bioRxiv Science⌕ Search
Home/Archive/bioRxiv

bioRxiv · 10.1101/2022.11.28.518182

Theory on the rate equations of Michaelis-Menten type enzyme kinetics with competitive inhibition

Murugan, R.
View original source ↗Export metadata ↓

Abstract

We derive approximate expressions under various conditions of validity over both pre- and post-steady state regimes of the velocity-substrate-inhibitor spaces of the Michaelis-Menten enzyme kinetic schemes with fully and partial competitive inhibition. Our refinement over the currently available standard quasi steady state approximations (sQSSA) seems to be valid over wide range of enzyme to substrate and enzyme to inhibitor ratios. Further, we show that under certain conditions the enzyme-inhibitor-substrate system can exhibit temporally well-separated two different steady states with respect to both enzyme-substrate and enzyme-inhibitor complexes. We define the ratios fS = vmax/(KMS + e0) and fI = umax/(KMI + e0) as the acceleration factors with respect to the catalytic conversion of substrate and inhibitor into their respective products. Here KMS and KMI are the Michaelis-Menten parameters associated with the binding of substrate and inhibitor with the enzyme, vmax and umax are the respective maximum reaction velocities and e0, s0, and i0 are total enzyme, substrate and inhibitor levels. When (fS / fI) < 1, then enzyme-substrate complex will show multiple steady states subsequently reaches the full-fledged steady state only after the depletion of enzyme-inhibitor complex. When (fS / fI) > 1, then the enzyme-inhibitor complex will show multiple steady states and subsequently reaches the full-fledged steady state only after the depletion of enzyme-substrate complex. This complex behavior exclusively when (fS / fI) = 1 is the root cause of large amount of error in the estimation of various kinetic parameters both in the cases of fully and partial competitive inhibition schemes using the sQSSA methods. Remarkably, we show that our refined expressions for the reaction velocities over enzyme-substrate-inhibitor space can control this error more significantly than the currently available sQSSA velocity expressions.

Source connections

Explore related subjects

biochemistryPreprint

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Murugan, R.. 2022-11-28. Theory on the rate equations of Michaelis-Menten type enzyme kinetics with competitive inhibition. https://doi.org/10.1101/2022.11.28.518182

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related preprints

bioRxiv2026

Hierarchical cysteine oxidation controls reversible amyloid formation in an ankyrin repeat protein

The formation of amyloids, including functional amyloids, is observed for an increasing number of proteins but the molecular mechanisms that control this structural transition remain poorly understood. Here we report that the kinase inhibitor protein P18 (drP18) from Danio rerio (zebrafish), which contains two cysteine residues, undergoes a complex and hierarchical redox switch that strictly governs reversible amyloid formation. We identify cysteine 50 (C50) acting as a regulatory residue. Upon oxidation, C50 forms an intramolecular disulfide bond with the executioner cysteine 128 (C128), thereby blocking it. C50 can become S-glutathionylated, and upon oxidation, C128 then forms intermolecular disulfides that lead to rapid transition into amyloid fibrils. S-glutathionylation of C50 therefore enables amyloid formation of drP18 and the outcome is oxidant-dependent with diamide, hydrogen peroxide, peroxymonocarbonate and hypothiocyanous acid each leading to amyloid assembly with distinct kinetics and morphologies. These amyloids are fully reversible, where disulfide reduction is leading to disassembly. Whereas monomeric drP18 inhibits CDK4-mediated retinoblastoma phosphorylation, the amyloid conformation abolishes this inhibition, and reduction restores both structure and function. Expression of drP18 in zebrafish embryos yields Congo red-positive, oxidation-dependent aggregates in vivo. Together, our findings show that a regulatory cysteine controls an executioner cysteine to induce reversible, functional amyloid formation, revealing that proteins can encode sophisticated mechanisms to control amyloid assembly.

biochemistry↗
bioRxiv2026

Snapshots from the Catalytic Landscape of Chalcone Isomerase

Chalcone isomerase (CHI) catalyzes the cyclization of 3-ring scaffolds of flavonoids, a class of plant-based natural products important for nutrition and disease prevention. A persistent question has been whether the enzyme uses dynamics to facilitate conformational rearrangements of substrates within the active site. To help resolve this question, CHI was crystallized with phloretin, a flexible substrate analogue that cannot undergo cyclization. The crystal structure possesses eight protein molecules per asymmetric unit, revealing different active site conformations that accommodate different bound conformers of phloretin. Together, the structural snapshots depict a series of coordinated, dynamic chemical interactions that lower barriers to substrate rearrangements approaching bond formation. Differential scanning fluorimetry combined with mutational analysis and enzyme kinetics further confirm that phloretin binds to the enzyme active site and that it acts as a competitive inhibitor of CHI. Together these findings answer outstanding questions about the flexibility and dynamics of CHI catalysis, information that may be useful for future biosynthetic design and enzyme engineering goals. Overall, this work supports a catalytic model in which the CHI enzyme operates as a dynamic ensemble of structures necessary to facilitate catalytic substrate rearrangements.

biochemistry↗
bioRxiv2026

Structures of pUG-fold RNA bound to DNMT1 reveal a mechanism for RNA-mediated epigenetic regulation

Many chromatin-associated proteins have been found to bind RNA as a means of epigenetic regulation. Specifically, DNA methyltransferase 1 (DNMT1), which maintains cytosine methylation at CpG dinucleotides, is inhibited by RNA at transcribed DNA loci in cells. However, the mechanisms by which RNA binds DNMT1 and inhibits its activity remain unknown. Here, we determine a series of cryogenic electron microscopy (cryo-EM) structures of human DNMT1 bound to pUG-fold RNA, a non-canonical G-quadruplex previously observed to inhibit activity, revealing two distinct RNA-binding modes. The pUG-fold RNA binds the surface of DNMT1 in its autoinhibited conformation across a positively charged surface between the methyltransferase domain and the CXXC domain, and it binds directly in the active site of an open DNMT1 conformation. RNA binding is sterically incompatible with substrate DNA engagement in both states. Our 2.5 [A] structure captures the intricate network of hydrogen bonds and electrostatic interactions between amino acids in the methyltransferase domain and the tetrad layers of pUG-fold RNA. Metadynamics molecular dynamics simulations provide an orthogonal view of the conformational landscape of DNMT1, revealing the two distinct RNA-binding modes. Furthermore, our analysis of published DNMT1 RIP-seq and eCLIP-seq data confirms that DNMT1-interacting RNAs in cells exhibit a strong propensity to form non-canonical G-quadruplex RNA structures. Collectively, our study provides the first structural basis for pUG-fold RNA recognition by a protein and illustrates how cryo-EM and AI-based methods for protein and RNA structure prediction synergize to inform the mechanism of RNA-mediated regulation of DNMT1.

biochemistry↗