Natural proteome diversity links aneuploidy tolerance to protein turnover.

Accessing the natural genetic diversity of species unveils hidden genetic traits, clarifies gene functions and allows the generalizability of laboratory findings to be assessed. One notable discovery made in natural isolates of Saccharomyces cerevisiae is that aneuploidy-an imbalance in chromosome copy numbers-is frequent1,2 (around 20%), which seems to contradict the substantial fitness costs and transient nature of aneuploidy when it is engineered in the laboratory3-5. Here we generate a proteomic resource and merge it with genomic1 and transcriptomic6 data for 796 euploid and aneuploid natural isolates. We find that natural and lab-generated aneuploids differ specifically at the proteome. In lab-generated aneuploids, some proteins-especially subunits of protein complexes-show reduced expression, but the overall protein levels correspond to the aneuploid gene dosage. By contrast, in natural isolates, more than 70% of proteins encoded on aneuploid chromosomes are dosage compensated, and average protein levels are shifted towards the euploid state chromosome-wide. At the molecular level, we detect an induction of structural components of the proteasome, increased levels of ubiquitination, and reveal an interdependency of protein turnover rates and attenuation. Our study thus highlights the role of protein turnover in mediating aneuploidy tolerance, and shows the utility of exploiting the natural diversity of species to attain generalizable molecular insights into complex biological processes.

The metabolic domestication syndrome of budding yeast.

Cellular metabolism evolves through changes in the structure and quantitative states of metabolic networks. Here, we explore the evolutionary dynamics of metabolic states by focusing on the collection of metabolite levels, the metabolome, which captures key aspects of cellular physiology. Using a phylogenetic framework, we profiled metabolites in 27 populations of nine budding yeast species, providing a graduated view of metabolic variation across multiple evolutionary time scales. Metabolite levels evolve more rapidly and independently of changes in the metabolic network's structure, providing complementary information to enzyme repertoire. Although metabolome variation accumulates mainly gradually over time, it is profoundly affected by domestication. We found pervasive signatures of convergent evolution in the metabolomes of independently domesticated clades of Saccharomyces cerevisiae. Such recurring metabolite differences between wild and domesticated populations affect a substantial part of the metabolome, including rewiring of the TCA cycle and several amino acids that influence aroma production, likely reflecting adaptation to human niches. Overall, our work reveals previously unrecognized diversity in central metabolism and the pervasive influence of human-driven selection on metabolite levels in yeasts.

Inorganic sulfur fixation via a new homocysteine synthase allows yeast cells to cooperatively compensate for methionine auxotrophy.

The assimilation, incorporation, and metabolism of sulfur is a fundamental process across all domains of life, yet how cells deal with varying sulfur availability is not well understood. We studied an unresolved conundrum of sulfur fixation in yeast, in which organosulfur auxotrophy caused by deletion of the homocysteine synthase Met17p is overcome when cells are inoculated at high cell density. In combining the use of self-establishing metabolically cooperating (SeMeCo) communities with proteomic, genetic, and biochemical approaches, we discovered an uncharacterized gene product YLL058Wp, herein named Hydrogen Sulfide Utilizing-1 (HSU1). Hsu1p acts as a homocysteine synthase and allows the cells to substitute for Met17p by reassimilating hydrosulfide ions leaked from met17Δ cells into O-acetyl-homoserine and forming homocysteine. Our results show that cells can cooperate to achieve sulfur fixation, indicating that the collective properties of microbial communities facilitate their basic metabolic capacity to overcome sulfur limitation.

Electronic Vector Potential from the Exact Factorization of a Complex Wavefunction.

We generalize the definitions of local scalar potentials named υ kin ${\upsilon _{{\rm{kin}}} }$ and υ N - 1 ${\upsilon _{N - 1} }$ , which are relevant to properly describe phenomena such as molecular dissociation with density-functional theory, to the case in which the electronic wavefunction corresponds to a complex current-carrying state. In such a case, an extra term in the form of a vector potential appears which cannot be gauged away. Both scalar and vector potentials are introduced via the exact factorization formalism which allows us to express the given Schrödinger equation as two coupled equations, one for the marginal and one for the conditional amplitude. The electronic vector potential is directly related to the paramagnetic current density carried by the total wavefunction and to the diamagnetic current density in the equation for the marginal amplitude. An explicit example of this vector potential in a triplet state of two non-interacting electrons is showcased together with its associated circulation, giving rise to a non-vanishing geometric phase. Some connections with the exact factorization for the full molecular wavefunction beyond the Born-Oppenheimer approximation are also discussed.

Vibrational Circular Dichroism Spectroscopy with a Classical Polarizable Force Field: Alanine in the Gas and Condensed Phases.

Polarizable force fields are an essential component for the chemically accurate modeling of complex molecular systems with a significant degree of fluxionality, beyond harmonic or perturbative approximations. In this contribution we examine the performance of such an approach for the vibrational spectroscopy of the alanine amino acid, in the gas and condensed phases, from the Fourier transform of appropriate time correlation functions generated along molecular dynamics (MD) trajectories. While the infrared (IR) spectrum only requires the electric dipole moment, the vibrational circular dichroism (VCD) spectrum further requires knowledge of the magnetic dipole moment, for which we provide relevant expressions to be used with polarizable force fields. The AMOEBA force field was employed here to model alanine in the neutral and zwitterionic isolated forms, solvated by water or nitrogen, and as a crystal. Within this framework, comparison of the electric and magnetic dipole moments to those obtained with nuclear velocity perturbation theory based on density-functional theory for the same MD trajectories are found to agree well with one another. The statistical convergence of the IR and VCD spectra is examined and found to be more demanding in the latter case. Comparisons with experimental frequencies are also provided for the condensed phases.

Exploring Exact-Factorization-Based Trajectories for Low-Energy Dynamics near a Conical Intersection.

We study low-energy dynamics generated by a two-dimensional two-state Jahn-Teller Hamiltonian in the vicinity of a conical intersection using quantum wave packet and trajectory dynamics. Recently, these dynamics were studied by comparing the adiabatic representation and the exact factorization, with the purpose to highlight the different nature of topological-phase and geometric-phase effects arising in the two theoretical representations of the same problem. Here, we employ the exact factorization to understand how to accurately model low-energy dynamics in the vicinity of a conical intersection using an approximate description of the nuclear motion that uses trajectories. We find that since nonadiabatic effects are weak but non-negligible, the trajectory-based description that invokes the classical approximation struggles to capture the correct behavior.

Nonadiabatic dynamics with classical trajectories: The problem of an initial coherent superposition of electronic states.

Advances in coherent light sources and development of pump-probe techniques in recent decades have opened the way to study electronic motion in its natural time scale. When an ultrashort laser pulse interacts with a molecular target, a coherent superposition of electronic states is created and the triggered electron dynamics is coupled to the nuclear motion. A natural and computationally efficient choice to simulate this correlated dynamics is a trajectory-based method where the quantum-mechanical electronic evolution is coupled to a classical-like nuclear dynamics. These methods must approximate the initial correlated electron-nuclear state by associating an initial electronic wavefunction to each classical trajectory in the ensemble. Different possibilities exist that reproduce the initial populations of the exact molecular wavefunction when represented in a basis. We show that different choices yield different dynamics and explore the effect of this choice in Ehrenfest, surface hopping, and exact-factorization-based coupled-trajectory schemes in a one-dimensional two-electronic-state model system that can be solved numerically exactly. This work aims to clarify the problems that standard trajectory-based techniques might have when a coherent superposition of electronic states is created to initialize the dynamics, to discuss what properties and observables are affected by different choices of electronic initial conditions and to point out the importance of quantum-momentum-induced electronic transitions in coupled-trajectory schemes.

Influence of the environment on the infrared spectrum of alanine: An effective mode analysis.

The vibrational spectrum of the alanine amino acid was computationally determined in the infrared range 1000-2000 cm-1, under various environments encompassing the gas, hydrated, and crystalline phases, by means of classical molecular dynamics trajectories, carried out with the Atomic Multipole Optimized Energetics for Biomolecular Simulation polarizable force field. An effective mode analysis was performed, in which the spectra are optimally decomposed into different absorption bands arising from well-defined internal modes. In the gas phase, this analysis allows us to unravel the significant differences between the spectra obtained for the neutral and zwitterionic forms of alanine. In condensed phases, the method provides invaluable insight into the molecular origins of the vibrational bands and further shows that peaks with similar positions can be traced to rather different molecular motions.

Quantum dynamics with curvilinear coordinates: models and kinetic energy operator.

In order to simplify the numerical solution of the time-dependent or time-independent Schrödinger equations associated with atomic and molecular motions, the use of well-adapted coordinates is essential. Usually, this set of curvilinear coordinates leads to a Hamiltonian operator that is as separable as possible. Although their corresponding kinetic energy operator (KEO) expressions can be derived analytically for small systems or special kinds of coordinates, a numerical and exact approach allows one to compute them in terms of sophisticated curvilinear coordinates. Furthermore, the numerical approach enables one to easily define reduced-dimensionality or constrained models. We present here a recent implementation of this numerical approach that allows nested coordinate transformations, therefore leading to great flexibility in the definition of the curvilinear coordinates. Furthermore, this implementation has no limitations in terms of numbers of atoms or coordinate transformations. The quantum dynamics of the cis-trans photoisomerization of part of the retinal chromophore illustrates the construction of the coordinates and KEO part of a three-dimensional model. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

A Photochemical Reaction in Different Theoretical Representations.

The Born-Oppenheimer picture has forged our representation and interpretation of photochemical processes, from photoexcitation down to the passage through a conical intersection, a funnel connecting different electronic states. In this work, we analyze a full in silico photochemical experiment, from the explicit electronic excitation by a laser pulse to the formation of photoproducts following a nonradiative decay through a conical intersection, by contrasting the picture offered by Born-Oppenheimer and that proposed by the exact factorization. The exact factorization offers an alternative understanding of photochemistry that does not rely on concepts such as electronic states, nonadiabatic couplings, and conical intersections. On the basis of nonadiabatic quantum dynamics performed for a two-state 2D model system, this work allows us to compare Born-Oppenheimer and exact factorization for (i) an explicit photoexcitation with and without the Condon approximation, (ii) the passage of a nuclear wavepacket through a conical intersection, (iii) the formation of excited stationary states in the Franck-Condon region, and (iv) the use of classical and quantum trajectories in the exact factorization picture to capture nonadiabatic processes triggered by a laser pulse.

Describing the photo-isomerization of a retinal chromophore model with coupled and quantum trajectories.

The exact factorization of the electron-nuclear wavefunction is applied to the study of photo-isomerization of a retinal chromophore model. We describe such an ultrafast nonadiabatic process by analyzing the time-dependent potentials of the theory and by mimicking nuclear dynamics with quantum and coupled trajectories. The time-dependent vector and scalar potentials are the signature of the exact factorization, as they guide nuclear dynamics by encoding the complete electronic dynamics and including excited-state effects. Analysis of the potentials is, thus, essential-when possible-to predict the time-dependent behavior of the system of interest. In this work, we employ the exact time-dependent potentials, available for the numerically exactly solvable model used here, to propagate quantum nuclear trajectories representing the isomerization reaction of the retinal chromophore. The quantum trajectories are the best possible trajectory-based description of the reaction when using the exact-factorization formalism and, thus, allow us to assess the performance of the coupled-trajectory, fully approximate schemes derived from the exact-factorization equations.

Exact Factorization Adventures: A Promising Approach for Non-Bound States.

Modeling the dynamics of non-bound states in molecules requires an accurate description of how electronic motion affects nuclear motion and vice-versa. The exact factorization (XF) approach offers a unique perspective, in that it provides potentials that act on the nuclear subsystem or electronic subsystem, which contain the effects of the coupling to the other subsystem in an exact way. We briefly review the various applications of the XF idea in different realms, and how features of these potentials aid in the interpretation of two different laser-driven dissociation mechanisms. We present a detailed study of the different ways the coupling terms in recently-developed XF-based mixed quantum-classical approximations are evaluated, where either truly coupled trajectories, or auxiliary trajectories that mimic the coupling are used, and discuss their effect in both a surface-hopping framework as well as the rigorously-derived coupled-trajectory mixed quantum-classical approach.

Electronic Structure and Excited States of the Collision Reaction O(3P) + C2H4: A Multiconfigurational Perspective.

We present a study of the O(3P) + C2H4 scattering reaction, a process that takes place in the interstellar medium and is of relevance in atmospheric chemistry as well. A comprehensive investigation of the electronic properties of the system has been carried out based on multiconfigurational ab initio CASSCF/CASPT2 calculations, using a robust and consistent active space that can deliver accurate potential energy surfaces in the key regions visited by the system. The paper discloses detailed description of the primary reaction pathways and the relevant singlet and triplet excited states at the CASSCF and CASPT2 level, including an accurate description of the critical configurations, such as minima and transition states. The chosen active space and the CASSCF/CASPT2 computational protocol are assessed against coupled-cluster calculations to further check the stability and reliability of the entire multiconfigurational procedure.

Relaxation dynamics through a conical intersection: Quantum and quantum-classical studies.

We study the relaxation process through a conical intersection of a photo-excited retinal chromophore model. The analysis is based on a two-electronic-state two-dimensional Hamiltonian developed by Hahn and Stock [J. Phys. Chem. B 104 1146 (2000)] to reproduce, with a minimal model, the main features of the 11-cis to all-trans isomerization of the retinal of rhodopsin. In particular, we focus on the performance of various trajectory-based schemes to nonadiabatic dynamics, and we compare quantum-classical results to the numerically exact quantum vibronic wavepacket dynamics. The purpose of this work is to investigate, by analyzing electronic and nuclear observables, how the sampling of initial conditions for the trajectories affects the subsequent dynamics.

Quantum-classical nonadiabatic dynamics of Floquet driven systems.

We develop a trajectory-based approach for excited-state molecular dynamics simulations of systems subject to an external periodic drive. We combine the exact-factorization formalism, allowing us to treat electron-nuclear systems in nonadiabatic regimes, with the Floquet formalism for time-periodic processes. The theory is developed starting with the molecular time-dependent Schrödinger equation with the inclusion of an external periodic drive that couples to the system dipole moment. With the support of the Floquet formalism, quantum dynamics is approximated by combining classical-like, trajectory-based, nuclear evolution with electronic dynamics represented in the Floquet basis. The resulting algorithm, which is an extension of the coupled-trajectory mixed quantum-classical scheme for periodically driven systems, is applied to a model study, exactly solvable, with different field intensities.

Spin-Orbit Interactions in Ultrafast Molecular Processes.

We investigate spin-orbit interactions in ultrafast molecular processes employing the exact factorization of the electron-nuclear wave function. We revisit the original derivation by including spin-orbit coupling, and show how the dynamics driven by the time-dependent potential energy surface alleviates inconsistencies arising from different electronic representations. We propose a novel trajectory-based scheme to simulate spin-forbidden non-radiative processes, and we show its performance in the treatment of excited-state dynamics where spin-orbit effects couple different spin multiplets.

Quantum Trajectories for the Dynamics in the Exact Factorization Framework: A Proof-of-Principle Test.

In the framework of the exact factorization of the time-dependent electron-nuclear wave function, we investigate the possibility of solving the nuclear time-dependent Schrödinger equation based on trajectories. The nuclear equation is separated in a Hamilton-Jacobi equation for the phase of the wave function, and a continuity equation for its (squared) modulus. For illustrative adiabatic and nonadiabatic one-dimensional models, we implement a procedure to follow the evolution of the nuclear density along the characteristics of the Hamilton-Jacobi equation. Those characteristics are referred to as quantum trajectories, since they are generated via ordinary differential equations similar to Hamilton's equations, but including the so-called quantum potential, and they can be used to reconstruct exactly the quantum-mechanical nuclear wave function, provided infinite initial conditions are propagated in time.

Biocatalysis with Unnatural Amino Acids: Enzymology Meets Xenobiology.

The goal of xenobiology is to design biological systems endowed with unusual biochemical functions, whereas enzymology concerns the study of enzymes, the workhorses of biocatalysis. Biocatalysis employs enzymes and organisms to perform useful biotransformations in synthetic chemistry and biotechnology. During the past few years, the effects of incorporating noncanonical amino acids (ncAAs) into enzymes with potential applications in biocatalysis have been increasingly investigated. In this Review, we provide an overview of the effects of new chemical functionalities that have been introduced into proteins to improve various facets of enzymatic catalysis. We also discuss future research avenues that will complement unnatural mutagenesis with standard protein engineering to produce novel and versatile biocatalysts with applications in synthetic organic chemistry and biotechnology.

Electronic Flux Density beyond the Born-Oppenheimer Approximation.

In the Born-Oppenheimer approximation, the electronic wave function is typically real-valued and hence the electronic flux density (current density) seems to vanish. This is unfortunate for chemistry, because it precludes the possibility to monitor the electronic motion associated with the nuclear motion during chemical rearrangements from a Born-Oppenheimer simulation of the process. We study an electronic flux density obtained from a correction to the electronic wave function. This correction is derived via nuclear velocity perturbation theory applied in the framework of the exact factorization of electrons and nuclei. To compute the correction, only the ground state potential energy surface and the electronic wave function are needed. For a model system, we demonstrate that this electronic flux density approximates the true one very well, for coherent tunneling dynamics as well as for over-the-barrier scattering, and already for mass ratios between electrons and nuclei that are much larger than the true mass ratios.