Kinetic versus Energetic Discrimination in Biological Copying

Abstract

We study stochastic copying schemes in which discrimination between a right and a wrong match is achieved via different kinetic barriers or different binding energies of the two matches. We demonstrate that, in single-step reactions, the two discrimination mechanisms are strictly alternative and can not be mixed to further reduce the error fraction. Close to the lowest error limit, kinetic discrimination results in a diverging copying velocity and dissipation per copied bit. On the opposite, energetic discrimination reaches its lowest error limit in an adiabatic regime where dissipation and velocity vanish. By analyzing experimentally measured kinetic rates of two DNA polymerases, T7 and Polγ, we argue that one of them operates in the kinetic and the other in the energetic regime. Finally, we show how the two mechanisms can be combined in copying schemes implementing error correction through a proofreading pathway.PACS numbers: 87.10. Vg, 87.18.Tt, 05.70.Ln Living organisms need to process signals in a fast and reliable way. Copying information is a task of particular relevance, as it is required for the replication of the genetic code, the transcription of DNA into mRNA, and its translation into a protein. Reliability is fundamental, since errors can result in the costly (or harmful) production of a non-functional protein. Indeed, cells have developed mechanisms to reduce the copying error rate η to values as low as η ∼ 10 −4 for protein transcription-translation [1] and η ∼ 10 −10 for DNA replication [2]. Such mechanisms include multiple discrimination steps [1, 2] and pathways to undo wrong copies as in proofreading [2,[4][5][6] or backtracking [7].Biological information is copied by thermodynamic machines that operate at a finite temperature. There is agreement that this fact alone implies a lower limit on the error rate. However, contrasting results have been obtained regarding the nature of this limit. In particular, it is not clear when it is reached in a slow and quasi-adiabiatic regime, or in a fast and dissipative one. As clarified by Bennett [8], information can be copied adiabatically. Indeed, the copying scheme proposed in Hopfield's seminal proofreading paper [2] reaches its minimum error at zero velocity and zero dissipation [9]. In contrast, a copolymerization model proposed few years later by Bennett [1,11,12], achieves its minimum error in a highly dissipative regime, where velocity and dissipation diverge. Some of the biological literature has favoured that the minimum error is achieved in near-equilibrium conditions [9]. This view is however not unanimous [13]. Recent biophysical literature supports a dissipative minimum error limit [11,12,14,15]. Similar disagreements are also present in models including proofreading. The proofreading model in [1] dissipates systematically less than the corresponding copying, while in other models [2, 4], at low errors, dissipation comes mainly from the proofreading step.In this Letter, we show how these contrasting results can be rationalized noting that...

Thermodynamic Uncertainty Relation for Biomolecular Processes

“…The role of energy dissipation in a variety of processes related to biological information processing has received much attention recently [1][2][3][4][5][6][7][8][9][10][11][12][13][14], to give just one class of examples for which one tries to uncover fundamental limits involving energy dissipation in biomolecular systems.…”

Thermodynamics of accuracy in kinetic proofreading: dissipation and efficiency trade-offs

“…The time-error and dissipation-error trade-offs are the same of those obtained by copolymerization models [16]. However, the definition of efficiency allows us to shed new light on this processes.…”

“…In other words, the network topology does not discriminate. According to [16], the substrates discrimination is embedded in the rate constants. Indeed, the substrates are distinguished either because of differences of chemical complex binding energies (the typical example is DNA replication and RNA transcription, in which there is an affinity difference between matching and mismatching nucleotide pairs), or because the activation energies related to the reaction involving the right substrate are lower than for the other ones (figure 2(left), describing the energy landscape of the Michaelis-Menten reaction scheme, can help in visualizing these ideas).…”

Computational investigations on polymerase actions in gene transcription and replication: Combining physical modeling and atomistic simulations

“…The study indicates that a sustained non--equilibrium steady state essentially drives the polymerization error rate to transit from a thermodynamically determined value to a kinetically determined one, i.e., the fidelity is achieved under the "flux--driven kinetic checkpoints" 75 . The two discrimination mechanisms involving either energetic (different binding energies) or kinetic (different kinetic barriers) differentiation are also analyzed more recently in 76 . It is shown that though the two mechanisms cannot be mixed in a single--step reaction to reduce errors, they can be combined in coping schemes with error correction through proofreading 76 .…”

“…The two discrimination mechanisms involving either energetic (different binding energies) or kinetic (different kinetic barriers) differentiation are also analyzed more recently in 76 . It is shown that though the two mechanisms cannot be mixed in a single--step reaction to reduce errors, they can be combined in coping schemes with error correction through proofreading 76 .…”