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.

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.

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.

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.

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.

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.

Diverse two-dimensional input functions control bacterial sugar genes.

Cells respond to signals by regulating gene expression. The relation between the level of input signals and the transcription rate of the gene is called the gene's input function. Because most genes are regulated by more than one signal, the input functions are usually multidimensional. To understand cellular responses, it is essential to know the shapes of these functions. Here, we map the two-dimensional input functions of 19 sugar-utilization genes at high resolution in living E. coli cells. We find diverse, intricately shaped input functions, despite the similarity in the regulatory circuitry of these genes. Surprisingly, some of the input functions are nonmonotonic, peaking at intermediate signal levels. Furthermore, most of the input functions show separation of variables, in the sense that they can be described as the product of simple functions that depend on a single input. This first broad survey of two-dimensional input functions can be extended to map the logic of gene regulation in other systems.

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.

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.

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 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.

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.

Optimality and evolutionary tuning of the expression level of a protein.

Different proteins have different expression levels. It is unclear to what extent these expression levels are optimized to their environment. Evolutionary theories suggest that protein expression levels maximize fitness, but the fitness as a function of protein level has seldom been directly measured. To address this, we studied the lac system of Escherichia coli, which allows the cell to use the sugar lactose for growth. We experimentally measured the growth burden due to production and maintenance of the Lac proteins (cost), as well as the growth advantage (benefit) conferred by the Lac proteins when lactose is present. The fitness function, given by the difference between the benefit and the cost, predicts that for each lactose environment there exists an optimal Lac expression level that maximizes growth rate. We then performed serial dilution evolution experiments at different lactose concentrations. In a few hundred generations, cells evolved to reach the predicted optimal expression levels. Thus, protein expression from the lac operon seems to be a solution of a cost-benefit optimization problem, and can be rapidly tuned by evolution to function optimally in new environments.

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.

The incoherent feed-forward loop can generate non-monotonic input functions for genes.

Gene regulation networks contain recurring circuit patterns called network motifs. One of the most common network motif is the incoherent type 1 feed-forward loop (I1-FFL), in which an activator controls both gene and repressor of that gene. This motif was shown to act as a pulse generator and response accelerator of gene expression. Here we consider an additional function of this motif: the I1-FFL can generate a non-monotonic dependence of gene expression on the input signal. Here, we study this experimentally in the galactose system of Escherichia coli, which is regulated by an I1-FFL. The promoter activity of two of the gal operons, galETK and galP, peaks at intermediate levels of the signal cAMP. We find that mutants in which the I1-FFL is disrupted lose this non-monotonic behavior, and instead display monotonic input functions. Theoretical analysis suggests that non-monotonic input functions can be achieved for a wide range of parameters by the I1-FFL. The models also suggest regimes where a monotonic input-function can occur, as observed in the mglBAC operon regulated by the same I1-FFL. The present study thus experimentally demonstrates how upstream circuitry can affect gene input functions and how an I1-FFL functions within its natural context in the cell.

Defined order of evolutionary adaptations: experimental evidence.

Organisms often adapt to new conditions by means of beneficial mutations that become fixed in the population. Often, full adaptation requires several different mutations in the same cell, each of which may affect a different aspect of the behavior. Can one predict order in which these mutations become fixed? To address this, we experimentally studied evolution of Escherichia coli in a growth medium in which the effects of different adaptations can be easily classified as affecting growth rate or the lag-phase duration. We find that adaptations are fixed in a defined and reproducible order: first reduction of lag phase, and then an increase of the exponential growth rate. A population genetics theory explains this order, and suggests growth conditions in which the order of adaptations is reversed. We experimentally find this order reversal under the predicted conditions. This study supports a view in which the evolutionary path to adaptation in a new environment can be captured by theory and experiment.

Microbial growth inhibition by alternating electric fields.

Weak electric currents generated using conductive electrodes have been shown to increase the efficacy of antibiotics against bacterial biofilms, a phenomenon termed "the bioelectric effect." The purposes of the present study were (i) to find out whether insulated electrodes that generate electric fields without "ohmic" electric currents, and thus are not associated with the formation of metal ions and free radicals, can inhibit the growth of planktonic bacteria and (ii) to define the parameters that are most effective against bacterial growth. The results obtained indicate that electric fields generated using insulated electrodes can inhibit the growth of planktonic Staphylococcus aureus and Pseudomonas aeruginosa and that the effect is amplitude and frequency dependent, with a maximum at 10 MHz. The combined effect of the electric field and chloramphenicol was found to be additive. Several possible mechanisms underlying the observed effect, as well as its potential clinical uses, are discussed.

Oscillations and variability in the p53 system.

Understanding the dynamics and variability of protein circuitry requires accurate measurements in living cells as well as theoretical models. To address this, we employed one of the best-studied protein circuits in human cells, the negative feedback loop between the tumor suppressor p53 and the oncogene Mdm2. We measured the dynamics of fluorescently tagged p53 and Mdm2 over several days in individual living cells. We found that isogenic cells in the same environment behaved in highly variable ways following DNA-damaging gamma irradiation: some cells showed undamped oscillations for at least 3 days (more than 10 peaks). The amplitude of the oscillations was much more variable than the period. Sister cells continued to oscillate in a correlated way after cell division, but lost correlation after about 11 h on average. Other cells showed low-frequency fluctuations that did not resemble oscillations. We also analyzed different families of mathematical models of the system, including a novel checkpoint mechanism. The models point to the possible source of the variability in the oscillations: low-frequency noise in protein production rates, rather than noise in other parameters such as degradation rates. This study provides a view of the extensive variability of the behavior of a protein circuit in living human cells, both from cell to cell and in the same cell over time.

Cost-benefit theory and optimal design of gene regulation functions.

Cells respond to the environment by regulating the expression of genes according to environmental signals. The relation between the input signal level and the expression of the gene is called the gene regulation function. It is of interest to understand the shape of a gene regulation function in terms of the environment in which it has evolved and the basic constraints of biological systems. Here we address this by presenting a cost-benefit theory for gene regulation functions that takes into account temporally varying inputs in the environment and stochastic noise in the biological components. We apply this theory to the well-studied lac operon of E. coli. The present theory explains the shape of this regulation function in terms of temporal variation of the input signals, and of minimizing the deleterious effect of cell-cell variability in regulatory protein levels. We also apply the theory to understand the evolutionary tradeoffs in setting the number of regulatory proteins and for selection of feed-forward loops in genetic circuits. The present cost-benefit theory can be used to understand the shape of other gene regulatory functions in terms of environment and noise constraints.

Disruption of cancer cell replication by alternating electric fields.

Low-intensity, intermediate-frequency (100-300 kHz), alternating electric fields, delivered by means of insulated electrodes, were found to have a profound inhibitory effect on the growth rate of a variety of human and rodent tumor cell lines (Patricia C, U-118, U-87, H-1299, MDA231, PC3, B16F1, F-98, C-6, RG2, and CT-26) and malignant tumors in animals. This effect, shown to be nonthermal, selectively affects dividing cells while quiescent cells are left intact. These fields act in two modes: arrest of cell proliferation and destruction of cells while undergoing division. Both effects are demonstrated when such fields are applied for 24 h to cells undergoing mitosis that is oriented roughly along the field direction. The first mode of action is manifested by interference with the proper formation of the mitotic spindle, whereas the second results in rapid disintegration of the dividing cells. Both effects, which are frequency dependent, are consistent with the computed directional forces exerted by these specific fields on charges and dipoles within the dividing cells. In vivo treatment of tumors in C57BL/6 and BALB/c mice (B16F1 and CT-26 syngeneic tumor models, respectively), resulted in significant slowing of tumor growth and extensive destruction of tumor cells within 3-6 days. These findings demonstrate the potential applicability of the described electric fields as a novel therapeutic modality for malignant tumors.