Universally valid reduction of multiscale stochastic biochemical systems using simple non-elementary propensities

Biochemical systems consist of numerous elementary reactions governed by the law of mass action. However, experimentally characterizing all the elementary reactions is nearly impossible. Thus, over a century, their deterministic models that typically contain rapid reversible bindings have been simplified with non-elementary reaction functions (e.g., Michaelis-Menten and Morrison equations). Although the non-elementary reaction functions are derived by applying the quasi-steady-state approximation (QSSA) to deterministic systems, they have also been widely used to derive propensities for stochastic simulations due to computational efficiency and simplicity. However, the validity condition for this heuristic approach has not been identified even for the reversible binding between molecules, such as protein-DNA, enzyme-substrate, and receptor-ligand, which is the basis for living cells. Here, we find that the non-elementary propensities based on the deterministic total QSSA can accurately capture the stochastic dynamics of the reversible binding in general. However, serious errors occur when reactant molecules with similar levels tightly bind, unlike deterministic systems. In that case, the non-elementary propensities distort the stochastic dynamics of a bistable switch in the cell cycle and an oscillator in the circadian clock. Accordingly, we derive alternative non-elementary propensities with the stochastic low-state QSSA, developed in this study. This provides a universally valid framework for simplifying multiscale stochastic biochemical systems with rapid reversible bindings, critical for efficient stochastic simulations of cell signaling and gene regulation. To facilitate the framework, we provide a user-friendly open-source computational package, ASSISTER, that automatically performs the present framework.

Mathematical Modeling Reveals Quantitative Properties of KEAP1-NRF2 Signaling

In response to oxidative and electrophilic stresses, cells launch an NRF2-mediated transcriptional antioxidant program. The activation of NRF2 depends on a redox sensor, KEAP1, which acts as an E3-ligase adaptor to promote the ubiquitination and degradation of NRF2. While a great deal has been learned about the molecular details of KEAP1, NRF2, and their interactions, the quantitative aspects of signal transfer conveyed by this redox duo are still largely unexplored. In the present study, we examined the signaling properties including response time, half-life, maximal activation, and response steepness (ultrasensitivity) of NRF2, through a suite of mathematical models. The models describe, with increasing complexity, the reversible binding of KEAP1 dimer and NRF2 via the ETGE and DLG motifs, NRF2 production, KEAP1-dependent and independent NRF2 degradation, and perturbations by different classes of NRF2 activators. Our simulations revealed that at the basal condition, NRF2 molecules are largely sequestered by KEAP1, with the KEAP1-NRF2 complex comparably distributed in either an ETGE-bound only (open) state or an ETGE and DLG dual-bound (closed) state, corresponding to the unlatched and latched configurations of the conceptual hinge-latch model. With two-step ETGE binding, the open and closed states operate in cycle mode at the basal condition and transition to equilibrium mode at stressed conditions. Class I-V, electrophilic NRF2 activators, which modify redox-sensing cysteine residues of KEAP1, shift the balance to a closed state that is unable to degrade NRF2 effectively. Total NRF2 has to accumulate to a level that nearly saturates existing KEAP1 to make sufficient free NRF2, therefore introducing a signaling delay. At the juncture of KEAP1 saturation, ultrasensitive NRF2 activation, i.e., a steep rise in the free NRF2 level, can occur through two simultaneous mechanisms, zero-order degradation mediated by DLG binding and protein sequestration (molecular titration) mediated by ETGE binding. These response characteristics of class I-V activators do not require disruption of DLG binding to unlatch the KEAP1-NRF2 complex. In comparison, class VI NRF2 activators, which directly compete with NRF2 for KEAP1 binding, can unlatch or even unhinge the KEAP1-NRF2 complex. This causes a shift to the open state of KEAP1-NRF2 complex and ultimately its complete dissociation, resulting in a fast release of free NRF2 followed by stabilization. Although class VI activators may induce free NRF2 to higher levels, ultrasensitivity is lost due to lower free KEAP1 and thus its NRF2-sequestering effect. Stress-induced NRF2 nuclear accumulation is enhanced when basal nuclear NRF2 turnover constitutes a small load to NRF2 production. Our simulation further demonstrated that optimal abundances of cytosolic and nuclear KEAP1 exist to maximize ultrasensitivity. In summary, by simulating the dual role of KEAP1 in repressing NRF2, i.e., sequestration and promoting degradation, our mathematical modeling provides key novel quantitative insights into the signaling properties of the crucial KEAP1-NRF2 module of the cellular antioxidant response pathway.

Recent Advances in Nucleic Acid Modulation for Functional Nanozyme

Nanozymes have the potential to replace natural enzymes, so they are widely used in energy conversion technologies such as biosensors and signal transduction (converting biological signals of a target into optical, electrical, or metabolic signals). The participation of nucleic acids leads nanozymes to produce richer interface effects and gives energy conversion events more attractive characteristics, creating what are called “functional nanozymes”. Since different nanozymes have different internal structures and external morphological characteristics, functional modulation needs to be compatible with these properties, and attention needs to be paid to the influence of nucleic acids on nanozyme activity. In this review, “functional nanozymes” are divided into three categories, (nanozyme precursor ion)/ (nucleic acid) self-assembly, nanozyme-nucleic acid irreversible binding, and nanozyme-nucleic acid reversible binding, and the effects of nucleic acids on modulation principles are summarized. Then, the latest developments of nucleic acid-modulated nanozymes are reviewed in terms of their use in energy conversion technology, and their conversion mechanisms are critically discussed. Finally, we outline the advantages and limitations of “functional nanozymes” and discuss the future development prospects and challenges in this field.

Universally valid reduction of multiscale stochastic biochemical systems using simple non-elementary propensities

Biochemical systems consist of numerous elementary reactions governed by the law of mass action. However, experimentally characterizing all the elementary reactions is nearly impossible. Thus, over a century, their deterministic models that typically contain rapid reversible bindings have been simplified with non-elementary reaction functions (e.g., Michaelis-Menten and Morrison equations). Although the non-elementary functions are derived by applying the quasi-steady-state approximation(QSSA) to deterministic systems, they have also been widely used to derive propensities for stochastic simulations due to computational efficiency and simplicity. However, the validity condition for this heuristic approach has not been identified even for the reversible binding between molecules, such as protein-DNA, enzyme-substrate, and receptor-ligand, which is the basis for living cells. Here, we find that the non-elementary propensities based on the deterministic total QSSA can accurately capture the stochastic dynamics of the reversible binding in general. However, serious errors occur when reactant molecules with similar levels tightly bind, unlike deterministic systems.In that case, the non-elementary propensities distort the stochastic dynamics of a bistable switch in the cell cycle and an oscillator in the circadian clock. Accordingly, we derive alternative non-elementary propensities with the stochastic low-state QSSA,developed in this study. This provides a universally valid framework for simplifying multiscale stochastic biochemical systems with rapid reversible bindings, critical for efficient stochastic simulations of cell signaling and gene regulation.

Enhanced diffusion by reversible binding to active polymers

Cells are known to use reversible binding to active biopolymer networks to allow diffusive transport of particles in an otherwise impenetrable mesh. We here determine the motion of a particle that experiences random forces during binding and unbinding events while being constrained by attached polymers. Using Monte-Carlo simulations and a statistical mechanics model, we find that enhanced diffusion is possible with active polymers. However, this is possible only under optimum conditions that has to do with the relative length of the chains to that of the plate. For example, in systems where the plate is shorter than the chains, diffusion is maximum when many chains have the potential to bind but few remain bound at any one time. Interestingly, if the chains are shorter than the plate, we find that diffusion is maximized when more active chains remain transiently bound. The model provides insight into these findings by elucidating the mechanisms for binding-mediated diffusion in biology and design rules for macromolecular transport in transient synthetic polymers.

Comparing lifeact and phalloidin for super-resolution imaging of actin in fixed cells

Visualizing actin filaments in fixed cells is of great interest for a variety of topics in cell biology such as cell division, cell movement, and cell signaling. We investigated the possibility of replacing phalloidin, the standard reagent for super-resolution imaging of F-actin in fixed cells, with the actin binding peptide ‘lifeact’. We compared the labels for use in single molecule based super-resolution microscopy, where AlexaFluor 647 labeled phalloidin was used in a dSTORM modality and Atto 655 labeled lifeact was used in a single molecule imaging, reversible binding modality. We found that imaging with lifeact had a comparable resolution in reconstructed images and provided several advantages over phalloidin including lower costs, the ability to image multiple regions of interest on a coverslip without degradation, simplified sequential super-resolution imaging, and more continuous labeling of thin filaments.