Kinetics of diffusion-controlled enzymatic reactions with charged substrates

Selective modulation of alkali metal ions on acetylcholinesterase

Acetylcholinesterase (AChE) is an important hydrolase in cholinergic synapses and a candidate target in the treatment of Alzheimer's disease. The lithium treatment widely used in neurological disorders can alter the AChE activity, yet the underlying mechanism of how the ion species regulate the enzymatic activity remains unclear. In this work, we performed combined quantum mechanics/molecular mechanics (QM/MM) and molecular dynamics (MD) simulations and well-tempered metadynamics to understand the modulation of human AChE (hAChE) activity using three alkali metal ions (Li+, Na+, and K+) in different concentrations. Our simulations show that the binding affinity and catalytic activity are affected by different ion species through allosteric ion coordination geometries on the hAChE complex and distant electrostatic screening effect. A Li+ cluster involving D330, E393, and D397 residues and three Li+ ions was found to be highly conserved and can be critical to the enzyme activity. Binding energy calculations indicate that the electrostatic screening from allosterically bound cations can affect the key residues at the catalytic site and active-site gorge, including E199. Furthermore, an increase in ion concentration can lead to lower reactivity, especially for Li+ ions, which exhibit more cation-hAChE contacts than Na+ and K+. The selective ion binding and their preferred modulation on hAChE are highly related to ion species. This work provides a molecular perspective on selective modulation by different ion species of the enzyme catalytic processes.

Competition and Synergy of Arp2/3 and Formins in Nucleating Actin Waves

The assembly and disassembly of actin filaments and their regulatory proteins are crucial for maintaining cell structure or changing physiological state. However, because of the tremendous global impact of actin on diverse cellular processes, dissecting the specific role of actin regulatory proteins remains challenging. In this study, we employ actin waves that propagate on the cortex of mast cell to investigate the interplay between formins and the Arp2/3 complex in the nucleating and turnover of cortical actin. Our findings reveal that the recruitment of FMNL1 and mDia3 precedes the Arp2/3 complex in cortical actin waves. Membrane and GTPase-interaction can drive oscillations of FMNL1 in an actin-dependent manner, but active Cdc42 waves or constitutively-active FMNL1 mutant can form without actin waves. In addition to the apparent coordinated assembly of formins and Arp2/3, we further reveal their antagonism, where inhibition of Arp2/3 complex by CK-666 led to a transient increase in the recruitment of formins and actin polymerization. Our analysis suggest that the antagonism could not be explained for the competition between FMNL1 and Arp2/3 for monomeric actin. Rather, it is regulated by a limited pool of their common upstream regulator, Cdc42, whose level is negatively regulated by Arp2/3. Collectively, our study highlights the multifaceted interactions, cooperative or competitive, between formins and Arp2/3 complex, in the intricate and dynamic control of actin cytoskeletal network.

Cortical waves mediate the cellular response to electric fields

Electrotaxis, the directional migration of cells in a constant electric field, is important in regeneration, development, and wound healing. Electrotaxis has a slower response and a smaller dynamic range than guidance by other cues, suggesting that the mechanism of electrotaxis shares both similarities and differences with chemical-gradient-sensing pathways. We examine a mechanism centered on the excitable system consisting of cortical waves of biochemical signals coupled to cytoskeletal reorganization, which has been implicated in random cell motility. We use electro-fused giant Dictyostelium discoideum cells to decouple waves from cell motion and employ nanotopographic surfaces to limit wave dimensions and lifetimes. We demonstrate that wave propagation in these cells is guided by electric fields. The wave area and lifetime gradually increase in the first 10 min after an electric field is turned on, leading to more abundant and wider protrusions in the cell region nearest the cathode. The wave directions display 'U-turn' behavior upon field reversal, and this switch occurs more quickly on nanotopography. Our results suggest that electric fields guide cells by controlling waves of signal transduction and cytoskeletal activity, which underlie cellular protrusions. Whereas surface receptor occupancy triggers both rapid activation and slower polarization of signaling pathways, electric fields appear to act primarily on polarization, explaining why cells respond to electric fields more slowly than to other guidance cues.

On Catalytic Kinetics of Enzymes

Classical enzyme kinetic theories are summarized and linked with modern discoveries here. The sequential catalytic events along time axis by enzyme are analyzed at the molecular level, and by using master equations, this writing tries to connect the microscopic molecular behavior of enzyme to kinetic data (like velocity and catalytic coefficient k) obtained in experiment: 1/k = t equals to the sum of the times taken by the constituent individual steps. The relationships between catalytic coefficient k, catalytic rate or velocity, the amount of time taken by each step and physical or biochemical conditions of the system are discussed, and the perspective and hypothetic equations proposed here regarding diffusion, conformational change, chemical conversion, product release steps and the whole catalytic cycle provide an interpretation of previous experimental observations and can be testified by future experiments.

Charged Substrate and Product Together Contribute Like a Nonreactive Species to the Overall Electrostatic Steering in Diffusion-Reaction Processes

The Debye-Hückel limiting law is used to study the binding kinetics of substrate-enzyme system as well as to estimate the reaction rate of a electrostatically steered diffusion-controlled reaction process. It is based on a linearized Poisson-Boltzmann model and known for its accurate predictions in dilute solutions. However, the substrate and product particles are in nonequilibrium states and are possibly charged, and their contributions to the total electrostatic field cannot be explicitly studied in the Poisson-Boltzmann model. Hence the influences of substrate and product on reaction rate coefficient were not known. In this work, we consider all the charged species, including the charged substrate, product, and mobile salt ions in a Poisson-Nernst-Planck model, and then compare the results with previous work. The results indicate that both the charged substrate and product can significantly influence the reaction rate coefficient with different behaviors under different setups of computational conditions. It is interesting to find that when substrate and product are both considered, under an overall neutral boundary condition for all the bulk charged species, the computed reaction rate kinetics recovers a similar Debye-Hückel limiting law again. This phenomenon implies that the charged product counteracts the influence of charged substrate on reaction rate coefficient. Our analysis discloses the fact that the total charge concentration of substrate and product, though in a nonequilibrium state individually, obeys an equilibrium Boltzmann distribution, and therefore contributes as a normal charged ion species to ionic strength. This explains why the Debye-Hückel limiting law still works in a considerable range of conditions even though the effects of charged substrate and product particles are not specifically and explicitly considered in the theory.

High-Throughput Screening for Positive Allosteric Modulators Identified Potential Therapeutics against Acetylcholinesterase Inhibition

The current standard of care for treatment of organophosphate (OP) poisoning includes pretreatment with the weak reversible acetylcholinesterase (AChE) inhibitor pyridostigmine bromide. Because this drug is an AChE inhibitor, similar side effects exist as with OP poisoning. In an attempt to provide a therapeutic capable of mitigating AChE inhibition without such side effects, high-throughput screening was performed to identify a compound capable of increasing the catalytic activity of AChE. Herein, two such novel positive allosteric modulators (PAMs) of AChE are presented. These PAMs increase AChE activity threefold, but they fail to upshift the apparent IC50 of a variety of OPs. Further development and optimization of these compounds may lead to pre- and/or postexposure therapeutics with broad-spectrum efficacy against pesticide and nerve agent poisoning. In addition, they could be used to complement the current therapeutic standard of care to increase the activity of uninhibited AChE, potentially increasing the efficacy of current therapeutics in addition to altering the therapeutic window.

Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smoothed particle hydrodynamics

Background

The calculation of diffusion-controlled ligand binding rates is important for understanding enzyme mechanisms as well as designing enzyme inhibitors.

Methods

We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) BC, is considered on the reactive boundaries. This new BC treatment allows for the analysis of enzymes with “imperfect” reaction rates.

Results

The numerical method is first verified in simple systems and then applied to the calculation of ligand binding to a mouse acetylcholinesterase (mAChE) monomer. Rates for inhibitor binding to mAChE are calculated at various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates.

Conclusions

Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.

Bacillus thuringiensis subsp. israelensis and its dipteran-specific toxins

Bacillus thuringiensis subsp. israelensis (Bti) is the first Bacillus thuringiensis to be found and used as an effective biological control agent against larvae of many mosquito and black fly species around the world. Its larvicidal activity resides in four major (of 134, 128, 72 and 27 kDa) and at least two minor (of 78 and 29 kDa) polypeptides encoded respectively by cry4Aa, cry4Ba, cry11Aa, cyt1Aa, cry10Aa and cyt2Ba, all mapped on the 128 kb plasmid known as pBtoxis. These six δ-endotoxins form a complex parasporal crystalline body with remarkably high, specific and different toxicities to Aedes, Culex and Anopheles larvae. Cry toxins are composed of three domains (perforating domain I and receptor binding II and III) and create cation-selective channels, whereas Cyts are composed of one domain that acts as well as a detergent-like membrane perforator. Despite the low toxicities of Cyt1Aa and Cyt2Ba alone against exposed larvae, they are highly synergistic with the Cry toxins and hence their combinations prevent emergence of resistance in the targets. The lack of significant levels of resistance in field mosquito populations treated for decades with Bti-bioinsecticide suggests that this bacterium will be an effective biocontrol agent for years to come.

Diffusion and association processes in biological systems: theory, computation and experiment

Macromolecular diffusion plays a fundamental role in biological processes. Here, we give an overview of recent methodological advances and some of the challenges for understanding how molecular diffusional properties influence biological function that were highlighted at a recent workshop, BDBDB2, the second Biological Diffusion and Brownian Dynamics Brainstorm.

Solutions to a reduced Poisson-Nernst-Planck system and determination of reaction rates

We study a reduced Poisson-Nernst-Planck (PNP) system for a charged spherical solute immersed in a solvent with multiple ionic or molecular species that are electrostatically neutralized in the far field. Some of these species are assumed to be in equilibrium. The concentrations of such species are described by the Boltzmann distributions that are further linearized. Others are assumed to be reactive, meaning that their concentrations vanish when in contact with the charged solute. We present both semi-analytical solutions and numerical iterative solutions to the underlying reduced PNP system, and calculate the reaction rate for the reactive species. We give a rigorous analysis on the convergence of our simple iteration algorithm. Our numerical results show the strong dependence of the reaction rates of the reactive species on the magnitude of its far field concentration as well as on the ionic strength of all the chemical species. We also find non-monotonicity of electrostatic potential in certain parameter regimes. The results for the reactive system and those for the non-reactive system are compared to show the significant differences between the two cases. Our approach provides a means of solving a PNP system which in general does not have a closed-form solution even with a special geometrical symmetry. Our findings can also be used to test other numerical methods in large-scale computational modeling of electro-diffusion in biological systems.