Binding of synthetic nanobodies to the SARS-CoV-2 receptor-binding domain: the importance of salt bridges.

In this study, five different SARS-CoV-2 receptor-binding domain (RBD) models were created based on the crystal structures of RBD complexes with two synthetic nanobodies (Sb16 and Sb45). Microsecond all-atom MD simulations revealed that Sb16 and Sb45 substantially stabilized the flexible RBD loop (residues GLU471-SER494) due to the salt bridges and hydrogen bonding interactions between RBD and the synthetic nanobodies. However, the calculation of binding free energy displayed that Sb45 had a higher binding affinity to RBD than Sb16, in agreement with the experimental result. This is because Sb45 has stronger electrostatic attraction to RBD as compared to Sb16. In particular, the salt bridge GLU484-ARG33 in Sb45-RBD is stronger than the GLU484-LYS32 in Sb16-RBD. Furthermore, by comparing the binding affinity of Sb16 for two RBD mutants (E484K and K417N), we found that E484K mutation substantially reduced the binding affinity to Sb16, and K417N mutation had no significant effect, qualitatively in agreement with experimental studies. According to the binding free energy calculation, the strong electrostatic repulsion between LYS32 and LYS484 caused by E484K mutation destroys the salt bridge between LYS32 and GLU484 in the RBD wild type (WT). In contrast, the binding of the K417N mutant to Sb16 effectively maintains the salt bridge between LYS32 and GLU484. Therefore, our research suggests that the salt bridges between RBD and synthetic nanobodies are crucial for binding synthetic nanobodies to RBD, and a SARS-CoV-2 variant can escape neutralization from nanobodies by creating electrostatic repulsion between them.

Simulating the isotropic Raman spectra of O-H stretching mode in liquid H2O based on a machine learning potential: the influence of vibrational couplings.

In this study, we trained a deep potential (DP) for H2O, an accurate machine learning (ML) potential. We performed molecular dynamics (MD) simulations of liquid water using the DP model (or DeePMD simulations). Our results showed that the DP model exhibits DFT-level accuracy, and the DeePMD simulation is a promising approach for modeling the structural properties of liquid water. Based on the DeePMD simulation trajectories, we calculated the isotropic Raman spectra of the O-H stretching mode using the surface-specific velocity-velocity correlation function (ssVVCF), showing that the DeePMD/ssVVCF approach can correctly capture the bimodal characteristics of the experimental Raman spectra, with one peak located near 3400 cm-1 and the other near 3250 cm-1. The success of the DeePMD/ssVVCF approach should be credited to (1) the DFT-level accuracy of the DP model for H2O, (2) the ssVVCF formulation considering the coupling between vibrational modes, and (3) non-Condon effects. Furthermore, the DeePMD simulations revealed that the anharmonic interactions between the coupled water molecules in the first and second hydration shells should play an essential role in the strong mixing of the H-O-H bending mode and the O-H stretching mode, leading to the delocalization of the O-H stretching band. In particular, increasing the strength of hydrogen bonds would enhance the bend-stretch coupling, leading to the red-shifting of the O-H vibrational spectra and the increase in the intensity of the shoulder around 3250 cm-1.

An intramolecular-locked strategy for designing nonlinear optical materials with remarkable first hyperpolarizability.

To meet the expanding demands of high performance nonlinear optical (NLO) materials, an unprecedented intramolecular-locked strategy is proposed to design NLO materials with remarkable static first hyperpolarizability (ß0). This strategy means that importing a large steric hindrance group diphenylmethane (DPM) decreases the torsion angles (θ) between the donor {triphenylamine (TPA)} and acceptor {9-H-thioxanthen-9-one-10,10-dioxide (TXO)} units, as well as between the donor (TPA) and π-bridge (benzene) fragments. The decrease of θ can accelerate the intramolecular charge transfer and enhance the contributions of the TPA, TXO and quinoxaline-6,7-dicarbo-nitrile (QCN) fragments to the axial component of the ß0 value, and then the ß0 values of TPA-TXO (ß0 = 10 762 au) and TPA-QCN (ß0 = 22 495 au) are increased by 14.9% and 34.4%, respectively. Overall, the intramolecular-locked strategy is very effective for designing high performance NLO materials.

Electronic Spin Moment As a Catalytic Descriptor for Fe Single-Atom Catalysts Supported on C2N.

The electrocatalytic activity of transition-metal-based compounds is strongly related to the spin states. However, the underlying relationship connecting spin to catalytic activity remains unclear. Herein, we carried out density functional theory calculations on oxygen reduction reaction (ORR) catalyzed by Fe single-atom supported on C2N (C2N-Fe) to shed light on this relationship. It is found that the change of electronic spin moments of Fe and O2 due to molecular-catalyst adsorption scales with the amount of electron transfer from Fe to O2, which promotes the catalytic activity of C2N-Fe for driving ORR. The nearly linear relationship between the catalytic activity and spin moment variation suggests electronic spin moment as a promising catalytic descriptor for Fe single-atom based catalysts. Following the revealed relationship, the ORR barrier on C2N-Fe was tuned to be as low as 0.10 eV through judicious manipulation of spin states. These findings thus provide important insights into the relationship between catalytic activity and spin, leading to new strategies for designing transition metal single-atom catalysts.

Extension of the CAVS model to the simulation of helical peptides in a membrane environment.

Considering the effect of peptide insertion on the dipole potential of the lipid membrane, we extend the CAVS coarse-grained (CG) model to the simulation of helical peptides in a membrane environment. In this approach, the CG scheme for a peptide backbone is similar to the treatment in the united-atom model, while we treated the side chain of an amino acid by grouping 1-3 heavy atoms into a CG unit. The CAVS CG force field for peptides is optimized by reproducing the experimental results for the backbone (φ, ψ) distribution and predicting the PMF profiles of transferring organic molecules in a lipid bilayer membrane obtained from all-atom simulations. The CAVS simulation of a helical peptide in a phosphatidylcholine (PC) lipid bilayer revealed that the insertion of a peptide increases the dipole potential of the PC lipid bilayer, in which the peptide and its neutralized ions make a significant contribution. Finally, we carried out the CAVS simulation for five different helical peptides in the PC lipid bilayer to explore the behavior of peptide tilt, showing excellent agreement with the all-atom simulations. Our work suggests that the peptide tilt should relieve the deformation stress from the lipid bilayer, and the peptide aggregation could reduce the peptide tilt by resisting the deformation stress from the surrounding lipids.

Adsorption of Organic Molecules and Surfactants on Graphene: A Coarse-Grained Study.

The research studies on the adsorption of surfactants on graphene help us to know how to use surfactants to exfoliate graphene from graphite or functionalize the graphene surface. Among them, molecular dynamics (MD) simulation has been widely used to investigate the adsorption of organic molecules and surfactants on graphene. In particular, coarse-grained (CG) MD simulation greatly improves the computational efficiency by simplifying the complexity of the studied systems, allowing us to explore the structure and dynamics of complex systems on larger spatial scales and longer time scales. However, an accurate prediction of the adsorption of surfactants on graphene is required by optimizing the interaction between surfactants and graphene, which is often overlooked by some CG models. In this work, we found that an accurate prediction of the adsorption enthalpies of organic molecules on graphene can be achieved by optimizing the interactions between organic molecules and benzene. Meanwhile, we simulated the adsorption of a surfactant on single-layer and double-layer graphene nanosheets, respectively. Our results revealed that increasing the temperature would favor the interactions between hydrophilic groups of surfactants. In addition, we discovered that the surfactant prefers to be adsorbed on the inner surfaces of double-layer graphene compared with the outer surfaces, and this is owing to the dehydration in the middle of double-layer graphene, which is beneficial to the hydrophilic interactions between surfactant molecules inside the double-layer graphene.

Effects of native defects and cerium impurity on the monoclinic BiVO4 photocatalyst obtained via PBE+U calculations.

In this article, we report a periodic density functional theory (DFT) investigation on the formation of the native defects and cerium doping in monoclinic BiVO4 (m-BiVO4) and their effect on the electronic structures, using the Perdew-Burke-Ernzerhof functionals corrected for on-site Coulombic interactions (PBE+U). From the point defect formation energies and transition levels, the Bivac (Bi vacancy), Vvac (V vacancy), Oint (O interstitial) and CeV (Ce doping on V site) defects in m-BiVO4 are identified as shallow acceptors. For Ce doping in m-BiVO4, the substitution of Bi by Ce is energetically favorable in the single positively charged state (Ce) under Bi/V-poor conditions, while the substitution of V by Ce is in the single negatively charged state (Ce) under O-rich conditions. The calculated electronic structures suggest that Ce degrades the activity by an unoccupied deep level in the gap region, mainly composed of Ce 4f orbitals, which makes this defect as the photogenerated electron-hole recombination center, in good agreement with the experimental results. For Ce, no localized state exists within the calculated band gap. Its formation energy is sensitive to the chemical potentials and Fermi energy, suggesting that the Bi/V-poor and O-rich conditions are desirable to eliminate the deep-level states and improve photocatalysis. Our results provide insights into enhancing the photocatalytic activity of m-BiVO4 for energy and environmental applications through the rational design of defect-controlled synthesis conditions.

Effect of Cholesterol and 6-Ketocholestanol on Membrane Dipole Potential and Sterol Flip-Flop Motion in Bilayer Membranes.

A variety of experimental and theoretical approaches have been employed to investigate the sterol flip-flop motion in lipid bilayer membranes. However, the sterol effect on the dipole potential of lipid bilayer membranes is less well studied and the influence of dipole potential on sterol flip-flop motion in lipid bilayer membranes is less well understood. In our previous works, we have demonstrated the performance of our coarse-grained (CG) model in the computation of the dipole potential. In this work, five 30 µs CG simulations of dimyristoylphosphatidylcholine (DMPC) bilayers were carried out at different sterol concentrations (in a range from 10 to 50% mole fraction). Then, a comparison was made between the effects of cholesterol (CHOL) and 6-ketocholestanol (6-KC) on the dipole potential of DMPC lipid bilayers as well as the sterol flip-flop motion. Our CG simulations show that the membrane dipole potential is impacted more significantly by 6-KC than by CHOL. This finding is consistent with recent experimental studies. Meanwhile, our work suggests that the sterol-sterol interactions (in particular, electrostatic interactions) should be critical to the formation of sterol-sterol clusters, which would hinder the sterol flip-flop motion inside the lipid bilayers. This is in support of the recent experimental study on the sterol transportation in lipid bilayer membranes.

Extension of CAVS coarse-grained model to phospholipid membranes: The importance of electrostatics.

It is evident from experiment that electrostatic potential (or dipole potential) is positive inside PC or PE lipid bilayers in the absence of ions. MARTINI coarse-grained (CG) model, which has been widely used in simulating physical properties of lipid bilayers, fails to reproduce the positive value for the dipole potential in the membrane interior. Although the total dipole potential can be correctly described by the BMW/MARTINI model, the contribution from the ester dipoles, playing a nontrivial role in the electrostatic potential across lipid membranes, is neglected by this hybrid approach. In the ELBA CG model, the role of the ester dipoles is considered, but it is overweighed because various atomistic models have consistently shown that water is actually the leading contributor of dipole potential. Here, we present a CG approach by combining the BMW-like water model (namely CAVS model) with the ELBA-like lipid model proposed in this work. Our CG model was designed not only to correctly reproduce the positive values for the dipole potential inside PC and PE lipid bilayers but also to properly balance the individual contributions from the ester dipoles and water, surmounting the limitations of current CG models in the calculations of dipole potential. © 2017 Wiley Periodicals, Inc.

Effects of electrostatic interaction on the properties of ionic liquids correlated with the change of free volume.

In this study, the amount of free volume in ionic liquids (ILs) was calculated and found to be almost half to that of their isoelectronic neutral analogues. MD simulations revealed that the significantly compressed free volume in the ILs was dominantly attributed to the strong inter-ion electrostatic interactions, which are comparable to the application of an external pressure of ∼250 MPa to the neutral analogues. Furthermore, the change in the free volume shows an interconnection with other properties of ILs, especially viscosity. The inherent high viscosity of ILs was quantitatively correlated to a low free volume available for mass transfer, and the sharp decrease in the viscosity of ILs with the addition of organic solvents was essentially caused by the introduction of free volume.

An anisotropic coarse-grained model based on Gay-Berne and electric multipole potentials and its application to simulate a DMPC bilayer in an implicit solvent model.

In this work, we aim at optimizing the performance of the anisotropic GBEMP model, which adopts a framework by combining a Gay-Berne (GB) anisotropic potential with an electric multipole (EMP) potential, in simulating a DMPC lipid bilayer in an implicit solvent model. First, the Gay-Berne parameters were initially obtained by fitting to atomistic profiles of van der Waals interactions between homodimers of molecular fragments while EMP parameters was directly derived from the expansion of point multipoles at predefined EMP sites. Second, the GB and EMP parameters for DMPC molecule were carefully optimized to be comparable to AMBER atomistic model in the calculations of the dipole moments of DMPC monomers adopting different conformations as well as the nonbonded interactions between two DMPC molecules adopting different conformations and separated at various distances. Finally, the GB parameters for DMPC were slightly adjusted in simulating a 72 DMPC bilayer system so that our GBEMP model would be able to reproduce a few important structural properties, namely, thickness (DHH), area per lipid ( AL) and volume per lipid ( VL). Meanwhile, the atomistic and experimental results for electron density profiles and order parameters were reproduced reasonably well by the GBEMP model, demonstrating the promising feature of GBEMP model in modeling lipid systems. Finally, we have shown that current GBEMP model is more efficient by a factor of about 25 than AMBER atomistic point charge model.

Binding modes and interaction mechanism between different base pairs and methylene blue trihydrate: a quantum mechanics study.

Different quantum mechanic methods have been evaluated for the calculation of binding modes and interactions between intercalators with different DNA base pairs by comparing with the results of MP2, which is very expensive, indicating that WB97XD method under 6-311+G* basis set is able to efficiently reproduce MP2 results. We discovered that the methylene blue trihydrate intercalated into the DNA base pairs, and DNA intercalation increased the distance between DNA base pairs, depending on the types of DNA bases. According to the binding energy results, it was found that the intercalation of methylene blue trihydrate into AA-TT base pair was more favorable in the orientation of nitrogen than other directions and intercalation, and the electric charge was transferred from methylene blue trihydrate to the AA-TT base pair. The analysis of change in the charge density shows that changes often take place in the heavy atom in the middle of the system which the charge density changes most remarkable.

Folding mechanisms of Trefoil Knot proteins studied by molecular dynamics simulations and Go-model.

Most proteins need to avoid the complex topologies when folding into the native structures, but some proteins with nontrivial topologies have been found in nature. Here we used protein unfolding simulations under high temperature and all-atom Go-model to investigate the folding mechanisms for two trefoil knot proteins. Results show that, the contacts in ß-sheet are important to the formation of knot protein, and if these contacts disappeared, the knot protein would be easy to untie. In the Go-model simulations, the folding processes of the two knot proteins are similar. The compact structures of the two knot proteins with the native contacts in ß-sheet are formed in transition state, and the intermediate state has loose C-terminal. This model also reveals the detailed folding mechanisms for the two proteins.

Theoretical studies on the folding mechanisms for different DNA G-quadruplexes.

The G-quadruplex DNA formed by the stack of guanines in human telomere sequence is a promising anticancer target. In this study we used the energy landscape theory to elucidate the folding mechanisms for the thrombin aptamer, Form 1 and Form 3 G-quadruplexes. The three G-quadruplexes were simulated with all-atom Go-model. Results show that, the three G-quadruplexes fold through a two-state mechanism. In the initial stage of the folding process, the compact structures are formed. The G-quadruplexes need to form G-triplex structures on the basis of the compact structures before folding to the native states. The folding free energy barrier of Form 3 G-quadruplex is higher than thrombin aptamer and Form 1, which shows that the structure of Form 3 G-quadruplex has more stability than the other two G-quadruplexes.

Modeling Vibrational Sum Frequency Generation Spectra of Interfacial Water on a Gold Surface: The Role of the Fermi Resonance.

Studying the hydrogen bonding structure of H2O at the metal-water interface is a highly complex yet fascinating endeavor. The intricate interactions and diverse orientations of water molecules on metal surfaces with varying potentials pose a significant challenge in elucidating the coupling between O-H stretching and H-O-H bending modes. In this study, we employed DFT-MD simulation to explore how the orientation of interfacial water molecules changes with the applied potential on the Au(111) surface. Based on the surface-specific velocity-velocity correlation function (ssVVCF) formula, we calculated vibrational sum frequency generation (VSFG) spectra for the O-H stretches. We found that three assigned peaks (∼3300, ∼3450, and 3650 cm-1) shifted toward lower frequencies as the potential moved toward more negative values. Our results align remarkably well with experimental Raman spectroscopy data. Notably, our VSFG analysis revealed a significant change in the VSFG spectra of the hydrogen-bonded O-H groups (∼3300 cm-1), switching from a negative to a positive sign with decreasing potential. This alteration suggests a substantial change in the orientation of these low-frequency O-H groups owing to their increased interactions with the Au surface. In contrast, the orientations of both the high-frequency O-H groups (∼3450 cm-1) and the dangling O-H groups (∼3650 cm-1) remained unaffected by the applied potentials. Furthermore, our analysis of the decomposed vibrational density of states (VDOS) for the H-O-H bending mode uncovered the coupling between the H-O-H bending and O-H stretching vibrations, known as the Fermi resonance. Our work suggests that the H-O-H bending vibration becomes restricted when water molecules transition from the ″one-H-down″ to the ″two-H-down″ conformation, leading to a redshift in the O-H stretching vibration through the Fermi resonance. By constructing the VSFG and decomposed VDOS spectra, we gained valuable insights into the structural changes that Raman spectra alone cannot fully interpret. Specifically, our analysis revealed the critical role of the Fermi resonance effect in shaping the spectroscopic signature of interfacial water molecules on the Au(111) surface.

What is the role of motif D in the nucleotide incorporation catalyzed by the RNA-dependent RNA polymerase from poliovirus?

Poliovirus (PV) is a well-characterized RNA virus, and the RNA-dependent RNA polymerase (RdRp) from PV (3D(pol)) has been widely employed as an important model for understanding the structure-function relationships of RNA and DNA polymerases. Many experimental studies of the kinetics of nucleotide incorporation by RNA and DNA polymerases suggest that each nucleotide incorporation cycle basically consists of six sequential steps: (1) an incoming nucleotide binds to the polymerase-primer/template complex; (2) the ternary complex (nucleotide-polymerase-primer/template) undergoes a conformational change; (3) phosphoryl transfer occurs (the chemistry step); (4) a post-chemistry conformational change occurs; (5) pyrophosphate is released; (6) RNA or DNA translocation. Recently, the importance of structural motif D in nucleotide incorporation has been recognized, but the functions of motif D are less well explored so far. In this work, we used two computational techniques, molecular dynamics (MD) simulation and quantum mechanics (QM) method, to explore the roles of motif D in nucleotide incorporation catalyzed by PV 3D(pol). We discovered that the motif D, exhibiting high flexibility in either the presence or the absence of RNA primer/template, might facilitate the transportation of incoming nucleotide or outgoing pyrophosphate. We observed that the dynamic behavior of motif A, which should be essential to the polymerase function, was greatly affected by the motions of motif D. In the end, through QM calculations, we attempted to investigate the proton transfer in enzyme catalysis associated with a few amino acid residues of motifs F and D.

Specific and sensitive fluorescence anisotropy sensing of guanine-quadruplex structures via a photoinduced electron transfer mechanism.

Fluorescence anisotropy (FA) is a homogeneous, ratiometric, and real-time analytical technology. By selective labeling of a guanine (G)-quadruplex motif with tetramethylrhodamine (TMR), here, it is established that a large reduction in FA response can be specifically associated with the unfolding → folding transition of G-quadruplex structures. On the basis of fluorescence intensity, polarization and lifetime analysis, and molecular docking simulation, the mechanism was found to be that the labeled fluorophore (TMR) can intramolecularly interact with adjacent G bases in an unfolded G-quadruplex motif, which allows for the photoinduced electron transfer (PET) occurring between the fluorophore and G bases, leading to a short fluorescence lifetime. Upon the folding of the motif to form a stable G-quadruplex structure, the intramolecular interactions and the concomitant PET could be eliminated with an increased fluorescence lifetime, leading to a large reduction in the FA response. On the basis of this mechanism, a novel, specific, and sensitive FA approach was developed for the detection of biologically and functionally important G-quadruplex structures. The approach is examined and validated using one normal G-quadruplex motif, five mutants, and six small cations and is potentially applicable to the study of G-quadruplexes at single molecule level, ligand screening, profiling of highly ordered DNA nanostructures, and biosensing.

Effect of Disulfide Bridge on the Binding of SARS-CoV-2 Fusion Peptide to Cell Membrane: A Coarse-Grained Study.

In this paper, we present the parameterization of the CAVS coarse-grained (CG) force field for 20 amino acids, and our CG simulations show that the CAVS force field could accurately predict the amino acid tendency of the secondary structure. Then, we used the CAVS force field to investigate the binding of a severe acute respiratory syndrome-associated coronavirus fusion peptide (SARS-CoV-2 FP) to a phospholipid bilayer: a long FP (FP-L) containing 40 amino acids and a short FP (FP-S) containing 26 amino acids. Our CAVS CG simulations displayed that the binding affinity of the FP-L to the bilayer is higher than that of the FP-S. We found that the FP-L interacted more strongly with membrane cholesterol than the FP-S, which should be attributed to the stable helical structure of the FP-L at the C-terminus. In addition, we discovered that the FP-S had one major and two minor membrane-bound states, in agreement with previous all-atom molecular dynamics (MD) studies. However, we found that both the C-terminal and N-terminal amino acid residues of the FP-L can strongly interact with the bilayer membrane. Furthermore, we found that the disulfide bond formed between Cys840 and Cys851 stabilized the helices of the FP-L at the C-terminus, enhancing the interaction between the FP-L and the bilayer membrane. Our work indicates that the stable helical structure is crucial for binding the SARS-CoV-2 FP to cell membranes. In particular, the helical stability of FP should have a significant influence on the FP-membrane binding.

Different Binding Modes of SARS-CoV-1 and SARS-CoV-2 Fusion Peptides to Cell Membranes: The Influence of Peptide Helix Length.

Although the amino acid sequences of SARS-CoV-1 and SARS-CoV-2 fusion peptides (FPs) are highly conserved, the cryo-electron microscopy structures of the SARS-CoV-1 and SARS-CoV-2 spike proteins show that the helix length of SARS-CoV-1 FP is longer than that of SARS-CoV-2 FP. In this work, we simulated the membrane-binding models of SARS-CoV-1 and SARS-CoV-2 FPs and compared the binding modes of the FPs with the POPC/POPE/cholesterol bilayer membrane. Our simulation results show that the SARS-CoV-2 FP binds to the bilayer membrane more effectively than the SARS-CoV-1 FP. It is seen that the short N-terminal helix of SARS-CoV-2 FP is more favorable to insert into the target membrane than the long N-terminal helix of SARS-CoV-1 FP. Meanwhile, the potential of mean force calculations showed that the SARS-CoV-2 FP would prefer only one binding mode (N-terminal binding), whereas the SARS-CoV-1 FP has two favorable membrane-binding modes (C-terminal and N-terminal binding modes). Moreover, in the case of SARS-CoV-1 FP binding to the target membrane, the transition between the two binding modes is relatively fast. Finally, we discovered that the membrane-binding mode would influence the helix length of SARS-CoV-1 FP, while the helix length of SARS-CoV-2 FP could be stably maintained in the membrane-bound configurations. This work suggests that the short helix might endow the FP with high membrane-anchoring strength. In particular, the membrane-penetrating residues (Phe, Ile, and Leu) of short α-helix interact with the cell membrane more strongly than those of long α-helix.

Second-Order Nonlinear Optics Response of the Boron-Dipyrromethenes-Based Mislinked Expanded Porphyrins: Revealing the Role of the -BF2 Group.

Here, the mislinked expanded porphyrins singly (labeled A) and doubly (labeled B) neo-confused [22]smaragdyrin, the boron-dipyrromethenes-based mislinked expanded porphyrins singly (labeled C) and doubly (labeled D) neo-confused [22]smaragdyrin, where both C and D include a -BF2 group, are chosen to serve as the study objects, and theoretical calculations are carried out to study the role of the -BF2 group in the second-order nonlinear optics (NLO) behaviors. Results highlighted that the -BF2 group plays an important role for the second-order behaviors in mislinked expanded porphyrins; namely, embedding the -BF2 group well enhanced the hyper-Rayleigh scattering (HRS) value {ßHRS(0;0,0)}, C{ßHRS(0;0,0)}A{ßHRS(0;0,0)} = 2.0 and D{ßHRS(0;0,0)}B{ßHRS(0;0,0)} = 2.9, main owning to the fact that installing -BF2 increases the electron delocalization degree and decreases the excited energy of the crucial excited state.