Competition between reactive species is commonplace in typical chemical reactions. Specifically the primary reaction between a substrate and its target enzyme may be altered when interactions with secondary species in the system are substantial. We explore this competition phenomenon for diffusion-limited reactions in the presence of neighboring particles through numerical solution of the diffusion equation. As a general model for globular proteins and small molecules, we consider spherical representations of the reactants and neighboring particles; these neighbors vary in local density, size, distribution, and relative distance from the primary target reaction, as well as their surface reactivity. Modulations of these model variables permit inquiry into the influence of excluded volume and competition on the primary reaction due to the presence of neighboring particles. We find that the surface reactivity effect is long-ranged and a strong determinant of reaction kinetics, whereas the excluded volume effect is relatively short-ranged and less influential in comparison. As a consequence, the effect of the excluded volume is only modestly dependent on the neighbor distribution and is approximately additive; this additivity permits a linear approximation to the many-body effect on the reaction kinetics. In contrast, the surface reactivity effect is non-additive, and thus it may require higher-order approximations to describe the reaction kinetics. Our model study has broad implications in the general understanding of competition and local crowding on diffusion-limited chemical reactions.

Biochemical reaction networks consisting of coupled enzymes connect substrate signaling events with biological function. Substrates involved in these reactions can be strongly influenced by diffusion "barriers" arising from impenetrable cellular structures and macromolecules, as well as interactions with biomolecules, especially within crowded environments. For diffusion-influenced reactions, the spatial organization of diffusion barriers arising from intracellular structures, non-specific crowders, and specific-binders (buffers) strongly controls the temporal and spatial reaction kinetics. In this study, we use two prototypical biochemical reactions, a Goodwin oscillator, and a reaction with a periodic source/sink term to examine how a diffusion barrier that partitions substrates controls reaction behavior. Namely, we examine how conditions representative of a densely packed cytosol, including reduced accessible volume fraction, non-specific interactions, and buffers, impede diffusion over nanometer length-scales. We find that diffusion barriers can modulate the frequencies and amplitudes of coupled diffusion-influenced reaction networks, as well as give rise to "compartments" of decoupled reactant populations. These effects appear to be intensified in the presence of buffers localized to the diffusion barrier. These findings have strong implications for the role of the cellular environment in tuning the dynamics of signaling pathways.

Troponin C (TnC) is an important regulatory molecule in cardiomyocytes. Calcium binding to site II in TnC initiates a series of molecular events that result in muscle contraction. The most direct change upon Ca(2+) binding is an opening motion of the molecule that exposes a hydrophobic patch on the surface allowing for Troponin I to bind. Molecular dynamics simulations were used to elucidate the dynamics of this crucial protein in three different states: apo, Ca(2+)-bound, and Ca(2+)-TnI-bound. Dynamics between the states are compared, and the Ca(2+)-bound system is investigated for opening motions. On the basis of the simulations, NMR chemical shifts and order parameters are calculated and compared with experimental observables. Agreement indicates that the simulations sample the relevant dynamics of the system. Brownian dynamics simulations are used to investigate the calcium association of TnC. We find that calcium binding gives rise to correlative motions involving the EF hand and collective motions conducive of formation of the TnI-binding interface. We furthermore indicate the essential role of electrostatic steering in facilitating diffusion-limited binding of Ca(2+).

We perform Brownian dynamics simulations and Smoluchowski continuum modeling of the bifunctional Plasmodium falciparum dihydrofolate reductase-thymidylate synthase (P. falciparum DHFR-TS) with the objective of understanding the electrostatic channeling of dihydrofolate generated at the TS active site to the DHFR active site. The results of Brownian dynamics simulations and Smoluchowski continuum modeling suggest that compared to Leishmania major DHFR-TS, P. falciparum DHFR-TS has a lower but significant electrostatic-mediated channeling efficiency (?15-25%) at physiological pH (7.0) and ionic strength (150 mM). We also find that removing the electric charges from key basic residues located between the DHFR and TS active sites significantly reduces the channeling efficiency of P. falciparum DHFR-TS. Although several protozoan DHFR-TS enzymes are known to have similar tertiary and quaternary structure, subtle differences in structure, active-site geometry, and charge distribution appear to influence both electrostatic-mediated and proximity-based substrate channeling.

Cardiac troponin (cTn) is a key molecule in the regulation of human cardiac muscle contraction. The N-terminal cardiac-specific peptide of the inhibitory subunit of troponin, cTnI (cTnI(1-39)), is a target for phosphorylation by protein kinase A (PKA) during β-adrenergic stimulation. We recently presented evidence indicating that this peptide interacts with the inhibitory peptide (cTnl(137-147)) when S23 and S24 are phosphorylated. The inhibitory peptide is also the target of the point mutation cTnI-R145G, which is associated with hypertrophic cardiomyopathy (HCM), a disease associated with sudden death in apparently healthy young adults. It has been shown that both phosphorylation and this mutation alter the cTnC-cTnI (C-I) interaction, which plays a crucial role in modulating contractile activation. However, little is known about the molecular-level events underlying this modulation. Here, we computationally investigated the effects of the cTnI-R145G mutation on the dynamics of cTn, cTnC Ca(2+) handling, and the C-I interaction. Comparisons were made with the cTnI-R145G/S23D/S24D phosphomimic mutation, which has been used both experimentally and computationally to study the cTnI N-terminal specific effects of PKA phosphorylation. Additional comparisons between the phosphomimic mutations and the real phosphorylations were made. For this purpose, we ran triplicate 150 ns molecular dynamics simulations of cTnI-R145G Ca(2+)-bound cTnC(1-161)-cTnI(1-172)-cTnT(236-285), cTnI-R145G/S23D/S24D Ca(2+)-bound cTnC(1-161)-cTnI(1-172)-cTnT(236-285), and cTnI-R145G/PS23/PS24 Ca(2+)-bound cTnC(1-161)-cTnI(1-172)-cTnT(236-285), respectively. We found that the cTnI-R145G mutation did not impact the overall dynamics of cTn, but stabilized crucial Ca(2+)-coordinating interactions. However, the phosphomimic mutations increased overall cTn fluctuations and destabilized Ca(2+) coordination. Interestingly, cTnI-R145G blunted the intrasubunit interactions between the cTnI N-terminal extension and the cTnI inhibitory peptide, which have been suggested to play a crucial role in modulating troponin function during β-adrenergic stimulation. These findings offer a molecular-level explanation for how the HCM mutation cTnI-R145G reduces the modulation of cTn by phosphorylation of S23/S24 during β-adrenergic stimulation.

We study models of two sequential enzyme-catalyzed reactions as a basic functional building block for coupled biochemical networks. We investigate the influence of enzyme distributions and long-range molecular interactions on reaction kinetics, which have been exploited in biological systems to maximize metabolic efficiency and signaling effects. Specifically, we examine how the maximal rate of product generation in a series of sequential reactions is dependent on the enzyme distribution and the electrostatic composition of its participant enzymes and substrates. We find that close proximity between enzymes does not guarantee optimal reaction rates, as the benefit of decreasing enzyme separation is countered by the volume excluded by adjacent enzymes. We further quantify the extent to which the electrostatic potential increases the efficiency of transferring substrate between enzymes, which supports the existence of electrostatic channeling in nature. Here, a major finding is that the role of attractive electrostatic interactions in confining intermediate substrates in the vicinity of the enzymes can contribute more to net reactive throughput than the directional properties of the electrostatic fields. These findings shed light on the interplay of long-range interactions and enzyme distributions in coupled enzyme-catalyzed reactions, and their influence on signaling in biological systems.

Mean-field methods, such as the Poisson-Boltzmann equation (PBE), are often used to calculate the electrostatic properties of molecular systems. In the past two decades, an enhancement of the PBE, the size-modified Poisson-Boltzmann equation (SMPBE), has been reported. Here, the PBE and the SMPBE are reevaluated for realistic molecular systems, namely, lipid bilayers, under eight different sets of input parameters. The SMPBE appears to reproduce the molecular dynamics simulation results better than the PBE only under specific parameter sets, but in general, it performs no better than the Stern layer correction of the PBE. These results emphasize the need for careful discussions of the accuracy of mean-field calculations on realistic systems with respect to the choice of parameters and call for reconsideration of the cost-efficiency and the significance of the current SMPBE formulation.

Contractile function of cardiac cells is driven by the sliding displacement of myofilaments powered by the cycling myosin crossbridges. Critical to this process is the availability of ATP, which myosin hydrolyzes during the cross-bridge cycle. The diffusion of adenine nucleotides through the myofilament lattice has been shown to be anisotropic, with slower radial diffusion perpendicular to the filament axis relative to parallel, and is attributed to the periodic hexagonal arrangement of the thin (actin) and thick (myosin) filaments. We investigated whether atomistic-resolution details of myofilament proteins can refine coarse-grain estimates of diffusional anisotropy for adenine nucleotides in the cardiac myofibril, using homogenization theory and atomistic thin filament models from the Protein Data Bank. Our results demonstrate considerable anisotropy in ATP and ADP diffusion constants that is consistent with experimental measurements and dependent on lattice spacing and myofilament overlap. A reaction-diffusion model of the half-sarcomere further suggests that diffusional anisotropy may lead to modest adenine nucleotide gradients in the myoplasm under physiological conditions.

The sodium-potassium ATPase (Na/K-ATPase, NKA) establishes ion gradients that facilitate many physiological functions including action potentials and secondary transport processes. NKA comprises a catalytic subunit (alpha) that interacts closely with an essential subunit (beta) and regulatory transmembrane micropeptides called FXYD proteins. In the heart, a key modulatory partner is the FXYD protein phospholemman (PLM, FXYD1), but the stoichiometry of the alpha-beta-PLM regulatory complex is unknown. Here, we used fluorescence lifetime imaging and spectroscopy to investigate the structure, stoichiometry, and affinity of the NKA-regulatory complex. We observed a concentration-dependent binding of the subunits of NKA-PLM regulatory complex, with avid association of the alpha subunit with the essential beta subunit as well as lower affinity alpha-alpha and alpha-PLM interactions. These data provide the first evidence that, in intact live cells, the regulatory complex is composed of two alpha subunits associated with two beta subunits, decorated with two PLM regulatory subunits. Docking and molecular dynamics (MD) simulations generated a structural model of the complex that is consistent with our experimental observations. We propose that alpha-alpha subunit interactions support conformational coupling of the catalytic subunits, which may enhance NKA turnover rate. These observations provide insight into the pathophysiology of heart failure, wherein low NKA expression may be insufficient to support formation of the complete regulatory complex with the stoichiometry (alpha-beta-PLM)₂.