Noise propagation in two-step series MAPK cascade

Retroactivity induced operating regime transition in an enzymatic futile cycle

Activated phosphorylation-dephosphorylation biochemical reaction cycles are a class of enzymatic futile cycles. A futile cycle such as a single MAPK cascade governed by two underlying enzymatic reactions permits Hyperbolic (H), Signal transducing (ST), Threshold-hyperbolic (TH) and Ultrasensitive (U) operating regimes that characterize input-output behaviour. Retroactive signalling caused by load due to sequestration of phosphorylated or unphosphorylated form of the substrate in a single enzymatic cascade without explicit feedback can introduce two-way communication, a feature not possible otherwise. We systematically characterize the operating regimes of a futile cycle subject to retroactivity in either of the substrate forms. We demonstrate that increasing retroactivity strength, which quantifies the downstream load, can trigger five possible regime transitions. Retroactivity strength is a reflection of the fraction of the substrate sequestered by its downstream target. Remarkably, the minimum required retroactivity strength to evidence any sequestration triggered regime transition demands 23% of the substrate bound to its downstream target. This minimum retroactivity strength corresponds to the transition of the dose-response curve from ST to H regime. We show that modulation of the saturation and unsaturation levels of the enzymatic reactions by retroactivity is the fundamental mechanism governing operating regime transition.

Noisy signal propagation and amplification in phenotypic transition cascade of colonic cells

Like genes and proteins, cells can use biochemical networks to sense and process information. The differentiation of the cell state in colonic crypts forms a typical unidirectional phenotypic transitional cascade, in which stem cells differentiate into the transit-amplifying cells (TACs), and TACs continue to differentiate into fully differentiated cells. In order to quantitatively describe the relationship between the noise of each compartment and the amplification of signals, the gain factor is introduced, and the gain-fluctuation relation is obtained by using the linear noise approximation of the master equation. Through the simulation of these theoretical formulas, the characters of noise propagation and amplification are studied. It is found that the transmitted noise is an important part of the total noise in each downstream cell. Therefore, a small number of downstream cells can only cause its small inherent noise, but the total noise may be very large due to the transmitted noise. The influence of the transmitted noise may be the indirect cause of colon cancer. In addition, the total noise of the downstream cells always has a minimum value. As long as a reasonable value of the gain factor is selected, the number of cells in colonic crypts will be controlled within the normal range. This may be a good method to intervene the uncontrollable growth of tumor cells and effectively control the deterioration of colon cancer.

Investigation of chemical noise in multisite phosphorylation chain using linear noise approximation

Quantitative and qualitative nature of chemical noise propagation in biochemical reaction networks depend crucially on the topology of the networks. Multisite reversible phosphorylation-dephosphorylation of target proteins is one such recurrently found topology that regulates host of key functions in living cells. Here we analytically calculated the stochasticity in multistep reversible chemical reactions by determining variance of phosphorylated species at the steady state using linear noise approximation to investigate the effect of mass action and Michaelis-Menten kinetics on the noise of phosphorylated species. We probed the dependence of noise on the number of phosphorylation sites and the equilibrium constants of the reaction equilibria to investigate the chemical noise propagation in the multisite phosphorylation chain.

Operating regimes in a single enzymatic cascade at ensemble-level

Single enzymatic cascade, ubiquitously found in cellular signaling networks, is a phosphorylation-dephosphorylation reaction cycle causing a transition between inactive and active states of a protein catalysed by kinase and phosphatase, respectively. Steady-state information processing ability of such a cycle (e.g., MAPK cascade) has been classified into four qualitatively different operating regimes, viz., hyperbolic (H), signal-transducing (ST), threshold-hyperbolic (TH) and ultrasensitive (U). These four regimes represent qualitatively different dose-response curves, that is, relationship between concentrations of input kinase (e.g., pMEK) and response activated protein (e.g., pERK). Regimes were identified using a deterministic model accounting for population-averaged behavior only. Operating regimes can be strongly influenced by the inherently present cell-to-cell variability in an ensemble of cells which is captured in the form of pMEK and pERK distributions using reporter-based single-cell experimentation. In this study, we show that such experimentally acquired snapshot pMEK and pERK distribution data of a single MAPK cascade can be directly used to infer the underlying operating regime even in the absence of a dose-response curve. This deduction is possible primarily due to the presence of a monotonic relationship between experimental observables R_IQR, ratio of the inter-quartile range of the pERK and pMEK distribution pairs and R_M, ratio of the medians of the distribution pair. We demonstrate this relationship by systematic analysis of a quasi-steady state approximated model superimposed with an input gamma distribution constrained by the stimulus strength specific pMEK distribution measured on Jurkat-T cells stimulated with PMA. As a first, we show that introduction of cell-to-cell variability only in the upstream kinase achieved by superimposition of an appropriate input pMEK distribution on the dose-response curve can predict bimodal response pERK distribution in ST regime. Implementation of the proposed method on the input-response distribution pair obtained in stimulated Jurkat-T cells revealed that while low-dosage PMA stimulation preserves the H regime observed in resting cells, high-dosage causes H to ST regime transition.

The role of stochastic sequestration dynamics for intrinsic noise filtering in signaling network motifs

The relation between design principles of signaling network motifs and their robustness against intrinsic noise still remains illusive. In this work we investigate the role of cascading for coping with intrinsic noise due to stochasticity in molecular reactions. We use stochastic approaches to quantify fluctuations in the terminal kinase of phosphorylation-dephosphorylation cascade motifs and demonstrate that cascading highly affects these fluctuations. We show that this purely stochastic effect can be explained by time-varying sequestration of upstream kinase molecules. In particular, we discuss conditions on time scales and parameter regimes which lead to a reduction of output fluctuations. Our results are put into biological context by adapting rate parameters of our modeling approach to biologically feasible ranges for general binding-unbinding and phosphorylation-dephosphorylation mechanisms. Overall, this study reveals a novel role of stochastic sequestration for dynamic noise filtering in signaling cascade motifs.

Increased gene expression noise in human cancers is correlated with low p53 and immune activities as well as late stage cancer

Gene expression in metazoans is delicately organized. As genetic information transmits from DNA to RNA and protein, expression noise is inevitably generated. Recent studies begin to unveil the mechanisms of gene expression noise control, but the changes of gene expression precision in pathologic conditions like cancers are unknown. Here we analyzed the transcriptomic data of human breast, liver, lung and colon cancers, and found that the expression noise of more than 74.9% genes was increased in cancer tissues as compared to adjacent normal tissues. This suggested that gene expression precision controlling collapsed during cancer development. A set of 269 genes with noise increased more than 2-fold were identified across different cancer types. These genes were involved in cell adhesion, catalytic and metabolic functions, implying the vulnerability of deregulation of these processes in cancers. We also observed a tendency of increased expression noise in patients with low p53 and immune activity in breast, liver and lung caners but not in colon cancers, which indicated the contributions of p53 signaling and host immune surveillance to gene expression noise in cancers. Moreover, more than 53.7% genes had increased noise in patients with late stage than early stage cancers, suggesting that gene expression precision was associated with cancer outcome. Together, these results provided genomic scale explorations of gene expression noise control in human cancers.

Ranking of Reactions Based on Sensitivity of Protein Noise Depends on the Choice of Noise Measure

Gene expression is a stochastic process. Identification of the step maximally affecting noise in the protein level is an important aspect of investigation of gene product distribution. There are numerous experimental and theoretical studies that seek to identify this important step. However, these studies have used two different measures of noise, viz. coefficient of variation and Fano factor, and have compared different processes leading to contradictory observations regarding the important step. In this study, we performed systematic global and local sensitivity analysis on two models of gene expression to investigate relative contribution of reaction rate parameters to steady state noise in the protein level using both the measures of noise. We analytically and computationally showed that the ranking of parameters based on the sensitivity of the noise to variation in a given parameter is a strong function of the choice of the noise measure. If the Fano factor is used as the noise measure, translation is the important step whereas for coefficient of variation, transcription is the important step. We derived an analytical expression for local sensitivity and used it to explain the distinct contributions of each reaction parameter to the two measures of noise. We extended the analysis to a generic linear catalysis reaction system and observed that the reaction network topology was an important factor influencing the local sensitivity of the two measures of noise. Our study suggested that, for the analysis of contributions of reactions to the noise, consideration of both the measures of noise is important.