but were also told that the odorant increases creativity and reduces inhibitions (n = 45). Subjects completed a recently developed automated test for creativity, the creative foraging game (CFG), and a randomly chosen subset (n = 57) also completed two manual standardized creativity tests, the alternate uses test (AUT) and the Torrance test (TTCT). In all three tests, participants were asked to create as many original solutions and were scored for originality, flexibility and fluency. RESULTS: The placebo group showed higher originality than the control group both in the CFG (p<0.04, effect size = 0.5) and in the AUT (p<0.05, effect size = 0.4), but not in the Torrance test. The placebo group also found more shapes outside of the standard categories found by a set of 100 CFG players in a previous study, a feature termed out-of-the-boxness (p<0.01, effect size = 0.6). CONCLUSIONS: The findings indicate that placebo can enhance the originality aspect of creativity. This strengthens the view that placebo can be used not only to reduce negative clinical symptoms, but also to enhance positive aspects of cognition. Furthermore, we find that the impact of placebo on creativity can be tested by CFG, which can quantify multiple aspects of creative search without need for manual coding. This approach opens the way to explore the behavioral and neural mechanisms by which placebo might amplify creativity.

Creative foraging: An experimental paradigm for studying exploration and discovery.

Creative exploration is central to science, art and cognitive development. However, research on creative exploration is limited by a lack of high-resolution automated paradigms. To address this, we present such an automated paradigm, the creative foraging game, in which people search for novel and valuable solutions in a large and well-defined space made of all possible shapes made of ten connected squares. Players discovered shape categories such as digits, letters, and airplanes as well as more abstract categories. They exploited each category, then dropped it to explore once again, and so on. Aligned with a prediction of optimal foraging theory (OFT), during exploration phases, people moved along meandering paths that are about three times longer than the shortest paths between shapes; when exploiting a category of related shapes, they moved along the shortest paths. The moment of discovery of a new category was usually done at a non-prototypical and ambiguous shape, which can serve as an experimental proxy for creative leaps. People showed individual differences in their search patterns, along a continuum between two strategies: a mercurial quick-to-discover/quick-to-drop strategy and a thorough slow-to-discover/slow-to-drop strategy. Contrary to optimal foraging theory, players leave exploitation to explore again far before categories are depleted. This paradigm opens the way for automated high-resolution study of creative exploration.

Automated Video Analysis of Non-verbal Communication in a Medical Setting.

Non-verbal communication plays a significant role in establishing good rapport between physicians and patients and may influence aspects of patient health outcomes. It is therefore important to analyze non-verbal communication in medical settings. Current approaches to measure non-verbal interactions in medicine employ coding by human raters. Such tools are labor intensive and hence limit the scale of possible studies. Here, we present an automated video analysis tool for non-verbal interactions in a medical setting. We test the tool using videos of subjects that interact with an actor portraying a doctor. The actor interviews the subjects performing one of two scripted scenarios of interviewing the subjects: in one scenario the actor showed minimal engagement with the subject. The second scenario included active listening by the doctor and attentiveness to the subject. We analyze the cross correlation in total kinetic energy of the two people in the dyad, and also characterize the frequency spectrum of their motion. We find large differences in interpersonal motion synchrony and entrainment between the two performance scenarios. The active listening scenario shows more synchrony and more symmetric followership than the other scenario. Moreover, the active listening scenario shows more high-frequency motion termed jitter that has been recently suggested to be a marker of followership. The present approach may be useful for analyzing physician-patient interactions in terms of synchrony and dominance in a range of medical settings.

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

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.

Would you like to play together? Adults' attachment and the mirror game.

Why is it easy for some people to play together and difficult for others? In this interdisciplinary pilot study, we looked at dyadic interaction in motion as a paradigm to explore the expression of attachment in adulthood. We used a device that gives simple, quantitative and automated indicators for the quality of interaction while playing the mirror game. Forty-seven participants played the mirror game with the same gender-matched expert players. In addition, participants were interviewed on the Adult Attachment Interview to assess their quality of attachment. Using high resolution kinematic measures, we found that secure attachment was correlated with high complexity of the game and low synchrony compared to insecure attachment. The findings suggest that security of attachment is related to a more exploratory and less rigid game than insecure-dismissing attachment. These preliminary findings imply that high resolution analysis of simple movement interaction could carry information about attachment behavior.

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.

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.

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.

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 person's 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.

Mutation rules and the evolution of sparseness and modularity in biological systems.

Biological systems exhibit two structural features on many levels of organization: sparseness, in which only a small fraction of possible interactions between components actually occur; and modularity--the near decomposability of the system into modules with distinct functionality. Recent work suggests that modularity can evolve in a variety of circumstances, including goals that vary in time such that they share the same subgoals (modularly varying goals), or when connections are costly. Here, we studied the origin of modularity and sparseness focusing on the nature of the mutation process, rather than on connection cost or variations in the goal. We use simulations of evolution with different mutation rules. We found that commonly used sum-rule mutations, in which interactions are mutated by adding random numbers, do not lead to modularity or sparseness except for in special situations. In contrast, product-rule mutations in which interactions are mutated by multiplying by random numbers--a better model for the effects of biological mutations--led to sparseness naturally. When the goals of evolution are modular, in the sense that specific groups of inputs affect specific groups of outputs, product-rule mutations also lead to modular structure; sum-rule mutations do not. Product-rule mutations generate sparseness and modularity because they tend to reduce interactions, and to keep small interaction terms small.

Comparing apples and oranges: fold-change detection of multiple simultaneous inputs.

Sensory systems often detect multiple types of inputs. For example, a receptor in a cell-signaling system often binds multiple kinds of ligands, and sensory neurons can respond to different types of stimuli. How do sensory systems compare these different kinds of signals? Here, we consider this question in a class of sensory systems - including bacterial chemotaxis- which have a property known as fold-change detection: their output dynamics, including amplitude and response time, depends only on the relative changes in signal, rather than absolute changes, over a range of several decades of signal. We analyze how fold-change detection systems respond to multiple signals, using mathematical models. Suppose that a step of fold F1 is made in input 1, together with a step of F2 in input 2. What total response does the system provide? We show that when both input signals impact the same receptor with equal number of binding sites, the integrated response is multiplicative: the response dynamics depend only on the product of the two fold changes, F1F2. When the inputs bind the same receptor with different number of sites n1 and n2, the dynamics depend on a product of power laws, [Formula: see text]. Thus, two input signals which vary over time in an inverse way can lead to no response. When the two inputs affect two different receptors, other types of integration may be found and generally the system is not constrained to respond according to the product of the fold-change of each signal. These predictions can be readily tested experimentally, by providing cells with two simultaneously varying input signals. The present study suggests how cells can compare apples and oranges, namely by comparing each to its own background level, and then multiplying these two fold-changes.

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.

Robust control of PEP formation rate in the carbon fixation pathway of C(4) plants by a bi-functional enzyme.

BACKGROUND: C(4) plants such as corn and sugarcane assimilate atmospheric CO(2) into biomass by means of the C(4) carbon fixation pathway. We asked how PEP formation rate, a key step in the carbon fixation pathway, might work at a precise rate, regulated by light, despite fluctuations in substrate and enzyme levels constituting and regulating this process. RESULTS: We present a putative mechanism for robustness in C(4) carbon fixation, involving a key enzyme in the pathway, pyruvate orthophosphate dikinase (PPDK), which is regulated by a bifunctional enzyme, Regulatory Protein (RP). The robust mechanism is based on avidity of the bifunctional enzyme RP to its multimeric substrate PPDK, and on a product-inhibition feedback loop that couples the system output to the activity of the bifunctional regulator. The model provides an explanation for several unusual biochemical characteristics of the system and predicts that the system's output, phosphoenolpyruvate (PEP) formation rate, is insensitive to fluctuations in enzyme levels (PPDK and RP), substrate levels (ATP and pyruvate) and the catalytic rate of PPDK, while remaining sensitive to the system's input (light levels). CONCLUSIONS: The presented PPDK mechanism is a new way to achieve robustness using product inhibition as a feedback loop on a bifunctional regulatory enzyme. This mechanism exhibits robustness to protein and metabolite levels as well as to catalytic rate changes. At the same time, the output of the system remains tuned to input levels.

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.

Rate constants rather than biochemical mechanism determine behaviour of genetic clocks.

Many biological systems contain both positive and negative feedbacks. These are often classified as resonators or integrators. Resonators respond preferentially to oscillating signals of a particular frequency. Integrators, on the other hand, accumulate a response to signals. Computational neuroscientists often refer to neurons showing integrator properties as type I neurons and those showing resonator properties as type II neurons. Guantes & Poyatos have shown that type I or type II behaviour can be seen in genetic clocks. They argue that when negative feedback occurs through transcription regulation and post-translationally, genetic clocks act as integrators and resonators, respectively. Here we show that either behaviour can be seen with either design and in a wide range of genetic clocks. This highlights the importance of parameters rather than biochemical mechanism in determining the system behaviour.

Escherichia coli glutamine synthetase adenylyltransferase (ATase, EC 2.7.7.49): kinetic characterization of regulation by PII, PII-UMP, glutamine, and alpha-ketoglutarate.

Glutamine synthetase adenylyltranferase (ATase, EC 2.7.7.49) catalyzes the adenylylation and deadenylylation of glutamine synthetase (GS), regulating GS activity. The adenylyltransferase (AT) reaction is activated by glutamine and by the unmodified form of the PII signal transduction protein and is inhibited by the uridylylated form of PII, PII-UMP. Conversely, the adenylyl-removing (AR) reaction is activated by PII-UMP and is inhibited by glutamine and by PII. Both AT and AR reactions are regulated by alpha-ketoglutarate, which binds to PII and PII-UMP. Here, we present a kinetic analysis of the AT and AR activities and their regulation. Both AT and AR reactions used a sequential mechanism of rapid equilibrium random binding of substrates and products. Activators and inhibitors had little effect on the binding of substrates, instead exerting their effects on catalysis. Our results were consistent with PII, PII-UMP, and glutamine shifting the enzyme among at least six different enzyme forms, two of which were inactive, one of which exhibited AR activity, and three of which exhibited AT activity. In addition to a site for glutamine, the enzyme appeared to contain two distinct sites for PII and PII-UMP. The PII, PII-UMP, and glutamine sites were in communication so that the apparent activation and inhibition constants for regulators depended upon each other. The binding of PII was favored by glutamine and its level reduced by PII-UMP, whereas glutamine and PII-UMP competed for the enzyme. alpha-Ketoglutarate, which acts exclusively through its binding to PII and PII-UMP, did not alter the binding of PII or PII-UMP to the enzyme. Rather, alpha-ketoglutarate dramatically affected the extent of activation or inhibition of the enzyme by PII or PII-UMP. A working hypothesis for the regulation of the AT and AR activities, consistent with all data, is presented.

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 gene's 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.

Hysteresis vs. graded responses: the connections make all the difference.

Biological regulatory systems have the potential to provide graded responses to stimuli or may demonstrate switch-like properties. Our understanding of the system design principles controlling these responses is still at a rudimentary stage, and here we consider several recent experimental and theoretical studies that focus on these system design principles. Overt positive feedback loops, or double-negative feedback loops, can produce bistable or multistable systems under the appropriate conditions and can produce graded responses under other conditions. Several design features favor bistability in negatively controlled genetic systems, including a high kinetic order for repression and a large difference in the rates of gene expression in the "on" and "off" states. In positive feedback, a high kinetic order for the activation of gene expression favors bistability. Multistability can result from the combined effects of positive and negative regulators, or from the combined effects of regulators that each demonstrate bistability. Finally, bistability can result in enzymatic systems in which multiple reversible covalent modifications occur, even when no overt feedback loops are present.