Validation of the CogDrisk Instrument as Predictive of Dementia in Four General Community-Dwelling Populations.

BACKGROUND: Lack of external validation of dementia risk tools is a major limitation for generalizability and translatability of prediction scores in clinical practice and research. OBJECTIVES: We aimed to validate a new dementia prediction risk tool called CogDrisk and a version, CogDrisk-AD for predicting Alzheimer's disease (AD) using cohort studies. DESIGN, SETTING, PARTICIPANTS AND MEASUREMENTS: Four cohort studies were identified that included majority of the dementia risk factors from the CogDrisk tool. Participants who were free of dementia at baseline were included. The predictors were component variables in the CogDrisk tool that include self-reported demographics, medical risk factors and lifestyle habits. Risk scores for Any Dementia and AD were computed and Area Under the Curve (AUC) was assessed. To examine modifiable risk factors for dementia, the CogDrisk tool was tested by excluding age and sex estimates from the model. RESULTS: The performance of the tool varied between studies. The overall AUC and 95% CI for predicting dementia was 0.77 (0.57, 0.97) for the Swedish National study on Aging and Care in Kungsholmen, 0.76 (0.70, 0.83) for the Health and Retirement Study - Aging, Demographics and Memory Study, 0.70 (0.67,0.72) for the Cardiovascular Health Study Cognition Study, and 0.66 (0.62,0.70) for the Rush Memory and Aging Project. CONCLUSIONS: The CogDrisk and CogDrisk-AD performed well in the four studies. Overall, this tool can be used to assess individualized risk factors of dementia and AD in various population settings.

The effect of missing data and imputation on the detection of bias in cognitive testing using differential item functioning methods.

BACKGROUND: Item response theory (IRT) methods for addressing differential item functioning (DIF) can detect group differences in responses to individual items (e.g., bias). IRT and DIF-detection methods have been used increasingly often to identify bias in cognitive test performance by characteristics (DIF grouping variables) such as hearing impairment, race, and educational attainment. Previous analyses have not considered the effect of missing data on inferences, although levels of missing cognitive data can be substantial in epidemiologic studies. METHODS: We used data from Visit 6 (2016-2017) of the Atherosclerosis Risk in Communities Neurocognitive Study (N = 3,580) to explicate the effect of artificially imposed missing data patterns and imputation on DIF detection. RESULTS: When missing data was imposed among individuals in a specific DIF group but was unrelated to cognitive test performance, there was no systematic error. However, when missing data was related to cognitive test performance and DIF group membership, there was systematic error in DIF detection. Given this missing data pattern, the median DIF detection error associated with 10%, 30%, and 50% missingness was -0.03, -0.08, and -0.14 standard deviation (SD) units without imputation, but this decreased to -0.02, -0.04, and -0.08 SD units with multiple imputation. CONCLUSIONS: Incorrect inferences in DIF testing have downstream consequences for the use of cognitive tests in research. It is therefore crucial to consider the effect and reasons behind missing data when evaluating bias in cognitive testing.

Assessing Bias in Cognitive Testing for Older Adults with Sensory Impairment: An Analysis of Differential Item Functioning in the Baltimore Longitudinal Study on Aging (BLSA) and the Atherosclerosis Risk in Communities Neurocognitive Study (ARIC-NCS).

OBJECTIVES: Vision and hearing impairments affect 55% of people aged 60+ years and are associated with lower cognitive test performance; however, tests rely on vision, hearing, or both. We hypothesized that scores on tests that depend on vision or hearing are different among those with vision or hearing impairments, respectively, controlling for underlying cognition. METHODS: Leveraging cross-sectional data from the Baltimore Longitudinal Study of Aging (BLSA) and the Atherosclerosis Risk in Communities Neurocognitive Study (ARIC-NCS), we used item response theory to test for differential item functioning (DIF) by vision impairment (better eye presenting visual acuity worse than 20/40) and hearing impairment (better ear .5-4 kHz pure-tone average > 25 decibels). RESULTS: We identified DIF by vision impairment for tests whose administrations do not rely on vision [e.g., Delayed Word Recall both in ARIC-NCS: .50 logit difference between impaired and unimpaired (p = .04) and in BLSA: .62 logits (p = .02)] and DIF by hearing impairment for tests whose administrations do not rely on hearing [Digit Symbol Substitution test in BLSA: 1.25 logits (p = .001) and Incidental Learning test in ARIC-NCS: .35 logits (p = .001)]. However, no individuals had differences between unadjusted and DIF-adjusted measures of greater than the standard error of measurement. CONCLUSIONS: DIF by sensory impairment in cognitive tests was independent of administration characteristics, which could indicate that elevated cognitive load among persons with sensory impairment plays a larger role in test performance than previously acknowledged. While these results were unexpected, neither of these samples are nationally representative and each has unique selection factors; thus, replication is critical.

Neuropsychologic assessment.

In this chapter, we review the use of neuropsychologic assessment in epidemiologic studies. First, we provide a brief introduction to the history of clinical neuropsychology and neuropsychologic assessment. We expand on the principal components of a neuropsychologic assessment and cognitive domains most commonly examined. This chapter also seeks to highlight specific domains and tests with validated psychometric properties that are widely accepted in clinical practice, as well as how data from a neuropsychologic test should be interpreted. Additionally, the important roles that neuropsychologic assessments play in tracking normative changes, patient diagnoses, care, and research will be discussed. Factors to consider when deciding on the inclusion of test instruments for a research study will also be reviewed. Lastly, we shed light on the contributions that neuropsychology has played in epidemiologic studies, as well as some challenges frequently faced when participating in this field of research.

The association of genetic variants in interleukin-1 genes with cognition: findings from the cardiovascular health study.

The inflammatory cytokine interleukin-1 (IL1) potentially plays a role in cognitive deterioration through pathology due to a dementing disorder or due to an aging process. Study of genetic variants in the IL1 genes has been mostly limited to diseases such as Alzheimer's, however, there may be benefit to studying a continuous measure of cognition. Using data from the Cardiovascular Health Study, we evaluate genetic variation in the genes encoding inflammatory agonists IL1A and IL1B, and the antagonist IL1RN, with repeated measures of global cognition (3MS) and processing speed (DSST), using mixed effects models. We found statistically significant minor allele SNP associations with baseline performance on the 3MS in the IL1RN gene for Caucasians (rs17042917: beta=0.47, 95%CI=0.09, 0.85, p=0.016; rs4251961: beta=-0.36, 95%CI=-0.13,-0.60, p=0.0027; rs931471: beta=0.39, 95%CI=0.13, 0.65, p=0.0032), and the IL1B gene for African Americans (rs1143627: beta=1.6, 95%CI=0.48, 2.8; p=0.006 and rs1143634: beta=2.09, 95%CI=0.39, 3.8; p=0.016). Associations appear to be weaker in a subgroup with higher education level. Upon removing those diagnosed with dementia, effect sizes and statistical significance attenuated. These results provide supporting evidence that genetic variants in IL1 genes may be involved in inflammatory-related lowered cognition, that higher education may modify genetic predisposition, and that these associations may be driven by a dementia process.

Functional and cognitive criteria produce different rates of mild cognitive impairment and conversion to dementia.

OBJECTIVE: To compare rates of mild cognitive impairment (MCI) and rates of progression to dementia using different MCI diagnostic systems. METHODS: MCI was investigated at baseline in 3063 community dwelling non-demented elderly in the Ginkgo Evaluation of Memory (GEM) study who were evaluated every 6 months to identify the presence of dementia. Overall MCI frequency was determined using (1) a Clinical Dementia Rating (CDR) score of 0.5 and (2) neuropsychological (NP) criteria, defined by impairment on standard cognitive tests. RESULTS: 40.2% of participants met CDR MCI criteria and 28.2% met NP MCI criteria (amnestic MCI = 16.6%). 15.7% were classified as MCI by both criteria and 47.4% as normal by both. Discordant diagnoses were observed in 24.5% who met NP normal/CDR MCI and in 12.4% who met NP MCI/CDR normal. Factors associated with CDR MCI among NP normal included lower education, lower NP scores, more instrumental activities of daily living impairment, greater symptoms of depression and subjective health problems. Individuals meeting NP MCI/CDR normal were significantly more likely to develop dementia over the median follow-up of 6.1 years than those meeting NP normal/CDR MCI. CONCLUSIONS: Different criteria produce different MCI rates and different conversion rates to dementia. Although a higher percentage of MCI was identified by CDR than NP, a higher percentage of NP MCI progressed to dementia. These findings suggest that the CDR is sensitive to subtle changes in cognition not identified by the NP algorithm but is also sensitive to demographic and clinical factors probably leading to a greater number of false positives. These results suggest that identifying all individuals with CDR scores of 0.5 as Alzheimer's disease is not advisable.

Knee height and arm span: a reflection of early life environment and risk of dementia.

OBJECTIVES: To determine if anthropometric measures, as markers of early life environment, are associated with risk of dementia, Alzheimer disease (AD), and vascular dementia (VaD). METHODS: A total of 2,798 subjects were followed as part of the Cardiovascular Health Cognition Study for an average of 5.4 years; 480 developed dementia. Knee height was measured 3 years prior to and arm span 4 years after the study's baseline. Cox proportional hazard models were used to examine their association with subsequent risk of dementia, AD, and VaD. RESULTS: Among women, greater knee height and arm span were associated with lower risks of dementia (knee height: HR per 1-inch increase 0.84; 95% CI 0.74-0.96; arm span: HR per 1-inch increase 0.93; 95% CI 0.88-0.98) and AD (knee height: HR per 1-inch increase 0.78; 95% CI 0.65-0.93; arm span: HR per 1-inch increase 0.90; 95% CI 0.85-0.96). Women in the lowest quartile of arm span had approximately 1.5 times greater risk of dementia (HR 1.45; 95% CI 1.03-2.05) and AD (HR 1.70; 95% CI 1.10-2.62) than other women. Among men, only arm span was associated with lower risks of dementia (HR per 1-inch increase 0.94; 95% CI 0.89-1.00) and AD (HR per 1-inch increase 0.92; 95% CI 0.84-1.00). For each gender, knee height was not associated with VaD, while arm span was associated with a nonsignificant lower risk of VaD. CONCLUSIONS: Our findings with knee height and arm span are consistent with previous reports and suggest early life environment may play an important role in the determination of future dementia risk.

The use of angiotensin-converting enzyme inhibitors and diuretics is associated with a reduced incidence of impairment on cognition in elderly women.

The effects of angiotensin-converting enzyme inhibitors (ACE-Is) and diuretics (used as antihypertensive agents) on global and domain-specific cognitive decline were evaluated in 326 non-demented community-dwelling participants over the age of 70 years in the Women's Health and Aging Study II. Time-dependent Cox proportional hazards regression analysis was used for evaluating the association between parameters. The use of ACE-I for more than 3 years was associated with reduced incidence of impairment on Mini-Mental State Examination (MMSE), Trail Making Test-Part A and Part B (TMT, Parts A and B), Hopkins Verbal Learning Test-Immediate Recall (HVLT-I), and Hopkins Verbal Learning Test-Delayed Recall (HVLT-D). The use of diuretics for more than 3 years was associated with reduced incidence of impairment on MMSE, TMT, Parts A and B, HVLT-I, and (HVLT-D). The presence of vascular disease did not make any difference to these effects. Therefore, the use of ACE-Is or diuretics was associated with reduced incidence of impairment of both global and domain-specific cognition in elderly women, and may help delay progression to dementia.

Environmental lead exposure and cognitive function in community-dwelling older adults.

OBJECTIVE: To determine if long-term exposure to high levels of lead in the environment is associated with decrements in cognitive ability in older Americans. METHODS: We completed a cross-sectional analysis using multiple linear regression to evaluate associations of recent (in blood) and cumulative (in tibia) lead dose with cognitive function in 991 sociodemographically diverse, community-dwelling adults, aged 50 to 70 years, randomly selected from 65 contiguous neighborhoods in Baltimore, MD. Tibia lead was measured with (109)Cd induced K-shell X-ray fluorescence. Seven summary measures of cognitive function were created based on standard tests in these domains: language, processing speed, eye-hand coordination, executive functioning, verbal memory and learning, visual memory, and visuoconstruction. RESULTS: The mean (SD) blood lead level was 3.5 (2.2) microg/dL and tibia lead level was 18.7 (11.2) microg/g. Higher tibia lead levels were consistently associated with worse cognitive function in all seven domains after adjusting for age, sex, APOE-epsilon4, and testing technician (six domains p

Neuropsychological characteristics of mild cognitive impairment subgroups.

OBJECTIVE: To describe the neuropsychological characteristics of mild cognitive impairment (MCI) subgroups identified in the Cardiovascular Health Study (CHS) cognition study. METHODS: MCI was classified as MCI-amnestic type (MCI-AT): patients with documented memory deficits but otherwise normal cognitive function; and MCI-multiple cognitive deficits type (MCI-MCDT): impairment of at least one cognitive domain (not including memory), or one abnormal test in at least two other domains, but who had not crossed the dementia threshold. The MCI subjects did not have systemic, neurological, or psychiatric disorders likely to affect cognition. RESULTS: MCI-AT (n = 10) had worse verbal and non-verbal memory performance than MCI-MCDT (n = 28) or normal controls (n = 374). By contrast, MCI-MCDT had worse language, psychomotor speed, fine motor control, and visuoconstructional function than MCI-AT or normal controls. MCI-MCDT subjects had memory deficits, though they were less pronounced than in MCI-AT. Of the MCI-MCDT cases, 22 (78.5%) had memory deficits, and 6 (21.5%) did not. MCI-MCDT with memory disorders had more language deficits than MCI-MCDT without memory disorders. By contrast, MCI-MCDT without memory deficits had more fine motor control deficits than MCI-MCDT with memory deficits. CONCLUSIONS: The most frequent form of MCI was the MCI-MCDT with memory deficits. However, the identification of memory impaired MCI groups did not reflect the true prevalence of MCI in a population, as 16% of all MCI cases and 21.5% of the MCI-MCDT cases did not have memory impairment. Study of idiopathic amnestic and non-amnestic forms of MCI is essential for an understanding of the aetiology of MCI.

Benefits of fatty fish on dementia risk are stronger for those without APOE epsilon4.

OBJECTIVE: To compare associations of lean fish vs fatty fish (tuna or other fish) intake with dementia, Alzheimer disease (AD), and vascular dementia (VaD) and in relation to APOE epsilon4 status in the Cardiovascular Health Cognition Study (CHCS). METHODS: Fish intake was assessed by food frequency questionnaires. Incident dementia, AD, and VaD were determined through a series of cognitive tests, physician's assessment, and committee consensus. We used Cox proportional hazards regression to calculate hazard ratios of dementia, AD, and VaD with lean fried fish, fatty fish, or total fish intake, which were then stratified by the presence of APOE epsilon4. RESULTS: Although consumption of lean fried fish had no protective effect, consumption of fatty fish more than twice per week was associated with a reduction in risk of dementia by 28% (95% CI: 0.51 to 1.02), and AD by 41% (95% CI: 0.36 to 0.95) in comparison to those who ate fish less than once per month. Stratification by APOE epsilon4 showed this effect to be selective to those without the epsilon4 allele. Adjustment by education and income attenuated the effect. CONCLUSION: In the Cardiovascular Health Cognition Study, consumption of fatty fish was associated with a reduced risk of dementia and Alzheimer disease for those without the APOE epsilon4 allele.

Preclinical Alzheimer disease: neuropsychological test performance 1.5 to 8 years prior to onset.

OBJECTIVE: To determine if individuals ultimately diagnosed with Alzheimer disease (AD) exhibited evidence of cognitive impairment on neuropsychological tests administered between 1.5 years and 8.1 years before dementia onset. METHODS: A total of 693 community-dwelling individuals, part of the Cardiovascular Health Study, completed a neuropsychological test battery in 1991/92. Subjects were followed annually over the next 8 years (median follow-up = 7.4 years). Seventy-two individuals were ultimately diagnosed with AD (median follow-up = 4.5 years): 24 with AD onset 1.5 to 3.4 years after baseline neuropsychological testing, 20 with AD onset 3.5 to 5.0 years after testing, and 28 with onset 5.1 to 8.1 years after testing. A total of 621 individuals remained nondemented throughout the 8 years of follow-up (median follow-up = 7.5 years). RESULTS: Subjects ultimately diagnosed with AD had poorer scores on baseline neuropsychological measures than subjects who remained nondemented. Although individuals closest to AD onset (i.e., 1.5 to 3.4 years) performed the most poorly, cognitive impairment was detected in individuals who did not develop AD until 5 to 8 years later. CONCLUSIONS: Cognitive changes can be detected well before onset of Alzheimer disease.

Stroke risk factors and loss of high cognitive function.

BACKGROUND: Modifiable stroke risk factors may contribute to age-associated declines in cognitive function. Individuals with high levels of cognitive function after midlife may have less exposure to these stroke risk factors or may be less susceptible to their effects on cognition. METHODS: The Cardiovascular Health Study (CHS)* is a population-based, longitudinal cohort study of 5,888 people age 65 years and older. Participants (n = 4,129) who were free of dementia, stroke, or TIA at the time of baseline cranial MRI were selected for analysis. High cognitive function at baseline was defined by performance at or above midlife norms on the Modified Mini-Mental State Examination (3MS). RESULTS: The odds of having high cognitive function at baseline decreased by quartile of stroke risk (highest vs lowest risk quartile, adjusted odds ratio [OR] 0.68; 95% CI 0.52 to 0.88; p for trend = 0.005). Stroke risk was a predictor of decline on the 3MS in those with typical levels of cognitive function at baseline, even in the absence of incident stroke or TIA (highest vs lowest risk quartile for 3MS decline, adjusted OR 2.11; 95% CI 1.42 to 3.13; p for trend < 0.001). In contrast, stroke risk was not associated with decline on the 3MS in those with high cognitive function at baseline (p = 0.03 for interaction). CONCLUSIONS: In a cohort of older adults without stroke, TIA, or dementia, cognitive function and incident cognitive decline were associated with risk for stroke. Additional studies are needed to determine whether modification of stroke risk factors can reduce the cognitive decline that is often attributed to normal aging.

Predictor index of mortality in dementia patients upon entry into long-term care.

BACKGROUND: The purpose of this study was to develop an algorithm that predicts survival in patients with dementia upon entry into long-term care. There are, as yet, no predictive equations developed for those in the late stages of Alzheimer's disease (AD). METHODS: This was a prospective, observational study of 132 patients with dementia (61% with AD) followed for up to 5.0 years (median of 41.0 months) after admission to a long-term care facility for dementia patients. Information on demographic characteristics, physical health, and cognitive, emotional, and behavioral characteristics was collected shortly after admission and entered as predictors of time until death in Cox regressions. Findings were used to derive an index predicting mortality. RESULTS: There were 60 deaths among the 132 patients (45.4% mortality), with an average survival of 22.4 months in those who died. Better physical health and the presence of delusions were associated with longer survival. These two variables were aggregated into the Copper Ridge Index (CRI). Each one-point increase on the CRI was associated with a four-fold greater likelihood of death over 5 years. CONCLUSIONS: A predictive equation incorporating measures of general physical health and delusions accurately predicted time to death in dementia patients in long-term care.

Hormone replacement therapy and reduced cognitive decline in older women: the Cache County Study.

OBJECTIVE: To examine the association between postmenopausal hormone replacement therapy (HRT) and the trajectory of global cognitive change with age. METHODS: The Modified Mini-Mental State Examination (MMSE) was administered to a population sample of 2,073 nondemented, community-dwelling female residents of Cache County, UT, aged 65 and older. Current and past HRT and other medications at a baseline interview and at follow-up 3 years later were assessed. Between interviews, a telephone Women's Health Questionnaire was administered to assess initial exposure, duration, and recency of HRT. Generalized estimating equation marginal models were used to evaluate the cross-sectional and longitudinal relations of HRT and modified MMSE score. Also assessed were effects with multivitamins and calcium supplements as exposures likely to reflect a "healthy lifestyle" among HRT users. Model covariates included the presence of APOE epsilon4 alleles, age, education, concurrent depression, several chronic diseases, and self-perceived general health. RESULTS: Age, lower education, depression, and APOE epsilon4 were all associated with lower baseline modified MMSE scores. With these covariates in the model, lifetime HRT use was associated with better baseline modified MMSE scores and a slower rate of decline. Stratification by APOE genotype did not alter these effects. Apparent benefits with HRT were attenuated but remained significant after elimination of scores from participants with incident dementia. A significant interaction between age and HRT indicated the strongest effects in women aged 85 and older. Measures of age at initial use of HRT, duration, and recency of exposure did not improve the models. No effects were seen with the "healthy lifestyle" control exposures. CONCLUSIONS: In a population cohort of older women, lifetime HRT exposure was associated with improved global cognition and attenuated decline over a 3-year interval. Improvements were greatest in the oldest old.

Importance of generativity for healthy aging in older women.

This article reviewed increasing evidence that remaining physically, cognitively, or socially active confers health benefits by delaying or preventing the onset of disease and disability in older adults. The desire to be generative, or to make a difference, has long been considered an important developmental objective in later years in order to give meaning to one's life, and may provide the necessary impetus for older women to initiate and maintain health-promoting activities. Because the prevalence of disability is greatest in older women, it is critical to find ways to maximize their opportunities for generative activity to promote healthier life-styles. Unfortunately, those who stand to gain most from the promotion of generative roles face many limiting factors, including low education, financial dependence and poverty, primary care-taking responsibilities, social isolation, and low self-efficacy. These obstacles may be too difficult and pervasive for an individual to overcome by oneself. Rather, these challenges need to be addressed through progressive changes in social programs that acknowledge the contributions that older adults can make in later years. Decreasing the structural lag between current social and demographic realities of older women's roles with increasing age will become ever more critical as a growing proportion of older women and men transition from a job outside the home to retirement.

Association between executive attention and physical functional performance in community-dwelling older women.

OBJECTIVES: Executive functions supervise the contents of working memory, where information from long-term memory is integrated with information in the immediate present. This study examined whether executive attentional abilities were uniquely associated with the performance of complex, instrumental activities of daily living (IADLs) in cognitively intact and physically high-functioning older women. METHODS: Participants were 406 community-residing, older women aged 70-80 years in the Women's Health and Aging Study (WHAS) II, screened to be physically high functioning and cognitively intact using the Mini-Mental State Exam. Hierarchical regression models, adjusted for demographic and disease variables, were used to evaluate the association of cognitive domains, including executive attention, memory, psychomotor speed, and spatial ability with summary measures of IADL (e.g., looking up and dialing a telephone number) and mobility-based ADL (e.g., walking 4 meters) function. RESULTS: Tests of executive attention were associated with performance on IADLs (6.6%) and, to a lesser degree, mobility-based ADLs (1%), adjusting for demographic and disease variables. In particular, the mental flexibility component of the Trail Making Test accounted for the majority of attentional variance in IADL performance. Older age, lower education, and African American race were also associated with poorer physical test performances. DISCUSSION: Executive difficulties in flexibly planning and initiating a course of action were selectively associated with slower performance of higher-order IADL tests, relative to other domains of cognition, in a high-functioning, community-based older cohort. These results suggest that executive functions may be important in mediating the onset and progression of physical functional declines.

Lack of relation between race and cognitive test performance in Alzheimer's disease.

This study evaluated cognitive test performance in African-American and European-American Alzheimer's disease patients with equivalent years of education. Group differences were negligible on a variety of memory, language, and attentional measures, including several widely used neuropsychological tests. Differences between racial groups observed in earlier studies may have stemmed, in part, from differences in education, which may itself serve as a proxy for other potentially important sociologic and health variables.

Aging, distraction, and the benefits of predictable location.

Three experiments examined the impact on reading time for younger and older adults in the absence vs. presence of distraction (marked by font type) in either fixed predictable locations (Experiments 1 and 2) or unpredictable locations (Experiment 3). Consistent with earlier work (S. L. Connelly, L. Hasher, & R. T. Zacks, 1991), older adults were markedly disrupted, relative to young adults, when distraction was present in unpredictable locations. When the location of distraction was fixed, however, the very large disadvantage that older adults otherwise experienced (slowed by as much as 46 s) diminished substantially (to as little as 2 s). Fixed location also eliminated the relatedness effect, by which older adults are especially susceptible to distraction from meaningfully related material.

Structure of phosphorylase kinase. A three-dimensional model derived from stained and unstained electron micrographs.

Phosphorylase kinase, the first protein kinase discovered, is a key regulatory enzyme in glycogen metabolism. Although its biochemical properties are well characterized, details of its three-dimensional structure and subunit topology are yet to be elucidated. This study describes four characteristic views of the hexadecameric holoenzyme (alpha 4 beta 4 gamma 4 delta 4) as observed in both negatively stained and unstained electron micrographs. The predominant views are the widely reported "butterfly" with two wing-like lobes connected by thin bridges, and the previously described "chalice", composed of "cup" and "stem" segments. Two additional views, a "cube", similar to the previously reported "tetrad", and a "cross" or "X" are less common, but illustrate the overall geometry of the particle. Based on these images, the first three-dimensional model of the enzyme has been constructed. It is composed of four identical protomers that associate with D2 symmetry to form the two major structural elements (the two lobes). Two protomers in a head to head arrangement make up each symmetrical lobe; to complete the holoenzyme, one lobe is inverted and placed perpendicular to the other. Thus, the overall structure has three 2-fold axes of symmetry, and the arrangement of the four protomers approximates a tetrahedron. Each lobe of the model corresponds to a wing of the butterfly projection. Two projections form the chalice: in the intra-lobe orientation, one lobe forms the cup and the other forms the stem, and in the inter-lobe view, one-half of each lobe contributes to each segment of the image. The cube and cross projections result from 90 degrees rotations from the butterfly orientation. In the cube, the distal portions of each lobe are projected separately. In the cross, one lobe is crossed over and is above the other. This model both accounts for and predicts all of the observed microscopic images.