A Model of Core Emotional Needs and Toxic Experiences: Their Links with Schema Domains, Well-Being, and Ill-Being.

This study examined the second-order schema domains of Early Maladaptive and Adaptive Schemas based on recent trends and compared them with the five theoretical second-order schema domains commonly used in schema therapy. Using six international Eastern and Western community samples-Singapore (n = 628), Malaysia (n = 229), USA (n = 396), South Africa (n = 390), Nigeria (n = 364), India (n = 306)-confirmatory factor analysis showed that the four second-order domains of EMSs and EASs, which ran almost parallel with each other, were the most robust models calling into question the validity of the five domain model. Given the hypothesized links between schemas and needs, these four categories of EMSs and EASs represent four categories of toxic experiences and core emotional needs, respectively. These categories were supported empirically and are useful to parents as well as to clinicians as they approach child rearing and the treatment of clients in schema therapy from the vantage point of needs. These four categories of psychological core emotional needs, as well as toxic experiences, were found, as expected, to be linked with various measures of well-being and ill-being.

Visualizing the Active Site Oxyanion Loop Transition Upon Ensitrelvir Binding and Transient Dimerization of SARS-CoV-2 Main Protease.

N-terminal autoprocessing from its polyprotein precursor enables creating the mature-like stable dimer interface of SARS-CoV-2 main protease (MPro), concomitant with the active site oxyanion loop equilibrium transitioning to the active conformation (E*) and onset of catalytic activity. Through mutagenesis of critical interface residues and evaluating noncovalent inhibitor (ensitrelvir, ESV) facilitated dimerization through its binding to MPro, we demonstrate that residues extending from Ser1 through Glu14 are critical for dimerization. Combined mutations G11A, E290A and R298A (MPro™) restrict dimerization even upon binding of ESV to monomeric MPro™ with an inhibitor dissociation constant of 7.4 ± 1.6 µM. Contrasting the covalent inhibitor NMV or GC373 binding to monomeric MPro, ESV binding enabled capturing the transition of the oxyanion loop conformations in the absence of a reactive warhead and independent of dimerization. Characterization of complexes by room-temperature X-ray crystallography reveals ESV bound to the E* state of monomeric MPro as well as an intermediate approaching the inactive state (E). It appears that the E* to E equilibrium shift occurs initially from G138-F140 residues, leading to the unwinding of the loop and formation of the 310-helix. Finally, we describe a transient dimer structure of the MPro precursor held together through interactions of residues A5-G11 with distinct states of the active sites, E and E*, likely representing an intermediate in the autoprocessing pathway.

Hemiparasite Phtheirospermum japonicum growth benefits from a second host and inflicts greater host damage with exogenous N supply.

While parasites are likely to connect to multiple host plants in nature, parasitism dynamics under multiple association conditions remain unclear and are difficult to separate from competitive effects. In this study, a five-compartment split root-box was constructed to allow a single facultative root hemiparasite, Phtheirospermum japonicum, to connect to zero, one or two Medicago sativa hosts while maintaining constant plant number and independently controlling nutrient supply. In the first experiment, we found that P. japonicum derived equal, additive benefits from attachment to a second host irrespective of parasite N status. In the second experiment, parasites were grown at four N levels in either parasitic or control conditions. Attachment caused a constant, absolute increase in parasite mass at all N levels, while host damage increased at higher parasite N levels despite an apparent decrease in host to parasite N transfer. Our findings suggest that host damage caused by P. japonicum may be strengthened by exogenous nitrogen supply to the parasite.

Supporting autistic communities through parent-led and child/young person-led digital social story interventions: an exploratory study.

Introduction: Social Stories (SS) is a socially-valid intervention for autistic children and young people (CYP) which is used widely by professionals and parents. Research suggests that whilst parents are in an ideal position to deliver interventions for their autistic CYP, a lack of procedural integrity can result in a great deal of variability in parent-mediated intervention outcomes. Methods: This exploratory study investigated the extent to which SS can be effectively developed and delivered, through digital mediation, by parents with little to no researcher input (n = 17, sample 1) and the factors that impact effectiveness. Furthermore, the study also investigated the extent to which digitally-mediated SS can support autistic CYP to develop and deliver their own stories, thereby utilising the intervention as a means for self-support and self-management (n = 5, sample 2). Results: The outcomes of the study indicate that digital mediation can effectively support parent-led SS intervention. Findings also indicate that receptive/expressive language skills of autistic CYP, their level of systemizing, as well as the practice of consulting with the autistic CYP whilst identifying goals and developing stories, are individual and procedural characteristics which positively influence the effectiveness of the parent-led intervention. The study also found that digitally-mediated SS can be utilised as a self-support tool by autistic CYP themselves. Discussion: The results inform the developing literature on digital interventions and support tools that aim to engage with, and involve further, the autistic community in the setting and authoring of interventions and research.

Insights into the mechanism of SARS-CoV-2 main protease autocatalytic maturation from model precursors.

A critical step for SARS-CoV-2 assembly and maturation involves the autoactivation of the main protease (MProWT) from precursor polyproteins. Upon expression, a model precursor of MProWT mediates its own release at its termini rapidly to yield a mature dimer. A construct with an E290A mutation within MPro exhibits time dependent autoprocessing of the accumulated precursor at the N-terminal nsp4/nsp5 site followed by the C-terminal nsp5/nsp6 cleavage. In contrast, a precursor containing E290A and R298A mutations (MProM) displays cleavage only at the nsp4/nsp5 site to yield an intermediate monomeric product, which is cleaved at the nsp5/nsp6 site only by MProWT. MProM and the catalytic domain (MPro1-199) fused to the truncated nsp4 region also show time-dependent conversion in vitro to produce MProM and MPro1-199, respectively. The reactions follow first-order kinetics indicating that the nsp4/nsp5 cleavage occurs via an intramolecular mechanism. These results support a mechanism involving an N-terminal intramolecular cleavage leading to an increase in the dimer population and followed by an intermolecular cleavage at the C-terminus. Thus, targeting the predominantly monomeric MPro precursor for inhibition may lead to the identification of potent drugs for treatment.

A rule-based theoretical account of social stories to address the double empathy problem.

Social Stories™ (SS) is one of the most popular and researched interventions for autistic children. To date, research that focuses on outcomes has been prioritized over the investigation of the psychological mechanisms that inform the intervention. In this article we consider theoretical accounts proposed thus far which could underpin SS. We argue that mechanisms that are based on social deficit theories lack validity, and propose a rule-based theoretical account to inform a strengths-based approach toward conceptualizing the mechanisms that underpin SS. We apply this account to the 'double-empathy problem' to propose that SS can be adapted to involve all parties in the development and delivery of SS support by adopting a rule-based perspective. We use the example of systemizing (the drive to analyze and explore systems in terms of 'if-and-then' rules), which is proposed to be a relative autistic strength, as a form of rule-based thinking that can provide a theoretical account of SS and a framework to address the double-empathy problem.

Contribution of the catalytic dyad of SARS-CoV-2 main protease to binding covalent and noncovalent inhibitors.

The effect of mutations of the catalytic dyad residues of SARS-CoV-2 main protease (MProWT) on the thermodynamics of binding of covalent inhibitors comprising nitrile [nirmatrelvir (NMV), NBH2], aldehyde (GC373), and ketone (BBH1) warheads to MPro is examined together with room temperature X-ray crystallography. When lacking the nucleophilic C145, NMV binding is ∼400-fold weaker corresponding to 3.5 kcal/mol and 13.3 °C decrease in free energy (ΔG) and thermal stability (Tm), respectively, relative to MProWT. The H41A mutation results in a 20-fold increase in the dissociation constant (Kd), and 1.7 kcal/mol and 1.4 °C decreases in ΔG and Tm, respectively. Increasing the pH from 7.2 to 8.2 enhances NMV binding to MProH41A, whereas no significant change is observed in binding to MProWT. Structures of the four inhibitor complexes with MPro1-304/C145A show that the active site geometries of the complexes are nearly identical to that of MProWT with the nucleophilic sulfur of C145 positioned to react with the nitrile or the carbonyl carbon. These results support a two-step mechanism for the formation of the covalent complex involving an initial non-covalent binding followed by a nucleophilic attack by the thiolate anion of C145 on the warhead carbon. Noncovalent inhibitor ensitrelvir (ESV) exhibits a binding affinity to MProWT that is similar to NMV but differs in its thermodynamic signature from NMV. The binding of ESV to MProC145A also results in a significant, but smaller, increase in Kd and decrease in ΔG and Tm, relative to NMV.

Structures of brain-derived 42-residue amyloid-ß fibril polymorphs with unusual molecular conformations and intermolecular interactions.

Fibrils formed by the 42-residue amyloid-ß peptide (Aß42), a main component of amyloid deposits in Alzheimer's disease (AD), are known to be polymorphic, i.e., to contain multiple possible molecular structures. Previous studies of Aß42 fibrils, including fibrils prepared entirely in vitro or extracted from brain tissue and using solid-state NMR (ssNMR) or cryogenic electron microscopy (cryo-EM) methods, have found polymorphs with differences in amino acid sidechain orientations, lengths of structurally ordered segments, and contacts between cross-ß subunit pairs within a single filament. Despite these differences, Aß42 molecules adopt a common S-shaped conformation in all previously described high-resolution Aß42 fibril structures. Here we report two cryo-EM-based structures of Aß42 fibrils that are qualitatively different, in samples derived from AD brain tissue by seeded growth. In type A fibrils, residues 12 to 42 adopt a ν-shaped conformation, with both intra-subunit and intersubunit hydrophobic contacts to form a compact core. In type B fibrils, residues 2 to 42 adopt an υ-shaped conformation, with only intersubunit contacts and internal pores. Type A and type B fibrils have opposite helical handedness. Cryo-EM density maps and molecular dynamics simulations indicate intersubunit K16-A42 salt bridges in type B fibrils and partially occupied K28-A42 salt bridges in type A fibrils. The coexistence of two predominant polymorphs, with differences in N-terminal dynamics, is supported by ssNMR data, as is faithful propagation of structures from first-generation to second-generation brain-seeded Aß42 fibril samples. These results demonstrate that Aß42 fibrils can exhibit a greater range of structural variations than seen in previous studies.

Positive Schemas: Replication, Associations With Negative Schemas, and the Dark Triad.

The purpose of the current study was to replicate the factor structure of the 14 positive schemas identified in the earlier study by Louis et al. (2018). Using confirmatory factor analysis (CFA), and Multi-group CFA, the 14 positive schemas were found to be robust across four new non-clinical English-speaking community samples - USA (n = 396), South Africa (n = 390), Nigeria (n = 364), and India (n = 306). Further, results from CFA, and chi square tests showed that positive and negative schemas were independent but related constructs, and that they do not reflect bipolarity. Using hierarchical regression and Pearson's correlations the negative schemas of Entitlement, Approval Seeking and Mistrust, and the positive schema of Empathic Consideration were found to be associated positively and negatively respectively with Machiavellianism, narcissism, and psychopathy of the Dark Triad scale in all four worldwide samples. Implications of this finding in Schema Therapy treatment were discussed.

Effective digital support for autism: digital social stories.

Social Stories™ is one of the most popular interventions for autistic children and has been researched extensively. However, effectiveness data has been gathered mainly through single-participant designs which generate outcomes which can lack generalizability and social validity. Stories Online For Autism (SOFA) is a digital application which supports the development and delivery of Social Stories in a real-world setting and has the potential to contribute toward furthering (1) Social Stories research and (2) research on digital applications for autism by gathering large data sets from multiple participants. Three data sets (N = 856) were gathered through the SOFA app and were analyzed to investigate three key variables: What predicted closeness-to-goal of the Social Stories (as rated by an adult/parent/guardian, n = 568); the child's comprehension of the Social Stories (assessed by story comprehension questions, n = 127); and the child's rating of the enjoyability of the Social Stories (n = 161). A merged data set then investigated correlations between these three key variables. Age range (≤15), gender, autism diagnosis, and the child's level of language understanding were the potential predictors for these three key variables. Regression analysis indicated that parental closeness-to-goal ratings for their children were highest for children who were younger and more verbal. Regression analysis also indicated that older children scored higher in comprehension assessment, and autistic children rated the Social Stories as more enjoyable. Closeness-to-goal, comprehension scores and enjoyment ratings did not significantly correlate with each other. This is the largest study of Social Stories effectiveness, which was enabled through the collection of data through a digital app from multiple participants. The results indicate that digital social stories are particularly effective for younger verbal children. While this was the case for all children, it was particularly true for autistic children and female (and gender-diverse) children. For the first time, the gathering of large digital data sets has highlighted that while digital Social Stories can be effective for autistic males, they can be more effective for autistic females and gender-diverse autistic individuals. Thus, the SOFA app can support the investigation of the factors which influence Social Stories outcomes that are generalizable and with high social validity.

Unmasking the Conformational Stability and Inhibitor Binding to SARS-CoV-2 Main Protease Active Site Mutants and Miniprecursor.

We recently demonstrated that inhibitor binding reorganizes the oxyanion loop of a monomeric catalytic domain of SARS CoV-2 main protease (MPro) from an unwound (E) to a wound (active, E*) conformation, independent of dimerization. Here we assess the effect of the flanking N-terminal residues, to imitate the MPro precursor prior to its autoprocessing, on conformational equilibria rendering stability and inhibitor binding. Thermal denaturation (Tm) of C145A mutant, unlike H41A, increases by 6.8 °C, relative to wild-type mature dimer. An inactivating H41A mutation to maintain a miniprecursor containing TSAVL[Q or E] of the flanking nsp4 sequence in an intact form [(-6)MProH41A and (-6*)MProH41A, respectively], and its corresponding mature MProH41A were systematically examined. While the H41A mutation exerts negligible effect on Tm and dimer dissociation constant (Kdimer) of MProH41A, relative to the wild type MPro, both miniprecursors show a 4-5 °C decrease in Tm and > 85-fold increase in Kdimer as compared to MProH41A. The Kd for the binding of the covalent inhibitor GC373 to (-6*)MProH41A increases ∼12-fold, relative to MProH41A, concomitant with its dimerization. While the inhibitor-free dimer exhibits a state in transit from E to E* with a conformational asymmetry of the protomers' oxyanion loops and helical domains, inhibitor binding restores the asymmetry to mature-like oxyanion loop conformations (E*) but not of the helical domains. Disorder of the terminal residues 1-2 and 302-306 observed in both structures suggest that N-terminal autoprocessing is tightly coupled to the E-E* equilibrium and stable dimer formation.

Autoprocessing and oxyanion loop reorganization upon GC373 and nirmatrelvir binding of monomeric SARS-CoV-2 main protease catalytic domain.

The monomeric catalytic domain (residues 1-199) of SARS-CoV-2 main protease (MPro1-199) fused to 25 amino acids of its flanking nsp4 region mediates its autoprocessing at the nsp4-MPro1-199 junction. We report the catalytic activity and the dissociation constants of MPro1-199 and its analogs with the covalent inhibitors GC373 and nirmatrelvir (NMV), and the estimated monomer-dimer equilibrium constants of these complexes. Mass spectrometry indicates the presence of the accumulated adduct of NMV bound to MProWT and MPro1-199 and not of GC373. A room temperature crystal structure reveals a native-like fold of the catalytic domain with an unwound oxyanion loop (E state). In contrast, the structure of a covalent complex of the catalytic domain-GC373 or NMV shows an oxyanion loop conformation (E* state) resembling the full-length mature dimer. These results suggest that the E-E* equilibrium modulates autoprocessing of the main protease when converting from a monomeric polyprotein precursor to the mature dimer.

RADIOACTIVITY ASSESSMENT OF SURFACE SOIL IN THE VICINITY OF A URANIUM MINE IN MALAWI.

The activity concentrations of 238U, 232Th and 40K in the soil of areas surrounding the Kayelekera uranium mine were assessed. This study aims to provide a comprehensive profile of soil radioactivity distribution in the area surrounding the uranium mine to determine radiological hazards associated with mining and processing activities. Soil samples were analysed using gamma-ray spectrometry with a high-purity germanium detector. Mean specific activities of 238U, 232Th and 40K were 58.3 ± 3.7, 40.3 ± 0.3 and 590.9 ± 63.9 Bq kg-1, respectively. Results from this study have indicated changes in radioactivity levels of naturally occurring radioactive materials in the area surrounding the understudied mine, with certain areas close to the mine site showing elevated levels of 238U, highlighting the need for systematic and periodic monitoring.

Global Dynamics of a Protein on the Surface of Anisotropic Lipid Nanoparticles Derived from Relaxation-Based NMR Spectroscopy.

The global motions of ubiquitin, a model protein, on the surface of anisotropically tumbling 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-(1'-rac-glycerol) (POPG):1,2-dihexanoyl-sn-glycero-3-phosphocholine (DHPC) bicelles are described. The shapes of POPG:DHPC bicelles prepared with high molar ratios q of POPG to DHPC can be approximated by prolate ellipsoids, with the ratio of ellipsoid dimensions and dimensions themselves increasing with higher values of q. Adaptation of the nuclear magnetic resonance (NMR) relaxation-based approach that we previously developed for interactions of ubiquitin with spherical POPG liposomes (Ceccon, A. J. Am. Chem. Soc. 2016, 138, 5789-5792) allowed us to quantitatively analyze the variation in lifetime line broadening of NMR signals (ΔR2) measured for ubiquitin in the presence of q = 2 POPG:DHPC bicelles and the associated transverse spin relaxation rates (R2,B) of bicelle-bound ubiquitin. Ubiquitin, transiently bound to POPG:DHPC bicelles, undergoes internal rotation about an axis orthogonal to the surface of the bicelle and perpendicular to the principal axis of its rotational diffusion tensor on the low microsecond time scale (∼3 µs), while the rotation axis itself wobbles in a cone on a submicrosecond time scale (≤ 500 ns).

Real-time Exchange of the Lipid-bound Intermediate and Post-fusion States of the HIV-1 gp41 Ectodomain.

The envelope glycoprotein gp41 of the HIV-1 virus mediates its entry into the host cell. During this process, gp41 undergoes large conformational changes and the energy released in the remodeling events is utilized to overcome the barrier associated with fusing the viral and host membranes. Although the structural intermediates of this fusion process are attractive targets for drug development, no detailed high-resolution structural information or quantitative thermodynamic characterization are available. By measuring the dynamic equilibrium between the lipid-bound intermediate and the post-fusion six-helical bundle (6HB) states of the gp41 ectodomain in the presence of bilayer membrane mimetics, we derived both the reaction kinetics and energies associated with these two states by solution NMR spectroscopy. At equilibrium, an exchange time constant of about 12 seconds at 38 °C is observed, and the post-fusion conformation is energetically more stable than the lipid-bound state by 3.4 kcal mol-1. The temperature dependence of the kinetics indicates that the folding occurs through a high-energy transition state which may resemble a 5HB structure. The energetics and kinetics of gp41 folding in the context of membrane bilayers provide a molecular basis for an improved understanding of viral membrane fusion.

Modulating the Excitability of Olfactory Output Neurons Affects Whole-Body Metabolism.

Metabolic state can alter olfactory sensitivity, but it is unknown whether the activity of the olfactory bulb (OB) may fine tune metabolic homeostasis. Our objective was to use CRISPR gene editing in male and female mice to enhance the excitability of mitral/tufted projection neurons (M/TCs) of the OB to test for improved metabolic health. Ex vivo slice recordings of MCs in CRISPR mice confirmed increased excitability due the targeted loss of Kv1.3 channels, which resulted in a less negative resting membrane potential (RMP), enhanced action potential (AP) firing, and insensitivity to the selective channel blocker margatoxin (MgTx). CRISPR mice exhibited enhanced odor discrimination using a habituation/dishabituation paradigm. CRISPR mice were challenged for 25 weeks with a moderately high-fat (MHF) diet, and compared with littermate controls, male mice were resistance to diet-induced obesity (DIO). Female mice did not exhibit DIO. CRISPR male mice gained less body weight, accumulated less white adipose tissue, cleared a glucose challenge more quickly, and had less serum leptin and liver triglycerides. CRISPR male mice consumed equivalent calories as control littermates, and had unaltered energy expenditure (EE) and locomotor activity, but used more fats for metabolic substrate over that of carbohydrates. Counter to CRISPR-engineered mice, by using chemogenetics to decrease M/TC excitability in male mice, activation of inhibitory designer receptors exclusively activated by designer drugs (DREADDs) caused a decrease in odor discrimination, and resulted in a metabolic profile that was obesogenic, mice had reduced EE and oxygen consumption (VO2). We conclude that the activity of M/TC projection neurons canonically carries olfactory information and simultaneously can regulate whole-body metabolism.SIGNIFICANCE STATEMENT The olfactory system drives food choice, and olfactory sensitivity is strongly correlated to hunger and fullness. Olfactory function thereby influences nutritional balance and obesity outcomes. Obesity has become a health and financial crisis in America, shortening life expectancy and increasing the severity of associated illnesses. It is expected that 51% of Americans will be obese by the year 2030. Using CRISPR gene editing and chemogenetic approaches, we discovered that changing the excitability of output neurons in the olfactory bulb (OB) affects metabolism and body weight stabilization in mice. Our results suggest that long-term therapeutic targeting of OB activity to higher processing centers may be a future clinical treatment of obesity or type II Diabetes.

Correction: The impact of using digitally-mediated social stories on the perceived competence and attitudes of parents and practitioners supporting children with autism.

[This corrects the article DOI: 10.1371/journal.pone.0262598.].

Development and Validation of the Young Parenting Inventory (YPI-R3) for Measuring Past Deviant and Normal Variations in Parenting.

Most measures of past parenting patterns have a restricted range of about two to three negative parenting constructs. The Young Parenting Inventory (YPI-R2) provides a more nuanced framework that measures a fuller spectrum of these negative parenting patterns and, therefore, holds the potential of being a more useful guide to parents and caretakers. The YPI-R2 is made up of six validated subscales. An additional four were identified but were not sufficiently robust to be included. The purpose of this study is to determine if these four scales can be strengthened through the development of additional items and be empirically validated. Using non-clinical, English-speaking community samples from Singapore (n = 592, 628) and Malaysia (n = 222, 229), these revised scales were tested using multiple exploratory factor analyses with fathers and mothers rated separately. After further scale refinement, the final model, which consisted of 10 subscales and 41 items, was then subjected to confirmatory factor analysis using 4 other non-clinical international samples with separate ratings for fathers and mothers-USA (n = 259, 281), South Africa (n = 318, 372), Nigeria (n = 328, 344) and India (n = 277, 289). The results show that the YPI-R3 with 10 subscales is a robust and cross-culturally acceptable model. Correlations and hierarchical multiple regression analyses showed that the YPI-R3 has good convergent validity and predictive capabilities with measures of psychopathology, personality traits, emotional distress, negative schemas and other distal measures of functioning in everyday life-gratitude, humor and satisfaction with life.

Covalent narlaprevir- and boceprevir-derived hybrid inhibitors of SARS-CoV-2 main protease.

Emerging SARS-CoV-2 variants continue to threaten the effectiveness of COVID-19 vaccines, and small-molecule antivirals can provide an important therapeutic treatment option. The viral main protease (Mpro) is critical for virus replication and thus is considered an attractive drug target. We performed the design and characterization of three covalent hybrid inhibitors BBH-1, BBH-2 and NBH-2 created by splicing components of hepatitis C protease inhibitors boceprevir and narlaprevir, and known SARS-CoV-1 protease inhibitors. A joint X-ray/neutron structure of the Mpro/BBH-1 complex demonstrates that a Cys145 thiolate reaction with the inhibitor's keto-warhead creates a negatively charged oxyanion. Protonation states of the ionizable residues in the Mpro active site adapt to the inhibitor, which appears to be an intrinsic property of Mpro. Structural comparisons of the hybrid inhibitors with PF-07321332 reveal unconventional F···O interactions of PF-07321332 with Mpro which may explain its more favorable enthalpy of binding. BBH-1, BBH-2 and NBH-2 exhibit comparable antiviral properties in vitro relative to PF-07321332, making them good candidates for further design of improved antivirals.

Modulation of the monomer-dimer equilibrium and catalytic activity of SARS-CoV-2 main protease by a transition-state analog inhibitor.

The role of dimer formation for the onset of catalytic activity of SARS-CoV-2 main protease (MProWT) was assessed using a predominantly monomeric mutant (MProM). Rates of MProWT and MProM catalyzed hydrolyses display substrate saturation kinetics and second-order dependency on the protein concentration. The addition of the prodrug GC376, an inhibitor of MProWT, to MProM leads to an increase in the dimer population and catalytic activity with increasing inhibitor concentration. The activity reaches a maximum corresponding to a dimer population in which one active site is occupied by the inhibitor and the other is available for catalytic activity. This phase is followed by a decrease in catalytic activity due to the inhibitor competing with the substrate. Detailed kinetics and equilibrium analyses are presented and a modified Michaelis-Menten equation accounts for the results. These observations provide conclusive evidence that dimer formation is coupled to catalytic activity represented by two equivalent active sites.