Single enzyme pathways and substrate fluctuations

TY - JOUR

T1 - Single enzyme pathways and substrate fluctuations

AU - Stéfanini, M. O.

AU - McKane, A. J.

AU - Newman, T. J.

PY - 2005/7

Y1 - 2005/7

N2 - The ability to dynamically probe single enzymes allows the experimental investigation of enzyme kinetics with unprecedented resolution. In this paper we develop a simple theory which predicts that certain classes of enzyme pathways can be distinguished by studying the turnover rate, V, as a function of substrate concentration, [S]. In particular, we study the steady state of a single enzyme interacting with a bath of substrate molecules, and analyse it as a stochastic process. The V([S]) relation is found to depend sensitively on the manner in which substrate molecules in the bath are replenished. We focus on a gedanken experiment in which the average substrate concentration is kept fixed by allowing molecules to enter the bath at a constant rate. We derive the exact relationship between V and [S], which has a relatively simple form, though different to that of the Michaelis-Menten (MM) equation. Interestingly, the MM equation is exactly recovered if the substrate concentration is instantaneously maintained with molecular precision. We examine the new V([S]) relation for a number of enzyme pathways and find that it differentiates between enzyme reactions involving one or many intermediate enzyme-substrate complexes. This, in principle, allows one to probe the internal conformations of enzymes by careful measurement of V([S]) curves in appropriately designed single enzyme experiments.

AB - The ability to dynamically probe single enzymes allows the experimental investigation of enzyme kinetics with unprecedented resolution. In this paper we develop a simple theory which predicts that certain classes of enzyme pathways can be distinguished by studying the turnover rate, V, as a function of substrate concentration, [S]. In particular, we study the steady state of a single enzyme interacting with a bath of substrate molecules, and analyse it as a stochastic process. The V([S]) relation is found to depend sensitively on the manner in which substrate molecules in the bath are replenished. We focus on a gedanken experiment in which the average substrate concentration is kept fixed by allowing molecules to enter the bath at a constant rate. We derive the exact relationship between V and [S], which has a relatively simple form, though different to that of the Michaelis-Menten (MM) equation. Interestingly, the MM equation is exactly recovered if the substrate concentration is instantaneously maintained with molecular precision. We examine the new V([S]) relation for a number of enzyme pathways and find that it differentiates between enzyme reactions involving one or many intermediate enzyme-substrate complexes. This, in principle, allows one to probe the internal conformations of enzymes by careful measurement of V([S]) curves in appropriately designed single enzyme experiments.

UR - https://www.scopus.com/pages/publications/21244456039

U2 - 10.1088/0951-7715/18/4/008

DO - 10.1088/0951-7715/18/4/008

M3 - Article

AN - SCOPUS:21244456039

SN - 0951-7715

VL - 18

SP - 1575

EP - 1595

JO - Nonlinearity

JF - Nonlinearity

IS - 4

ER -