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.

Glucose becomes one of the worst carbon sources for E.coli on poor nitrogen sources due to suboptimal levels of cAMP.

In most conditions, glucose is the best carbon source for E. coli: it provides faster growth than other sugars, and is consumed first in sugar mixtures. Here we identify conditions in which E. coli strains grow slower on glucose than on other sugars, namely when a single amino acid (arginine, glutamate, or proline) is the sole nitrogen source. In sugar mixtures with these nitrogen sources, E. coli still consumes glucose first, but grows faster rather than slower after exhausting glucose, generating a reversed diauxic shift. We trace this counterintuitive behavior to a metabolic imbalance: levels of TCA-cycle metabolites including α-ketoglutarate are high, and levels of the key regulatory molecule cAMP are low. Growth rates were increased by experimentally increasing cAMP levels, either by adding external cAMP, by genetically perturbing the cAMP circuit or by inhibition of glucose uptake. Thus, the cAMP control circuitry seems to have a 'bug' that leads to slow growth under what may be an environmentally rare condition.

Dynamics inside the cancer cell attractor reveal cell heterogeneity, limits of stability, and escape.

The observed intercellular heterogeneity within a clonal cell population can be mapped as dynamical states clustered around an attractor point in gene expression space, owing to a balance between homeostatic forces and stochastic fluctuations. These dynamics have led to the cancer cell attractor conceptual model, with implications for both carcinogenesis and new therapeutic concepts. Immortalized and malignant EBV-carrying B-cell lines were used to explore this model and characterize the detailed structure of cell attractors. Any subpopulation selected from a population of cells repopulated the whole original basin of attraction within days to weeks. Cells at the basin edges were unstable and prone to apoptosis. Cells continuously changed states within their own attractor, thus driving the repopulation, as shown by fluorescent dye tracing. Perturbations of key regulatory genes induced a jump to a nearby attractor. Using the Fokker-Planck equation, this cell population behavior could be described as two virtual, opposing influences on the cells: one attracting toward the center and the other promoting diffusion in state space (noise). Transcriptome analysis suggests that these forces result from high-dimensional dynamics of the gene regulatory network. We propose that they can be generalized to all cancer cell populations and represent intrinsic behaviors of tumors, offering a previously unidentified characteristic for studying cancer.

Hierarchy of non-glucose sugars in Escherichia coli.

BACKGROUND: Understanding how cells make decisions, and why they make the decisions they make, is of fundamental interest in systems biology. To address this, we study the decisions made by E. coli on which genes to express when presented with two different sugars. It is well-known that glucose, E. coli's preferred carbon source, represses the uptake of other sugars by means of global and gene-specific mechanisms. However, less is known about the utilization of glucose-free sugar mixtures which are found in the natural environment of E. coli and in biotechnology. RESULTS: Here, we combine experiment and theory to map the choices of E. coli among 6 different non-glucose carbon sources. We used robotic assays and fluorescence reporter strains to make precise measurements of promoter activity and growth rate in all pairs of these sugars. We find that the sugars can be ranked in a hierarchy: in a mixture of a higher and a lower sugar, the lower sugar system shows reduced promoter activity. The hierarchy corresponds to the growth rate supported by each sugar- the faster the growth rate, the higher the sugar on the hierarchy. The hierarchy is 'soft' in the sense that the lower sugar promoters are not completely repressed. Measurement of the activity of the master regulator CRP-cAMP shows that the hierarchy can be quantitatively explained based on differential activation of the promoters by CRP-cAMP. Comparing sugar system activation as a function of time in sugar pair mixtures at sub-saturating concentrations, we find cases of sequential activation, and also cases of simultaneous expression of both systems. Such simultaneous expression is not predicted by simple models of growth rate optimization, which predict only sequential activation. We extend these models by suggesting multi-objective optimization for both growing rapidly now and preparing the cell for future growth on the poorer sugar. CONCLUSION: We find a defined hierarchy of sugar utilization, which can be quantitatively explained by differential activation by the master regulator cAMP-CRP. The present approach can be used to understand cell decisions when presented with mixtures of conditions.

Linear superposition and prediction of bacterial promoter activity dynamics in complex conditions.

Bacteria often face complex environments. We asked how gene expression in complex conditions relates to expression in simpler conditions. To address this, we obtained accurate promoter activity dynamical measurements on 94 genes in E. coli in environments made up of all possible combinations of four nutrients and stresses. We find that the dynamics across conditions is well described by two principal component curves specific to each promoter. As a result, the promoter activity dynamics in a combination of conditions is a weighted average of the dynamics in each condition alone. The weights tend to sum up to approximately one. This weighted-average property, called linear superposition, allows predicting the promoter activity dynamics in a combination of conditions based on measurements of pairs of conditions. If these findings apply more generally, they can vastly reduce the number of experiments needed to understand how E. coli responds to the combinatorially huge space of possible environments.

Promoters maintain their relative activity levels under different growth conditions.

Most genes change expression levels across conditions, but it is unclear which of these changes represents specific regulation and what determines their quantitative degree. Here, we accurately measured activities of ~900 S. cerevisiae and ~1800 E. coli promoters using fluorescent reporters. We show that in both organisms 60-90% of promoters change their expression between conditions by a constant global scaling factor that depends only on the conditions and not on the promoter's identity. Quantifying such global effects allows precise characterization of specific regulation-promoters deviating from the global scale line. These are organized into few functionally related groups that also adhere to scale lines and preserve their relative activities across conditions. Thus, only several scaling factors suffice to accurately describe genome-wide expression profiles across conditions. We present a parameter-free passive resource allocation model that quantitatively accounts for the global scaling factors. It suggests that many changes in expression across conditions result from global effects and not specific regulation, and provides means for quantitative interpretation of expression profiles.

The last generation of bacterial growth in limiting nutrient.

BACKGROUND: Bacterial growth as a function of nutrients has been studied for decades, but is still not fully understood. In particular, the growth laws under dynamically changing environments have been difficult to explore, because of the rapidly changing conditions. Here, we address this challenge by means of a robotic assay and measure bacterial growth rate, promoter activity and substrate level at high temporal resolution across the entire growth curve in batch culture. As a model system, we study E. coli growing under nitrogen or carbon limitation, and explore the dynamics in the last generation of growth where nutrient levels can drop rapidly. RESULTS: We find that growth stops abruptly under limiting nitrogen or carbon, but slows gradually when nutrients are not limiting. By measuring growth rate at a 3 min time resolution, and inferring the instantaneous substrate level, s, we find that the reduction in growth rate µ under nutrient limitation follows Monod's law, µ=µ0(s/(k(s)+s)). By following promoter activity of different genes we found that the abrupt stop of growth under nitrogen or carbon limitation is accompanied by a pulse-like up-regulation of the expression of genes in the relevant nutrient assimilation pathways. We further find that sharp stop of growth is conditional on the presence of regulatory proteins in the assimilation pathway. CONCLUSIONS: The observed sharp stop of growth accompanied by a pulsed expression of assimilation genes allows bacteria to compensate for the drop in nutrients, suggesting a strategy used by the cells to prolong exponential growth under limiting substrate.

Response to comment on "Evolutionary trade-offs, Pareto optimality, and the geometry of phenotype space".

Edelaar raises concerns about the way we tested our theory. Our mathematical theorem predicts that despite the high dimensionality of trait space, trade-offs between tasks leads to phenotypes in low-dimensional regions in trait space, such as lines and triangles. We address Edelaar's questions with statistical tests that eliminate pseudoreplication concerns, finding that our predictions remain convincingly supported.

Promoter activity dynamics in the lag phase of Escherichia coli.

BACKGROUND: Lag phase is a period of time with no growth that occurs when stationary phase bacteria are transferred to a fresh medium. Bacteria in lag phase seem inert: their biomass does not increase. The low number of cells and low metabolic activity make it difficult to study this phase. As a consequence, it has not been studied as thoroughly as other bacterial growth phases. However, lag phase has important implications for bacterial infections and food safety. We asked which, if any, genes are expressed in the lag phase of Escherichia coli, and what is their dynamic expression pattern. RESULTS: We developed an assay based on imaging flow cytometry of fluorescent reporter cells that overcomes the challenges inherent in studying lag phase. We distinguish between lag1 phase- in which there is no biomass growth, and lag2 phase--in which there is biomass growth but no cell division. We find that in lag1 phase, most promoters are not active, except for the enzymes that utilize the specific carbon source in the medium. These genes show promoter activities that increase exponentially with time, despite the fact that the cells do not measurably increase in size. An oxidative stress promoter, katG, is also active. When cells enter lag2 and begin to grow in size, they switch to a full growth program of promoter activity including ribosomal and metabolic genes. CONCLUSIONS: The observed exponential increase in enzymes for the specific carbon source followed by an abrupt switch to production of general growth genes is a solution of an optimal control model, known as bang-bang control. The present approach contributes to the understanding of lag phase, the least studied of bacterial growth phases.

Mode of regulation and the insulation of bacterial gene expression.

A gene can be said to be insulated from environmental variations if its expression level depends only on its cognate inducers, and not on variations in conditions. We tested the insulation of the lac promoter of E. coli and of synthetic constructs in which the transcription factor CRP acts as either an activator or a repressor, by measuring their input function-their expression as a function of inducers-in different growth conditions. We find that the promoter activities show sizable variation across conditions of 10%-100% (SD/mean). When the promoter is bound to its cognate regulator(s), variation across conditions is smaller than when it is unbound. Thus, mode of regulation affects insulation: activators seem to show better insulation at high expression levels, and repressors at low expression levels. This may explain the Savageau demand rule, in which E. coli genes needed often in the natural environment tend to be regulated by activators, and rarely needed genes by repressors. The present approach can be used to study insulation in other genes and organisms.

Using bleach-chase to measure protein half-lives in living cells.

Protein removal has a central role in numerous cellular processes. Obtaining systematic measurements of multiple protein removal rates is necessary to understand the principles that govern these processes, but it is currently a major technical challenge. To address this, we developed 'bleach-chase', a noninvasive method for measuring the half-lives of multiple proteins at high temporal resolution in living cells. The method uses a library of annotated human reporter cell clones, each with a unique fluorescently tagged protein expressed from its native chromosomal location. In this protocol, we detail a simple procedure that bleaches the cells and uses time-lapse fluorescence microscopy and automated image analysis to systematically measure the half-life dynamics of multiple proteins. The duration of the protocol is 4-5 d. The method may be applicable to a wide range of fluorescently tagged proteins and cell lines.

The mirror game as a paradigm for studying the dynamics of two people improvising motion together.

Joint improvisation is the creative action of two or more people without a script or designated leader. Examples include improvisational theater and music, and day-to-day activities such as conversations. In joint improvisation, novel action is created, emerging from the interaction between people. Although central to creative processes and social interaction, joint improvisation remains largely unexplored due to the lack of experimental paradigms. Here we introduce a paradigm based on a theater practice called the mirror game. We measured the hand motions of two people mirroring each other at high temporal and spatial resolution. We focused on expert actors and musicians skilled in joint improvisation. We found that players can jointly create novel complex motion without a designated leader, synchronized to less than 40 ms. In contrast, we found that designating one player as leader deteriorated performance: The follower showed 2-3 Hz oscillation around the leader's smooth trajectory, decreasing synchrony and reducing the range of velocities reached. A mathematical model suggests a mechanism for these observations based on mutual agreement on future motion in mirrored reactive-predictive controllers. This is a step toward understanding the human ability to create novelty by improvising together.

Cell-to-cell spread of HIV permits ongoing replication despite antiretroviral therapy.

Latency and ongoing replication have both been proposed to explain the drug-insensitive human immunodeficiency virus (HIV) reservoir maintained during antiretroviral therapy. Here we explore a novel mechanism for ongoing HIV replication in the face of antiretroviral drugs. We propose a model whereby multiple infections per cell lead to reduced sensitivity to drugs without requiring drug-resistant mutations, and experimentally validate the model using multiple infections per cell by cell-free HIV in the presence of the drug tenofovir. We then examine the drug sensitivity of cell-to-cell spread of HIV, a mode of HIV transmission that can lead to multiple infection events per target cell. Infections originating from cell-free virus decrease strongly in the presence of antiretrovirals tenofovir and efavirenz whereas infections involving cell-to-cell spread are markedly less sensitive to the drugs. The reduction in sensitivity is sufficient to keep multiple rounds of infection from terminating in the presence of drugs. We examine replication from cell-to-cell spread in the presence of clinical drug concentrations using a stochastic infection model and find that replication is intermittent, without substantial accumulation of mutations. If cell-to-cell spread has the same properties in vivo, it may have adverse consequences for the immune system, lead to therapy failure in individuals with risk factors, and potentially contribute to viral persistence and hence be a barrier to curing HIV infection.

Negative auto-regulation increases the input dynamic-range of the arabinose system of Escherichia coli.

BACKGROUND: Gene regulation networks are made of recurring regulatory patterns, called network motifs. One of the most common network motifs is negative auto-regulation, in which a transcription factor represses its own production. Negative auto-regulation has several potential functions: it can shorten the response time (time to reach halfway to steady-state), stabilize expression against noise, and linearize the gene's input-output response curve. This latter function of negative auto-regulation, which increases the range of input signals over which downstream genes respond, has been studied by theory and synthetic gene circuits. Here we ask whether negative auto-regulation preserves this function also in the context of a natural system, where it is embedded within many additional interactions. To address this, we studied the negative auto-regulation motif in the arabinose utilization system of Escherichia coli, in which negative auto-regulation is part of a complex regulatory network. RESULTS: We find that when negative auto-regulation is disrupted by placing the regulator araC under constitutive expression, the input dynamic range of the arabinose system is reduced by 10-fold. The apparent Hill coefficient of the induction curve changes from about n = 1 with negative auto-regulation, to about n = 2 when it is disrupted. We present a mathematical model that describes how negative auto-regulation can increase input dynamic-range, by coupling the transcription factor protein level to the input signal. CONCLUSIONS: Here we demonstrate that the negative auto-regulation motif in the native arabinose system of Escherichia coli increases the range of arabinose signals over which the system can respond. In this way, negative auto-regulation may help to increase the input dynamic-range while maintaining the specificity of cooperative regulatory systems. This function may contribute to explaining the common occurrence of negative auto-regulation in biological systems.

Proteome half-life dynamics in living human cells.

Cells remove proteins by two processes: degradation and dilution due to cell growth. The balance between these basic processes is poorly understood. We addressed this by developing an accurate and noninvasive method for measuring protein half-lives, called "bleach-chase," that is applicable to fluorescently tagged proteins. Assaying 100 proteins in living human cancer cells showed half-lives that ranged between 45 minutes and 22.5 hours. A variety of stresses that stop cell division showed the same general effect: Long-lived proteins became longer-lived, whereas short-lived proteins remained largely unaffected. This effect is due to the relative strengths of degradation and dilution and suggests a mechanism for differential killing of rapidly growing cells by growth-arresting drugs. This approach opens a way to understand proteome half-life dynamics in living cells.

Fourier analysis and systems identification of the p53 feedback loop.

A key circuit in the response of cells to damage is the p53-mdm2 feedback loop. This circuit shows sustained, noisy oscillations in individual human cells following DNA breaks. Here, we apply an engineering approach known as systems identification to quantify the in vivo interactions in the circuit on the basis of accurate measurements of its power spectrum. We obtained oscillation time courses of p53 and Mdm2 protein levels from several hundred cells and analyzed their Fourier spectra. We find characteristic spectra with distinct low-frequency components that are well-described by a third-order linear model with white noise. The model identifies the sign and strength of the known interactions, including a negative feedback loop between p53 and its upstream regulator. It also implies that noise can trigger and maintain the oscillations. The model also captures the power spectra of p53 dynamics without DNA damage. Parameters such as noise amplitudes and protein lifetimes are estimated. This approach employs natural biological noise as a diagnostic that stimulates the system at many frequencies at once. It seems to be a useful way to find the in vivo design of circuits and may be applied to other systems by monitoring their power spectrum in individual cells.

Cost of unneeded proteins in E. coli is reduced after several generations in exponential growth.

When E. coli cells express unneeded protein, they grow more slowly. Such penalty to fitness associated with making proteins is called protein cost. Protein cost is an important component in the cost-benefit tradeoffs that underlie the evolution of protein circuits, but its origins are still poorly understood. Here, we ask how the protein cost varies during the exponential growth phase of E. coli. We find that cells growing exponentially following an upshift from overnight culture show a large cost when producing unneeded proteins. However, after several generations, while still in exponential growth, the cells enter a phase where cost is much reduced despite vigorous unneeded protein production. We find that this reduced-cost phase depends on the ppGpp system, which adjusts the amount of ribosomes in the cell and does not occur after a downshift from rich to poor medium. These findings suggest that protein cost is a transient phenomenon that happens upon an upshift in conditions and that cost is reduced when ribosomes and other cellular systems have increased to their appropriate steady-state level in the new condition.

Protein dynamics in drug combinations: a linear superposition of individual-drug responses.

Drugs and drug combinations have complex biological effects on cells and organisms. Little is known about how drugs affect protein dynamics that determine these effects. Here, we use a dynamic proteomics approach to accurately follow 15 protein levels in human cells in response to 13 different drugs. We find that protein dynamics in response to combinations of drugs are described accurately by a linear superposition (weighted sum) of their response to individual drugs. The weights in this superposition describe the relative impact of each drug on each protein. Using these weights, we show that one can predict the dynamics in a three-drug or four-drug combination on the basis of the dynamics in drug pairs. Our approach might eliminate the need to increase the number of experiments exponentially with the number of drugs and suggests that it might be possible to rationally control protein dynamics with specific drug combinations.

Invariant distribution of promoter activities in Escherichia coli.

Cells need to allocate their limited resources to express a wide range of genes. To understand how Escherichia coli partitions its transcriptional resources between its different promoters, we employ a robotic assay using a comprehensive reporter strain library for E. coli to measure promoter activity on a genomic scale at high-temporal resolution and accuracy. This allows continuous tracking of promoter activity as cells change their growth rate from exponential to stationary phase in different media. We find a heavy-tailed distribution of promoter activities, with promoter activities spanning several orders of magnitude. While the shape of the distribution is almost completely independent of the growth conditions, the identity of the promoters expressed at different levels does depend on them. Translation machinery genes, however, keep the same relative expression levels in the distribution across conditions, and their fractional promoter activity tracks growth rate tightly. We present a simple optimization model for resource allocation which suggests that the observed invariant distributions might maximize growth rate. These invariant features of the distribution of promoter activities may suggest design constraints that shape the allocation of transcriptional resources.

Adaptive prediction of environmental changes by microorganisms.

Natural habitats of some microorganisms may fluctuate erratically, whereas others, which are more predictable, offer the opportunity to prepare in advance for the next environmental change. In analogy to classical Pavlovian conditioning, microorganisms may have evolved to anticipate environmental stimuli by adapting to their temporal order of appearance. Here we present evidence for environmental change anticipation in two model microorganisms, Escherichia coli and Saccharomyces cerevisiae. We show that anticipation is an adaptive trait, because pre-exposure to the stimulus that typically appears early in the ecology improves the organism's fitness when encountered with a second stimulus. Additionally, we observe loss of the conditioned response in E. coli strains that were repeatedly exposed in a laboratory evolution experiment only to the first stimulus. Focusing on the molecular level reveals that the natural temporal order of stimuli is embedded in the wiring of the regulatory network-early stimuli pre-induce genes that would be needed for later ones, yet later stimuli only induce genes needed to cope with them. Our work indicates that environmental anticipation is an adaptive trait that was repeatedly selected for during evolution and thus may be ubiquitous in biology.