Molecular switch architecture determines response properties of signaling pathways.

Many intracellular signaling pathways are composed of molecular switches, proteins that transition between two states-on and off Typically, signaling is initiated when an external stimulus activates its cognate receptor that, in turn, causes downstream switches to transition from off to on using one of the following mechanisms: activation, in which the transition rate from the off state to the on state increases; derepression, in which the transition rate from the on state to the off state decreases; and concerted, in which activation and derepression operate simultaneously. We use mathematical modeling to compare these signaling mechanisms in terms of their dose-response curves, response times, and abilities to process upstream fluctuations. Our analysis elucidates several operating principles for molecular switches. First, activation increases the sensitivity of the pathway, whereas derepression decreases sensitivity. Second, activation generates response times that decrease with signal strength, whereas derepression causes response times to increase with signal strength. These opposing features allow the concerted mechanism to not only show dose-response alignment, but also to decouple the response time from stimulus strength. However, these potentially beneficial properties come at the expense of increased susceptibility to upstream fluctuations. We demonstrate that these operating principles also hold when the models are extended to include additional features, such as receptor removal, kinetic proofreading, and cascades of switches. In total, we show how the architecture of molecular switches govern their response properties. We also discuss the biological implications of our findings.

Towards resolution of a paradox in plant G-protein signaling.

G-proteins are molecular on-off switches that are involved in transmitting a variety of extracellular signals to their intracellular targets. In animal and yeast systems, the switch property is encoded through nucleotides: a GDP-bound state is the "off-state" and the GTP-bound state is the "on-state". The G-protein cycle consists of the switch turning on through nucleotide exchange facilitated by a G-protein coupled receptor and the switch turning off through hydrolysis of GTP back to GDP, facilitated by a protein designated REGULATOR OF G SIGNALING 1 (RGS). In plants, G-protein signaling dramatically differs from that in animals and yeast. Despite stringent conservation of the nucleotide binding and catalytic structures over the 1.6 billion years that separate the evolution of plants and animals, genetic and biochemical data indicate that nucleotide exchange is less critical for this switch to operate in plants. Also, the loss of the single RGS protein in Arabidopsis (Arabidopsis thaliana) confers unexpectedly weaker phenotypes consistent with a diminished role for the G cycle, at least under static conditions. However, under dynamic conditions, genetic ablation of RGS in Arabidopsis results in a strong phenotype. We explore explanations to this conundrum by formulating a mathematical model that takes into account the accruing evidence for the indispensable role of phosphorylation in G-protein signaling in plants and that the G-protein cycle is needed to process dynamic signal inputs. We speculate that the plant G-protein cycle and its attendant components evolved to process dynamic signals through signaling modulation rather than through on-off, switch-like regulation of signaling. This so-called change detection may impart greater fitness for plants due to their sessility in a dynamic light, temperature, and pest environment.

Towards a platform quantitative systems pharmacology (QSP) model for preclinical to clinical translation of antibody drug conjugates (ADCs).

A next generation multiscale quantitative systems pharmacology (QSP) model for antibody drug conjugates (ADCs) is presented, for preclinical to clinical translation of ADC efficacy. Two HER2 ADCs (trastuzumab-DM1 and trastuzumab-DXd) were used for model development, calibration, and validation. The model integrates drug specific experimental data including in vitro cellular disposition data, pharmacokinetic (PK) and tumor growth inhibition (TGI) data for T-DM1 and T-DXd, as well as system specific data such as properties of HER2, tumor growth rates, and volumes. The model incorporates mechanistic detail at the intracellular level, to account for different mechanisms of ADC processing and payload release. It describes the disposition of the ADC, antibody, and payload inside and outside of the tumor, including binding to off-tumor, on-target sinks. The resulting multiscale PK model predicts plasma and tumor concentrations of ADC and payload. Tumor payload concentrations predicted by the model were linked to a TGI model and used to describe responses following ADC administration to xenograft mice. The model was translated to humans and virtual clinical trial simulations were performed that successfully predicted progression free survival response for T-DM1 and T-DXd for the treatment of HER2+ metastatic breast cancer, including differential efficacy based upon HER2 expression status. In conclusion, the presented model is a step toward a platform QSP model and strategy for ADCs, integrating multiple types of data and knowledge to predict ADC efficacy. The model has potential application to facilitate ADC design, lead candidate selection, and clinical dosing schedule optimization.

First-passage time approach to controlling noise in the timing of intracellular events.

In the noisy cellular environment, gene products are subject to inherent random fluctuations in copy numbers over time. How cells ensure precision in the timing of key intracellular events despite such stochasticity is an intriguing fundamental problem. We formulate event timing as a first-passage time problem, where an event is triggered when the level of a protein crosses a critical threshold for the first time. Analytical calculations are performed for the first-passage time distribution in stochastic models of gene expression. Derivation of these formulas motivates an interesting question: Is there an optimal feedback strategy to regulate the synthesis of a protein to ensure that an event will occur at a precise time, while minimizing deviations or noise about the mean? Counterintuitively, results show that for a stable long-lived protein, the optimal strategy is to express the protein at a constant rate without any feedback regulation, and any form of feedback (positive, negative, or any combination of them) will always amplify noise in event timing. In contrast, a positive feedback mechanism provides the highest precision in timing for an unstable protein. These theoretical results explain recent experimental observations of single-cell lysis times in bacteriophage [Formula: see text] Here, lysis of an infected bacterial cell is orchestrated by the expression and accumulation of a stable [Formula: see text] protein up to a threshold, and precision in timing is achieved via feedforward rather than feedback control. Our results have broad implications for diverse cellular processes that rely on precise temporal triggering of events.

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.

Exact lower and upper bounds on stationary moments in stochastic biochemical systems.

In the stochastic description of biochemical reaction systems, the time evolution of statistical moments for species population counts is described by a linear dynamical system. However, except for some ideal cases (such as zero- and first-order reaction kinetics), the moment dynamics is underdetermined as lower-order moments depend upon higher-order moments. Here, we propose a novel method to find exact lower and upper bounds on stationary moments for a given arbitrary system of biochemical reactions. The method exploits the fact that statistical moments of any positive-valued random variable must satisfy some constraints that are compactly represented through the positive semidefiniteness of moment matrices. Our analysis shows that solving moment equations at steady state in conjunction with constraints on moment matrices provides exact lower and upper bounds on the moments. These results are illustrated by three different examples-the commonly used logistic growth model, stochastic gene expression with auto-regulation and an activator-repressor gene network motif. Interestingly, in all cases the accuracy of the bounds is shown to improve as moment equations are expanded to include higher-order moments. Our results provide avenues for development of approximation methods that provide explicit bounds on moments for nonlinear stochastic systems that are otherwise analytically intractable.

Reported differences in the flg22 response of the null mutation of AtRGS1 correlates with fixed genetic variation in the background of Col-0 isolates.

A role for the heterotrimeric G protein complex in the induction of a transient burst of reactive oxygen species (ROS) by the Microbial-Associated Molecular Pattern, flg22, a 22-amino acid peptide derived from bacterial flagella, is well established. However, the evidence for a negative or positive role for one component of the Arabidopsis G protein complex, namely, Regulator of G Signaling 1 (AtRGS1) leads to opposing conclusions. We show that the reason for this difference is due to the isolate of Col-0 ecotype used as the wildtype control in flg22-induced ROS and our data further support the idea that AtRGS1 is a negative regulator of the flg22-induced ROS response. Whole-genome genotyping led to the identification and validation of polymorphism in five genes between two Col-0 isolates that are candidates for the different ROS response relative to the rgs1 null mutant.

Cell size control and gene expression homeostasis in single-cells.

Growth of a cell and its subsequent division into daughters is a fundamental aspect of all cellular living systems. During these processes, how do individual cells correct size aberrations so that they do not grow abnormally large or small? How do cells ensure that the concentration of essential gene products are maintained at desired levels, in spite of dynamic/stochastic changes in cell size during growth and division? Both these questions have fascinated researchers for over a century. We review how advances in singe-cell technologies and measurements are providing unique insights into these questions across organisms from prokaryotes to human cells. More specifically, diverse strategies based on timing of cell-cycle events, regulating growth, and number of daughters are employed to maintain cell size homeostasis. Interestingly, size homeostasis often results in size optimality - proliferation of individual cells in a population is maximized at an optimal cell size. We further discuss how size-dependent expression or gene-replication timing can buffer concentration of a gene product from cell-to-cell size variations within a population. Finally, we speculate on an intriguing hypothesis that specific size control strategies may have evolved as a consequence of gene-product concentration homeostasis.

A mechanistic stochastic framework for regulating bacterial cell division.

How exponentially growing cells maintain size homeostasis is an important fundamental problem. Recent single-cell studies in prokaryotes have uncovered the adder principle, where cells add a fixed size (volume) from birth to division, irrespective of their size at birth. To mechanistically explain the adder principle, we consider a timekeeper protein that begins to get stochastically expressed after cell birth at a rate proportional to the volume. Cell-division time is formulated as the first-passage time for protein copy numbers to hit a fixed threshold. Consistent with data, the model predicts that the noise in division timing increases with size at birth. Intriguingly, our results show that the distribution of the volume added between successive cell-division events is independent of the newborn cell size. This was dramatically seen in experimental studies, where histograms of the added volume corresponding to different newborn sizes collapsed on top of each other. The model provides further insights consistent with experimental observations: the distribution of the added volume when scaled by its mean becomes invariant of the growth rate. In summary, our simple yet elegant model explains key experimental findings and suggests a mechanism for regulating both the mean and fluctuations in cell-division timing for controlling size.

Synthesis of robust tunable oscillators using mitogen activated protein kinase cascades.

Mitogen activated protein kinase (MAPK) cascade is evolutionally preserved in all eukaryotic cells, and regulates various cellular activities such as gene expression, mitosis, differentiation, and apoptosis. Recently, Bashor et al. have shown that Ste5 scaffold protein can be used to reshape the MAPK cascade through engineered feedback loops, and have used heuristic tuning mechanisms to synthesize the feedback. A problem of interest is to determine whether information regarding the underlying biochemical reactions can be used to synthesize robust feedback that will ensure that the resultant circuit has the desired properties. In this paper, we consider the problem of engineering feedback in MAPK cascade to synthesize an oscillator of the desired frequency. Our approach builds on the MAPK cascade model derived by Chikarmane et al. who have exploited the existence of a Hopf bifurcation point in the Markevich model of the MAPK cascade to synthesize the exciting kinase as a function of the doubly phosphorylated protein. We show how the [Formula: see text]-control theory can be used for a robust synthesis of the oscillator and present the simulation results.