Extending the linear-noise approximation to biochemical systems influenced by intrinsic noise and slow lognormally distributed extrinsic noise

The contribution and mechanism of hypoxia/USP19/Beclin-1 feed-forward loop in cervical cancer

Cervical cancer ranks fourth in female mortality. Since the mechanisms for pathogenesis of cervical cancer are still poorly understood, the effective treatment options are lacking. Beclin-1 exhibits an inhibitory role in cervical cancer via suppressing the proliferation, invasion, and migration of cervical cancer cells. It is reported that USP19 removes the K11-linked ubiquitination of Beclin-1 to protect Beclin-1 from proteasomal degradation. Interestingly, we found that hypoxia induced a significant decrease of both Beclin-1 and USP19, suggesting that hypoxia could dually inhibit the protein level of Beclin-1 through a type 2 coherent feed-forward loop (C2-FFL, hypoxia ⊸ Beclin-1 integrating with hypoxia ⊸ USP19 → Beclin-1) to promote the occurrence and development of cervical cancer. Furthermore, mathematical modeling revealed that under the hypoxic environment of solid tumor, the hypoxia/USP19/Beclin-1 coherent feed-forward loop could significantly reduce the protein level of Beclin-1, greatly enhance the sensitivity of Beclin-1 to hypoxia, strikingly restrict the heterogeneity of Beclin-1, and contribute to the low positive rate of Beclin-1 in cervical cancer. It is expected to have significance for elucidating the underlying mechanisms of the occurrence and development of cervical cancer and to provide novel targets and strategies for prevention and treatment of cervical cancer.

Bye bye, linearity, bye: quantification of the mean for linear CRNs in a random environment

Molecular reactions within a cell are inherently stochastic, and cells often differ in morphological properties or interact with a heterogeneous environment. Consequently, cell populations exhibit heterogeneity both due to these intrinsic and extrinsic causes. Although state-of-the-art studies that focus on dissecting this heterogeneity use single-cell measurements, the bulk data that shows only the mean expression levels is still in routine use. The fingerprint of the heterogeneity is present also in bulk data, despite being hidden from direct measurement. In particular, this heterogeneity can affect the mean expression levels via bimolecular interactions with low-abundant environment species. We make this statement rigorous for the class of linear reaction systems that are embedded in a discrete state Markov environment. The analytic expression that we provide for the stationary mean depends on the reaction rate constants of the linear subsystem, as well as the generator and stationary distribution of the Markov environment. We demonstrate the effect of the environment on the stationary mean. Namely, we show how the heterogeneous case deviates from the quasi-steady state (Q.SS) case when the embedded system is fast compared to the environment.

RNA velocity unraveled

We perform a thorough analysis of RNA velocity methods, with a view towards understanding the suitability of the various assumptions underlying popular implementations. In addition to providing a self-contained exposition of the underlying mathematics, we undertake simulations and perform controlled experiments on biological datasets to assess workflow sensitivity to parameter choices and underlying biology. Finally, we argue for a more rigorous approach to RNA velocity, and present a framework for Markovian analysis that points to directions for improvement and mitigation of current problems.

The chemical Langevin equation for biochemical systems in dynamic environments

Modelling and simulation of complex biochemical reaction networks form cornerstones of modern biophysics. Many of the approaches developed so far capture temporal fluctuations due to the inherent stochasticity of the biophysical processes, referred to as intrinsic noise. Stochastic fluctuations, however, predominantly stem from the interplay of the network with many other - and mostly unknown - fluctuating processes, as well as with various random signals arising from the extracellular world; these sources contribute extrinsic noise. Here we provide a computational simulation method to probe the stochastic dynamics of biochemical systems subject to both intrinsic and extrinsic noise. We develop an extrinsic chemical Langevin equation-a physically motivated extension of the chemical Langevin equation- to model intrinsically noisy reaction networks embedded in a stochastically fluctuating environment. The extrinsic CLE is a continuous approximation to the Chemical Master Equation (CME) with time-varying propensities. In our approach, noise is incorporated at the level of the CME, and can account for the full dynamics of the exogenous noise process, irrespective of timescales and their mismatches. We show that our method accurately captures the first two moments of the stationary probability density when compared with exact stochastic simulation methods, while reducing the computational runtime by several orders of magnitude. Our approach provides a method that is practical, computationally efficient and physically accurate to study systems that are simultaneously subject to a variety of noise sources.

Data-based stochastic modeling reveals sources of activity bursts in single-cell TGF-β signaling

Cells sense their surrounding by employing intracellular signaling pathways that transmit hormonal signals from the cell membrane to the nucleus. TGF-β/SMAD signaling encodes various cell fates, controls tissue homeostasis and is deregulated in diseases such as cancer. The pathway shows strong heterogeneity at the single-cell level, but quantitative insights into mechanisms underlying fluctuations at various time scales are still missing, partly due to inefficiency in the calibration of stochastic models that mechanistically describe signaling processes. In this work we analyze single-cell TGF-β/SMAD signaling and show that it exhibits temporal stochastic bursts which are dose-dependent and whose number and magnitude correlate with cell migration. We propose a stochastic modeling approach to mechanistically describe these pathway fluctuations with high computational efficiency. Employing high-order numerical integration and fitting to burst statistics we enable efficient quantitative parameter estimation and discriminate models that assume noise in different reactions at the receptor level. This modeling approach suggests that stochasticity in the internalization of TGF-β receptors into endosomes plays a key role in the observed temporal bursting. Further, the model predicts the single-cell dynamics of TGF-β/SMAD signaling in untested conditions, e.g., successfully reflects memory effects of signaling noise and cellular sensitivity towards repeated stimulation. Taken together, our computational framework based on burst analysis, noise modeling and path computation scheme is a suitable tool for the data-based modeling of complex signaling pathways, capable of identifying the source of temporal noise.

Pathway-resolved decomposition demonstrates correlation and noise dependencies of redundant information processing in recurrent feed-forward topologies

In a biochemical assay that converts fan-in networks into feed-forward loops (FFLs), we show that the inter-regulator redundant information about the output gene product can be decomposed into finer components, mediated by the constituent pathways. Variance-based information within the linear noise regime facilitates quantifying these submodular redundancies. Contrary to the conventional wisdom on information decomposition, we report that information redundancy depends nontrivially on inter-regulator correlation. For the type-1 coherent (C1) and incoherent (I1) FFLs, the direct regulatory path-mediated redundancy is certainly correlation independent. However, components induced by the indirect regulatory path and interpathway interference are correlation dependent in (non)linear fashion. The trade-off between information redundancy and similarly decomposable extrinsic noise from input to output node has been demonstrated for the pathways and full motifs. Our analyses suggest that the interpathway cross redundancy positively and negatively influences the superposition of elementary redundancies in the C1- and I1-FFLs, respectively. Their corresponding total extrinsic noise is produced by the weighted sum and difference of the pathway-specific components. We find that the I1-FFL is able to manufacture more varied redundancy and extrinsic noise responses compared to the C1-FFL. Underlying the differing characteristics of the composite metrics across FFL variants, there exist uniformly behaving pathway-dependent elements. The decomposition framework has been meticulously explored in biologically rational parametric realizations through analytical estimates and stochastic simulations.

Coloured noise induces phenotypic diversity with energy dissipation

Genes integrate many different sources of noise to adapt their survival strategy with energy costs, but how this noise impacts gene phenotype switching is not fully understood. Here, we refine a mechanistic model with multiplicative and additive coloured noise and analyse the influence of noise strength (NS) and autocorrelation time (AT) on gene phenotypic diversity. Different from white noise, we found that in the autocorrelation time-scale plane, increasing the multiplicative noise will broaden the bimodal region of the gene product, and additive noise will induce bimodal region drift from the lower level to the higher level, while the AT will promote this transition. Specifically, the effect of AT on gene expression is similar to a feedback loop; that is, the AT of multiplicative noise will elongate the mean first passage time (MFPT) from the low stable state to the high stable state, but it will reduce the MFPT from the high stable state to the low stable state, and the opposite is true for additive noise. Moreover, these transitions will violate the detailed equilibrium and then consume energy. By effective topology network reconstruction, we found that when the NS is small, the more obvious the bimodality is, the lower the energy dissipation; however, when the NS is large, it will consume more energy with a tendency for bimodality. The overall analysis implies that living organisms will utilize noise strength and its autocorrelation time for better survival in complex and fluctuating environments.

Variance of filtered signals: Characterization for linear reaction networks and application to neurotransmission dynamics

Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance of the synaptic vesicle to the calcium channels determines the release probability and consequently the postsynaptic signal. Suitable models of the process need to capture both the mean and the variance observed in electrophysiological measurements of the postsynaptic current. In this work, we propose a method to directly compute the exact first- and second-order moments for signals generated by a linear reaction network under convolution with an impulse response function, rendering computationally expensive numerical simulations of the underlying stochastic counting process obsolete. We show that the autocorrelation of the process is central for the calculation of the filtered signal's second-order moments, and derive a system of PDEs for the cross-correlation functions (including the autocorrelations) of linear reaction networks with time-dependent rates. Finally, we employ our method to efficiently compare different spatial coarse graining approaches for a specific model of synaptic vesicle fusion. Beyond the application to neurotransmission processes, the developed theory can be applied to any linear reaction system that produces a filtered stochastic signal.

Information transmission in a two-step cascade: interplay of activation and repression

We present an information-theoretic formalism to study signal transduction in four architectural variants of a model two-step cascade with increasing input population. Our results categorize these four types into two classes depending upon the effect of activation and repression on mutual information, net synergy, and signal-to-noise ratio. Using the Gaussian framework and linear noise approximation, we derive the analytic expressions for these metrics to establish their underlying relationships in terms of the biochemical parameters. We also verify our approximations through stochastic simulations.

Extrinsic noise of the target gene governs abundance pattern of feed-forward loop motifs

Feed-forward loop (FFL) is found to be a recurrent structure in bacterial and yeast gene transcription regulatory networks. In a generic FFL, transcription factor (TF) S regulates production of another TF X while both of these TFs regulate production of final gene-product Y. Depending upon the regulatory programs (activation or repression), FFLs are grouped into two broad classes: coherent (C) and incoherent (I), each class containing four distinct types (C1-C4 and I1-I4). These FFL types are experimentally observed to occur with varied frequencies, C1 and I1 being the abundant ones. Here we present a stochastic framework singling out the absolute value of the normalized covariance of X and Y to be the determining factor behind the abundance of FFLs while considering differential promoter activities of X and Y. Our theoretical construct employs two possible signal integration mechanisms (additive and multiplicative) to synthesize Y while steady-state population level of S remains fixed or becomes tunable reflecting two possible environmental signaling scenarios. Our model categorically points out that abundant FFLs exhibit higher amount of the designated metric which has a biophysical connotation of extrinsic noise for the target gene Y. Our predictions emanating from an overarching analytical expression utilizing biologically plausible parametric conditions are substantiated by stochastic simulation.

Modeling the neuro-protection of theaflavic acid from black tea and its synergy with nimodipine via mitochondria apoptotic pathway

Ischemic stroke presents a leading cause of mortality and morbidity worldwide. Theaflavic acid (TFA) is a theaflavin isolated from black tea that exerts a potentially neuro-protective effect. However, the dynamic properties of TFA-mediated protection remain largely unknown. In the current study, we evaluated the function of TFA in the mitochondria apoptotic pathway using mathematical modeling. We found that TFA-enhanced B-cell lymphoma 2 (Bcl-2) overexpression can theoretically give rise to bistability. The bistability is highly robust against parametric stochasticity while also conferring considerable variability in survival threshold. Stochastic simulations faithfully match the TFA dose response pattern seen in experimental studies. In addition, we identified a dose- and time-dependent synergy between TFA and nimodipine, a clinically used neuro-protective drug. This synergistic effect was enhanced by bistability independent of temporal factors. Precise application of pulsed doses of TFA can also promote survival compared with sustained TFA treatment. These data collectively demonstrate that TFA treatment can give rise to bistability and that synergy between TFA and nimodipine may offer a promising strategy for developing therapeutic neuro-protection against ischemic stroke.

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.

Frequency spectrum of chemical fluctuation: A probe of reaction mechanism and dynamics

Even in the steady-state, the number of biomolecules in living cells fluctuates dynamically, and the frequency spectrum of this chemical fluctuation carries valuable information about the dynamics of the reactions creating these biomolecules. Recent advances in single-cell techniques enable direct monitoring of the time-traces of the protein number in each cell; however, it is not yet clear how the stochastic dynamics of these time-traces is related to the reaction mechanism and dynamics. Here, we derive a rigorous relation between the frequency-spectrum of the product number fluctuation and the reaction mechanism and dynamics, starting from a generalized master equation. This relation enables us to analyze the time-traces of the protein number and extract information about dynamics of mRNA number and transcriptional regulation, which cannot be directly observed by current experimental techniques. We demonstrate our frequency spectrum analysis of protein number fluctuation, using the gene network model of luciferase expression under the control of the Bmal 1a promoter in mouse fibroblast cells. We also discuss how the dynamic heterogeneity of transcription and translation rates affects the frequency-spectra of the mRNA and protein number.