A classic problem in population and evolutionary biology is to understand how a population optimizes its fitness in fluctuating environments. A population might enhance its fitness by allowing individual cells to stochastically transition among multiple phenotypes, thus ensuring that some cells are always prepared for an unforeseen environmental fluctuation. Here we experimentally explore how switching affects population growth by using the galactose utilization network of Saccharomyces cerevisiae. We engineered a strain that randomly transitions between two phenotypes as a result of stochastic gene expression. Each phenotype was designed to confer a growth advantage over the other phenotype in a certain environment. When we compared the growth of two populations with different switching rates, we found that fast-switching populations outgrow slow switchers when the environment fluctuates rapidly, whereas slow-switching phenotypes outgrow fast switchers when the environment changes rarely. These results suggest that cells may tune inter-phenotype switching rates to the frequency of environmental changes.

The propagation of information through signaling cascades spans a wide range of time-scales, including the rapid ligand-receptor interaction and the much slower response of downstream gene expression. To determine which dynamic range dominates a response, we used periodic stimuli to measure the frequency dependence of signal transduction in the osmo-adaptation pathway of Saccharomyces cerevisiae. We applied system identification methods to infer a concise predictive model. We found that the dynamics of the osmo-adaptation response are dominated by a fast-acting negative feedback through the kinase Hog1 that does not require protein synthesis. After large osmotic shocks, an additional, much slower, negative feedback through gene expression allows cells to respond faster to future stimuli.The mechanisms cells use to sense and respond to environmental changes include complicated systems of biochemical reactions that occur with rates spanning a wide dynamic range. Reactions can be fast, such as association and dissociation between a ligand and its receptor (< 1 s), or slow, such as protein synthesis (> 10 3 s). Though a system may comprise hundreds of reactions, often only a few of them dictate the system dynamics. Unfortunately, identification of the dominant processes is often difficult, and many models instead incorporate knowledge of all reactions in the system. Although occasionally successful (1-4), this exhaustive approach often suffers from missing information, such as unknown interactions or parameters.Here we used systems engineering tools to study how oscillatory signals propagate through a signal transduction cascade, allowing us to identify and concisely model the interactions that dominate system dynamics. The cornerstone of this approach is to measure the cascade output in response to input signals oscillating at a range of frequencies (5,6). By comparing the frequency response of the wild-type network to that of mutants, the molecular underpinnings of network dynamics can be determined. Studies of neural and other physiological systems have used systems theory (6), while control-theory has also been applied to cellular networks (7-14).We focused on the high osmolarity glycerol (HOG) Mitogen-activated protein kinase (MAPK) cascade in the budding yeast Saccharomyces cerevisiae. This cascade forms a core module of the hyperosmotic-shock-response system and is particularly well suited to frequency-response * To whom correspondence should be addressed: avano@mit.edu. NIH Public Access Author ManuscriptScience. Author manuscript; available in PMC 2010 August 5. analysis for several reasons. First, both the input (extracellular osmolyte concentration) and output (activity of the MAPK Hog1) of the network are easily measured and manipulated. Second, the molecular components of the network have been well studied, facilitating connection of dynamic models with molecular events. Finally, the system contains multiple negative feedback loops that operate on different time-scales (4,15,16). It is still unc...

SUMMARY Negative feedback can serve many different cellular functions, including noise reduction in transcriptional networks and the creation of circadian oscillations. However, only one special type of negative feedback (“integral feedback”) ensures perfect adaptation, where steady-state output is independent of steady-state input. Here we quantitatively measure single-cell dynamics in the Saccharomyces cerevisiae hyperosmotic shock network, which regulates membrane turgor pressure. Importantly, we find that the nuclear enrichment of the MAP kinase Hog1 perfectly adapts to changes in external osmolarity, a feature robust to signaling fidelity and operating with very low noise. By monitoring multiple system quantities (e.g., cell volume, Hog1, glycerol) and using varied input waveforms (e.g., steps and ramps), we assess the network location of the mechanism responsible for perfect adaptation in a minimally invasive manner. We conclude that the system contains only one effective integrating mechanism, which requires Hog1 kinase activity and regulates glycerol synthesis but not leakage.

In 2011, AstraZeneca embarked on a major revision of its research and development (R&D) strategy with the aim of improving R&D productivity, which was below industry averages in 2005-2010. A cornerstone of the revised strategy was to focus decision-making on five technical determinants (the right target, right tissue, right safety, right patient and right commercial potential). In this article, we describe the progress made using this '5R framework' in the hope that our experience could be useful to other companies tackling R&D productivity issues. We focus on the evolution of our approach to target validation, hit and lead optimization, pharmacokinetic/pharmacodynamic modelling and drug safety testing, which have helped improve the quality of candidate drug nomination, as well as the development of the right culture, where 'truth seeking' is encouraged by more rigorous and quantitative decision-making. We also discuss where the approach has failed and the lessons learned. Overall, the continued evolution and application of the 5R framework are beginning to have an impact, with success rates from candidate drug nomination to phase III completion improving from 4% in 2005-2010 to 19% in 2012-2016.

Fluctuations in protein numbers (noise) due to inherent stochastic effects in single cells can have large effects on the dynamic behavior of gene regulatory networks. Although deterministic models can predict the average network behavior, they fail to incorporate the stochasticity characteristic of gene expression, thereby limiting their relevance when single cell behaviors deviate from the population average. Recently, stochastic models have been used to predict distributions of steady-state protein levels within a population but not to predict the dynamic, presteadystate distributions. In the present work, we experimentally examine a system whose dynamics are heavily influenced by stochastic effects. We measure population distributions of protein numbers as a function of time in the Escherichia coli lactose uptake network (lac operon). We then introduce a dynamic stochastic model and show that prediction of dynamic distributions requires only a few noise parameters in addition to the rates that characterize a deterministic model. Whereas the deterministic model cannot fully capture the observed behavior, our stochastic model correctly predicts the experimental dynamics without any fit parameters. Our results provide a proof of principle for the possibility of faithfully predicting dynamic population distributions from deterministic models supplemented by a stochastic component that captures the major noise sources.gene networks ͉ systems biology O ne of the central goals of systems biology is to predict the dynamic behavior of a cell's genetic and metabolic networks. These predictions traditionally stem from models in which discrete molecular events, such as transcription and translation, are represented by continuous and deterministic differential equations. Such equations are valid when behavior of individual cells is very similar to the average behavior of the population. However, in many cases, the inherently stochastic nature of biological systems leads to significant cell-to-cell variability (1-3), and previous studies indicate that individual cells often behave very differently from the population average in response to external stimuli. For example, studies of bacterial persistence indicate that the population survival rate can be fundamentally different from the average cell's survival rate in response to environmental stress (4, 5). The impact of noise-induced population heterogeneity is also relevant when studying cellular memory, where fluctuations in protein numbers can cause the stability of epigenetic memory to degrade by effectively causing cells to forget their original states (6, 7). In these cases, stochastic modeling techniques must be used to describe the large cell-tocell variability. Although deterministic models can describe dynamic network behavior and analytical stochastic models can faithfully predict steady-state population distributions (8), little work has been done to connect dynamic cellular behavior with noise models. It is important that stochastic models of biological systems...

Human tumor xenograft studies are the primary means to evaluate the biological activity of anticancer agents in late-stage preclinical drug discovery. The variability in the growth rate of human tumors established in mice and the small sample sizes make rigorous statistical analysis critical. The most commonly used summary of antitumor activity for these studies is the T/C ratio. However, alternative methods based on growth rate modeling can be used. Here, we describe a summary metric called the rate-based T/C, derived by fitting each animal’s tumor growth to a simple exponential model. The rate-based T/C uses all of the data, in contrast with the traditional T/C, which only uses a single measurement. We compare the rate-based T/C with the traditional T/C and assess their performance through a bootstrap analysis of 219 tumor xenograft studies. We find that the rate-based T/C requires fewer animals to achieve the same power as the traditional T/C. We also compare 14-day studies with 21-day studies and find that 14-day studies are more cost efficient. Finally, we perform a power analysis to determine an appropriate sample size.

The partitioning and subsequent inheritance of cellular factors like proteins and RNAs is a ubiquitous feature of cell division. However, direct quantitative measures of how such nongenetic inheritance affects subsequent changes in gene expression have been lacking. We tracked families of the yeast Saccharomyces cerevisiae as they switch between two semi-stable epigenetic states. We found that long after two cells have divided, they continued to switch in a synchronized manner, whereas individual cells have exponentially distributed switching times. By comparing these results to a Poisson process, we show that the time evolution of an epigenetic state depends initially on inherited factors, with stochastic processes requiring several generations to decorrelate closely related cells. Finally, a simple stochastic model demonstrates that a single fluctuating regulatory protein that is synthesized in large bursts can explain the bulk of our results.

It is generally assumed that single cells in an isogenic population, when exposed to identical environments, exhibit the same behavior. However, it is becoming increasingly clear that, even in a genetically identical population, cellular behavior can vary significantly among cells. Here we explore this variability in the gradientsensing response of Dictyostelium cells when exposed to repeated spatiotemporal pulses of chemoattractant. Our experiments show the response of a single cell to be highly reproducible from pulse to pulse. In contrast, a large variability in the response direction and magnitude is observed from cell to cell, even when different cells are exposed to the same pulse. First, these results indicate that the gradient-sensing network has inherent asymmetries that can significantly impact the ability of cells to faithfully sense the direction of extracellular signals (cellular asymmetry). Second, we find that the magnitude of this asymmetry varies greatly among cells. Some cells are able to accurately follow the direction of an extracellular stimulus, whereas, in other cells, the intracellular asymmetry dominates, resulting in a polarization axis that is independent of the direction of the extracellular cue (cellular individuality). We integrate these experimental findings into a model that treats the effective signal a cell detects as the product of the extracellular signal and the asymmetric intracellular signal. With this model we successfully predict the population response. This cellular individuality and asymmetry might fundamentally limit the fidelity of signal detection; in contrast, however, it might be beneficial by diversifying phenotypes in isogenic populations.T he low number of molecules involved in biological systems can lead to large stochastic effects and population heterogeneity even within a genetically identical population (1-3). For example, the swimming behavior of Escherichia coli cells varies greatly from cell to cell (4), and recent studies start to link this variability in swimming behavior to concentration fluctuations in regulatory proteins (5-7). It is an open question whether a similar variability can be observed in eukaryotic chemotactic cells, such as the slime mold Dictyostelium discoideum, which has the exquisite ability to sense and respond to shallow gradients of chemoattractants. In these spatially sensitive systems, signaling errors might be introduced in two different ways. First, the concentrations of intracellular signaling components might vary from cell to cell; second, spatial inhomogeneities or asymmetries in the cellular distributions of molecules might influence the ability of cells to sense slight spatial differences in the extracellular environment.To explore this question, we employ a quantitative approach to systematically study directional sensing in single Dictyostelium cells. Recent experiments have demonstrated that an extracellular signal induces spatial localization of several signaling proteins along the plasma membrane (8-12). The localiz...