A novel Bayesian generative approach for estimating tumor dynamics from published studies.

Tumor growth inhibition (TGI) modeling attempts to describe the time course changes in tumor size for patients undergoing cancer therapy. TGI models present several advantages over traditional exposure-response models that are based explicitly on clinical end points and have become a popular tool in the pharmacometrics community. Unfortunately, the data required to fit TGI models, namely longitudinal tumor measurements, are sparse or often not available in literature or publicly accessible databases. On the contrary, common end points such as progression-free survival (PFS) and objective response rate (ORR) are directly derived from longitudinal tumor measurements and are routinely published. To this end, a Bayesian generative model relating underlying tumor dynamics to summary PFS and ORR data is introduced to learn TGI model parameters using only published summary data. The parameterized model can describe the tumor dynamics, quantify treatment effect, and account for differences in the study population. The utility of this model is shown by applying it to several published studies, and learned parameters are combined to simulate an in silico trial of a novel combination therapy in a novel setting.

Noise suppression in stochastic genetic circuits using PID controllers.

Inside individual cells, protein population counts are subject to molecular noise due to low copy numbers and the inherent probabilistic nature of biochemical processes. We investigate the effectiveness of proportional, integral and derivative (PID) based feedback controllers to suppress protein count fluctuations originating from two noise sources: bursty expression of the protein, and external disturbance in protein synthesis. Designs of biochemical reactions that function as PID controllers are discussed, with particular focus on individual controllers separately, and the corresponding closed-loop system is analyzed for stochastic controller realizations. Our results show that proportional controllers are effective in buffering protein copy number fluctuations from both noise sources, but this noise suppression comes at the cost of reduced static sensitivity of the output to the input signal. In contrast, integral feedback has no effect on the protein noise level from stochastic expression, but significantly minimizes the impact of external disturbances, particularly when the disturbance comes at low frequencies. Counter-intuitively, integral feedback is found to amplify external disturbances at intermediate frequencies. Next, we discuss the design of a coupled feedforward-feedback biochemical circuit that approximately functions as a derivate controller. Analysis using both analytical methods and Monte Carlo simulations reveals that this derivative controller effectively buffers output fluctuations from bursty stochastic expression, while maintaining the static input-output sensitivity of the open-loop system. In summary, this study provides a systematic stochastic analysis of biochemical controllers, and paves the way for their synthetic design and implementation to minimize deleterious fluctuations in gene product levels.

Controlling organism size by regulating constituent cell numbers.

How living cells employ counting mechanisms to regulate their numbers or density is a long-standing problem in developmental biology that ties directly with organism or tissue size. Diverse cells types have been shown to regulate their numbers via secretion of factors in the extracellular space. These factors act as a proxy for the number of cells and function to reduce cellular proliferation rates creating a negative feedback. It is desirable that the production rate of such factors be kept as low as possible to minimize energy costs and detection by predators. Here we formulate a stochastic model of cell proliferation with feedback control via a secreted extracellular factor. Our results show that while low levels of feedback minimizes random fluctuations in cell numbers around a given set point, high levels of feedback amplify Poisson fluctuations in secreted-factor copy numbers. This trade-off results in an optimal feedback strength, and sets a fundamental limit to noise suppression in cell numbers with short-lived factors providing more efficient noise buffering. We further expand the model to consider external disturbances in key physiological parameters, such as, proliferation and factor synthesis rates. Intriguingly, while negative feedback effectively mitigates disturbances in the proliferation rate, it amplifies disturbances in the synthesis rate. In summary, these results provide unique insights into the functioning of feedback-based counting mechanisms, and apply to organisms ranging from unicellular prokaryotes and eukaryotes to human cells.

Analysis of Noise Mechanisms in Cell-Size Control.

At the single-cell level, noise arises from multiple sources, such as inherent stochasticity of biomolecular processes, random partitioning of resources at division, and fluctuations in cellular growth rates. How these diverse noise mechanisms combine to drive variations in cell size within an isoclonal population is not well understood. Here, we investigate the contributions of different noise sources in well-known paradigms of cell-size control, such as adder (division occurs after adding a fixed size from birth), sizer (division occurs after reaching a size threshold), and timer (division occurs after a fixed time from birth). Analysis reveals that variation in cell size is most sensitive to errors in partitioning of volume among daughter cells, and not surprisingly, this process is well regulated among microbes. Moreover, depending on the dominant noise mechanism, different size-control strategies (or a combination of them) provide efficient buffering of size variations. We further explore mixer models of size control, where a timer phase precedes/follows an adder, as has been proposed in Caulobacter crescentus. Although mixing a timer and an adder can sometimes attenuate size variations, it invariably leads to higher-order moments growing unboundedly over time. This results in a power-law distribution for the cell size, with an exponent that depends inversely on the noise in the timer phase. Consistent with theory, we find evidence of power-law statistics in the tail of C. crescentus cell-size distribution, although there is a discrepancy between the observed power-law exponent and that predicted from the noise parameters. The discrepancy, however, is removed after data reveal that the size added by individual newborns in the adder phase itself exhibits power-law statistics. Taken together, this study provides key insights into the role of noise mechanisms in size homeostasis, and suggests an inextricable link between timer-based models of size control and heavy-tailed cell-size distributions.