Shear viscosity of two-state enzyme solutions

Abstract

We discuss the shear viscosity of a Newtonian solution of catalytic enzymes and substrate molecules. The enzyme is modeled as a two-state dimer consisting of two spherical domains connected with an elastic spring. We take into account the enzymatic conformational dynamics, which is induced by the binding of an additional elastic spring that represents a bond between the substrate and enzyme. Employing the Boltzmann distribution weighted by the waiting times of enzymatic species in each catalytic cycle, we obtain the shear viscosity of dilute enzyme solutions as a function of substrate concentration and its physical properties. The substrate affinity distinguishes between fast and slow enzymes, and the corresponding viscosity expressions are obtained. Furthermore, we connect the obtained viscosity with the diffusion coefficient of a tracer particle in enzyme solutions.

Acceleration of enzymatic catalysis by active hydrodynamic fluctuations

“…Hydrodynamic forces induced by active processes. We consider a solution of stochastic force dipoles [63,69] representing active processes such as enzymatic catalysis and the motion of molecular motors. In this coarse-grained view, each force dipole consists of two beads connected by a spring of equilibrium length ℓ 0 .…”

“…Linkage between intrinsic motion and catalysis was reported in adenylate kinase (ADK) [43][44][45][46][47], dihydrofolate reductase (DHFR) [48][49][50][51][52][53][54], and other enzymes [51,55,56]-though the existence, extent and physical nature of this linkage remain open questions [20,21,57]. All this invokes a notion of enzymes as stochastic molecular machines whose chemical performance and evolution are linked to their internal mechanics [51,[58][59][60][61][62][63][64].…”

Diffusion and steady state distributions of flexible chemotactic enzymes

“…Noting the form of Γ I and Γ D in (18) and (19), we see that such a choice of g(l) does not exist in general, and thus no center of diffusion exists in general for such a flexible object. A center of diffusion does exist in the particular case in which the dumbbell is symmetric, with µ 11 = µ 22 , in which case we have Γ I = Γ D = 0 if the tracking point is chosen as the midpoint between subunits, i.e. g(l) = 1/2.…”

“…Enzymes have attracted much attention in recent years as biocompatible nanomachines that may perform work and undergo directed motion, with many biomedical and nanoengineering applications [1][2][3][4]. In particular, much work has been devoted to understanding and further exploring experimental observations of enhanced diffusion [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and chemotaxis [6,13,14,[23][24][25][26][27][28][29][30] of enzymes in the presence of their substrate. Chemotaxis, in particular, may have important implications in the self-organization of enzymes that participate in a common catalytic pathway [28,[31][32][33].…”

Mechanochemical enzymes and protein machines as hydrodynamic force dipoles: the active dimer model

“…[5][6][7] Following the original publication, 12 extensive further research has been performed. [13][14][15][16][17][18][19][20] The effects of rotational diffusion and of possible nematic ordering for enzymes were considered, 14 the phenomena in biomembranes were extensively analyzed, 15,16 and the theory was extended to viscoelastic media as well. 17,18 Recently, it was shown that viscosity in dilute solutions of mechanochemically active enzymes should become also reduced.…”