*Nat Struct Mol Biol ; 27(1): 62-70, 2020 01.*

##### RESUMO

ABCB4 is an ATP-binding cassette transporter that extrudes phosphatidylcholine into the bile canaliculi of the liver. Its dysfunction or inhibition by drugs can cause severe, chronic liver disease or drug-induced liver injury. We determined the cryo-EM structure of nanodisc-reconstituted human ABCB4 trapped in an ATP-bound state at a resolution of 3.2 Å. The nucleotide binding domains form a closed conformation containing two bound ATP molecules, but only one of the ATPase sites contains bound Mg2+. The transmembrane domains adopt a collapsed conformation at the level of the lipid bilayer, but we observed a large, hydrophilic and fully occluded cavity at the level of the cytoplasmic membrane boundary, with no ligand bound. This indicates a state following substrate release but prior to ATP hydrolysis. Our results rationalize disease-causing mutations in human ABCB4 and suggest an 'alternating access' mechanism of lipid extrusion, distinct from the 'credit card swipe' model of other lipid transporters.

##### Assuntos

Subfamília B de Transportador de Cassetes de Ligação de ATP/química , Subfamília B de Transportador de Cassetes de Ligação de ATP/metabolismo , Subfamília B de Transportador de Cassetes de Ligação de ATP/ultraestrutura , Trifosfato de Adenosina/metabolismo , Sítios de Ligação , Microscopia Crioeletrônica , Humanos , Hidrólise , Bicamadas Lipídicas/química , Modelos Moleculares , Conformação Proteica , Especificidade por Substrato*J Chem Phys ; 151(8): 084108, 2019 Aug 28.*

##### RESUMO

A simple two-state model has previously been shown to be able to describe and rationalize the convergence of the most common perturbation method for including electron correlation, the Møller-Plesset expansion. In particular, this simple model has been able to predict the convergence rate and the form of the higher-order corrections for typical Møller-Plesset expansions of the correlation energy. In this paper, the convergence of nondegenerate perturbation expansions in the two-state model is analyzed in detail for a general form of two-state perturbation expansion by examining the analytic expressions of the corrections and series of the values of the corrections for various choices of the perturbation. The previous analysis that covered only a single form of the perturbation is thereby generalized to arbitrary forms of the perturbation. It is shown that the convergence may be described in terms of four characteristics: archetype, rate of convergence, length of recurring period, and sign pattern. The archetype defines the overall form of a plot of the energy-corrections, and the remaining characteristics specify details of the archetype. For symmetric (Hermitian) perturbations, five archetypes are observed: zigzag, interspersed zigzag, triadic, ripples, and geometric. Two additional archetypes are obtained for an asymmetric perturbation: zigzag-geometric and convex-geometric. For symmetric perturbations, each archetype has a distinctive pattern that recurs with a period which depends on the perturbation parameters, whereas no such recurrence exists for asymmetric perturbations from a series of numerical corrections. The obtained relations between the form of a two-state perturbation and the energy corrections allow us to obtain additional insights into the convergence behavior of the Møller-Plesset and other forms of perturbation expansions. This is demonstrated by analyzing several diverging or slowly converging perturbation expansions of ground state and excitation energies. It is demonstrated that the higher-order corrections of these expansions can be described using the two-state model and each expansion can therefore be described in terms of an archetype and the other three characteristics. Examples of all archetypes except the zigzag and convex-geometric archetypes are given. For each example, it is shown how the characteristics may be extracted from the higher-order corrections and used to identify the term in the perturbation that is the cause of the observed slow convergence or divergence.

*J Chem Phys ; 150(13): 134109, 2019 Apr 07.*

##### RESUMO

In cluster perturbation (CP) theory, we consider a target excitation space relative to a Hartree-Fock state and partition the target excitation space into a parent excitation space and an auxiliary excitation space. The zeroth-order state is in CP theory a coupled cluster (CC) state in the parent excitation space, and the target state is a CC state in the target excitation space. In this paper, we derive CP series for excitation energies in orders of the CC parent-state similarity-transformed fluctuation potential where the zeroth-order term in the series is an excitation energy for the CC parent state response eigenvalue equation and where the series formally converge to an excitation energy for the CC target state response eigenvalue equation. We give explicit expressions for the lowest-order excitation energy corrections. We also report calculations for CP excitation energy series for various parent and target excitation spaces and examine how well the lower-order corrections can reproduce the total excitation energies. Considering the fast local convergence we have observed for the CP excitation energy series, it becomes computationally attractive to use low-order corrections in CP series to obtain excitation energies of CC target state quality. For the CPS(D-n) series, the first-order correction vanishes, the second-order correction becomes the CIS(D) model, and for the CPS(D-3) model, our calculations suggest that excitation energies of CCSD quality are obtained. The numerical results also suggest that a similar behavior can be seen for the low-order excitation energy corrections for CP series where the parent state contains more than a singles excitation space, e.g., for the CPSD(T) model. We therefore expect the low-order excitation energy corrections in CP series soon to become state-of-the-art models for determining excitation energies of CC target state quality.

*J Chem Phys ; 150(13): 134108, 2019 Apr 07.*

##### RESUMO

We introduce a new class of perturbation models-the cluster perturbation (CP) models-where the major drawbacks of Møller-Plesset perturbation theory and coupled cluster perturbation theory have been eliminated. In CP theory, we consider a target excitation space relative to the Hartree-Fock state and partition the target excitation space into a parent and an auxiliary excitation space. The zeroth-order state is a coupled cluster (CC) state in the parent excitation space, and the target state is either a cluster linear or a CC state in the target excitation space. In CP theory, perturbation series are determined in orders of the CC parent state similarity-transformed fluctuation potential for the energy and for a molecular property, where the zeroth-order term in the series is the energy or a molecular property for the CC parent state and where the series formally converge to the energy or a molecular property for the target state. In CP theory, we use a generalized order concept, where the zeroth-order component of the extended parent-state Jacobian contains a fluctuation potential contribution, and use this new generalized order to treat internal relaxation in the parent excitation space at zeroth order and hence remove it from the perturbation calculation. Even more importantly, using this new generalized order concept, CP series can be determined for molecular properties of ground and excited states and for transition properties between these states, including excitation energies and energies of the excited states. The applicability of CP theory to both the energy and molecular properties and numerical results for the CP energy and molecular property series demonstrate the superiority of CP theory compared to previous perturbation models. Low-order corrections in the CP perturbation series can be expected soon to become state-of-the-art electronic structure models for the determination of energies and molecular properties of target-state quality for single-configuration dominated molecular systems.

*J Chem Phys ; 150(13): 134111, 2019 Apr 07.*

##### RESUMO

The theoretical foundation has been developed for establishing whether cluster perturbation (CP) series for the energy, molecular properties, and excitation energies are convergent or divergent and for using a two-state model to describe the convergence rate and convergence patterns of the higher-order terms in the CP series. To establish whether the perturbation series are convergent or divergent, a fictitious system is introduced, for which the perturbation is multiplied by a complex scaling parameter z. The requirement for convergent perturbation series becomes that the energy or molecular property, including an excitation energy, for the fictitious system is an analytic, algebraic function of z that has no singularities when the norm |z| is smaller than one. Examples of CP series for the energy and molecular properties, including excitation energies, are also presented, and the two-state model is used for the interpretation of the convergence rate and the convergence patterns of the higher-order terms in these series. The calculations show that the perturbation series effectively become a two-state model at higher orders.

*J Chem Phys ; 150(13): 134110, 2019 Apr 07.*

##### RESUMO

The cluster perturbation series, CPS(D), for coupled cluster singles and doubles excitation energies is considered. It is demonstrated that the second-order model CPS(D-2) is identical to the configuration interaction singles with perturbative doubles, CIS(D) model. The third-order model, CPS(D-3), provides excitation energies of coupled cluster singles and doubles (CCSD) quality in the sense that the difference between CPS(D-3) and CCSD excitation energies is of the same size or smaller than the effect of adding triples corrections to CCSD excitation energies. We further show that the third-order corrections can be efficiently implemented, in particular, when the resolution of the identity approximation is used for integrals. We also show that the CPS(D-3) excitation energies can be determined for system sizes that are far beyond what can be considered in conventional CCSD excitation energy calculations.

*J Chem Phys ; 150(13): 134112, 2019 Apr 07.*

##### RESUMO

Cluster perturbation (CP) theory was developed in Paper I [F. Pawlowski et al., J. Chem. Phys. 150, 134108 (2019)] for a coupled cluster (CC) target state and is extended in this paper to comprehend a cluster linear (CL) target state, for which the embedding of a CC parent state in the target excitation space is described using a linear parametrization. The theory is developed for determining the energy and molecular properties for a CL state. When CP theory is applied to a CL target state, a series of corrections is determined in orders of the CC parent-state similarity-transformed fluctuation potential, where the zeroth-order term is the energy or molecular property of the CC parent state and where the series formally converges to the energy or molecular property of the CL target state. The determination of energies and molecular properties is simpler for a CL state than for a CC state because the CL state is linearly parametrized. The amplitude equations are quadratic for a CL target state, while quartic for a CC target state, and molecular property expressions for a CL target state have the same simple structure as for a configuration interaction state. The linear parametrization introduces non-size-extensive contributions in the energy and molecular property expressions. However, since the linear parametrization describes the embedding of the CC parent state in the target excitation space, the energy and molecular properties for a CL state are weakly size-extensive. For the energy, weak size-extensivity means that non-size-extensive contributions enter in sixth and higher orders in the CP energy series, whereas for molecular properties, weak size-extensivity means that non-size-extensive contributions enter in second and higher orders. Weak size-extensivity therefore has a little or vanishing effect on calculated energies or molecular properties. The determination of the CP energy and molecular property corrections does not require that amplitude or response equations are solved explicitly for the target state and it becomes computationally tractable to use low-order corrections from these series to obtain energies and molecular properties of CL target state quality. For three simple molecules, HF, N2, and CH2, the accuracy of the CL approach for ground-state energies is tested using a parent state including single and double excitations (i.e., the CC singles-and-doubles state, CCSD) and a target state that includes triple excitations. It is found that the size-extensive fifth-order CL energies deviate by less than 0.0001 hartree from the energies of a target CC that includes triple excitations (i.e., the CC singles-doubles-and-triples state, CCSDT). CP theory with a CL target state therefore becomes a very attractive replacement of standard CC theory for high-accuracy energy and molecular property calculations, in which triple and higher excitation levels are considered.

*J Chem Phys ; 149(14): 144104, 2018 Oct 14.*

##### RESUMO

The use of non-orthogonal orbitals allows the construction and use of more compact wave functions than offered by standard methods using orthogonal molecular orbitals; in particular, for molecules containing partly occupied atomic orbitals as present, for example, in transition metal complexes. With the purpose of developing efficient dynamic correlation methods, we discuss several new internal correlation methods employing a reference state containing non-orthogonal active orbitals. The non-orthogonal internally contracted perturbation theory approach is improved in several directions. The major improvements are the use of the Dyall Hamiltonian including two-electron interactions within the active space as the zero-order operator, the calculation of third-order energy-corrections, and the inclusion of excitations in the space of active orbitals. The latter improvement corrects for the use of an incomplete reference state. The improvements are tested for the nitrogen molecule and the challenging chromium dimer. The combined use of the improved zero-order Hamiltonian and the inclusion of active space excitations allow us to obtain potential curves for the chromium dimer that are close to those obtained using the larger complete active space reference wave function.

*Integr Psychol Behav Sci ; 52(4): 565-594, 2018 12.*

##### RESUMO

Motor intention/intentionality (MI) has been investigated from many different angles. Some researchers focus on the purely physical and mechanical aspects of the human motor system, while others emphasize the subjectivity involved in intentionality. While bridging this seemingly dualistic gap between the two concepts ought to be the researcher's' main task, different schools of thought have instead specialized in stressing one (objective) or the other (subjective) part of this construct. Thus, we find everything from neuroscientific to phenomenologically inspired approaches to MI. The purpose of this article is to review the literature regarding these different approaches to the MI construct. In reviewing the literature, we introduce a broadened conception of associationism. In organizing our data in relation to the laws of association, a lack of methodology clearly manifests itself. Hence, 123 articles out of 143 meet the criteria of our definition of associationism. It seems that this old doctrine sneaks in to a big part of the research rather implicitly through a lack of methodology. To shed light on how this happens in the 123 articles, we develop a continuum to show to which extend associationism operates on a transcendent or substantial level in each article. We find only very few articles that seem to try to gap the bridge between motor and intention/intentionality, and thus we suggest that future MI research reintroduce methodological debates concerning the conceptual character of this construct.

##### Assuntos

Associação , Intenção , Atividade Motora/fisiologia , Teoria Psicológica , Humanos*J Chem Phys ; 147(18): 184111, 2017 Nov 14.*

##### RESUMO

A new large-scale parallel multiconfigurational self-consistent field (MCSCF) implementation in the open-source NWChem computational chemistry code is presented. The generalized active space approach is used to partition large configuration interaction (CI) vectors and generate a sufficient number of batches that can be distributed to the available cores. Massively parallel CI calculations with large active spaces can be performed. The new parallel MCSCF implementation is tested for the chromium trimer and for an active space of 20 electrons in 20 orbitals, which can now routinely be performed. Unprecedented CI calculations with an active space of 22 electrons in 22 orbitals for the pentacene systems were performed and a single CI iteration calculation with an active space of 24 electrons in 24 orbitals for the chromium tetramer was possible. The chromium tetramer corresponds to a CI expansion of one trillion Slater determinants (914 058 513 424) and is the largest conventional CI calculation attempted up to date.

*J Chem Phys ; 147(17): 174106, 2017 Nov 07.*

##### RESUMO

A computational method is presented for systems that require high-level treatments of static and dynamic electron correlation but cannot be treated using conventional complete active space self-consistent field-based methods due to the required size of the active space. Our method introduces an efficient algorithm for perturbative dynamic correlation corrections for compact non-orthogonal MCSCF calculations. In the algorithm, biorthonormal expansions of orbitals and CI-wave functions are used to reduce the scaling of the performance determining step from quadratic to linear in the number of configurations. We describe a hierarchy of configuration spaces that can be chosen for the active space. Potential curves for the nitrogen molecule and the chromium dimer are compared for different configuration spaces. Already the most compact spaces yield qualitatively correct potentials that with increasing size of configuration spaces systematically approach complete active space results.

*J Chem Phys ; 145(22): 224104, 2016 Dec 14.*

##### RESUMO

The convergence of a recently proposed coupled cluster (CC) family of perturbation series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)], in which the energetic difference between two CC models-a low-level parent and a high-level target model-is expanded in orders of the Møller-Plesset (MP) fluctuation potential, is investigated for four prototypical closed-shell systems (Ne, singlet CH2, distorted HF, and F-) in standard and augmented basis sets. In these investigations, energy corrections of the various series have been calculated to high orders and their convergence radii have been determined by probing for possible front- and back-door intruder states, the existence of which would make the series divergent. In summary, we conclude how it is primarily the choice of the target state, and not the choice of the parent state, which ultimately governs the convergence behavior of a given series. For example, restricting the target state to, say, triple or quadruple excitations might remove intruders present in series which target the full configuration interaction limit, such as the standard MP series. Furthermore, we find that whereas a CC perturbation series might converge within standard correlation consistent basis sets, it may start to diverge whenever these become augmented by diffuse functions, similar to the MP case. However, unlike for the MP case, such potential divergences are not found to invalidate the practical use of the low-order corrections of the CC perturbation series.

*J Chem Theory Comput ; 12(7): 3208-13, 2016 Jul 12.*

##### RESUMO

A multireference second-order perturbation theory approach based on the generalized active space self-consistent-field (GASSCF) wave function is presented. Compared with the complete active space (CAS) and restricted active space (RAS) wave functions, GAS wave functions are more flexible and can employ larger active spaces and/or different truncations of the configuration interaction expansion. With GASSCF, one can explore chemical systems that are not affordable with either CASSCF or RASSCF. Perturbation theory to second order on top of GAS wave functions (GASPT2) has been implemented to recover the remaining electron correlation. The method has been benchmarked by computing the chromium dimer ground-state potential energy curve. These calculations show that GASPT2 gives results similar to CASPT2 even with a configuration interaction expansion much smaller than the corresponding CAS expansion.

*J Chem Phys ; 144(6): 064103, 2016 Feb 14.*

##### RESUMO

We consider two distinct coupled cluster (CC) perturbation series that both expand the difference between the energies of the CCSD (CC with single and double excitations) and CCSDT (CC with single, double, and triple excitations) models in orders of the Møller-Plesset fluctuation potential. We initially introduce the E-CCSD(T-n) series, in which the CCSD amplitude equations are satisfied at the expansion point, and compare it to the recently developed CCSD(T-n) series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)], in which not only the CCSD amplitude, but also the CCSD multiplier equations are satisfied at the expansion point. The computational scaling is similar for the two series, and both are term-wise size extensive with a formal convergence towards the CCSDT target energy. However, the two series are different, and the CCSD(T-n) series is found to exhibit a more rapid convergence up through the series, which we trace back to the fact that more information at the expansion point is utilized than for the E-CCSD(T-n) series. The present analysis can be generalized to any perturbation expansion representing the difference between a parent CC model and a higher-level target CC model. In general, we demonstrate that, whenever the parent parameters depend upon the perturbation operator, a perturbation expansion of the CC energy (where only parent amplitudes are used) differs from a perturbation expansion of the CC Lagrangian (where both parent amplitudes and parent multipliers are used). For the latter case, the bivariational Lagrangian formulation becomes more than a convenient mathematical tool, since it facilitates a different and faster convergent perturbation series than the simpler energy-based expansion.

*J Chem Phys ; 144(2): 024102, 2016 Jan 14.*

##### RESUMO

Molecular response properties for ground and excited states and for transitions between these states are defined by solving the time-dependent Schrödinger equation for a molecular system in a field of a time-periodic perturbation. In equation of motion coupled cluster (EOM-CC) theory, molecular response properties are commonly obtained by replacing, in configuration interaction (CI) molecular response property expressions, the energies and eigenstates of the CI eigenvalue equation with the energies and eigenstates of the EOM-CC eigenvalue equation. We show here that EOM-CC molecular response properties are identical to the molecular response properties that are obtained in the coupled cluster-configuration interaction (CC-CI) model, where the time-dependent Schrödinger equation is solved using an exponential (coupled cluster) parametrization to describe the unperturbed system and a linear (configuration interaction) parametrization to describe the time evolution of the unperturbed system. The equivalence between EOM-CC and CC-CI molecular response properties only holds when the CI molecular response property expressions-from which the EOM-CC expressions are derived-are determined using projection and not using the variational principle. In a previous article [F. Pawlowski, J. Olsen, and P. Jørgensen, J. Chem. Phys. 142, 114109 (2015)], it was stated that the equivalence between EOM-CC and CC-CI molecular response properties only held for a linear response function, whereas quadratic and higher order response functions were mistakenly said to differ in the two approaches. Proving the general equivalence between EOM-CC and CC-CI molecular response properties is a challenging task, that is undertaken in this article. Proving this equivalence not only corrects the previous incorrect statement but also first and foremost leads to a new, time-dependent, perspective for understanding the basic assumptions on which the EOM-CC molecular response property expressions are founded. Further, the equivalence between EOM-CC and CC-CI molecular response properties highlights how static molecular response properties can be obtained from finite-field EOM-CC energy calculations.

*J Chem Phys ; 143(11): 114102, 2015 Sep 21.*

##### RESUMO

A novel algorithm for performing configuration interaction (CI) calculations using non-orthogonal orbitals is introduced. In the new algorithm, the explicit calculation of the Hamiltonian matrix is replaced by the direct evaluation of the Hamiltonian matrix times a vector, which allows expressing the CI-vector in a bi-orthonormal basis, thereby drastically reducing the computational complexity. A new non-orthogonal orbital optimization method that employs exponential mappings is also described. To allow non-orthogonal transformations of the orbitals, the standard exponential mapping using anti-symmetric operators is supplemented with an exponential mapping based on a symmetric operator in the active orbital space. Expressions are obtained for the orbital gradient and Hessian, which involve the calculation of at most two-body density matrices, thereby avoiding the time-consuming calculation of the three- and four-body density matrices of the previous approaches. An approach that completely avoids the calculation of any four-body terms with limited degradation of convergence is also devised. The novel methods for non-orthogonal configuration interaction and orbital optimization are applied to the chromium dimer and trimer. For internuclear distances that are typical for chromium clusters, it is shown that a reference configuration consisting of optimized singly occupied active orbitals is sufficient to give a potential curve that is in qualitative agreement with complete active space self-consistent field (CASSCF) calculations containing more than 500 × 10(6) determinants. To obtain a potential curve that deviates from the CASSCF curve by less than 1 mHartree, it is sufficient to add single and double excitations out from the reference configuration.

*Mol Pharmacol ; 88(4): 697-707, 2015 Oct.*

##### RESUMO

Neuronal α4ß2 nicotinic acetylcholine receptors are attractive drug targets for psychiatric and neurodegenerative disorders and smoking cessation aids. Recently, a third agonist binding site between two α4 subunits in the (α4)(3)(ß2)(2) receptor subpopulation was discovered. In particular, three residues, H142, Q150, and T152, were demonstrated to be involved in the distinct pharmacology of the α4-α4 versus α4-ß2 binding sites. To obtain insight into the three-dimensional structure of the α4-α4 binding site, a surrogate protein reproducing α4-α4 binding characteristics was constructed by introduction of three point mutations, R104H, L112Q, and M114T, into the binding pocket of Lymnaea stagnalis acetylcholine-binding protein (Ls-AChBP). Cocrystallization with two agonists possessing distinct pharmacologic profiles, NS3920 [1-(6-bromopyridin-3-yl)-1,4-diazepane] and NS3573 [1-(5-ethoxypyridin-3-yl)-1,4-diazepane], highlights the roles of the three residues in determining binding affinities and functional properties of ligands at the α4-α4 interface. Confirmed by mutational studies, our structures suggest a unique ligand-specific role of residue H142 on the α4 subunit. In the cocrystal structure of the mutated Ls-AChBP with the high-efficacy ligand NS3920, the corresponding histidine forms an intersubunit bridge that reinforces the ligand-mediated interactions between subunits. The structures further reveal that the binding site residues gain different and ligand-dependent interactions that could not be predicted based on wild-type Ls-AChBP structures in complex with the same agonists. The results show that an unprecedented correlation between binding in engineered AChBPs and functional receptors can be obtained and provide new opportunities for structure-based design of drugs targeting specific nicotinic acetylcholine receptor interfaces.

##### Assuntos

Proteínas de Transporte/química , Proteínas de Transporte/metabolismo , Mimetismo Molecular/fisiologia , Engenharia de Proteínas/métodos , Receptores Nicotínicos/química , Receptores Nicotínicos/metabolismo , Animais , Sítios de Ligação/fisiologia , Cristalografia por Raios X , Relação Dose-Resposta a Droga , Feminino , Humanos , Insetos , Ligação Proteica/fisiologia , Estrutura Secundária de Proteína , Xenopus laevis*J Chem Phys ; 142(11): 114109, 2015 Mar 21.*

##### RESUMO

The time-dependent Schrödinger equation for a time-periodic perturbation is recasted into a Hermitian eigenvalue equation, where the quasi-energy is an eigenvalue and the time-periodic regular wave function an eigenstate. From this Hermitian eigenvalue equation, a rigorous and transparent formulation of response function theory is developed where (i) molecular properties are defined as derivatives of the quasi-energy with respect to perturbation strengths, (ii) the quasi-energy can be determined from the time-periodic regular wave function using a variational principle or via projection, and (iii) the parametrization of the unperturbed state can differ from the parametrization of the time evolution of this state. This development brings the definition of molecular properties and their determination on par for static and time-periodic perturbations and removes inaccuracies and inconsistencies of previous response function theory formulations. The development where the parametrization of the unperturbed state and its time evolution may differ also extends the range of the wave function models for which response functions can be determined. The simplicity and universality of the presented formulation is illustrated by applying it to the configuration interaction (CI) and the coupled cluster (CC) wave function models and by introducing a new model-the coupled cluster configuration interaction (CC-CI) model-where a coupled cluster exponential parametrization is used for the unperturbed state and a linear parametrization for its time evolution. For static perturbations, the CC-CI response functions are shown to be the analytical analogues of the static molecular properties obtained from finite field equation-of-motion coupled cluster (EOMCC) energy calculations. The structural similarities and differences between the CI, CC, and CC-CI response functions are also discussed with emphasis on linear versus non-linear parametrizations and the size-extensivity of the obtained molecular properties.

*Neuropharmacology ; 92: 135-45, 2015 May.*

##### RESUMO

The nicotinic acetylcholine receptor α4ß2 is important for normal mammalian brain function and is known to express in two different stoichiometries, (α4)2(ß2)3 and (α4)3(ß2)2. While these are similar in many aspects, the (α4)3(ß2)2 stoichiometry differs by harboring a third orthosteric acetylcholine binding site located at the α4-α4 interface. Interestingly, the third binding site has, so far, only been documented using electrophysiological assays, actual binding affinities of nicotinic receptor ligands to this site are not known. The present study was therefore aimed at determining binding affinities of nicotinic ligands to the α4-α4 interface. Given that epibatidine shows large functional potency differences at α4-ß2 vs. α4-α4 interfaces, biphasic binding properties would be expected at (α4)3(ß2)2 receptors. However, standard saturation binding experiments with [(3)H]epibatidine did not reveal biphasic binding under the conditions utilized. Therefore, an engineered ß2 construct (ß2(HQT)), which converts the ß(-) face to resemble that of an α4(-) face, was utilized to create (α4)3(ß2(HQT))2 receptors harboring three α4-α4 interfaces. With this receptor, low affinity binding of epibatidine with a Kd of â¼5 nM was observed in sharp contrast to a Kd value of â¼10 pM observed for wild-type receptors. A strong correlation between binding affinities at the (α4)3(ß2(HQT))2 receptor and functional potencies at the wild-type receptor of a range of nicotinic ligands highlighted the validity of using the mutational approach. Finally, large differences in activities at α4-ß2 vs. α4-α4 interfaces were observed for structurally related agonists underscoring the need for establishing all binding parameters of compounds at α4ß2 receptors.