Multi-Site Mild Traumatic Brain Injury Classification with Machine Learning and Harmonization.

Traumatic brain injury (TBI) can drastically affect an individual's cognition, physical, emotional wellbeing, and behavior. Even patients with mild TBI (mTBI) may suffer from a variety of long-lasting symptoms, which motivates researchers to find better biomarkers. Machine learning algorithms have shown promising results in detecting mTBI from resting-state functional network connectivity (rsFNC) data. However, data collected at multiple sites introduces additional noise called site-effects, resulting in erroneous conclusions. Site errors are controlled through a process called harmonization, but its use in classifying neuroimaging data has been addressed lightly. With the ongoing need to improve mTBI detection, this study shows that harmonization should be integrated into the machine learning process when working with multi-site neuroimaging datasets.

Identifying Alcohol Use Disorder With Resting State Functional Magnetic Resonance Imaging Data: A Comparison Among Machine Learning Classifiers.

Alcohol use disorder (AUD) is a burden to society creating social and health problems. Detection of AUD and its effects on the brain are difficult to assess. This problem is enhanced by the comorbid use of other substances such as nicotine that has been present in previous studies. Recent machine learning algorithms have raised the attention of researchers as a useful tool in studying and detecting AUD. This work uses AUD and controls samples free of any other substance use to assess the performance of a set of commonly used machine learning classifiers detecting AUD from resting state functional network connectivity (rsFNC) derived from independent component analysis. The cohort used included 51 alcohol dependent subjects and 51 control subjects. Despite alcohol, none of the 102 subjects reported use of nicotine, cannabis or any other dependence or habit formation substance. Classification features consisted of whole brain rsFNC estimates undergoing a feature selection process using a random forest approach. Features were then fed to 10 different machine learning classifiers to be evaluated based on their classification performance. A neural network classifier showed the highest performance with an area under the curve (AUC) of 0.79. Other good performers with similar AUC scores were logistic regression, nearest neighbor, and support vector machine classifiers. The worst results were obtained with Gaussian process and quadratic discriminant analysis. The feature selection outcome pointed to functional connections between visual, sensorimotor, executive control, reward, and salience networks as the most relevant for classification. We conclude that AUD can be identified using machine learning classifiers in the absence of nicotine comorbidity.

Dynamic connectivity predicts acute motor impairment and recovery post-stroke.

Thorough assessment of cerebral dysfunction after acute lesions is paramount to optimize predicting clinical outcomes. We here built random forest classifier-based prediction models of acute motor impairment and recovery post-stroke. Predictions relied on structural and resting-state fMRI data from 54 stroke patients scanned within the first days of symptom onset. Functional connectivity was estimated via static and dynamic approaches. Motor performance was phenotyped in the acute phase and 6 months later. A model based on the time spent in specific dynamic connectivity configurations achieved the best discrimination between patients with and without motor impairments (out-of-sample area under the curve, 95% confidence interval: 0.67 ± 0.01). In contrast, patients with moderate-to-severe impairments could be differentiated from patients with mild deficits using a model based on the variability of dynamic connectivity (0.83 ± 0.01). Here, the variability of the connectivity between ipsilesional sensorimotor cortex and putamen discriminated the most between patients. Finally, motor recovery was best predicted by the time spent in specific connectivity configurations (0.89 ± 0.01) in combination with the initial impairment. Here, better recovery was linked to a shorter time spent in a functionally integrated configuration. Dynamic connectivity-derived parameters constitute potent predictors of acute impairment and recovery, which, in the future, might inform personalized therapy regimens to promote stroke recovery.

Acute ischaemic stroke alters the brain's preference for distinct dynamic connectivity states.

Acute ischaemic stroke disturbs healthy brain organization, prompting subsequent plasticity and reorganization to compensate for the loss of specialized neural tissue and function. Static resting state functional MRI studies have already furthered our understanding of cerebral reorganization by estimating stroke-induced changes in network connectivity aggregated over the duration of several minutes. In this study, we used dynamic resting state functional MRI analyses to increase temporal resolution to seconds and explore transient configurations of motor network connectivity in acute stroke. To this end, we collected resting state functional MRI data of 31 patients with acute ischaemic stroke and 17 age-matched healthy control subjects. Stroke patients presented with moderate to severe hand motor deficits. By estimating dynamic functional connectivity within a sliding window framework, we identified three distinct connectivity configurations of motor-related networks. Motor networks were organized into three regional domains, i.e. a cortical, subcortical and cerebellar domain. The dynamic connectivity patterns of stroke patients diverged from those of healthy controls depending on the severity of the initial motor impairment. Moderately affected patients (n = 18) spent significantly more time in a weakly connected configuration that was characterized by low levels of connectivity, both locally as well as between distant regions. In contrast, severely affected patients (n = 13) showed a significant preference for transitions into a spatially segregated connectivity configuration. This configuration featured particularly high levels of local connectivity within the three regional domains as well as anti-correlated connectivity between distant networks across domains. A third connectivity configuration represented an intermediate connectivity pattern compared to the preceding two, and predominantly encompassed decreased interhemispheric connectivity between cortical motor networks independent of individual deficit severity. Alterations within this third configuration thus closely resembled previously reported ones originating from static resting state functional MRI studies post-stroke. In summary, acute ischaemic stroke not only prompted changes in connectivity between distinct networks, but it also caused characteristic changes in temporal properties of large-scale network interactions depending on the severity of the individual deficit. These findings offer new vistas on the dynamic neural mechanisms underlying acute neurological symptoms, cortical reorganization and treatment effects in stroke patients.

Determining the number of states in dynamic functional connectivity using cluster validity indexes.

BACKGROUND: Clustering analysis is employed in brain dynamic functional connectivity (dFC) to cluster the data into a set of dynamic states. These states correspond to different patterns of functional connectivity that iterate through time. Although several cluster validity index (CVI) methods to determine the best clustering partition exists, the appropriateness of methods to apply in the case of dynamic connectivity analysis has not been determined. NEW METHOD: Currently employed indexes do not provide a crisp answer on what is the best number of clusters. In addition, there is a lack of CVI testing in the context of dFC data. This work tests a comprehensive set of twenty four cluster validity indexes applied to addiction data and suggest the best ones for clustering dynamic functional connectivity. RESULTS: Out of the twenty four considered CVIs, Davies-Bouldin and Ray-Turi were the most suitable methods to find the number of clusters in both simulation and real data. The solution for these two CVIs is to find a local minimum critical point, which can be automated using computational algorithms. COMPARISON WITH EXISTING METHODS: Elbow-Criterion, Silhouette and GAP-Statistic methods have been widely used in dFC studies. These methods are included among the tested CVIs where the performances of all twenty four CVIs are compared. CONCLUSIONS: Davies-Bouldin and Ray-Turi CVIs showed better performance among a group of twenty four CVIs in determining the number of clusters to use in dFC analysis.

Functional outcome is tied to dynamic brain states after mild to moderate traumatic brain injury.

The current study set out to investigate the dynamic functional connectome in relation to long-term recovery after mild to moderate traumatic brain injury (TBI). Longitudinal resting-state functional MRI data were collected (at 1 and 3 months postinjury) from a prospectively enrolled cohort consisting of 68 patients with TBI (92% mild TBI) and 20 healthy subjects. Patients underwent a neuropsychological assessment at 3 months postinjury. Outcome was measured using the Glasgow Outcome Scale Extended (GOS-E) at 6 months postinjury. The 57 patients who completed the GOS-E were classified as recovered completely (GOS-E = 8; n = 37) or incompletely (GOS-E < 8; n = 20). Neuropsychological test scores were similar for all groups. Patients with incomplete recovery spent less time in a segregated brain state compared to recovered patients during the second visit. Also, these patients moved less frequently from one meta-state to another as compared to healthy controls and recovered patients. Furthermore, incomplete recovery was associated with disruptions in cyclic state transition patterns, called attractors, during both visits. This study demonstrates that poor long-term functional recovery is associated with alterations in dynamics between brain networks, which becomes more marked as a function of time. These results could be related to psychological processes rather than injury-effects, which is an interesting area for further work. Another natural progression of the current study is to examine whether these dynamic measures can be used to monitor treatment effects.

Resting-state fMRI dynamic functional network connectivity and associations with psychopathy traits.

Studies have used resting-state functional magnetic resonance imaging (rs-fMRI) to examine associations between psychopathy and brain connectivity in selected regions of interest as well as networks covering the whole-brain. One of the limitations of these approaches is that brain connectivity is modeled as a constant state through the scan duration. To address this limitation, we apply group independent component analysis (GICA) and dynamic functional network connectivity (dFNC) analysis to uncover whole-brain, time-varying functional network connectivity (FNC) states in a large forensic sample. We then examined relationships between psychopathic traits (PCL-R total scores, Factor 1 and Factor 2 scores) and FNC states obtained from dFNC analysis. FNC over the scan duration was better represented by five states rather than one state previously shown in static FNC analysis. Consistent with prior findings, psychopathy was associated with networks from paralimbic regions (amygdala and insula). In addition, whole-brain FNC identified 15 networks from nine functional domains (subcortical, auditory, sensorimotor, cerebellar, visual, salience, default mode network, executive control and attentional) related to psychopathy traits (Factor 1 and PCL-R scores). Results also showed that individuals with higher Factor 1 scores (affective and interpersonal traits) spend more time in a state with weaker connectivity overall, and changed states less frequently compared to those with lower Factor 1 scores. On the other hand, individuals with higher Factor 2 scores (impulsive and antisocial behaviors) showed more dynamism (changes to and from different states) than those with lower scores.

Characterizing Whole Brain Temporal Variation of Functional Connectivity via Zero and First Order Derivatives of Sliding Window Correlations.

Brain functional connectivity has been shown to change over time during resting state fMRI experiments. Close examination of temporal changes have revealed a small set of whole-brain connectivity patterns called dynamic states. Dynamic functional network connectivity (dFNC) studies have demonstrated that it is possible to replicate the dynamic states across several resting state experiments. However, estimation of states and their temporal dynamicity still suffers from noisy and imperfect estimations. In regular dFNC implementations, states are estimated by comparing connectivity patterns through the data without considering time, in other words only zero order changes are examined. In this work we propose a method that includes first order variations of dFNC in the searching scheme of dynamic connectivity patterns. Our approach, referred to as temporal variation of functional network connectivity (tvFNC), estimates the derivative of dFNC, and then searches for reoccurring patterns of concurrent dFNC states and their derivatives. The tvFNC method is first validated using a simulated dataset and then applied to a resting-state fMRI sample including healthy controls (HC) and schizophrenia (SZ) patients and compared to the standard dFNC approach. Our dynamic approach reveals extra patterns in the connectivity derivatives complementing the already reported state patterns. State derivatives consist of additional information about increment and decrement of connectivity among brain networks not observed by the original dFNC method. The tvFNC shows more sensitivity than regular dFNC by uncovering additional FNC differences between the HC and SZ groups in each state. In summary, the tvFNC method provides a new and enhanced approach to examine time-varying functional connectivity.

Concurrent Cross-Sectional and Longitudinal Analyses of Multivariate White Matter Profiles and Clinical Functioning in Pre-Diagnosis Huntington Disease.

BACKGROUND: Gray matter (GM) atrophy in the striatum and across the brain is a consistently reported feature of the Huntington Disease (HD) prodrome. More recently, widespread prodromal white matter (WM) degradation has also been detected. However, longitudinal WM studies are limited and conflicting, and most analyses comparing WM and clinical functioning have also been cross-sectional. OBJECTIVE: We simultaneously assessed changes in WM and cognitive and motor functioning at various prodromal HD stages. METHODS: Data from 1,336 (1,047 prodromal, 289 control) PREDICT-HD participants were analyzed (3,700 sessions). MRI images were used to create GM, WM, and cerebrospinal fluid probability maps. Using source-based morphometry, independent component analysis was applied to WM probability maps to extract covarying spatial patterns and their subject profiles. WM profiles were analyzed in two sets of linear mixed model (LMM) analyses: one to compare WM profiles across groups cross-sectionally and longitudinally, and one to concurrently compare WM profiles and clinical variables cross-sectionally and longitudinally within each group. RESULTS: Findings illustrate widespread prodromal changes in GM-adjacent-WM, with premotor, supplementary motor, middle frontal and striatal changes early in the prodrome that subsequently extend sub-gyrally with progression. Motor functioning agreed most with WM until the near-onset prodromal stage, when Stroop interference was the best WM indicator. Across groups, Trail-Making Test part A outperformed other cognitive variables in its similarity to WM, particularly cross-sectionally. CONCLUSIONS: Results suggest that distinct regions coincide with cognitive compared to motor functioning. Furthermore, at different prodromal stages, distinct regions appear to align best with clinical functioning. Thus, the informativeness of clinical measures may vary according to the type of data available (cross-sectional or longitudinal) as well as age and CAG-number.

Dynamic functional network connectivity in Huntington's disease and its associations with motor and cognitive measures.

Dynamic functional network connectivity (dFNC) is an expansion of traditional, static FNC that measures connectivity variation among brain networks throughout scan duration. We used a large resting-state fMRI (rs-fMRI) sample from the PREDICT-HD study (N = 183 Huntington disease gene mutation carriers [HDgmc] and N = 78 healthy control [HC] participants) to examine whole-brain dFNC and its associations with CAG repeat length as well as the product of scaled CAG length and age, a variable representing disease burden. We also tested for relationships between functional connectivity and motor and cognitive measurements. Group independent component analysis was applied to rs-fMRI data to obtain whole-brain resting state networks. FNC was defined as the correlation between RSN time-courses. Dynamic FNC behavior was captured using a sliding time window approach, and FNC results from each window were assigned to four clusters representing FNC states, using a k-means clustering algorithm. HDgmc individuals spent significantly more time in State-1 (the state with the weakest FNC pattern) compared to HC. However, overall HC individuals showed more FNC dynamism than HDgmc. Significant associations between FNC states and genetic and clinical variables were also identified. In FNC State-4 (the one that most resembled static FNC), HDgmc exhibited significantly decreased connectivity between the putamen and medial prefrontal cortex compared to HC, and this was significantly associated with cognitive performance. In FNC State-1, disease burden in HDgmc participants was significantly associated with connectivity between the postcentral gyrus and posterior cingulate cortex, as well as between the inferior occipital gyrus and posterior parietal cortex.

Selection of Efficient Clustering Index to Estimate the Number of Dynamic Brain States from Functional Network Connectivity.

Clustering analysis is employed in brain dynamic functional connectivity to cluster the data into a set of dynamic states. These states correspond to different patterns of functional connectivity that iterate through time. Although several methods to determine the best clustering partition exists, the appropriateness of methods to apply in the case of dynamic connectivity analysis has not been determined. In this work we examine the use of the Davies-Bouldin clustering validity index via simulation and real data analysis. Currently employed indexes, such as the Silhouette index, do not provide an effective estimation requiring the use of an elbow criterion. All elbow criteria rely on users experience and introduce uncertainty into the estimation. We demonstrate the feasibility of using the Davies-Bouldin index as a method delivering a unique discrete response to provide automated selection of the number of clusters.

High and Low Levels of an NTRK2-Driven Genetic Profile Affect Motor- and Cognition-Associated Frontal Gray Matter in Prodromal Huntington's Disease.

This study assessed how BDNF (brain-derived neurotrophic factor) and other genes involved in its signaling influence brain structure and clinical functioning in pre-diagnosis Huntington's disease (HD). Parallel independent component analysis (pICA), a multivariate method for identifying correlated patterns in multimodal datasets, was applied to gray matter concentration (GMC) and genomic data from a sizeable PREDICT-HD prodromal cohort (N = 715). pICA identified a genetic component highlighting NTRK2, which encodes BDNF's TrkB receptor, that correlated with a GMC component including supplementary motor, precentral/premotor cortex, and other frontal areas (p < 0.001); this association appeared to be driven by participants with high or low levels of the genetic profile. The frontal GMC profile correlated with cognitive and motor variables (Trail Making Test A (p = 0.03); Stroop Color (p = 0.017); Stroop Interference (p = 0.04); Symbol Digit Modalities Test (p = 0.031); Total Motor Score (p = 0.01)). A top-weighted NTRK2 variant (rs2277193) was protectively associated with Trail Making Test B (p = 0.007); greater minor allele numbers were linked to a better performance. These results support the idea of a protective role of NTRK2 in prodromal HD, particularly in individuals with certain genotypes, and suggest that this gene may influence the preservation of frontal gray matter that is important for clinical functioning.

Genetics Modulate Gray Matter Variation Beyond Disease Burden in Prodromal Huntington's Disease.

Huntington's disease (HD) is a neurodegenerative disorder caused by an expansion mutation of the cytosine-adenine-guanine (CAG) trinucleotide in the HTT gene. Decline in cognitive and motor functioning during the prodromal phase has been reported, and understanding genetic influences on prodromal disease progression beyond CAG will benefit intervention therapies. From a prodromal HD cohort (N = 715), we extracted gray matter (GM) components through independent component analysis and tested them for associations with cognitive and motor functioning that cannot be accounted for by CAG-induced disease burden (cumulative effects of CAG expansion and age). Furthermore, we examined genetic associations (at the genomic, HD pathway, and candidate region levels) with the GM components that were related to functional decline. After accounting for disease burden, GM in a component containing cuneus, lingual, and middle occipital regions was positively associated with attention and working memory performance, and the effect size was about a tenth of that of disease burden. Prodromal participants with at least one dystonia sign also had significantly lower GM volume in a bilateral inferior parietal component than participants without dystonia, after controlling for the disease burden. Two single-nucleotide polymorphisms (SNPs: rs71358386 in NCOR1 and rs71358386 in ADORA2B) in the HD pathway were significantly associated with GM volume in the cuneus component, with minor alleles being linked to reduced GM volume. Additionally, homozygous minor allele carriers of SNPs in a candidate region of ch15q13.3 had significantly higher GM volume in the inferior parietal component, and one minor allele copy was associated with a total motor score decrease of 0.14 U. Our findings depict an early genetical GM reduction in prodromal HD that occurs irrespective of disease burden and affects regions important for cognitive and motor functioning.

Aberrant functional network connectivity in psychopathy from a large (N = 985) forensic sample.

Psychopathy is a personality disorder characterized by antisocial behavior, lack of remorse and empathy, and impaired decision making. The disproportionate amount of crime committed by psychopaths has severe emotional and economic impacts on society. Here we examine the neural correlates associated with psychopathy to improve early assessment and perhaps inform treatments for this condition. Previous resting-state functional magnetic resonance imaging (fMRI) studies in psychopathy have primarily focused on regions of interest. This study examines whole-brain functional connectivity and its association to psychopathic traits. Psychopathy was hypothesized to be characterized by aberrant functional network connectivity (FNC) in several limbic/paralimbic networks. Group-independent component and regression analyses were applied to a data set of resting-state fMRI from 985 incarcerated adult males. We identified resting-state networks (RSNs), estimated FNC between RSNs, and tested their association to psychopathy factors and total summary scores (Factor 1, interpersonal/affective; Factor 2, lifestyle/antisocial). Factor 1 scores showed both increased and reduced functional connectivity between RSNs from seven brain domains (sensorimotor, cerebellar, visual, salience, default mode, executive control, and attentional). Consistent with hypotheses, RSNs from the paralimbic system-insula, anterior and posterior cingulate cortex, amygdala, orbital frontal cortex, and superior temporal gyrus-were related to Factor 1 scores. No significant FNC associations were found with Factor 2 and total PCL-R scores. In summary, results suggest that the affective and interpersonal symptoms of psychopathy (Factor 1) are associated with aberrant connectivity in multiple brain networks, including paralimbic regions.

Whole-Brain Connectivity in a Large Study of Huntington's Disease Gene Mutation Carriers and Healthy Controls.

Huntington's disease (HD) is an inherited brain disorder characterized by progressive motor, cognitive, and behavioral dysfunctions. It is caused by abnormally large trinucleotide cytosine-adenine-guanine (CAG) repeat expansions on exon 1 of the Huntingtin gene. CAG repeat length (CAG-RL) inversely correlates with an earlier age of onset. Region-based studies have shown that HD gene mutation carrier (HDgmc) individuals (CAG-RL ≥36) present functional connectivity alterations in subcortical (SC) and default mode networks. In this analysis, we expand on previous HD studies by investigating associations between CAG-RL and connectivity in the whole brain, as well as between CAG-dependent connectivity and motor and cognitive performances. We used group-independent component analysis on resting-state functional magnetic resonance imaging scans of 261 individuals (183 HDgmc and 78 healthy controls) from the PREDICT-HD study, to obtain whole-brain resting state networks (RSNs). Regression analysis was applied within and between RSNs connectivity (functional network connectivity [FNC]) to identify CAG-RL associations. Connectivity within the putamen RSN is negatively correlated with CAG-RL. The FNC between putamen and insula decreases with increasing CAG-RL, and also shows significant associations with motor and cognitive measures. The FNC between calcarine and middle frontal gyri increased with CAG-RL. In contrast, FNC in other visual (VIS) networks declined with increasing CAG-RL. In addition to observed effects in SC areas known to be related to HD, our study identifies a strong presence of alterations in VIS regions less commonly observed in previous reports and provides a step forward in understanding FNC dysfunction in HDgmc.

Optimal aggregation of FcεRI with a structurally defined trivalent ligand overrides negative regulation driven by phosphatases.

To investigate why responses of mast cells to antigen-induced IgE receptor (FcεRI) aggregation depend nonlinearly on antigen dose, we characterized a new artificial ligand, DF3, through complementary modeling and experimentation. This ligand is a stable trimer of peptides derived from bacteriophage T4 fibritin, each conjugated to a hapten (DNP). We found low and high doses of DF3 at which degranulation of mast cells sensitized with DNP-specific IgE is minimal, but ligand-induced receptor aggregation is comparable to aggregation at an intermediate dose, optimal for degranulation. This finding makes DF3 an ideal reagent for studying the balance of negative and positive signaling in the FcεRI pathway. We find that the lipid phosphatase SHIP and the protein tyrosine phosphatase SHP-1 negatively regulate mast cell degranulation over all doses considered. In contrast, SHP-2 promotes degranulation. With high DF3 doses, relatively rapid recruitment of SHIP to the plasma membrane may explain the reduced degranulation response. Our results demonstrate that optimal secretory responses of mast cells depend on the formation of receptor aggregates that promote sufficient positive signaling by Syk to override phosphatase-mediated negative regulatory signals.

Phospholipid scramblase-1-induced lipid reorganization regulates compensatory endocytosis in neuroendocrine cells.

Calcium-regulated exocytosis in neuroendocrine cells and neurons is accompanied by the redistribution of phosphatidylserine (PS) to the extracellular space, leading to a disruption of plasma membrane asymmetry. How and why outward translocation of PS occurs during secretion are currently unknown. Immunogold labeling on plasma membrane sheets coupled with hierarchical clustering analysis demonstrate that PS translocation occurs at the vicinity of the secretory granule fusion sites. We found that altering the function of the phospholipid scramblase-1 (PLSCR-1) by expressing a PLSCR-1 calcium-insensitive mutant or by using chromaffin cells from PLSCR-1⁻/⁻ mice prevents outward translocation of PS in cells stimulated for exocytosis. Remarkably, whereas transmitter release was not affected, secretory granule membrane recapture after exocytosis was impaired, indicating that PLSCR-1 is required for compensatory endocytosis but not for exocytosis. Our results provide the first evidence for a role of specific lipid reorganization and calcium-dependent PLSCR-1 activity in neuroendocrine compensatory endocytosis.

Insights into cell membrane microdomain organization from live cell single particle tracking of the IgE high affinity receptor FcϵRI of mast cells.

Current models propose that the plasma membrane of animal cells is composed of heterogeneous and dynamic microdomains known variously as cytoskeletal corrals, lipid rafts and protein islands. Much of the experimental evidence for these membrane compartments is indirect. Recently, live cell single particle tracking studies using quantum dot-labeled IgE bound to its high affinity receptor FcϵRI, provided direct evidence for the confinement of receptors within micrometer-scale cytoskeletal corrals. In this study, we show that an innovative time-series analysis of single particle tracking data for the high affinity IgE receptor, FcϵRI, on mast cells provides substantial quantitative information about the submicrometer organization of the membrane. The analysis focuses on the probability distribution function of the lengths of the jumps in the positions of the quantum dots labeling individual IgE FcϵRI complexes between frames in movies of their motion. Our results demonstrate the presence, within the micrometer-scale cytoskeletal corrals, of smaller subdomains that provide an additional level of receptor confinement. There is no characteristic size for these subdomains; their size varies smoothly from a few tens of nanometers to a over a hundred nanometers. In QD-IGE labeled unstimulated cells, jumps of less than 70 nm predominate over longer jumps. Addition of multivalent antigen to crosslink the QD-IgE-FcϵRI complexes causes a rapid slowing of receptor motion followed by a long tail of mostly jumps less than 70 nm. The reduced receptor mobility likely reflects both the membrane heterogeneity revealed by the confined motion of the monomeric receptor complexes and the antigen-induced cross linking of these complexes into dimers and higher oligomers. In both cases, the probability distribution of the jump lengths is well fit, from 10 nm to over 100 nm, by a novel power law. The fit for short jumps suggests that the motion of the quantum dots can be modeled as diffusion in a fractal space of dimension less than two.

Using hierarchical clustering and dendrograms to quantify the clustering of membrane proteins.

Cell biologists have developed methods to label membrane proteins with gold nanoparticles and then extract spatial point patterns of the gold particles from transmission electron microscopy images using image processing software. Previously, the resulting patterns were analyzed using the Hopkins statistic, which distinguishes nonclustered from modestly and highly clustered distributions, but is not designed to quantify the number or sizes of the clusters. Clusters were defined by the partitional clustering approach which required the choice of a distance. Two points from a pattern were put in the same cluster if they were closer than this distance. In this study, we present a new methodology based on hierarchical clustering to quantify clustering. An intrinsic distance is computed, which is the distance that produces the maximum number of clusters in the biological data, eliminating the need to choose a distance. To quantify the extent of clustering, we compare the clustering distance between the experimental data being analyzed with that from simulated random data. Results are then expressed as a dimensionless number, the clustering ratio that facilitates the comparison of clustering between experiments. Replacing the chosen cluster distance by the intrinsic clustering distance emphasizes densely packed clusters that are likely more important to downstream signaling events.We test our new clustering analysis approach against electron microscopy images from an experiment in which mast cells were exposed for 1 or 2 minutes to increasing concentrations of antigen that crosslink IgE bound to its high affinity receptor, FcϵRI, then fixed and the FcϵRI ß subunit labeled with 5 nm gold particles. The clustering ratio analysis confirms the increase in clustering with increasing antigen dose predicted from visual analysis and from the Hopkins statistic. Access to a robust and sensitive tool to both observe and quantify clustering is a key step toward understanding the detailed fine scale structure of the membrane, and ultimately to determining the role of spatial organization in the regulation of transmembrane signaling.