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.

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.

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.

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.

Alternating electric fields arrest cell proliferation in animal tumor models and human brain tumors.

We have recently shown that low intensity, intermediate frequency, electric fields inhibit by an anti-microtubule mechanism of action, cancerous cell growth in vitro. Using implanted electrodes, these fields were also shown to inhibit the growth of dermal tumors in mice. The present study extends these findings to additional cell lines [human breast carcinoma; MDA-MB-231, and human non-small-cell lung carcinoma (H1299)] and to animal tumor models (intradermal B16F1 melanoma and intracranial F-98 glioma) using external insulated electrodes. These findings led to the initiation of a pilot clinical trial of the effects of TTFields in 10 patients with recurrent glioblastoma (GBM). Median time to disease progression in these patients was 26.1 weeks and median overall survival was 62.2 weeks. These time to disease progression and OS values are more than double the reported medians of historical control patients. No device-related serious adverse events were seen after >70 months of cumulative treatment in all of the patients. The only device-related side effect seen was a mild to moderate contact dermatitis beneath the field delivering electrodes. We conclude that TTFields are a safe and effective new treatment modality which effectively slows down tumor growth in vitro, in vivo and, as demonstrated here, in human cancer patients.

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.

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.