Synergy among Pausing, Intrinsic Proofreading, and Accessory Proteins Results in Optimal Transcription Speed and Tolerable Accuracy.

Cleavage of dinucleotides after the misincorporational pauses serves as a proofreading mechanism that increases transcriptional elongation accuracy. The accuracy is further improved by accessory proteins such as GreA and TFIIS. However, it is not clear why RNAP pauses and why cleavage-factor-assisted proofreading is necessary despite transcriptional errors in vitro being of the same order as those in downstream translation. Here, we developed a chemical-kinetic model that incorporates most relevant features of transcriptional proofreading and uncovers how the balance between speed and accuracy is achieved. We found that long pauses are essential for high accuracy, whereas cleavage-factor-stimulated proofreading optimizes speed. Moreover, in comparison to the cleavage of a single nucleotide or three nucleotides, RNAP backtracking and dinucleotide cleavage improve both speed and accuracy. Our results thereby show how the molecular mechanism and the kinetic parameters of the transcriptional process were evolutionarily optimized to achieve maximal speed and tolerable accuracy.

Theoretical Analysis Reveals the Cost and Benefit of Proofreading in Coronavirus Genome Replication.

Severe acute respiratory syndrome coronaviruses have unusually large RNA genomes replicated by a multiprotein complex containing an RNA-dependent RNA polymerase (RdRp). Exonuclease activity enables the RdRp complex to remove wrongly incorporated bases via proofreading, a process not utilized by other RNA viruses. However, it is unclear why the RdRp complex needs proofreading and what the associated trade-offs are. Here we investigate the interplay among the accuracy, speed, and energetic cost of proofreading in the RdRp complex using a kinetic model and bioinformatics analysis. We find that proofreading nearly optimizes the rate of functional virus production. However, we find that further optimization would lead to a significant increase in the proofreading cost. Unexpected importance of the cost minimization is further supported by other global analyses. We speculate that cost optimization could help avoid cell defense responses. Thus, proofreading is essential for the production of functional viruses, but its rate is limited by energy costs.

Do We Understand the Mechanisms Used by Biological Systems to Correct Their Errors?

Most cellular processes involved in biological information processing display a surprisingly low error rate despite the stochasticity of the underlying biochemical reactions and the presence of competing chemical species. Such high fidelity is the result of nonequilibrium kinetic proofreading mechanisms, i.e., the existence of dissipative pathways for correcting the reactions that went in the wrong direction. While proofreading was often studied from the perspective of error minimization, a number of recent studies have demonstrated that the underlying mechanisms need to consider the interplay of other characteristic properties such as speed, energy dissipation, and noise reduction. Here, we present current views and new insights on the mechanisms of error-correction phenomena and various trade-off scenarios in the optimization of the functionality of biological systems. Existing challenges and future directions are also discussed.

Trade-Offs between Speed, Accuracy, and Dissipation in tRNAIle Aminoacylation.

Living systems maintain a high fidelity in information processing through kinetic proofreading, a mechanism for preferentially removing incorrect substrates at the cost of energy dissipation and slower speed. Proofreading mechanisms must balance their demand for higher speed, fewer errors, and lower dissipation, but it is unclear how rates of individual reaction steps are evolutionarily tuned to balance these needs, especially when multiple proofreading mechanisms are present. Here, using a discrete-state stochastic model, we analyze the optimization strategies in Escherichia coli isoleucyl-tRNA synthetase. Surprisingly, this enzyme adopts an economic proofreading strategy and improves speed and dissipation as long as the error is tolerable. Through global parameter sampling, we reveal a fundamental dissipation-error relation that bounds the enzyme's optimal performance and explains the importance of the post-transfer editing mechanism. The proximity of native system parameters to this bound demonstrates the importance of energy dissipation as an evolutionary force affecting fitness.

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

One of the most intriguing features of biological systems is their ability to regulate the steady-state fluxes of the underlying biochemical reactions; however, the regulatory mechanisms and their physicochemical properties are not fully understood. Fundamentally, flux regulation can be explained with a chemical kinetic formalism describing the transitions between discrete states, with the reaction rates defined by an underlying free energy landscape. Which features of the energy landscape affect the flux distribution? Here we prove that the ratios of the steady-state fluxes of quasi-first-order biochemical processes are invariant to energy perturbations of the discrete states and are only affected by the energy barriers. In other words, the nonequilibrium flux distribution is under kinetic and not thermodynamic control. We illustrate the generality of this result for three biological processes. For the network describing protein folding along competing pathways, the probabilities of proceeding via these pathways are shown to be invariant to the stability of the intermediates or to the presence of additional misfolded states. For the network describing protein synthesis, the error rate and the energy expenditure per peptide bond is proven to be independent of the stability of the intermediate states. For molecular motors such as myosin-V, the ratio of forward to backward steps and the number of adenosine 5'-triphosphate (ATP) molecules hydrolyzed per step is demonstrated to be invariant to energy perturbations of the intermediate states. These findings place important constraints on the ability of mutations and drug perturbations to affect the steady-state flux distribution for a wide class of biological processes.

Magic numbers, quantum delocalization, and orientational disordering in anionic hydrogen and deuterium clusters.

The Diffusion Monte Carlo (DMC) method was applied to anionic hydrogen clusters H-(H2)n (n = 1-16, 32) and their deuterated analogs using a polarizable all-atom potential energy surface (PES) developed by Calvo and Yurtsever. For the hydrogen clusters, the binding energy ΔEn appears to be a smooth function of the cluster size n, thus contradicting the previous claim that n = 12 is a "magic number" cluster. The structures of the low energy minima of the PES for these clusters belong to the icosahedral motif with the H2 molecules aligned toward the central H- ion. However, their ground state wavefunctions are highly delocalized and resemble neither the structures of the global nor local minima. Moreover, the strong nuclear quantum effects result in a nearly complete orientational disordering of the H2 molecules. For the deuterium clusters, the ground state wavefunctions are localized and the D2 molecules are aligned toward the central D- ion. However, their structures are still characterized as disordered and, as such, do not display size sensitivity. In addition, DMC simulations were performed on the mixed H-(H2)n(D2)p clusters with (n, p) = (6, 6) and (16, 16). Again, in contradiction to the previous claim, we found that the "more quantum" H2 molecules prefer to reside farther from the central H- ion than the D2 molecules.

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

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.

Quantum-induced solid-solid transitions and melting in the Lennard-Jones LJ38 cluster.

The solid-solid and melting transitions that occur in Lennard-Jones LJ n clusters have been both fascinating and challenging for the computational physics community over the last several decades. A number of attempts to extend these studies to the quantum case have also been made. Particularly interesting is the exploration of the parallel between the thermally induced and quantum-induced transitions. Yet, both numerically accurate and systematic studies of the latter are still lacking. In this paper, we apply the diffusion Monte Carlo method to the especially difficult case of LJ38. Starting with the truncated octahedral global minimum configuration, as the de Boer quantum delocalization parameter Λ increases, the system undergoes two consecutive solid-solid transitions, switching to anti-Mackay configurations. At sufficiently large values of Λ, the cluster is completely "melted," which is manifested by delocalization of the ground state wavefunction over a very large number of minima that represent several structural motifs.

Nuclear Quantum Effects and Thermodynamic Properties for Small (H2O)1-21X- Clusters (X- = F-, Cl-, Br-, I-).

We carried out accurate diffusion Monte Carlo (DMC) studies for small (H2O) NX- clusters ( N = 1-5; X- = F-, Cl-, Br-, I-) and their D2O isotopologues. We found remarkably good agreement (i.e., ∼0.1 kcal/mol or better) with no exceptions between the DMC solvation energies and the corresponding harmonic approximation (HA) estimates, due, apparently, to massive error cancellations. This is surprising, in particular, because HA does not account for a substantial (i.e., ∼ 3%) increase of the mean O-O distances, caused by the anharmonicity in conjunction with the nuclear quantum effects, although the other distances in the system are affected to a much lesser extent. This agreement for the solvation energies motivated us to extend the current study to larger ( N = 6-21) clusters to explore their thermodynamic properties using the harmonic superposition method (HSM). The HSM results for the solvation free energies in turn reveal that at finite temperatures the nuclear quantum effects (including the isotope effects) in these systems are miniscule.

Quantum Melting and Isotope Effects from Diffusion Monte Carlo Studies of p-H2 Clusters.

We present a rigorous characterization of the ground state structures of p-H2 clusters and their isotopologues using diffusion Monte Carlo combined with the inherent structures analysis. For the N = 19 cluster we explore the effect of "quantum melting" by quantifying the contributions of local minima to the ground state as a function of continuously varying particle mass. Doubling the cluster size leads to an enormous increase of its complexity: the ground state of (p-H2)38 is highly delocalized over a large number of minima representing all the funnels of the potential energy surface. The ground state of (o-D2)38 is also delocalized, but over a smaller subset of minima, which exclusively belong to the same disordered motif.

Binding energies from diffusion Monte Carlo for the MB-pol H2O and D2O dimer: A comparison to experimental values.

The diffusion Monte Carlo (DMC) method is applied to compute the ground state energies of the water monomer and dimer and their D2O isotopomers using MB-pol; the most recent and most accurate ab inito-based potential energy surface (PES). MB-pol has already demonstrated excellent agreement with high level electronic structure data, as well as agreement with some experimental, spectroscopic, and thermodynamic data. Here, the DMC binding energies of (H2O)2 and (D2O)2 agree with the corresponding values obtained from velocity map imaging within, respectively, 0.01 and 0.02 kcal/mol. This work adds two more valuable data points that highlight the accuracy of the MB-pol PES.

Assessing the Performance of the Diffusion Monte Carlo Method As Applied to the Water Monomer, Dimer, and Hexamer.

The diffusion Monte Carlo (DMC) method is applied to the water monomer, dimer, and hexamer using q-TIP4P/F, one of the most simple empirical water models with flexible monomers. The bias in the time step (Δτ) and population size (Nw) is investigated. For the binding energies, the bias in Δτ cancels nearly completely, whereas a noticeable bias in Nw remains. However, for the isotope shift (e.g, in the dimer binding energies between (H2O)2 and (D2O)2), the systematic errors in Nw do cancel. Consequently, very accurate results for the latter (within ∼0.01 kcal/mol) are obtained with moderate numerical effort (Nw ∼ 10(3)). For the water hexamer and its (D2O)6 isotopomer, the DMC results as a function of Nw are examined for the cage and prism isomers. For a given isomer, the issue of the walker population leaking out of the corresponding basin of attraction is addressed by using appropriate geometric constraints. The population size bias for the hexamer is more severe, and to maintain accuracy similar to that of the dimer, Nw must be increased by ∼2 orders of magnitude. Fortunately, when the energy difference between the cage and prism is taken, the biases cancel, thereby reducing the systematic errors to within ∼0.01 kcal/mol when using a population of Nw = 4.8 × 10(5) walkers. Consequently, a very accurate result for the isotope shift is also obtained. Notably, both the quantum and isotope effects for the prism-cage energy difference are small.

Metallophilic interactions from dispersion-corrected density-functional theory.

In this article, we present the first comprehensive study of metallophilic (aurophilic) interactions using dispersion-corrected density-functional theory. Dispersion interactions (an essential component of metallophilicity) are treated using the exchange-hole dipole moment (XDM) model. By comparing against coupled-cluster benchmark calculations on simple dimers, we show that LC-ωPBE-XDM is a viable functional to study interactions between closed-shell transition metals and that it performs uniformly better than second-order Møller-Plesset theory, the basic computational technique used in previous works. We apply LC-ωPBE-XDM to address several open questions regarding metallophilicity, such as the interplay between dispersion and relativistic effects, the interaction strength along group 11, the additivity of homo- and hetero-metallophilic effects, the stability of [E(AuPH3)4](+) cations (E = N, P, As, Sb), and the role of metallophilic effects in crystal packing. We find that relativistic effects explain the prevalence of aurophilicity not by stabilizing metal-metal contacts, but by preventing gold from forming ionic structures involving bridge anions (which are otherwise common for Ag and Cu) as a result of the increased electron affinity of the metal. Dispersion effects are less important than previously assumed and their stabilization contribution is relatively independent of the metal.