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All proteins are translated in the cytoplasm, yet many, including transcription factors, play vital roles in the nucleus. While previous research has concentrated on molecular motors for the transport of these proteins to the nucleus, recent observations reveal perinuclear accumulation even in the absence of an energy source, hinting at alternative mechanisms. Here, we propose that structural properties of the cellular environment, specifically the endoplasmic reticulum (ER), can promote molecular transport to the perinucleus without requiring additional energy expenditure. Specifically, physical interaction between proteins and the ER impedes their diffusion and leads to their accumulation near the nucleus. This result explains why larger proteins, more frequently interacting with the ER membrane, tend to accumulate at the perinucleus. Interestingly, such diffusion in a heterogeneous environment follows Chapman’s law rather than the popular Fick’s law. Our findings suggest a novel protein transport mechanism arising solely from characteristics of the intracellular environment. 

Abstract Long-term behaviors of biochemical reaction networks (BRNs) are described by steady states in deterministic models and stationary distributions in stochastic models. Unlike deterministic steady states, stationary distributions capturing inherent fluctuations of reactions are extremely difficult to derive analytically due to the curse of dimensionality. Here, we develop a method to derive analytic stationary distributions from deterministic steady states by transforming BRNs to have a special dynamic property, called complex balancing. Specifically, we merge nodes and edges of BRNs to match in- and out-flows of each node. This allows us to derive the stationary distributions of a large class of BRNs, including autophosphorylation networks of EGFR, PAK1, and Aurora B kinase and a genetic toggle switch. This reveals the unique properties of their stochastic dynamics such as robustness, sensitivity, and multi-modality. Importantly, we provide a user-friendly computational package, CASTANET, that automatically derives symbolic expressions of the stationary distributions of BRNs to understand their long-term stochasticity. 

Multisite phosphorylation of the PERIOD 2 (PER2) protein is the key step that determines the period of the mammalian circadian clock. Previous studies concluded that an unidentified kinase is required to prime PER2 for subsequent phosphorylation by casein kinase 1 (CK1), an essential clock component that is conserved from algae to humans. These subsequent phosphorylations stabilize PER2, delay its degradation, and lengthen the period of the circadian clock. Here, we perform a comprehensive biochemical and biophysical analysis of mouse PER2 (mPER2) priming phosphorylation and demonstrate, surprisingly, that CK1δ/ε is indeed the priming kinase. We find that both CK1ε and a recently characterized CK1δ2 splice variant more efficiently prime mPER2 for downstream phosphorylation in cells than the well-studied splice variant CK1δ1. While CK1 phosphorylation of PER2 was previously shown to be robust to changes in the cellular environment, our phosphoswitch mathematical model of circadian rhythms shows that the CK1 carboxyl-terminal tail can allow the period of the clock to be sensitive to cellular signaling. These studies implicate the extreme carboxyl terminus of CK1 as a key regulator of circadian timing. 

Abstract MotivationAdvances in experimental and imaging techniques have allowed for unprecedented insights into the dynamical processes within individual cells. However, many facets of intracellular dynamics remain hidden, or can be measured only indirectly. This makes it challenging to reconstruct the regulatory networks that govern the biochemical processes underlying various cell functions. Current estimation techniques for inferring reaction rates frequently rely on marginalization over unobserved processes and states. Even in simple systems this approach can be computationally challenging, and can lead to large uncertainties and lack of robustness in parameter estimates. Therefore we will require alternative approaches to efficiently uncover the interactions in complex biochemical networks. ResultsWe propose a Bayesian inference framework based on replacing uninteresting or unobserved reactions with time delays. Although the resulting models are non-Markovian, recent results on stochastic systems with random delays allow us to rigorously obtain expressions for the likelihoods of model parameters. In turn, this allows us to extend MCMC methods to efficiently estimate reaction rates, and delay distribution parameters, from single-cell assays. We illustrate the advantages, and potential pitfalls, of the approach using a birth–death model with both synthetic and experimental data, and show that we can robustly infer model parameters using a relatively small number of measurements. We demonstrate how to do so even when only the relative molecule count within the cell is measured, as in the case of fluorescence microscopy. Availability and implementationAccompanying code in R is available at https://github.com/cbskust/DDE_BD. Supplementary informationSupplementary data are available at Bioinformatics online.