Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2012 Jul 24;109(30):12034-9.
doi: 10.1073/pnas.1119911109. Epub 2012 Jul 11.

Speed, Dissipation, and Error in Kinetic Proofreading

Affiliations
Free PMC article

Speed, Dissipation, and Error in Kinetic Proofreading

Arvind Murugan et al. Proc Natl Acad Sci U S A. .
Free PMC article

Abstract

Proofreading mechanisms increase specificity in biochemical reactions by allowing for the dissociation of intermediate complexes. These mechanisms disrupt and reset the reaction to undo errors at the cost of increased time of reaction and free energy expenditure. Here, we draw an analogy between proofreading and microtubule growth which share some of the features described above. Our analogy relates the statistics of growth and shrinkage of microtubules in physical space to the cycling of intermediate complexes in the space of chemical states in proofreading mechanisms. Using this analogy, we find a new kinetic regime of proofreading in which an exponential speed-up of the process can be achieved at the cost of a somewhat larger error rate. This regime is analogous to the transition region between two known growth regimes of microtubules (bounded and unbounded) and is sharply defined in the limit of large proofreading networks. We find that this advantageous regime of speed-error tradeoff might be present in proofreading schemes studied earlier in the charging of tRNA by tRNA synthetases, in RecA filament assembly on ssDNA, and in protein synthesis by ribosomes.

Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
Proofreading mechanism proposed by Hopfield (1). Substrates R, W compete to react with E, and form either the right product PR or the wrong one PW. The ESES reactions (S = R, W) are coupled to external out-of-equilibrium ATP- hydrolysis reactions.
Fig. 2.
Fig. 2.
Dominant transitions for Hopfield’s proofreading scheme in different kinetic limits. (A) In the limit of [1], both substrates S = W, R cycle many times around the loop in the reaction network which helps achieve the lowest possible error rate of η ∼ e-2Δ. (B) In the limit of [11], substrate S = R completes the reaction without much backtracking as shown here while W still backtracks as shown in (A).
Fig. 3.
Fig. 3.
A generalized proofreading network. (A) The enzyme E forms a complex with one with one of two substrates R, W and explores the network shown by executing a random walk on it. PR is the desired product (or final state) while PW is an incorrect product (an error). For good proofreading, one of the paths (bold line) must dominate the walk. (B) Schematic redrawing of the generalized network in (A) emphasizing the central reaction path from the initial free enzyme state E to final product molecules PR, PW. A typical trajectory involves moving a certain distance along the dominant path towards PR or PW before randomly taking one of the sideways paths back, undoing part or all of the reaction. The probability of taking a sideways path is higher for W than for R and hence the final product is reached exponentially less often for the incorrect substrate W.
Fig. 4.
Fig. 4.
Ladder network for kinetic proofreading. For both substrates, the reaction can proceed only in the forward direction along the top “rails” of their subgraphs and only backwards along the lower rail. This network can be defined using kinetic rate constants f, d, u and b, or equivalently using probabilities cR, cW and r.
Fig. 5.
Fig. 5.
Stochastic trajectory of bounded enzyme kinetics on a ladder network. The trajectory consists of forward moves on one rail, alternating with backward moves on the other rail. After many such stochastic cycles, the reaction ultimately reaches the final product S. For better visualization, enzyme kinetics were chosen to be close to the bounded-unbounded transition (but on the bounded side).
Fig. 6.
Fig. 6.
Examples of bounded and unbounded growth of microtubules. The fluctuations in the bounded walk are of size comparable to the mean displacement (σ ∼ μ). The unbounded walk amounts to a random walk and the fluctuations scale as the square root of the mean (formula image).
Fig. 7.
Fig. 7.
Behavior in different regions of parameter space (log(μ), log(λ)), where formula image and formula image. λ is related to events of “rescues” (r is the probability of rescue for both R and W), while μ is related to the probability of “catastrophes” for R, cR. We distinguish three regions in this parameter space—in the upper region, both R and W undergo bounded walks kinetics, giving very low error rate at the cost of slow product formation. In the diagonal central strip, R exhibits unbounded walk kinetics, while kinetics of W is that of bounded walks. Such kinetics save much time for proofreading, at a small expense in error rate. The shaded subregion minimizes the small expense in error rate and hence is particularly advantageous. In the third, lower region, both R and W exhibit unbounded walks. The width of the central strip is proportional to Δ.
Fig. 8.
Fig. 8.
An abstract one-dimensional representation of the space of possible kinetics for a proofreading model. The kinetics of R and W can differ only by a fixed amount, determined by their enzyme binding energy difference Δ, but can be shifted together within this space. Placing both R, W kinetics well within the bounded walk region is the traditional choice, leading to the minimal error rate η at the cost of slow product formation. However, placing them at transition area between the bounded and unbounded walks regimes offers a great speed-up of the reaction at a relatively small cost in the error rate η.

Similar articles

See all similar articles

Cited by 22 articles

See all "Cited by" articles

Publication types

LinkOut - more resources

Feedback