Trade-Offs between Error, Speed, Noise, and Energy Dissipation in Biological Processes with Proofreading

Abstract

High accuracy of major biological processes relies on the ability of the participating enzymatic molecules to preferentially select the correct substrate from a pool of chemically similar substrates by activating the so-called proofreading mechanisms. While the importance of such mechanisms is widely accepted, it is still unclear how evolution has optimized the biological systems with respect to certain characteristic properties. Here, using a discrete-state stochastic framework with a first-passage analysis, we theoretically investigate trade-offs between four characteristic properties of enzymatic systems, namely, error, speed, noise, and energy dissipation. Specifically, two fundamental biological processes are examined, i.e., DNA replication in the T7 bacteriophage and tRNA selection during protein translation in Escherichia coli. Notably, all of the characteristic properties cannot be completely optimized at the same time due to trade-offs between them. To understand the relative importance of the computed quantities to the enzymatic functionality, we introduce a new quantitative metric to rank the properties. The results demonstrate that the reaction speed is the principal characteristic property that evolution optimizes in both enzymatic systems and that the energy dissipation comes in second. In addition, the error and the noise are always ranked third and fourth, respectively, regardless of the system considered. Physicochemical arguments to explain these observations are presented.

Kinetic control of stationary flux ratios for a wide range of biochemical processes

“…Our examination of the biochemical network for aa-tRNA selection in the E. Coli ribosome 18,21,24,29,30 demostrates that our invariance statement holds in the presence of energy-dissipating cycles on the network. We show that both the error fraction and the normalized energy dissipation can be expressed as flux ratios, and therefore, they are invariant to changes in the energies of the intermediate states on the underlying free-energy landscape.…”

“…The kinetic parameters (rate constants) that correspond to the various reactions on the corresponding biochemical networks are given in the SI Tabs. S1-S3 23,26,[29][30][31][32] . For simplicity of the notation, we drop all of the prime and ω superscripts on the perturbed steady-state fluxes.…”

“…We illustrate the generality and the biological implications of our results by specifically studying three diverse biological systems. The examples include: (i) two alternative pathways for protein folding in the presence of misfolded error states, which is motivated by folding pathways in hen egg-white lysozyme 25,26 , (ii) a Hopfield KPR network describing aminoacyl(aa)-tRNA selection during protein translation in the Escherichia coli ribosome 18,24,[27][28][29][30] , and (iii) the myosin-V motor protein that walks along actin cytoskeleton filaments 20,23 . These results have wide-ranging implications for the types of genetic or chemical perturbations capable of changing the steady-state flux distribution through biochemical reaction networks.…”

Kinetic Proofreading and the Limits of Thermodynamic Uncertainty

“…where ∆µ = ∆µ KPR for proofreading cycles (N = 3) or ∆µ p for production cycle (N = p) and chemical potentials are hereafter measured in k B T units. We take the approximate physiological values of the chemical potential differences, ∆µ p ∼ 26k B T for poly-peptide elongation, ∆µ p ∼ 11k B T for nucleotide ligation and ∆µ KPR ∼ 20k B T for the hydrolysis KPR step in both systems [40]. For convenience, we also define discrimination factors f i which relate the R and rate constants as f…”

“…Taking the physiological state as a reference point, they investigated the speed-accuracy trade-off as a function of the kinetic rates, finding that speed is prioritized over error rate. In a follow-up work on the same systems, they found that speed is also prioritized over energy dissipation and output noise [40].…”