Stochastic kinetics of ribosomes: Single motor properties and collective behavior

Abstract

Synthesis of protein molecules in a cell are carried out by ribosomes. A ribosome can be regarded as a molecular motor which utilizes the input chemical energy to move on a messenger RNA (mRNA) track that also serves as a template for the polymerization of the corresponding protein. The forward movement, however, is characterized by an alternating sequence of translocation and pause. Using a quantitative model, which captures the mechanochemical cycle of an individual ribosome, we derive an exact analytical expression for the distribution of its dwell times at the successive positions on the mRNA track. Inverse of the average dwell time satisfies a "Michaelis-Menten-like" equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle. Extending this formula appropriately, we also derive the exact force-velocity relation for a ribosome. Often many ribosomes simultaneously move on the same mRNA track, while each synthesizes a copy of the same protein. We extend the model of a single ribosome by incorporating steric exclusion of different individuals on the same track. We draw the phase diagram of this model of ribosome traffic in 3-dimensional spaces spanned by experimentally controllable parameters. We suggest new experimental tests of our theoretical predictions.

Mechanistic constraints from the substrate concentration dependence of enzymatic fluctuations

“…In contrast to the expressions currently in use (1,13,15,19,(22)(23)(24)(25)(26)(27), Eq. 4 makes very limited assumptions about the underlying kinetic model.…”

“…Here we consider the substrate concentration dependence of n min for an important family of kinetic models and show that there is a single, compact expression that contains, as a subset, all previous equations (1,13,15,19,(22)(23)(24)(25)(26)(27). We discuss the kinetic parameters introduced by this expression and derive the mechanistic constraints they provide.…”

“…Thus, n min , as an estimate of the number of "effective" rate-limiting states, will vary with substrate concentration. Such substrate dependence has been calculated for a variety of specific kinetic models (1,13,15,19,(22)(23)(24)(25)(26)(27), and these expressions have been fit to experimental measurements (when available) (13,15,28). However, by assuming a specific kinetic model, the expressions derived previously are only applicable to the assumed models, and, thus, do not exploit the model independence of [2].…”

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

“…Subsequent to its introduction, many groups have derived analytical expressions for the randomness parameter for a variety of specific kinetic models. 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.…”

“…(B) Randomness parameter for a system with different forms of dynamic disorder [51]. (C) Randomness parameter for different kinetic models for the ribosome [62]. (D) n min for a different model of the ribosome [61].…”