Beyond homogeneity: Assessing the validity of the Michaelis-Menten rate law in spatially heterogeneous environments.

The Michaelis-Menten (MM) rate law has been a fundamental tool in describing enzyme-catalyzed reactions for over a century. When substrates and enzymes are homogeneously distributed, the validity of the MM rate law can be easily assessed based on relative concentrations: the substrate is in large excess over the enzyme-substrate complex. However, the applicability of this conventional criterion remains unclear when species exhibit spatial heterogeneity, a prevailing scenario in biological systems. Here, we explore the MM rate law's applicability under spatial heterogeneity by using partial differential equations. In this study, molecules diffuse very slowly, allowing them to locally reach quasi-steady states. We find that the conventional criterion for the validity of the MM rate law cannot be readily extended to heterogeneous environments solely through spatial averages of molecular concentrations. That is, even when the conventional criterion for the spatial averages is satisfied, the MM rate law fails to capture the enzyme catalytic rate under spatial heterogeneity. In contrast, a slightly modified form of the MM rate law, based on the total quasi-steady state approximation (tQSSA), is accurate. Specifically, the tQSSA-based modified form, but not the original MM rate law, accurately predicts the drug clearance via cytochrome P450 enzymes and the ultrasensitive phosphorylation in heterogeneous environments. Our findings shed light on how to simplify spatiotemporal models for enzyme-catalyzed reactions in the right context, ensuring accurate conclusions and avoiding misinterpretations in in silico simulations.

scLENS: data-driven signal detection for unbiased scRNA-seq data analysis.

High dimensionality and noise have limited the new biological insights that can be discovered in scRNA-seq data. While dimensionality reduction tools have been developed to extract biological signals from the data, they often require manual determination of signal dimension, introducing user bias. Furthermore, a common data preprocessing method, log normalization, can unintentionally distort signals in the data. Here, we develop scLENS, a dimensionality reduction tool that circumvents the long-standing issues of signal distortion and manual input. Specifically, we identify the primary cause of signal distortion during log normalization and effectively address it by uniformizing cell vector lengths with L2 normalization. Furthermore, we utilize random matrix theory-based noise filtering and a signal robustness test to enable data-driven determination of the threshold for signal dimensions. Our method outperforms 11 widely used dimensionality reduction tools and performs particularly well for challenging scRNA-seq datasets with high sparsity and variability. To facilitate the use of scLENS, we provide a user-friendly package that automates accurate signal detection of scRNA-seq data without manual time-consuming tuning.

Beyond microtubules: The cellular environment at the endoplasmic reticulum attracts proteins to the nucleus, enabling nuclear transport.

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.

Spatially coordinated collective phosphorylation filters spatiotemporal noises for precise circadian timekeeping.

The circadian (∼24h) clock is based on a negative-feedback loop centered around the PERIOD protein (PER), translated in the cytoplasm and then enters the nucleus to repress its own transcription at the right time of day. Such precise nucleus entry is mysterious because thousands of PER molecules transit through crowded cytoplasm and arrive at the perinucleus across several hours. To understand this, we developed a mathematical model describing the complex spatiotemporal dynamics of PER as a single random time delay. We find that the spatially coordinated bistable phosphoswitch of PER, which triggers the phosphorylation of accumulated PER at the perinucleus, leads to the synchronous and precise nuclear entry of PER. This leads to robust circadian rhythms even when PER arrival times are heterogeneous and perturbed due to changes in cell crowdedness, cell size, and transcriptional activator levels. This shows how the circadian clock compensates for spatiotemporal noise.