Single-molecule enzyme kinetics in the presence of inhibitors

Abstract

Recent studies in single-molecule enzyme kinetics reveal that the turnover statistics of a single enzyme is governed by the waiting time distribution that decays as mono-exponential at low substrate concentration and multi-exponential at high substrate concentration. The multi-exponentiality arises due to protein conformational fluctuations, which act on the time scale longer than or comparable to the catalytic reaction step, thereby inducing temporal fluctuations in the catalytic rate resulting in dynamic disorder. In this work, we study the turnover statistics of a single enzyme in the presence of inhibitors to show that the multi-exponentiality in the waiting time distribution can arise even when protein conformational fluctuations do not influence the catalytic rate. From the Michaelis-Menten mechanism of inhibited enzymes, we derive exact expressions for the waiting time distribution for competitive, uncompetitive, and mixed inhibitions to quantitatively show that the presence of inhibitors can induce dynamic disorder in all three modes of inhibitions resulting in temporal fluctuations in the reaction rate. In the presence of inhibitors, dynamic disorder arises due to transitions between active and inhibited states of enzymes, which occur on time scale longer than or comparable to the catalytic step. In this limit, the randomness parameter (dimensionless variance) is greater than unity indicating the presence of dynamic disorder in all three modes of inhibitions. In the opposite limit, when the time scale of the catalytic step is longer than the time scale of transitions between active and inhibited enzymatic states, the randomness parameter is unity, implying no dynamic disorder in the reaction pathway.

Extracting signal from noise: kinetic mechanisms from a Michaelis–Menten‐like expression for enzymatic fluctuations

“…Can these dependencies be classified based on the observed modification of N L , N S and a, as well as k cat and K M ? Although there has been some initial work on similar questions [9,44,47,55]; there has not yet been a systematic study of the effects of such external variables on the parameters of Eqn (23). We predict that general trends will emerge, and that the effect of inhibitors and force can be classified based on their effect of N L , N S and a.…”

“…Panel (C) is reproduced with permission [62]. Panel (E) is reproduced with permission [55]. Panel (F) is reproduced with permission [63].…”

“…For example, expressions have been derived for molecular motors such as kinesin [12,41,44,46] and myosin [47]; polymerization enzymes such as the ribosome [61,62]; metabolic enzymes such as b-galactosidase [51]; and ion transporting enzymes such as channel proteins [36]. Generic models, such as the Michaelis-Menten mechanism in the presence [9,55] and absence [9,41,51] of inhibitors have also been considered. Finally, the randomness parameter has even been calculated for non-enzymatic, nanoparticle-assisted, single-molecule catalysis [63].…”

“…(D) n min for a different model of the ribosome [61]. (E) Randomness parameter for a model of mixed inhibition [55]. (F) Randomness parameter for nanoparticle-assisted catalysis [63].…”

“…Previous work [24,51] revealed that parallel branches can produce r > 1. In addition, we [9] and others [55] have also shown that mechanisms with single off-pathway states, such as the inhibitor state in Eqn (13), can also produce r > 1. Thus, r > 1 does not necessarily imply the existence of dynamic disorder in the system but rather indicates that the enzyme contains transitions not included in Eqn (21).…”