Cracking phase diagram for the dynamics of an enzyme

Abstract

We measure the ensemble averaged deformation of an enzyme for an oscillating applied force. From the low frequency divergence of the mechanical susceptibility for the hinge motion of Guanylate Kinase we obtain a non-equilibrium phase diagram in the frequency -force plane. A phase line separates linear elasticity dynamics from softer (viscoelastic) dynamics. The hinge motion corresponds to crossing this phase line (not to a soft linear elastic mode). The phase line is dramatically shifted in the closed state compared to the open state of the enzyme.Introduction. Virtually all enzymes couple catalysis to conformational motion. Evident in motor proteins, mechano-chemical coupling is also the basis for substrate specificity [1,2] and activity regulation [3][4][5] in these molecular machines. Conformational changes coupled to catalysis are often large, with amplitudes of ∼ 1 nm compared to an overall size of the enzyme of ∼ 5 nm. The folded protein being a solid, these huge strains pose an interesting question about the nature of conformational dynamics and the associated materials properties of the system. Surely this motion is not within the linear elasticity regime, and a specific nonlinear mechanism for these transitions, called "cracking", was proposed some years ago [6,7]. Cracking connects initial and final states through a local melting and refolding event. Translated into stress-strain relations, this should give rise to an interesting dynamics. Here we measure directly the stress-strain relations for the hinge motion of the enzyme Guanylate Kinase (GK), a molecule quite similar to the enzyme considered in [6,7]. Specifically, we report comparative nano-rheology [8] measurements on the open (no substrate) and closed (with the substrate GMP) forms of the enzyme and find that while the linear elasticity regime is almost the same, the nonlinear behavior, or what we have called the viscoelastic regime [9,10] is dramatically different in the two cases. A phase diagram in the frequency -force plane maps out regions of linear elastic vs softer (viscoelastic) dynamics. The existence of this phase line may be a universal feature of the dynamics of enzymes.

How Enzymes Work: A Look through the Perspective of Molecular Viscoelastic Properties

“…The enzyme structure exhibits long-lived nonequilibrium states during the catalytic cycle, and rates for the forward and backward reaction are, in general, different. These same ideas are reflected in the present model, which in addition contains an explicit representation of the mechanical ''relaxation'' cycle based on the experimental data now available on the viscoelastic transition of enzyme dynamics [25]. Indeed, this paper can be thought of as fulfilling, to some extent, Blumenfeld's program as expressed in [26], where we read the following statement in his conclusion: ''.…”

Plasmon resonance enhanced mechanical detection of ligand binding

“…Previous measurements with this setup were performed in this evanescent wave scattering (EWS) regime. [4][5][6][7] In Fig. 3, we show the low frequency viscoelastic response of the enzyme GK measured using SPR (squares) and EWS (i.e., off resonance: circles).…”

“…4,6,7 Briefly, the molecule under study (here, the enzyme Guanylate Kinase: GK) tethers 20 nm gold nanoparticles (GNPs) to a 30 nm thick gold layer deposited on a glass slide (Fig. 1).…”

Dissipation at the angstrom scale: Probing the surface and interior of an enzyme

“…In the following we will often use, in discussing the data, the simplest model of visco-elasticity, which is the Maxwell model. While it is a linear model, it describes the frequency dependence of the deformation amplitude measured in the experiments remarkably well [11]. We therefore summarize it here.…”

“…High and low refers to a characteristic corner frequency ω c ∼ 100 rad/s well defined in the experiments. The system is nonlinear in that, for example, the characteristic frequency ω c depends on the amplitude F 0 of the applied force [11]. Indeed, at fixed forcing frequency ω and for increasing F 0 , the system undergoes an abrupt dynamic softening transition at a critical deformation amplitude x c ∼ 1Å (rms) [12].…”