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Although molecular dynamics (MD) simulations have been used extensively to study the structural dynamics of proteins, the role of MD simulation in studies of nucleic acid based systems has been more limited. One contributing factor to this disparity is the historically lower level of accuracy of the physical models used in such simulations to describe interactions involving nucleic acids. By modifying nonbonded and torsion parameters of a force field from the Amber family of models, we recently developed force field parameters for RNA that achieve a level of accuracy comparable to that of state-of-the-art protein force fields. Here we report force field parameters for DNA, which we developed by transferring nonbonded parameters from our recently reported RNA force field and making subsequent adjustments to torsion parameters. We have also modified the backbone charges in both the RNA and DNA parameter sets to make the treatment of electrostatics compatible with our recently developed variant of the Amber protein and ion force field. We name the force field resulting from the union of these three parameter sets (the new DNA parameters, the revised RNA parameters, and the existing protein and ion parameters)

Because lipid bilayers can bend and stretch in ways similar to thin elastic sheets, physical models of bilayer deformation have utilized mechanical constants such as the moduli for bending rigidity (κC) and area compressibility (KA). However, the use of these models to quantify the energetics of membrane deformation associated with protein-membrane interactions and the membrane response to stress is often hampered by the shortage of experimental data suitable for the estimation of the mechanical constants of various lipid mixtures. While computational tools such as Molecular Dynamics (MD) simulations can provide alternative means to estimateKAvalues, current approaches suffer significant technical limitations. Here, we present a novel computational framework that allows for a direct estimation ofKAvalues for individual bilayer leaflets. The theory is based on the concept of elasticity and derivesKAfrom real-space analysis of local thickness fluctuations sampled in MD simulations. We explore and validate the model on a large set of single and multicomponent bilayers of different lipid composition and sizes, simulated at different temperatures. The calculated bilayer compressibility moduli agree with values estimated previously from experiments and those obtained from a standard computational method based on a series of constrained tension simulations. We further validate our framework in a comparison with an existing polymer brush model (PBM) and confirm the PBM’s predicted linear relationship with proportionality coefficient of 24 using elastic parameters calculated from the simulation trajectories. The robustness of the results that emerge from the new method allows us to revisit the origins of the bilayer mechanical (compressible) thickness and in particular, its dependence on acyl chain unsaturation and the presence of cholesterol.

Neurotransmitter:sodium symporters (NSS), targets of antidepressants and psychostimulants, clear neurotransmitters from the synaptic cleft through sodium (Na+)-coupled transport. Substrate and Na+ are thought to be transported from the extracellular to intracellular space through an alternating access mechanism by coordinated conformational rearrangements in the symporter that alternately expose the binding sites to each side of the membrane. However, the mechanism by which the binding of ligands coordinates conformational changes occurring on opposite sides of the membrane is not well understood. Here, we report the use of single-molecule fluorescence resonance energy transfer (smFRET) techniques to image transitions between distinct conformational states on both the extracellular and intracellular sides of the prokaryotic NSS LeuT, including partially open intermediates associated with transport activity. The nature and functional context of these hitherto unidentified intermediate states shed new light on the allosteric mechanism that couples substrate and Na+ symport by the NSS family through conformational dynamics.

Allostery plays a crucial role in the mechanism of neurotransmitter-sodium symporters, such as the human dopamine transporter. To investigate the molecular mechanism that couples the transport-associated inward release of the Na+ ion from the Na2 site to intracellular gating, we applied a combination of the thermodynamic coupling function (TCF) formalism and Markov state model analysis to a 50-μs data set of molecular dynamics trajectories of the human dopamine transporter, in which multiple spontaneous Na+ release events were observed. Our TCF approach reveals a complex landscape of thermodynamic coupling between Na+ release and inward-opening, and identifies diverse, yet well-defined roles for different Na+-coordinating residues. In particular, we identify a prominent role in the allosteric coupling for the Na+-coordinating residue D421, where mutation has previously been associated with neurological disorders. Our results highlight the power of the TCF analysis to elucidate the molecular mechanism of complex allosteric processes in large biomolecular systems.

Many of the functions of transmembrane proteins involved in signal processing and transduction across the cell membrane are determined by allosteric couplings that propagate the functional effects well beyond the original site of activation. Data gathered from breakthroughs in biochemistry, crystallography, and single molecule fluorescence have established a rich basis of information for the study of molecular mechanisms in the allosteric couplings of such transmembrane proteins. The mechanistic details of these couplings, many of which have therapeutic implications, however, have only become accessible in synergy with molecular modeling and simulations. Here, we review some recent computational approaches that analyze allosteric coupling networks (ACNs) in transmembrane proteins, and in particular the recently developed Protein Interaction Analyzer (PIA) designed to study ACNs in the structural ensembles sampled by molecular dynamics simulations. The power of these computational approaches in interrogating the functional mechanisms of transmembrane proteins is illustrated with selected examples of recent experimental and computational studies pursued synergistically in the investigation of secondary active transporters and GPCRs. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Significance The combination of molecular dynamics simulation, single-molecule imaging, and functional assays described here reveals a mechanism of substrate selectivity in the SLC6 family of neurotransmitter transporters. We show that the rotameric state of a volumetric sensor in the substrate binding site is allosterically coupled to conformational changes necessary for transport, and as a consequence, upon binding large substrates, the transporter becomes stabilized in an inactive, nontransporting state upon binding larger substrates. This mechanistic insight suggests the possibility that medically relevant SLC6 transporters may be targeted by inhibitors that specifically modulate this sensor., Neurotransmitter:sodium symporters (NSSs) in the SLC6 family terminate neurotransmission by coupling the thermodynamically favorable transport of ions to the thermodynamically unfavorable transport of neurotransmitter back into presynaptic neurons. Results from many structural, functional, and computational studies on LeuT, a bacterial NSS homolog, have provided critical insight into the mechanism of sodium-coupled transport, but the mechanism underlying substrate-specific transport rates is still not understood. We present a combination of molecular dynamics simulations, single-molecule fluorescence resonance energy transfer (smFRET) imaging, and measurements of Na+ binding and substrate transport that reveals an allosteric substrate specificity mechanism. In this mechanism, residues F259 and I359 in the substrate binding pocket couple the binding of substrate to Na+ release from the Na2 site by allosterically modulating the stability of a partially open, inward-facing state. We propose a model for transport selectivity in which residues F259 and I359 act as a volumetric sensor that inhibits the transport of bulky amino acids.

Solute transport across cell membranes is ubiquitous in biology as an essential physiological process. Secondary active transporters couple the unfavorable process of solute transport against its concentration gradient to the energetically favorable transport of one or several ions. The study of such transporters over several decades indicates that their function involves complex allosteric mechanisms that are progressively being revealed in atomistic detail. We focus on two well-characterized sodium-coupled symporters: the bacterial amino acid transporter LeuT, which is the prototype for the "gated pore" mechanism in the mammalian synaptic monoamine transporters, and the archaeal GltPh, which is the prototype for the "elevator" mechanism in the mammalian excitatory amino acid transporters. We present the evidence for the role of allostery in the context of a quantitative formalism that can reconcile biochemical and biophysical data and thereby connects directly to recent insights into the molecular structure and dynamics of these proteins. We demonstrate that, while the structures and mechanisms of these transporters are very different, the available data suggest a common role of specific models of allostery in their functions. We argue that such allosteric mechanisms appear essential not only for sodium-coupled symport in general but also for the function of other types of molecular machines in the membrane.

Recent work has shown that the choice of the type and concentration of detergent used for the solubilization of membrane proteins can strongly influence the results of functional experiments. In particular, the amino acid transporter LeuT can bind two substrate molecules in low concentrations of n-dodecyl β-d-maltopyranoside (DDM), whereas high concentrations reduce the molar binding stoichiometry to 1:1. Subsequent molecular dynamics (MD) simulations of LeuT in DDM proteomicelles revealed that DDM can penetrate to the extracellular vestibule and make stable contacts in the functionally important secondary substrate binding site (S2), suggesting a potential competitive mechanism for the reduction in binding stoichiometry. Because annular lipids can be retained during solubilization, we performed MD simulations of LeuT proteomicelles at various stages of the solubilization process. We find that at low DDM concentrations, lipids are retained around the protein and penetration of detergent into the S2 site does not occur, whereas at high concentrations, lipids are displaced and the probability of DDM binding in the S2 site is increased. This behavior is dependent on the type of detergent, however, as we find in the simulations that the detergent lauryl maltose-neopentyl glycol, which is approximately twice the size of DDM and structurally more closely resembles lipids, does not penetrate the protein even at very high concentrations. We present functional studies that confirm the computational findings, emphasizing the need for careful consideration of experimental conditions, and for cautious interpretation of data in gathering mechanistic information about membrane proteins.

We present the dynamic mechanism of concerted motions in a full-length molecular model of the human dopamine transporter (hDAT), a member of the neurotransmitter/sodium symporter (NSS) family, involved in state-to-state transitions underlying function. The findings result from an analysis of unbiased atomistic molecular dynamics simulation trajectories (totaling >14 μs) of the hDAT molecule immersed in lipid membrane environments with or without phosphatidylinositol 4,5-biphosphate (PIP2) lipids. The N-terminal region of hDAT (N-term) is shown to have an essential mechanistic role in correlated rearrangements of specific structural motifs relevant to state-to-state transitions in the hDAT. The mechanism involves PIP2-mediated electrostatic interactions between the N-term and the intracellular loops of the transporter molecule. Quantitative analyses of collective motions in the trajectories reveal that these interactions correlate with the inward-opening dynamics of hDAT and are allosterically coupled to the known functional sites of the transporter. The observed large-scale motions are enabled by specific reconfiguration of the network of ionic interactions at the intracellular end of the protein. The isomerization to the inward-facing state in hDAT is accompanied by concomitant movements in the extracellular vestibule and results in the release of an Na(+) ion from the Na2 site and destabilization of the substrate dopamine in the primary substrate binding S1 site. The dynamic mechanism emerging from the findings highlights the involvement of the PIP2-regulated interactions between the N-term and the intracellular loop 4 in the functionally relevant conformational transitions that are also similar to those found to underlie state-to-state transitions in the leucine transporter (LeuT), a prototypical bacterial homologue of the NSS. This work was supported by the National Institutes of Health grants P01DA012408, R01DA035263, and U54GM087519. J.M. is supported by the “Caja Madrid” Graduate Fellowship and the “La Caixa” Graduate Fellowship. M.V.L. is supported by a Ruth L. Kirschstein National Research Service Award F31DA035533.

Neurotransmitter:sodium symporters (NSS), targets of antidepressants and psychostimulants, clear neurotransmitters from the synaptic cleft through sodium (Na+)-coupled transport. Substrate and Na+ are thought to be transported from the extracellular to intracellular space through an alternating access mechanism by coordinated conformational rearrangements in the symporter that alternately expose the binding sites to each side of the membrane. However, the mechanism by which the binding of ligands coordinates conformational changes occurring on opposite sides of the membrane is not well understood. Here, we report the use of single-molecule fluorescence resonance energy transfer (smFRET) techniques to image transitions between distinct conformational states on both the extracellular and intracellular sides of the prokaryotic NSS LeuT, including partially open intermediates associated with transport activity. The nature and functional context of these hitherto unidentified intermediate states shed new light on the allosteric mechanism that couples substrate and Na+ symport by the NSS family through conformational dynamics., Neurotransmitter:sodium symporters (NSS) modulate the duration and magnitude of signaling via the sodium-coupled reuptake of neurotransmitters. Here the authors describe quantitative single molecule imaging of ligand-induced, functional dynamics of both intracellular and extracellular surfaces of LeuT, further defining the mechanism for NSS transport.

GPCRs regulate all aspects of human physiology, and biophysical studies have deepened our understanding of GPCR conformational regulation by different ligands. Yet there is no experimental evidence for how sidechain dynamics control allosteric transitions between GPCR conformations. To address this deficit, we generated samples of a wild-type GPCR (A2AR) that are deuterated apart from 1H/13C NMR probes at isoleucine δ1 methyl groups, which facilitated 1H/13C methyl TROSY NMR measurements with opposing ligands. Our data indicate that low [Na+] is required to allow large agonist-induced structural changes in A2AR, and that patterns of sidechain dynamics substantially differ between agonist (NECA) and inverse agonist (ZM241385) bound receptors, with the inverse agonist suppressing fast ps-ns timescale motions at the G protein binding site. Our approach to GPCR NMR creates a framework for exploring how different regions of a receptor respond to different ligands or signaling proteins through modulation of fast ps-ns sidechain dynamics., eLife digest Almost every aspect of the human body – from our senses to our moods – depends, in one way or another, on a large family of proteins called G-protein-coupled receptors. These receptor proteins, known as GPCRs for short, detect signals from outside the cell and trigger activity within the cell. This allows cells to gather information from their surroundings and to communicate with each other. Importantly, since GPCRs regulate many processes in the body that are involved in disease, it is perhaps unsurprising that over a third of all approved drugs target these receptors. Like all proteins, GPCRs are long chain-like molecules with a repetitive backbone and short branches called sidechains. Each sidechain has its own chemical properties and electrical charge, which can affect how different parts of the chain interact with each other and what shape the protein can adopt. This in turn can influence how strongly a drug or other molecule can bind to a receptor protein. Protein crystallography is one technique that has been used to better understand how the different GPCRs are built and how they work. The technique involves growing crystals from pure samples of the protein; this locks millions of copies of the protein in place and provides a snapshot of its shape. However, GPCRs – and especially their sidechains – are flexible and can adopt different shapes, which cannot be seen fully by only looking at protein crystals. Now, Clark, Dikiy et al. used another technique called nuclear magnetic resonance spectroscopy, or NMR for short, to understand how drugs affect the fast moving sidechains within a GPCR. First, genetically modified yeast was used to create samples of a GPCR called the adenosine receptor A2A that were labelled with specific markers which made it easier to measure the structure and flexibility of the protein by NMR. This approach revealed that too much sodium in the sample’s solution supresses the large structural changes that occur in the A2A receptor when it binds to a drug. Moreover, it showed that the sidechains of several regions on the receptor move in different ways depending on whether the receptor binds to an activating drug or an inhibiting drug. These findings lay the groundwork for understanding how the movements of sidechains help to activate or inhibit GPCRs, and will complement on-going studies using protein crystals. Moreover, the new approach to producing labelled proteins could be applied to other types of proteins that until now could not be studied with NMR due to practical limitations. In future, this may help scientists to better understand how drugs affect these proteins and to develop new treatments for a whole range of diseases.

Structural and functional properties of integral membrane proteins are often studied in detergent micellar environments (proteomicelles), but how such proteomicelles form and organize is not well understood. This makes it difficult to evaluate the relationship between the properties of the proteins measured in such a detergent-solubilized form and under native conditions. To obtain mechanistic information about this relationship for the leucine transporter (LeuT), a prokaryotic homologue of the mammalian neurotransmitter/sodium symporters (NSSs), we studied the properties of proteomicelles formed by n-dodecyl-β,D-maltopyranoside (DDM) detergent. Extensive atomistic molecular dynamics simulations of different protein/detergent/water number ratios revealed the formation of a proteomicelle characterized by a constant-sized shell of detergents surrounding LeuT protecting its transmembrane segments from unfavorable hydrophobic/hydrophilic exposure. Regardless of the DDM content in the simulated system, this shell consisted of a constant number of DDM molecules (∼120 measured at a 4 Å cutoff distance from LeuT). In contrast, the overall number of DDMs in the proteomicelle (aggregation number) was found to depend on the detergent concentration, reaching a saturation value of 226±17 DDMs in the highest concentration regime simulated. Remarkably, we found that at high detergent-to-protein ratios we observed two independent ways of DDM penetration into LeuT, both leading to a positioning of the DDM molecule in the second substrate (S2) binding site of LeuT. Consonant with several recent experimental studies demonstrating changes in functional properties of membrane proteins due to detergent, our findings highlight how the environment in which the membrane proteins are examined may affect the outcome and interpretation of their mechanistic features.

Proteins carrying out the many biological processes essential to cellular function act as biomolecular machines utilizing mechanisms that are most often allosteric in nature, i.e. the structural components involved in the mechanism, which are sometimes separated by large distances at the molecular scale, are coupled energetically. Although it is a ubiquitous mechanism, allostery is still poorly understood as an experimentally validated molecular mechanism underlying particular instances, and lacks a general theoretical approach to describe it quantitatively. We will present our efforts to address both of these inadequacies using the secondary active transporter LeuT as an example. First, we will introduce a model for secondary active transport (LeVine, Cuendet, Khelashvili, and Weinstein. In review) that implicitly includes the allosteric coupling between two separate processes: i) sodium and substrate binding, and ii) substrate binding and intracellular opening of the transporter to allow release. Next, a general theoretical approach for allostery will be addressed with a statistical mechanical model based on the Ising Model (LeVine and Weinstein, Entropy, 2015). This will be shown to provide analytical insight into how long-distance allosteric couplings, such as that occurring between substrate binding and intracellular opening in LeuT, can arise in a complex system of interacting structural components. Finally, we will address the lack of experimentally validated molecular mechanisms underlying allostery. We will discuss a proposed model for substrate binding/intracellular opening coupling in LeuT, discovered using a novel information theory-based analysis framework, N-body Information Theory (NbIT) (LeVine and Weinstein, PLoS Comp Biol, 2014), and will present a recent experimental validation of this model. This presentation of combined theoretical, computational, and experimental work will demonstrate how deeper mechanistic understanding of biomolecular machines can be achieved through improved models of allosteric behavior.

This paper advances nonparametric multidimensional item response theory by reporting experimental results on the use of nonmetric multidimensional scaling (MDS) to synthesize a multidimensional model from several approximating one-dimensional models. A two-dimensional simulation data set contains items in which the two-component traits combine linearly (dominance model items) and items in which the two-component traits combine quadratically (ideal point items). Several unidimensional approximations of the two-dimensional model were obtained by running unidimensional estimation software on the simulated data set. The graphs reconstructed from MDS of the unidimensional approximations at selected points clearly separate dominance items from ideal point items, and also various types of dominance or ideal point models. MDS also succeeded in determining the dimensionality of the simulation model items from the observable item responses.

Psychologists would like to say that a probability distribution on {0,1} n is d -dimensional if (1) the distribution can be represented by some smooth d -dimensional latent variable model and (2) the distribution cannot be represented by any smooth d −1 dimensional model. This does not work out because for d >1, every distribution that can be represented by a smooth d -dimensional model can also be represented by a smooth one-dimensional model. A proof and discussion of some implications of this mathematical result follow.

GPCRs regulate all aspects of human physiology, and biophysical studies have deepened our understanding of GPCR conformational regulation by different ligands. Yet there is no experimental evidence for how sidechain dynamics control allosteric transitions between GPCR conformations. To address this deficit, we generated samples of a wild-type GPCR (A2AR) that are deuterated apart from 1H/13C NMR probes at isoleucine δ1 methyl groups, which facilitated 1H/13C methyl TROSY NMR measurements with opposing ligands. Our data indicate that low [Na+] is required to allow large agonist-induced structural changes in A2AR, and that patterns of sidechain dynamics substantially differ between agonist (NECA) and inverse agonist (ZM241385) bound receptors, with the inverse agonist suppressing fast ps-ns timescale motions at the G protein binding site. Our approach to GPCR NMR creates a framework for exploring how different regions of a receptor respond to different ligands or signaling proteins through modulation of fast ps-ns sidechain dynamics.

With recent progress in determination of G protein-coupled receptor (GPCR) structure with crystallography, a variety of other experimental approaches (e.g., NMR spectroscopy, fluorescent-based assays, mass spectrometry techniques) are also being used to characterize state-specific and ligand-specific conformational states. MD simulations offer a powerful complementary approach to elucidate the dynamic features associated with ligand-specific GPCR conformations. To shed light on the conformational elements and dynamics of the important aspect of GPCR functional selectivity, we carried out unbiased microsecond-length MD simulations of the human serotonin 2A receptor (5-HT(2A)R) in the absence of ligand and bound to four distinct serotonergic agonists. The 5-HT(2A)R is a suitable system to study the structural features involved in the ligand-dependent conformational heterogeneity of GPCRs because it is well-characterized experimentally and exhibits a strong agonist-specific phenotype in that some 5-HT(2A)R agonists induce LSD-like hallucinations, while others lack this psychoactive property entirely. Here we report evidence for structural and dynamic differences in 5-HT(2A)R interacting with such pharmacologically distinct ligands, hallucinogens, and nonhallucinogens obtained from all-atom MD simulations. Differential ligand binding contacts were identified for structurally similar hallucinogens and nonhallucinogens and found to correspond to different conformations in the intracellular loop 2 (ICL2). From the different ICL2 conformations, functional selective phenotypes are suggested through effects on dimerization and/or distinct direct interaction with effector proteins. The findings are presented in the context of currently proposed hallucinogenesis mechanisms, and ICL2 is proposed as a fine-tuning selective switch that can differentiates modes of 5-HT(2A)R activation.

Complex networks of interacting residues and microdomains in the structures of biomolecular systems underlie the reliable propagation of information from an input signal, such as the concentration of a ligand, to sites that generate the appropriate output signal, such as enzymatic activity. This information transduction often carries the signal across relatively large distances at the molecular scale in a form of allostery that is essential for the physiological functions performed by biomolecules. While allosteric behaviors have been documented from experiments and computation, the mechanism of this form of allostery proved difficult to identify at the molecular level. Here, we introduce a novel analysis framework, called N-body Information Theory (NbIT) analysis, which is based on information theory and uses measures of configurational entropy in a biomolecular system to identify microdomains and individual residues that act as (i)-channels for long-distance information sharing between functional sites, and (ii)-coordinators that organize dynamics within functional sites. Application of the new method to molecular dynamics (MD) trajectories of the occluded state of the bacterial leucine transporter LeuT identifies a channel of allosteric coupling between the functionally important intracellular gate and the substrate binding sites known to modulate it. NbIT analysis is shown also to differentiate residues involved primarily in stabilizing the functional sites, from those that contribute to allosteric couplings between sites. NbIT analysis of MD data thus reveals rigorous mechanistic elements of allostery underlying the dynamics of biomolecular systems., Author Summary We developed the new information theory-based analysis framework presented here, NbIT analysis, for the study of allosteric mechanisms in biomolecular systems from Molecular Dynamics trajectories. The illustrative application of NbIT to the analysis of the occluded state in the bacterial transporter LeuT, produced a quantitative representation of the allosteric behavior, and identified intramolecular channels that enable the long-distance information transmission. Our findings, identifying the roles of specific residues in the communication of the allosteric information, were validated by the recognition of residues that have been previously shown to play functional roles in this very well studied system. In addition, we show that application of NbIT analysis leads to the discrimination of functional roles by differentiating between residues that are essential to the dynamics within functional sites (e.g., the substrate binding sites), and residues whose role is to communicate between such functional sites. These results demonstrate that the information theoretical analysis presented here is a powerful tool for quantifying complex allosteric behavior in biomolecular systems and for identifying the crucial components underlying those behaviors.

Optimal appropriateness measurement statistically provides the most powerful methods for identifying individuals who are mismeasured by a standardized psychological test or scale. These methods use a likelihood ratio test to compare the hypothesis of normal responding versus the alternative hypothesis that an individual's responses are aberrant in some specified way. According to the Neyman-Pearson Lemma, no other statistic computed from an individual's item responses can achieve a higher rate of detection of the hypothesized measure- ment anomaly at the same false positive rate. Use of optimal methods requires a psychometric model for normal responding, which can be readily obtained from the item response theory literature, and a model for aberrant responding. In this article, several concerns about measurement anomalies are described and transformed into quantitative models. We then show how to compute the likeli- hood of a response pattern u* for each of the aberrance models.

Biophysical studies of structure-function relations of membrane proteins are often done in detergent micelles. However, the scarce molecular understanding of the way in which such micelles form and organize around guest proteins makes it difficult to evaluate the relation between the experimental models and the properties of the membrane proteins in their native environment. Because experimental conditions were shown to have a major effect on structure-function relations of the leucine transporter (LeuT), a prokaryotic homolog of the mammalian neurotransmitter:sodium symporter proteins and a prototype for their study, we investigated LeuT in dodecyl-β-maltoside (DDM) detergent micelles. Atomistic molecular dynamics (MD) simulations revealed the formation of a constant-sized “detergent core” within 4A of LeuT consisting of ∼120 DDM molecules regardless of the DDM-to-protein number ratio. However, we found that the aggregation number of the protein-detergent complex (i.e., the number of DDMs associated with the micelle surrounding the protein) depends on detergent concentration. Notably, this aggregation number appears to determine the extent of detergent penetration into the LeuT extracellular vestibule. Thus, we observed DDM penetration into LeuT via two pathways, but the penetration was detected only in the constructs with high detergent content. In constructs with low DDM concentration, any detergent penetration was at most transient. Entering from the “side” of LeuT, a DDM molecule passes between the extracellular segments of transmembrane helix 6 (TMH6) and TMH10, and interacts with TMH1 residues Arg30 and Gln34 in the secondary substrate-binding site (S2) of LeuT. When insertion is “from the top”, the DDM passes by extracellular loop 4 (ECL4) before it penetrates the S2 site at the level of Phe320 (in ECL4) and Leu400 (in TMH10). These findings are discussed in light of experiments that established a modulatory effect of DDM concentration on LeuT activity.

This study examined how well current software implementations of four polytomous item response theory models fit several multiple-choice tests. The models were Bock's (1972) nominal model, Samejima's (1979) multiple-choice Model C, Thissen & Steinberg's (1984) multiple-choice model, and Levine's (1993) maximum-likelihood formula scoring model. The parameters of the first three of these models were estimated with Thissen's (1986) MULTILOG computer program; Williams & Levine's (1993) FORSCORE program was used for Levine's model. Tests from the Armed Services Vocational Aptitude Battery,the Scholastic Aptitude Test, and the American College Test Assessment were analyzed. The models were fit in estimation samples of approximately 3,000; cross-validation samples of approximately 3,000 were used to evaluate goodness of fit. Both fit plots and X2 statistics were used to determine the adequacy of fit. Bock's model provided surprisingly good fit; adding parameters to the nominal model did not yield improvements in fit. FORSCORE provided generally good fit for Levine's nonparametric model across all tests. Index terms: Bock's nominal model, FORSCORE, maximum likelihood formula scoring, MULTILOG, polytomous IRT.

With the ability to perform all-atoms Molecular Dynamics (MD) simulations of complex biological systems on the micro- and even millisecond time-scales, the need to extract the interesting features of the molecular behavior inherent in the resulting trajectories has become more pressing. For the large molecules, short simulations on the order of nanoseconds are often considered to be metastable and quasi-harmonic, representing small fluctuations around a single local minimum in the free energy landscape; longer simulations, on the order of microseconds, must be treated as non-equilibrium trajectories, as they often include large, anharmonic transitions between more than one minima that can lead to significant changes in the protein topology. Because of their complexity, these long simulations are generally subjected to extensive, detailed analysis of many parameters (distances, angles, etc.), often causing the interesting dynamics to be lost in a sea of minutiae. We present a new analysis method that can be used to simultaneously identify, visualize, and compare complex events in MD trajectories of proteins. The statistical approach uses sliding window principal component analysis (sw-PCA) to identify collective motions that are large but transient, which is followed by projection techniques to compare motions between trajectories. We illustrate the method by analyzing microsecond MD simulations of the bacterial leucine transporter LeuT in complex with the substrates leucine, valine, and alanine that have been shown to produce different transport phenotypes. In all three systems we identified transient, hundred nanosecond time-scale collective motions in the intracellular domains, and found that these motions were coupled to different, substrate-specific, conformational changes in the primary substrate site. Our results indicate that the method can be a powerful tool in the analysis of all-atoms MD simulations as both system size and trajectory length increase.

Two psychometric models with very different parametric formulas and item response functions can make virtually the same predictions in all applications. By applying some basic results from the theory of hypothesis testing and from signal detection theory, the power of the most powerful test for distinguishing the models can be com puted. Measuring model misspecification by com puting the power of the most powerful test is proposed. If the power of the most powerful test is low, then the two models will make nearly the same prediction in every application. If the power is high, there will be applications in which the models will make different predictions. This measure, that is, the power of the most powerful test, places various types of model misspecifica tion— item parameter estimation error, multidi mensionality, local independence failure, learning and/or fatigue during testing—on a common scale. The theory supporting the method is presented and illustrated with a systematic study of misspecifica tion due to item response function estimation error. In these studies, two joint maximum likelihood estimation methods (LOGIST 2B and LOGIST 5) and two marginal maximum likelihood estimation methods (BILOG and ForScore) were contrasted by measuring the difference between a simulation model and a model obtained by applying an estimation method to simulation data. Marginal estimation was found generally to be superior to joint estimation. The parametric marginal method (BILOG) was superior to the nonparametric method only for three- parameter logistic models. The nonparametric mar ginal method (ForScore) excelled for more general models. Of the two joint maximum likelihood methods studied, LOGIST s appeared to be more accurate than LOGIST 2B.

Model-based methods for the detection of in dividuals inadequately measured by a test have generally been limited to unidimensional tests. Ex tensions of unidimensional appropriateness indices are developed here for multi-unidimensional tests (i.e., multidimensional tests composed of unidimensional subtests). Simulated and real data were used to evaluate the effectiveness of the mul titest appropriateness indices. Very high rates of detection of spuriously high and spuriously low response patterns were obtained with the simulated data. These detection rates were comparable to rates obtained for long unidimensional tests (both simulated and real) with approximately the same number of items. For real data, similarly high de tection rates were obtained in the spuriously high condition; slightly lower detection rates were ob served for the spuriously low condition. Several directions for future research are described.

In his recent review of probability learning, Estes (1972, p. 96) notes that “the chief limitation on effective application” of the models for learning with a continuum of responses to have emerged from the linear and pattern learning models is the failure to specify the smearing or generalization function. He notes that “a useful technique has been developed by Levine for estimating this function from individual data.” This paper describes, gives the rationale, and proves the validity of the previously unpublished technique.

Periodic functions and functional equations remove the major remaining obstacle to the direct application of the logic of physical length and mass measurement to psychological data.

The test scores of some examinees on a multiple-choice test may not provide satisfactory measures of their abilities. The goal of appropriateness measurement is to identify such individuals. Earlier theoretical and experimental work considered examinees answering all, or almost all, test items. This article reports research that extends appropriateness measurement methods to examinees with moderately high nonresponse rates. These methods treat non-response as if it were a deliberate option choice and then attempt to measure the 'appropriateness' of the pattern of option choices. Earlier studies used only the dichotomous pattern of right and 'not right' answers. A general polychotomous model is introduced along with a technique called 'standardization' designed to reduce the observed confounding between measured appropriateness and ability. A standardized appropriateness index based on a polychotomous model yielded higher rates of detection of simulated spuriously low examinees than the analogous index based on a dichotomous model. However, the converse was true for simulated spuriously high examinees. Standardization was found to reduce greatly the interaction between ability and measured appropriateness.

Multilinear formula score theory (Levine, 1984, 1985, 1989a, 1989b) provides powerful methods for addressing important psychological measurement prob lems. In this paper, a brief review of multilinear for mula scoring (MFS) is given, with specific emphasis on estimating option characteristic curves (occs). MFS was used to estimate occs for the Arithmetic Reason ing subtest of the Armed Services Vocational Aptitude Battery. A close match was obtained between empiri cal proportions of option selection for examinees in 25 ability intervals and the modeled probabilities of op tion selection. In a second analysis, accurately esti mated occs were obtained for simulated data. To eval uate the utility of modeling incorrect responses to the Arithmetic Reasoning test, the amounts of statistical information about ability were computed for dichoto mous and polychotomous scorings of the items. Con sistent with earlier studies, moderate gains in informa tion were obtained for low to slightly above average abilities.

Two different procedures were used to measure the difficulties of Scholastic Aptitude Test items: a new distribution-free procedure that uses periodic functions and LOGIST, a well-developed optimization procedure that fits a logistic model. Despite the fact that the two procedures used different data in very different ways, they obtained virtually the same numbers. The new method exemplifies “fundamental” psychological measurement in as much as it is based on counting and ordinal properties of data only.

The test-taking behavior of some examinees may be so idiosyncratic that their test scores may not be comparable to the scores of more typical examinees. Appropriateness measurement attempts to use answer patterns to recognize atypical examinees. In this report appropriateness measurement procedures are viewed as statistical tests for choosing between a null hypothesis of normal test-taking behavior and an alternative hypothesis of atypical test-taking behavior. Most powerful tests for inappropriateness are described together with methods for computing their power. A recursion greatly simplifying the calculation of optimal test statistics is described and illustrated.

The possibility that certain features of items on a reading comprehension test may lead to biased esti mates of the reading achievement of particular sub groups of students was investigated. Eight nonover lapping subgroups of students were defined by the combinations of three factors: student grade level (fifth or sixth), income level of the neighborhood in which the school was located (low and middle or above), and race of the student (black or white). Es timates of student ability and item parameters were obtained separately for each of the eight subgroups using the three-parameter logistic model. Bias in dices were computed based on differences in item characteristic curves for pairs of subgroups. A cri terion for labeling an item as biased was developed using the distribution of bias indices for subgroups of the same race that differed only in income level or grade level. Using this criterion, three items were consistently identified as biased in four independent comparisons of subgroups of black and white stu dents. Comparisons of content and format charac teristics of items that were identified as biased with those that were not, or between items biased in dif ferent directions, did not lead to the identification of any systematic content differences. The study did provide strong support for the viability of the esti mation procedure; item characteristics, estimated with samples from different populations were very similar. Some suggestions for improvements in methodology are offered.

The test-taking behaviour of some examinees may be so unusual that their test scores cannot be regarded as appropriate measures of their ability. Appropriateness measurement is a model-based approach to the problem of identifying these test scores. The intuitions and basic theory supporting appropriateness measurement are presented together with a critical review of earlier work and a series of interrelated experiments. We conclude that appropriateness measurement techniques are robust to errors in parameter estimation and robust to the presence of unidentified aberrant examinees in the test norming sample. In addition, the frequently criticized ‘three-parameter logistic’ latent trait model was found to be adequate for the detection of spuriously low scores in actual test data.

Optimal appropriateness indices, recently introduced by Levine and Drasgow (1984), provide the highest rates of detection of aberrant response patterns that can be obtained from item responses. In this article they are used to study three important problems in ap propriateness measurement. First, the maximum detec tion rates of two particular forms of aberrance are de termined for a long unidimensional test. These detection rates are shown to be moderately high. Sec ond, two versions of the standardized l0 appropriate ness index are compared to optimal indices. At low false alarm rates, one standardized l0 index has detec tion rates that are about 65% as large as optimal for spuriously high (cheating) test scores. However, for the spuriously low scores expected from persons with ill-advised testing strategies or reading problems, both standardized l0 indices are far from optimal. Finally, detection rates for polychotomous and dichotomous scorings of the item responses are compared. It is shown that dichotomous scoring causes serious de creases in the detectability of some aberrant response patterns. Consequently, appropriateness measurement constitutes one practical testing problem in which sig nificant gains result from the use of a polychotomous item response model.

The relation between incorrect option choice and estimated ability level was examined for two widely used aptitude tests, the Scholastic Aptitude Test and the Graduate Record Examination. Incorrect option choice was found to be related to estimated ability for many items. Implications of these findings are briefly discussed.

Several statistics have been proposed as quantitative indices of the appropriateness of a test score as a mea sure of ability. Two criteria have been used to evalu ate such indices in previous research. The first crite rion, standardization, refers to the extent to which the conditional distributions of an index, given ability, are invariant across ability levels. The second criterion, relative power, refers to indices' relative effectiveness for detecting inappropriate test scores. In this paper the effectiveness of nine appropriateness indices is de termined in an absolute sense by comparing them to optimal indices; an optimal index is the most powerful index for a particular form of aberrance that can be computed from item responses. Three indices were found to provide nearly optimal rates of detection of very low ability response patterns modified to simulate cheating, as well as very high ability response patterns modified to simulate spuriously low responding. Opti mal indices had detection rates from 50% to 200% higher than any other index when average ability re sponse vectors were manipulated to appear spuriously high and spuriously low.

Curves are considered to have the same shape when they are related by a similarity transformation of a certain kind. This paper extends earlier work on parallel curves to curves with the same shape. Some examples are given more or less explicitly. A generalization is used to show that the theory is ordinal and to show how the theory may be applied to measure sensation. The problem of actually transforming curves into curves with the same shape is reduced to the problem of rendering another set of curves parallel. Connections with groups and rings are developed to place the work in a familiar context. These connections and the earlier work on parallel curves are used to obtain necessary and sufficient conditions for the existence of transformations, to study the uniqueness of transformations and to show how transformations can be calculated.

The effects of an initial sequence of random responses to 15-, 20-, and 25-item adaptive tests were examined in a series of simulation studies. Random responding on as two items had a substantial effect on an examinee's score. Thus it is important to determine whether--as a result of carelessness, test anxiety, computer anxiety, failure to understand instructions, or other reasons--an examinee has answered the first several items haphazardly. It was shown by use of an optimal appropriateness index, the likelihood ratio (LR) index, that a large proportion of faulty test scores can be identified. The performance of LR was evaluated by determining hit rates and false positive rates in a series of studies concerning: (a) comparisons with other indices, (b) the use of a security procedure during item selection for the adaptive test, (c) standardization, and (d) misspecification of the number of items with random answers. The LR index detected initial sequences of random responses with high accuracy with and without a security procedure during item selection. Other appropriateness indices were considerably less accurate. Standardization greatly decreased the power of LR at low false positive rates. Finally, misspecification of the length of the initial segment of random responses systematically reduced the power of the LR index to detect aberrance. Keywords: Appropriateness measurement; Aptitude tests; Computerized adaptive test.