The main goal of this tutorial is to introduce young scientists to the theoretical
foundations of state-of-the-art ab-initio techniques through keynote lectures given by
world-leading experts. On the same occasion, young scientist will have the opportunity
to put this knowledge into practice through hands-on exercises with the software package
exciting based on density-functional theory (DFT). Therefore, exploring the fundamental
physical concepts in combination with practical exercises also comprises the important
pedagogical aspect of learning by doing. Each of the presented topic will be treated in
a twofold way, first introducing the general concepts and, then, presenting applications
to real materials. We will focus on the treatment of various excitations, crucial to
understand and predict electronic, optical, and thermodynamic properties of materials.
This is exactly the point where basic research meets the needs of industrial applications.
The development of new theoretical and computational approaches requires a flexible
organization of the program package as well as a developer-friendly environment.
The codes must be able to handle reliably sophisticated implementations of theoretical
concepts to allow for forefront basic research. At the same time, employing such codes
for practical purposes by non-specialists in programming or DFT asks for well documented
packages and a user-friendly environment. Only this way codes can be utilized in applied
materials research, i.e., also by industries. exciting fulfills all these needs, and the
program package covers a variety of tools for calculating and analyzing both ground-state
properties and excitations in condensed matter. We wish to provide training on this
package to the young generation of scientists and developers.
Besides the fundamentals related to the method and hands-on exercises, we will provide
keynote lectures given by world-leading experts in the various fields we want to focus on.
They will comprise the cornerstones of DFT, time-dependent DFT (TDDFT), many-body
perturbation theory (MBPT), linear response and phonons, superconductivity,
the GW method, thermoelectricity, and the physics of carbon monolayers.
The outcome of this tutorial will be manifold: (i) Since exciting solves the Kohn-Sham
equations very accurately and exhibits various unique features in terms of excited-state
properties, exciting can be more and more utilized as a benchmark for other methods which
make use of different approximations. (ii) Equipped with modern programming instruments
(e.g., XML input and output, a series of scripts for automatizing the computation of various
physical properties, and graphical analysis tools) exciting can be straightforwardly
interfaced with other packages. Since we will invite keynote speakers from various areas,
including experts in code-development, we also aim at confronting different techniques and
fostering possible collaborations towards future code development. Hence, the trainees will
have not only the chance to deeply work into the linearized augmented planewave (LAPW)
method, but also can benefit from a honest comparison with other methods. (iii) Introducing
the code to the young generation will contribute to its dissemination and future development.
The main goal of this tutorial is to introduce young scientists to the theoretical foundations of state-of-the-art first-principles techniques based on and going beyond densitiy-functional theory (DFT) through keynote lectures given by world-leading experts. On the same occasion, young scientist will have the opportunity to put this knowledge into practice through hands-on exercises with the software package This CECAM workshop aims at providing training to young people, making them familiar with the exciting code (see web site: http://exciting-code.org).
exciting is a young public-domain all-electron package based on DFT for the investigation of condensed matter on the atomic scale. It combines several major advantages: (i) It is a full-potential all-electron code based on the linearized augmented plane-wave (LAPW) method, which stands for highest precision and the fact that it can be used for any material. (ii) It is the only all-electron package comprising vast implementations of excited-state properties within TDDFT as well as many-body perturbation theory. (iii) It is developers-friendly through a clean and fully documented programming style, being written from scratch and handled with a modern version-control system (git). (iv) It is user-friendly through an easy-to-handle user interface comprising various tools to create and validate input files and analyze results. (v) It is seminal by being interfaced to packages operating on the next higher length scale and by the development of tools which allow for the handling by users from an industrial environment.Each of the presented topic will be treated in a twofold way: introducing the general concepts as well as presenting applications to real materials. We will focus on the treatment of various excitations, crucial to understand and predict electronic, optical, and lattice-dynamical properties of materials.
We will provide keynote lectures given by world-leading experts in the various fields we want to focus on. They will comprise the cornerstones of DFT, time-dependent DFT (TDDFT), many-body perturbation theory (MBPT) for one- and two-body Green functions, linear-response theory. Besides the fundamental theory, some presentations will be dedicated to cutting-edge applications such as thermoelectricity or the physics of carbon monolayers.
The typical session block of 1/2 a day will have the following structure:
Tutorial lecture
Talk about LAPW-specific features and implementation within the exciting code
Hands-on exercise
We plan 11 session blocks which results in a total of six and a half conference days including one day for the conference excursion.
Tutorial topics
Density-functional theory: Introduction and advances
Linear response to lattice excitations: Theory and applications
The GW approach: Survey, limitations, challenges, and applications
The Bethe-Salpeter equation (BSE): Survey, limitations, challenges, and applications
Time-dependent DFT: Survey, limitations, challenges, and applications
Applications: From thermoelectrics to the physics of carbon monolayer
Challenges in large-scale computations
LAPW-specific talks
The family of APW methods
Structural optimization with exciting
ElaStic@exciting
Phonons@exciting
TDDFT@exciting
GW@exciting
BSE@exciting
Core-excitations@exciting
exciting input and output
exciting templates & more
Hands-on exercises
Input/output and templating
Structure optimization
Kohn-Sham band structure and density of states
Elastic properties
Exchange-correlation functionals
Van-der-Waals interactions
Phonons and related properties
Quasi-partilce band structure from GW
Optical spectra and electron loss from TDDFT
Exciton spectra from BSE
Core excitations from BSE
exciting@web
References
[1] J.P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996)
[2] K. Burke and R. Magyar, ABC of DFT, http://dft.uci.edu/
[3] P. Giannozzi, S. de Gironcoli, P. Pavone, and S. Baroni, Ab-initio calculation of phonon dispersions in semiconductors, Phys. Rev. B 43, 7231 (1991)
[4] S. Baroni, S. de Gironcoli, A. Dal Corso, and P. Giannozzi, Phonons and related crystal properties from density-functional perturbation theory, Rev. Mod. Phys. 73, 515-562 (2001)
[5] S. Albrecht, L. Reining, R. Del Sole, and G. Onida, Ab initio calculation of excitonic effects in the optical spectra of semiconductors, Phys. Rev. Lett. 80, 4510 (1998)
[6] G. Onida, L. Reining, and A. Rubio, Electronic excitations: density-functional vs many-body Green's-function approaches, Rev. Mod. Phys. 74, 601 (2002)
[7] L.N. Oliveira, E.K.U. Gross, W. Kohn, Density-Functional Theory for Superconductors, Phys. Rev. Lett. 60, 2430 (1988)
[8] M.A.L. Marques and E.K.U. Gross, Time-Dependent Density-Functional Theory in "A Primer in Density Functional Theory", edited by C. Fiolhais, F. Nogueira, and M. Marques (Springer-Verlag, NY, 2003)
[9] M.S. Hybertsen and S.G. Louie, Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies, Phys. Rev. B 34, 5390 (1986)
[10] M.S. Hybertsen and S.G. Louie, First-Principles Theory of Quasiparticles: Calculation of Band Gaps in Semiconductors and Insulators, Phys. Rev. Lett. 55, 1418 (1985)
[11] J.O. Sofo, A.S. Chaudhari, and G.D. Barber, Graphane: A two-dimensional hydrocarbon, Phys. Rev. B 75, 153401 (2007)
[12] G.D. Mahan and J.O. Sofo, The best thermoelectric, Proc. Nat. Acad. Sci. U.S.A. 93, 7436 (1996)
[13] J.C. Grossman, E. Schwegler, E.W. Draeger, F. Gygi, and G. Galli, Towards an assessment of the accuracy of DFT for first principles simulations of water, J. Chem. Phys. 120, 300 (2004)
The first principles description of strongly correlated materials (typically materials containing partially filled d- or f-shells, but also e.g. low-dimensional organic systems) is currently one of the great challenges in condensed matter physics. Different approaches to tackle the problem beyond density-functional theory (DFT) within the local-density or generalized gradient approximation (LDA/GGA) are being pursued in the different subfields of the electronic structure community. We envisage that a symposium dedicated to the first principles treatment of correlations, covering approaches from Hedin's GW approximation, "LDA+U", or hybrid functionals up to random-phase approximation (RPA) and dynamical mean field (DMFT) techniques will provide the synergy to shape the future development in this important field.
We plan to have several well-known international experts as well as young, bright researchers who have already significantly contributed to the field. We expect this symposium to attract a diverse audience: those involved in formalism development and/or software implementation, as well as theoreticians and experimentalists working in physics, chemistry and material science.
The first principles description of strongly correlated materials (typically materials containing partially filled d- or f-shells, but also e.g. low-dimensional organic systems) is currently one of the great challenges in condensed matter physics. Different approaches to tackle the problem beyond density-functional theory (DFT) within the local-density or generalized gradient approximation (LDA/GGA) are being pursued in the different subfields of the electronic structure community. We envisage that a symposium dedicated to the first principles treatment of correlations, covering approaches from Hedin's GW approximation, "LDA+U", or hybrid functionals up to random-phase approximation (RPA) and dynamical mean field (DMFT) techniques will provide the synergy to shape the future development in this important field.We plan to have several well-known international experts as well as young, bright researchers who have already significantly contributed to the field. We expect this symposium to attract a diverse audience: those involved in formalism development and/or software implementation, as well as theoreticians and experimentalists working in physics, chemistry and material science.
中文摘要:设计并实现了一种采用微机械制造(MEMS)技术加工的D波段矩形波导膜片滤波器。采用有限元仿真软件HFSS分析了滤波器内腔镀膜厚度、粗糙度以及感性膜片厚度对滤波器主要性能的影响。采用MEMS深刻蚀工艺(DRIE)成功加工出了滤波器主体结构。通过完成结构深刻蚀、金属电镀和键合等关键工艺,首次制造出了D波段 MEMS波导滤波器。样品测试结果为插入损耗0.4-0.7dB,中心频率140?3GHz,带外抑制为≥18dB,样品主要技术指标与设计值符合。 中文关键词:微细加工 波导滤波器 太赫兹 DRIE
MEMS rectangular waveguide filter at 140GHz Xinghai Zhao, Guangcun Shan, Yingbin Zheng, Yijia Du, Yinghui Chen, Jie Liu, Cheng Wang, Jingfu Bao, Yang Gao
Abstract:The D-band MEMS rectangular waveguide iris filter is deigned and fabricated. The effects of metallized layer and iris thickness, roughness on filter main performances are investigated. The prototypes are fabricated using DRIE method. The key technique problems including deep etching, electroplating and bonding are researched and settled, the MEMS waveguide iris filter at 140GHz has been accomplished for the first time. The measured insert loss can get to be 0.4-0.7dB, central frequency is 140?3GHz,the isolation is larger than 18dB. The test results are in agreement with the simulations. keywords:RF MEMS Waveguide Filter THz DRIE
Figure 1 (a) The magnetic dipole field produced by an electron spin. Note that the magnetic field experienced by the nuclear spin has a transverse component along the x-axis, even though the electron spin is aligned with the external field along the -axis. Therefore, flipping the electron spin would lead to changes in both the magnitude and the direction of the magnetic field experienced by the nuclear spin. This is the essence of the anisotropic hyperfine interaction (AHF). (b) A malonic acid molecule. The red spheres are oxygen nuclei, the larger dark gray spheres are carbon nuclei, and the smaller light gray spheres are protons. One proton has been knocked off by x-ray irradiation, to leave a radical electron localized at the central carbon-13 nucleus. AHF is used in Ref. [7] to couple the nuclear spins of the carbon-13 and the proton via the electron spin.
Many nuclei have a magnetic moment that arises from their intrinsic spin. In an external magnetic field, these nuclei tend to align their moment with the field, just as a compass points to the North Pole in the Earth’s magnetic field. In many material systems, the nuclear spins are extremely well isolated from their environments, so that the dynamics of an individual nuclear spin is completely quantum coherent and governed by the Schrödinger equation of nonrelativistic quantum mechanics [1]. This high degree of quantum coherence makes some of the nuclear spins enticing candidates for bits for a quantum-mechanical computer [2]. However, the fact that these nuclear spins enjoy a quantum coherent “quiet life” also means that they are hard to access with external means, making them difficult to manipulate rapidly.
One of the established means to initialize, manipulate, and readout individual nuclear spins in a nanostructure is via an electron spin [2]. If an electron has a finite probability to be right on top of a nuclear spin, they interact through the so-called contact hyperfine interaction [1]. Otherwise they would still interact with each other through magnetic dipolar interaction, which decays as an inverse cubic function of the electron-nucleus distance, and is, in general, anisotropic (thus the name anisotropic hyperfine interaction), as shown in Fig.1(a). Electron spins are much easier and faster to control than nuclear spins because they interact strongly with both electric and magnetic fields, and their energies are in the microwave frequency regime. Indeed, in recent years there has been tremendous experimental progress in controlling and reading out single electron-spin states in a variety of systems, such as double dots [3, 4], nitrogen-vacancy (NV) centers in diamond [5], and phosphorus (P) donors [6]. Therefore, controlling nuclear spins via their hyperfine interaction with electron spins is becoming experimentally feasible.
In a paper appearing in Physical Review Letters, Yingjie Zhang and colleagues from the University of Waterloo, Canada, have demonstrated how two nuclear spins can be coupled by an electron via anisotropic hyperfine interaction in a solid-state environment [7]. The material system studied is an x-ray-irradiated crystal of malonic acid molecules, in which a radical electron is hyperfine coupled to a 13C nucleus and a proton, as shown in Fig.1(b). By applying various optimized electron-spin resonance (ESR) pulses in the microwave frequency range, Zhang et al. were able to create quantum coherence between the two nuclear spins, starting from an initial nuclear-spin state that is completely thermal and uncorrelated. The key for this experiment is the existence of the anisotropic component of the hyperfine interaction (AHF), which drives a nuclear spin to precess differently, depending on the electron-spin orientation, therefore allowing conditional operations on the nuclear spin. When such operations are applied to both nuclear spins, they acquire quantum-mechanical correlations between themselves from the common electron spin. In other words, the two nuclear spins can now get into lockstep in their precession—even though they do not talk to each other directly—because of the “directions” they receive from the ESR pulses via the common electron.
The current experiment points to a new way to enable nuclear-spin qubits in nanostructured systems, going beyond the complete reliance on the contact hyperfine interaction in past nuclear-spin qubit proposals [2]. Indeed, the presence of AHF allows complete control in the three-spin system, making malonic acid crystal at low temperature an interesting test bed of nuclear-spin qubit manipulations in a solid-state environment. In addition, with AHF one uses only microwave pulses (instead of both microwave and radio-frequency pulses) to control the nuclear spins, which speeds up the nuclear-spin manipulations significantly. In the current room-temperature experiment, nuclear-spin entanglement cannot be measured because they are pushed only slightly away from their initial thermal state. However, if the experiment is done at low temperature, the same experimental procedure would have led to nuclear-spin entanglement, which is the hallmark of quantum-mechanical correlation. Measurement of such correlation can be done using the microwave toolkit developed in the current experiment as well.
The future of the technique described in this paper seems bright. While malonic acid molecules may only be used to demonstrate the principle of nuclear-spin control and coupling, the same type of interactions are present in other more scalable systems. Among the most promising qubit candidates are the phosphorus donor nuclear spins in silicon (Si) [2] and NV centers in diamond [5]. The former takes advantage of the strong contact hyperfine interaction between the phosphorus nuclear spin and the localized donor electron spin, and is set in silicon, the dominant semiconductor of today. The latter uses the spin states of a strongly localized defect in diamond, has extremely good coherence properties even at room temperature, and can be manipulated optically. Like malonic acid molecules, both these spin qubit systems have hyperfine interactions that are strongly anisotropic, which has been clearly revealed in spin-echo experiments [8, 9]. Furthermore, an experiment has already been done to perform error correction encoding between an NV-center electron spin and an environmental 13C nuclear spin, and to couple two nuclear spins through the NV-center electron, helped by both microwave and radio-frequency pulses and optical readout [10]. Using the technique developed in the current paper, these and other experiments in and NV centers can potentially be done with less complexity, more efficiency, and faster speed, giving these materials systems a distinct advantage in terms of maneuverability.
From a broader perspective, AHF is already being used in biology and chemistry for the purpose of single nucleus recognition [1]. An all-microwave approach that can controllably couple multiple nuclear spins would enhance the toolkit of all the electron- and nuclear-spin spectroscopists. It is not clear whether such a new tool could be useful to applications such as magnetic resonance imaging, but that should hardly be an impediment to further explorations.
References
A. Schweiger and G. Jeschke, Principles of Pulse Electron Paramagnetic Resonance (Oxford University Press, New York, 2001).
A. Morello, J. J. Pla, F. A. Zwanenburg, K. W. Chan, K. Y. Tan, H. Huebl, M. Mottonen, C. D. Nugroho, C. Y, Yang, J. A. van Donkelaar, A. D. C. Alves, D. N. Jamieson, C. C. Escott, L. C. L. Hollenberg, R. G. Clark, and A. S. Dzurak, Nature467, 687 (2010).
W. M. Witzel, X. Hu, and S. Das Sarma, Phys. Rev. B76, 035212 (2007); E. Abe, A. M. Tyryshkin, S. Tojo, J. J. L. Morton, W. M. Witzel, A. Fujimoto, J. W. Ager, E. E. Haller, J. Isoya, S. A. Lyon, M. L. W. Thewalt, and K. M. Itoh, Phys. Rev. B82, 121201R (2010).
L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, Science314, 281 (2006).
L. Jiang, J. S. Hodges, J. R. Maze, P. Maurer, J. M. Taylor, D. G. Cory, P. R. Hemmer, R. L. Walsworth, A. Yacoby, A. S. Zibrov, and M. D. Lukin, Science326, 267 (2009).
PubMed Abstract: Understanding the energetics of molecular interactions is fundamental to all of the central quests of structural biology including structure prediction and design, mapping evolutionary pathways, learning how mutations cause disease, drug design, and relating structure to function. Hydrogen-bonding is widely...
Nature 453, 1266-1270 (26 June 2008) | doi:10.1038/nature06977; Received 24 January 2008; Accepted 8 April 2008;
Published online 25 May 2008
Modest stabilization by most hydrogen-bonded side-chain interactions in membrane proteins
Nathan HyunJoong Joh1, Andrew Min1, Salem Faham2, Julian P. Whitelegge3, Duan Yang1, Virgil L. Woods4 & James U. Bowie1
Department of Chemistry and Biochemistry, UCLA-DOE Center for Genomics and Proteomics, Molecular Biology Institute,
Department of Physiology, and,
The NPI-Semel Institute, Pasarow Mass Spec Laboratory, University of California, Los Angeles, California 90095, USA
Department of Medicine and Biomedical Sciences Graduate Program, University of California, San Diego, La Jolla, California 92093-0656, USA
Correspondence to: James U. Bowie1 Correspondence and requests for materials should be addressed to J.U.B. (Email: bowie@mbi.ucla.edu).
Abstract
Understanding the energetics of molecular interactions is fundamental to all of the central quests of structural biology including structure prediction and design, mapping evolutionary pathways, learning how mutations cause disease, drug design, and relating structure to function. Hydrogen-bonding is widely regarded as an important force in a membrane environment because of the low dielectric constant of membranes and a lack of competition from water1, 2, 3, 4, 5, 6. Indeed, polar residue substitutions are the most common disease-causing mutations in membrane proteins6, 7. Because of limited structural information and technical challenges, however, there have been few quantitative tests of hydrogen-bond strength in the context of large membrane proteins. Here we show, by using a double-mutant cycle analysis, that the average contribution of eight interhelical side-chain hydrogen-bonding interactions throughout bacteriorhodopsin is only 0.6kcalmol-1. In agreement with these experiments, we find that 4% of polar atoms in the non-polar core regions of membrane proteins have no hydrogen-bond partner and the lengths of buried hydrogen bonds in soluble proteins and membrane protein transmembrane regions are statistically identical. Our results indicate that most hydrogen-bond interactions in membrane proteins are only modestly stabilizing. Weak hydrogen-bonding should be reflected in considerations of membrane protein folding, dynamics, design, evolution and function.
The few evaluations of hydrogen-bond contributions in membrane proteins have tested the effect of single point mutants on either the free energy of unfolding or the free energy of dissociation4, 8, 9. However, these measurements combine hydrogen-bond contributions with desolvation and many other factors10, so the hydrogen-bond contribution cannot necessarily be extracted without the incorporation of correction factors11 that are particularly uncertain for membrane proteins.
The energetic complexities of single side-chain alterations can be illustrated by mutations in bacteriorhodopsin residues T90 and D115 that make two hydrogen bonds near the centre of the membrane (Fig. 1). We eliminated the hydrogen bonds by making T90A and D115A mutations and measured the change in the free energy of unfolding with an SDS unfolding assay9. The T90A mutation decreases stability by 1.3±0.1kcalmol-1, whereas the D115A mutant increases stability by 0.5±0.1kcalmol-1. The large variation suggests that hydrogen-bonding alone does not dominate the stability effects, and other energetic contributions must be accounted for. Below we present evidence that a principal factor is changes in solvation free energy in the unfolded protein.
For each cycle shown, the difference in free energies of unfolding (black number by the arrow) was measured for the pair of proteins connected by the arrow. Free energies of unfolding are compared at an SDS concentration at which the wild-type protein (WT) is 50% unfolded to minimize extrapolations needed. Errors are s.d. for three separate measurements. Next to each double-mutant cycle is a close-up view of the relevant hydrogen bond shown as blue dotted line between the altered side chains along with the heavy atom donor–acceptor distance. Donor and acceptor residues are labelled in green and blue, respectively. Donor–acceptor distinction in the two strongest interactions was arbitrary. On the basis of hydrogen-bonding patterns and nearest neighbours, it seems that all the potentially charged residues are the neutral species. The inset (bottom right) shows the location of each interaction in the context of the protein (PDB ID 1C3W). The planes of green dots indicate the estimated position of the edge of the hydrocarbon region of the bilayer as defined previously28. Any interaction mediated by the residues that contain at least one atom in the hydrocarbon region is mapped with the red line, and the interaction in the lipid/water interface region is mapped with a blue line.
To examine the effects of the T90A and D115A mutations on the folded state of bacteriorhodopsin, we solved the structures of the D115A mutant and a T90A/D115A double mutant (T90A proved too unstable to crystallize). We were unable to detect any structural changes in the mutant proteins that would obviously explain the contrasting energetic consequences, beyond the loss of density around the deleted side chains (see Fig. 2a).
a, Omit electron density maps and overlay of refined mutant and wild-type structures for D115A (top) and T90A/D115A (bottom) mutants. The wild-type structure (PDB ID 1PY6) is shown in rust, D115A in blue and T90A/D115A in grey. The mutated side chains are shown in ball-and-stick representation and labelled. The side chains of all residues within 4Å of T90 and D115 of the wild-type (WT) structure were eliminated during refinement for the omit map and are shown here with the exception of W182, which was left out for clarity. The electron density map is contoured at 1.0σ and 1.5σ for D115A and T90A/D115A, respectively. b, Plot of the number of hydrogens exchanged in the denatured state against time for peptides overlapping the T90A mutation (top), a region between T90A and D115A mutation (middle) and the D115A mutation (bottom). In brief, wild-type and mutant proteins were unfolded in SDS and incubated in D2O; the exchange reaction was quenched by rapidly lowering the temperature and pH. The proteins were then digested with pepsin, distinct peptides were separated chromatographically and the change in the mass envelope was measured by electrospray ionization-mass spectroscopy. The maximum scale on the y axis is the maximum number of exchangeable backbone amide hydrogens. Error bars are s.d. estimated with results from triplicate experiments. c, A plot of average exchange rates for peptides throughout the protein (top) and a schematic illustration of the bacteriorhodopsin structure (bottom) showing the sequences covered by the deuterium exchange experiment in light red. Error bars on the xaxis reflect the range of the peptic peptides, and those on the yaxis are s.d. for ten simulated data sets incorporating the experimental errors observed in the exchange time courses (see Methods).
To probe the consequences of the mutations on the unfolded state, we developed a hydrogen-exchange assay. Unfolded-state backbone hydrogens that are shielded from solvent by burial in the detergent micelle will exchange at a slower rate than backbone hydrogens exposed to the aqueous phase12, 13. Figure 2b shows the detailed time course of exchange for the unfolded state of the wild-type and mutant proteins at three regions, one resolved by the peptide overlapping the site of the T90A mutation, the second overlapping a region in between the sites of the T90A and D115A mutations, and the third overlapping the site of the D115A mutation. Figure 2c summarizes the average exchange rates of peptides throughout the unfolded states.
The T90A mutation modestly slows the exchange in the vicinity of position 90, whereas D115A markedly slows exchange in the vicinity of position 115. Although the sequence effects on intrinsic exchange rates14 are uncertain in an SDS environment15, the results suggest that the polar to non-polar substitutions alter the unfolded state by increasing burial in the detergent micelle at the sites of mutation. The larger change in polarity in D115A than in T90A is consistent with the larger effect on exchange rate and probably explains the stabilizing effect of the D115A mutation. In particular, the loss of the favourable escape of D115 to solvent could increase the free energy of the unfolded state in the D115A mutant, compensating for the increased free energy of the folded state. Thus, solvation effects in the unfolded state may mask the hydrogen-bond contribution that we wish to measure.
In an effort to obtain side-chain interaction energies within the folded state, we turned to double-mutant cycle analysis. Double-mutant cycle analysis has the potential to measure the free energy of side-chain interaction directly in the context of the folded protein by cancelling out energetic perturbations in both the folded and unfolded states that are not due to the interactions between the side chains16, 17. Thus, desolvation contributions and any other new interactions made in the unfolded state can be eliminated. As a result, double-mutant cycle analysis can be interpreted as reporting the contribution of the hydrogen-bonded interaction to the free energy of the folded state, not the difference in free energy between the folded and unfolded states. The unfolded state becomes simply a common reference state in which the interaction of interest is broken (see Supplementary Methods).
We were able to express and purify complete single-mutant and double-mutant sets for eight interhelical hydrogen-bonding interactions as shown in Fig. 1. Four of the hydrogen bonds are in the middle of the hydrocarbon core region of the bilayer, three are on the edge of the hydrocarbon core and one is in the interfacial region. The strongest interactions were T46–D96 and T90–D115, each contributing -1.7±0.3kcalmol-1, and T170–S226, contributing -0.8±0.3kcalmol-1. The strongest interactions, between T46 and D96 and between T90 and D115, both involve two hydrogen bonds, corresponding to about -0.9kcalmol-1 per hydrogen bond. Y185–D212 and S193–E204 make weaker, but favourable, interactions contributing -0.4±0.4 and -0.5±0.3kcalmol-1, respectively. The K30–Y43 and E9–Y79 interactions were found to make no measurable contribution to stability, and W189–Y83 was found to be slightly destabilizing, contributing +0.4±0.2kcalmol-1.
The results of the double-mutant cycles suggest three main conclusions. First, hydrogen-bonded side-chain contributions are quite variable and depend on the characteristics and local environment of each hydrogen bond. Second, the strength of a hydrogen-bonded interaction is not strongly correlated with the location in the protein. For example, the T170–S226 interaction in the interfacial region contributes -0.8±0.3kcalmol-1, whereas the T185–D212 interaction in the centre of the hydrocarbon core contributes only -0.4±0.4kcalmol-1. Third, the eight hydrogen-bonding interactions studied here make a remarkably modest average contribution of only about 0.6kcalmol-1, which corresponds to a roughly threefold effect on an equilibrium constant at room temperature.
Protein folding experiments are complex and not all variables can be eliminated, so we sought an additional, independent evaluation of the hydrogen-bond contribution in membrane proteins. We reasoned that if hydrogen-bond strengths were low, we would see a large number of unsatisfied hydrogen-bonding groups in membrane protein structures18. To test this idea, we examined six membrane protein structures solved at 1.7Å resolution or better. HBPLUS was used to identify the hydrogen-bonding of all polar atoms within the hydrocarbon core region of the bilayer. Any polar atoms that made no hydrogen bonds were further verified by eye.
The results are summarized in Table 1 and reveal that unsatisfied hydrogen bonds are not rare in the hydrocarbon core region (also see Supplementary Information). Of 2,892 protein donors and acceptors examined in the hydrocarbon core region, 111 have no hydrogen-bonding partner (about 4%). We believe this to be a low estimate of the number of unsatisfied hydrogen bonds because the HBPLUS criteria permit even marginal hydrogen bonds to be counted. Moreover, the crystal structure reports the predominant conformation and does not report the fraction of time for which a hydrogen bond is broken.
The hydrogen-bonded interaction strengths we measured in a membrane protein are very similar to hydrogen-bond strengths in soluble proteins measured in a variety of double-mutant cycle analyses (see Supplementary Fig. 1). Retrospectively, this finding is not unreasonable because the polarities of the interiors of soluble proteins and membrane proteins are quite similar19, 20. Because folding studies in soluble proteins are well accepted, we decided to validate our findings further by comparing hydrogen-acceptor distance distributions in membrane and soluble proteins. As summarized in Fig. 3, the buried hydrogen-bond distances in the interior of soluble and membrane protein transmembrane regions are statistically indistinguishable (see Supplementary Fig. 3 for full distributions), both averaging 2.02Å. However, the hydrogen-bond distances in surface residues are markedly different. For the transmembrane regions of membrane proteins, the hydrogen-acceptor distances on the surface are slightly shortened to 1.98Å on average, whereas for soluble proteins the average distance lengthens to 2.08Å. These results further validate our results, indicating similar contributions from interior hydrogen bonds in soluble and membrane proteins. It also hints that hydrogen bonds at the surface of membrane proteins may be stronger than what we have measured here for interior ones.
The arrows point towards the shorter hydrogen bonds. The Pvalue is the probability that the distance distributions are different by random chance based on Student’s t-test. The distributions are shown in Supplementary Information.
Many of the hydrogen-bonded residues we tested are involved in function, so it is possible that they are in a separate class from structural hydrogen-bonded side chains. However, previous work eliminating hydrogen bonds in structural residues is consistent with our findings. For example, a Gln residue that makes two hydrogen bonds across the interface of an OMPLA dimer contributes less than 1kcalmol-1 to dimerization (less than 0.5kcalmol-1 per hydrogen bond)21. An Asp to Ala substitution in a designed transmembrane helix oligomer decreases the free energy of association by 1.8kcalmol-1 (0.9kcalmol-1 per potential hydrogen bond)4. A T87A substitution in glycophorin A decreases the free energy of dimerization by 0.9kcalmol-1 (about 0.5kcalmol-1 per hydrogen bond in the dimer)22. Mutations in hydrogen-bonding polar residues in the T-cell receptor ζ-subunit dimer affected dimerization by a maximum of 7.7-fold, as indirectly measured by assembly rate, which corresponds to a maximum of about 1.2kcalmol-1 (0.6kcalmol-1 per residue in the dimer)8. Analysis of hydrogen-bonding mutations in bacteriorhodopsin (ref. 9) suggest a contribution of about 1kcalmol-1 (ref. 23). Because double-mutant cycle analysis was not employed in these cases, however, the results combine hydrogen-bond contributions with other effects that could contribute favourably or unfavourably10, 24.
Although our results indicate that most hydrogen-bond interactions observed in membrane proteins make modest energetic contributions, it does not mean that polar interactions cannot be strong. It has been found16 that charge-stabilized salt-bridge interactions can contribute 5.6kcalmol-1, and mutations in residues that hydrogen-bond to ligands in the β-adrenergic receptor can have marked effects on ligand binding25.
Why, then, are hydrogen-bond interactions not much stronger on average? It is possible that optimal geometries are difficult to achieve, that there are entropic costs to fixing hydrogen-bonded groups, and that polar groups in the protein can increase the local dielectric constant26. In addition to possible physical limitations, there may also be evolutionary pressure favouring weak hydrogen bonds. Evolutionary pressure for weak hydrogen bonds could come in the form of the conformational flexibility needed for protein function6. Moreover, the helical distortions that are common in membrane proteins would be hard to create by random mutation if the breakage of hydrogen bonds presented a large energy barrier. It is also possible that weak hydrogen bonds are more robust evolutionarily. Strong side-chain hydrogen bonds, once established, could no longer be altered by mutation without destroying fitness. Thus, proteins that rely on a strong hydrogen bond for stability would be more likely to be lost from a population than proteins that rely on more broadly distributed stabilizing interactions. Whatever the mechanism, our results indicate that it is not difficult to make and break interactions between polar residues, enabling the structural variation and dynamic flexibility necessary to optimize membrane protein function and folding. The results also suggest that a primary mechanism for the prevalence of disease-causing substitutions of polar residues may not be inappropriate hydrogen-bond formation but, instead, alterations in bilayer partitioning6. However, the loss or gain of even a weak hydrogen bond could tip the balance between biological function and dysfunction.
Stability measurements were performed essentially as described previously9. In brief, purple membrane was dissolved in a DMPC (1,2-dimyristoyl-sn-glycerol-3-phosphocholine)/CHAPSO (3((3-cholamidopropyl)dimethylammonio)-2-hydroxy-1-propanesulphonate) mixture and unfolded by adding increasing concentrations of SDS. Unfolding was monitored either by retinal absorbance at 560nm or far-ultraviolet circular dichroism at 228nm. Unfolding free energies were compared at the SDS concentration at which wild-type bacteriorhodopsin was 50% unfolded, to minimize the extrapolation error due to the varying m values.
X-ray crystallography
Crystals were grown by the bicelle method27 and, diffraction data were phased by molecular replacement.
Deuterium exchange
Unfolded proteins in SDS were deuterium-exchanged for various periods. The exchange reactions were then quenched by rapid cooling and the addition of low-pH buffer containing an acid-labile detergent to maintain solubility during digestion with pepsin. K+ was also included to precipitate SDS. Quenched reactions were flash-frozen and stored at -80°C. For analysis of deuterium exchange, the quenched reactions were rapidly thawed, treated with pepsin at 0°C and immediately analysed by liquid chromatography–mass spectrometry (LC–MS).
Structure analysis
To analyse unsatisfied hydrogen-bond donors and acceptors, the transmembrane regions were first identified as described28 and hydrogen bonds were identified with HBPLUS29. To obtain hydrogen-bond distance distributions, hydrogen-acceptor distances of all α-helix backbone–backbone hydrogen bonds in six high-resolution membrane protein structures and 839 unique soluble protein structures were calculated with HBPLUS. The soluble proteins chosen were solved in the same resolution range as the membrane proteins used.
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