Sensitivity of peptide conformational dynamics on clustering of a classical molecular dynamics trajectory

We investigate the sensitivity of a Markov model with states and transition probabilities obtained from clustering a molecular dynamics trajectory. We have examined a 500 ns molecular dynamics trajectory of the peptide valine-proline-alanine-leucine in explicit water. The sensitivity is quantified by varying the boundaries of the clusters and investigating the resulting variation in transition probabilities and the average transition time between states. In this way, we represent the effect of clustering using different clustering algorithms. It is found that in terms of the investigated quantities, the peptide dynamics described by the Markov model is sensitive to the clustering; in particular, the average transition times are found to vary up to 46%. Moreover, inclusion of nonphysical sparsely populated clusters can lead to serious errors of up to 814%. In the investigation, the time step used in the transition matrix is determined by the minimum time scale on which the system behaves approximately Markovian. This time step is found to be about 100 ps. It is concluded that the description of peptide dynamics with transition matrices should be performed with care, and that using standard clustering algorithms to obtain states and transition probabilities may not always produce reliable results.

What to do when K-means clustering fails:a simple yet principled alternative algorithm

The K-means algorithm is one of the most popular clustering algorithms in current use as it is relatively fast yet simple to understand and deploy in practice. Nevertheless, its use entails certain restrictive assumptions about the data, the negative consequences of which are not always immediately apparent, as we demonstrate. While more flexible algorithms have been developed, their widespread use has been hindered by their computational and technical complexity. Motivated by these considerations, we present a flexible alternative to K-means that relaxes most of the assumptions, whilst remaining almost as fast and simple. This novel algorithm which we call MAP-DP (maximum a-posteriori Dirichlet process mixtures), is statistically rigorous as it is based on nonparametric Bayesian Dirichlet process mixture modeling. This approach allows us to overcome most of the limitations imposed by K-means. The number of clusters K is estimated from the data instead of being fixed a-priori as in K-means. In addition, while K-means is restricted to continuous data, the MAP-DP framework can be applied to many kinds of data, for example, binary, count or ordinal data. Also, it can efficiently separate outliers from the data. This additional flexibility does not incur a significant computational overhead compared to K-means with MAP-DP convergence typically achieved in the order of seconds for many practical problems. Finally, in contrast to K-means, since the algorithm is based on an underlying statistical model, the MAP-DP framework can deal with missing data and enables model testing such as cross validation in a principled way. We demonstrate the simplicity and effectiveness of this algorithm on the health informatics problem of clinical sub-typing in a cluster of diseases known as parkinsonism.

A statistical method for the identification and aggregation of regional linguistic variation

This paper introduces a method for the analysis of regional linguistic variation. The method identifies individual and common patterns of spatial clustering in a set of linguistic variables measured over a set of locations based on a combination of three statistical techniques: spatial autocorrelation, factor analysis, and cluster analysis. To demonstrate how to apply this method, it is used to analyze regional variation in the values of 40 continuously measured, high-frequency lexical alternation variables in a 26-million-word corpus of letters to the editor representing 206 cities from across the United States.

A statistical comparison of regional phonetic and lexical variation in American English

This paper presents a statistical comparison of regional phonetic and lexical variation in American English. Both the phonetic and lexical datasets were first subjected to separate multivariate spatial analyses in order to identify the most common dimensions of spatial clustering in these two datasets. The dimensions of phonetic and lexical variation extracted by these two analyses were then correlated with each other, after being interpolated over a shared set of reference locations, in order to measure the similarity of regional phonetic and lexical variation in American English. This analysis shows that regional phonetic and lexical variation are remarkably similar in Modern American English.

"Belonging” in the gentrified Golden Horn/Halic neighbourhoods of Istanbul

Mainstream gentrification research predominantly examines experiences and motivations of the middle-class gentrifier groups, while overlooking experiences of non-gentrifying groups including the impact of in situ local processes on gentrification itself. In this paper, I discuss gentrification, neighbourhood belonging and spatial distribution of class in Istanbul by examining patterns of belonging both of gentrifiers and non-gentrifying groups in historic neighbourhoods of the Golden Horn/Halic. I use multiple correspondence analysis (MCA), a methodology rarely used in gentrification research, to explore social and symbolic borders between these two groups. I show how gentrification leads to spatial clustering by creating exclusionary practices and eroding social cohesion, and illuminate divisions that are inscribed into the physical space of the neighbourhood.

Fuzzy c-means variants for medical image segmentation

Segmentation is an important step in many medical imaging applications and a variety of image segmentation techniques exist. One group of segmentation algorithms is based on clustering concepts. In this article we investigate several fuzzy c-means based clustering algorithms and their application to medical image segmentation. In particular we evaluate the conventional hard c-means (HCM) and fuzzy c-means (FCM) approaches as well as three computationally more efficient derivatives of fuzzy c-means: fast FCM with random sampling, fast generalised FCM, and a new anisotropic mean shift based FCM. © 2010 by IJTS, ISDER.

Clustering and spatial correlations of the neuronal cytoplasmic inclusions, astrocytic plaques and ballooned neurons in corticobasal degeneration

This study tested three hypotheses: (1) that there is clustering of the neuronal cytoplasmic inclusions (NCI), astrocytic plaques (AP) and ballooned neurons (BN) in corticobasal degeneration (CBD), (2) that the clusters of NCI and BN are not spatially correlated, and (3) that the lesions are correlated with disease ‘stage’. In 50% of the regions, clusters of lesions were 400–800 µm in diameter and regularly distributed parallel to the tissue boundary. Clusters of NCI and BN were larger in laminae II/III and V/VI, respectively. In a third of regions, the clusters of BN and NCI were negatively spatially correlated. Cluster size of the BN in the parahippocampal gyrus (PHG) was positively correlated with disease ‘stage’. The data suggest the following: (1) degeneration of the cortico-cortical pathways in CBD, (2) clusters of NCI and BN may affect different anatomical pathways and (3) BN may develop after the NCI in the PHG.

Higher-order co-occurrences for exploratory point pattern analysis and decision tree clustering on spatial data

Analyzing geographical patterns by collocating events, objects or their attributes has a long history in surveillance and monitoring, and is particularly applied in environmental contexts, such as ecology or epidemiology. The identification of patterns or structures at some scales can be addressed using spatial statistics, particularly marked point processes methodologies. Classification and regression trees are also related to this goal of finding "patterns" by deducing the hierarchy of influence of variables on a dependent outcome. Such variable selection methods have been applied to spatial data, but, often without explicitly acknowledging the spatial dependence. Many methods routinely used in exploratory point pattern analysis are2nd-order statistics, used in a univariate context, though there is also a wide literature on modelling methods for multivariate point pattern processes. This paper proposes an exploratory approach for multivariate spatial data using higher-order statistics built from co-occurrences of events or marks given by the point processes. A spatial entropy measure, derived from these multinomial distributions of co-occurrences at a given order, constitutes the basis of the proposed exploratory methods. © 2010 Elsevier Ltd.

Higher-order co-occurrences for exploratory point pattern analysis and decision tree clustering on spatial data

Analyzing geographical patterns by collocating events, objects or their attributes has a long history in surveillance and monitoring, and is particularly applied in environmental contexts, such as ecology or epidemiology. The identification of patterns or structures at some scales can be addressed using spatial statistics, particularly marked point processes methodologies. Classification and regression trees are also related to this goal of finding "patterns" by deducing the hierarchy of influence of variables on a dependent outcome. Such variable selection methods have been applied to spatial data, but, often without explicitly acknowledging the spatial dependence. Many methods routinely used in exploratory point pattern analysis are2nd-order statistics, used in a univariate context, though there is also a wide literature on modelling methods for multivariate point pattern processes. This paper proposes an exploratory approach for multivariate spatial data using higher-order statistics built from co-occurrences of events or marks given by the point processes. A spatial entropy measure, derived from these multinomial distributions of co-occurrences at a given order, constitutes the basis of the proposed exploratory methods. © 2010 Elsevier Ltd.

Measuring the spatial arrangement patterns of pathological lesions in histological sections of brain tissue

The development of abnormal protein aggregates in the form of extracellular plaques and intracellular inclusions is a characteristic feature of many neurodegenerative diseases such as Alzheimer's disease (AD), Creutzfeldt-Jakob disease (CJD) and the fronto-temporal dementias (FTD). An important aspect of a pathological protein aggregate is its spatial topography in the tissue. Lesions may not be randomly distributed within a histological section but exhibit spatial pattern, a departure from randomness either towards regularity or clustering. Information on the spatial pattern of a lesion may be useful in elucidating its pathogenesis and in studying the relationships between different lesions. This article reviews the methods that have been used to study the spatial topography of lesions. These include simple tests of whether the distribution of a lesion departs significantly from random using randomized points or sample fields, and more complex methods that employ grids or transects of contiguous fields and which can detect the intensity of aggregation and the sizes, distribution and spacing of the clusters. The usefulness of these methods in elucidating the pathogenesis of protein aggregates in neurodegenerative disease is discussed.

What does the study of the spatial patterns of pathological lesions tell us about the pathogenesis of neurodegenerative disorders?

Discrete pathological lesions, which include extracellular protein deposits, intracellular inclusions and changes in cell morphology, occur in the brain in the majority of neurodegenerative disorders. These lesions are not randomly distributed in the brain but exhibit a spatial pattern, that is, a departure from randomness towards regularity or clustering. The spatial pattern of a lesion may reflect pathological processes affecting particular neuroanatomical structures and, therefore, studies of spatial pattern may help to elucidate the pathogenesis of a lesion and of the disorders themselves. The present article reviews first, the statistical methods used to detect spatial patterns and second, the types of spatial patterns exhibited by pathological lesions in a variety of disorders which include Alzheimer's disease, Down syndrome, dementia with Lewy bodies, Creutzfeldt-Jakob disease, Pick's disease and corticobasal degeneration. These studies suggest that despite the morphological and molecular diversity of brain lesions, they often exhibit a common type of spatial pattern (i.e. aggregation into clusters that are regularly distributed in the tissue). The pathogenic implications of spatial pattern analysis are discussed with reference to the individual disorders and to studies of neurodegeneration as a whole.

Clustering of Pick bodies in the dentate gyrus in Pick's disease

In patients with Pick's disease (PD), high densities of tau positive Pick bodies (PB) have been observed within the granule cell layer of the dentate gyrus. This study investigated the spatial patterns of PB along the granule cell layer in coronal sections of the hippocampus in eight patients with PD. In all patients, there was evidence of clustering of PB within the granule cell layer; however, there was considerable variation in the pattern of clustering. In five patients, the clusters of PB were regularly distributed along the dentate gyms, and in two of these patients, the smaller clusters were aggregated into larger superclusters. In three patients, a single large cluster of PB, more than 1200 μm in diameter, was present. Clustering of PB may reflect a primary degenerative process within the granule cells or the degeneration of pathways that project to the dentate gyrus.

Clustering and periodicity of neurofibrillary tangles in the upper and lower cortical laminae in Alzheimer's disease

In Alzheimer's disease (AD), neurofibrillary tangles (NFT) occur within neurons in both the upper and lower cortical laminae. Using a statistical method that estimates the size and spacing of NFT clusters along the cortex parallel to the pia mater, two hypotheses were tested: 1) that the cluster size and distribution of the NFT in gyri of the temporal lobe reflect degeneration of the feedforward (FF) and feedback (FB) cortico-cortical pathways, and 2) that there is a spatial relationship between the clusters of NFT in the upper and lower laminae. In 16 temporal lobe gyri from 10 cases of sporadic AD, NFT were present in both the upper and lower laminae in 11/16 (69%) gyri and in either the upper or lower laminae in 5/16 (31%) gyri. Clustering of the NFT was observed in all gyri. A significant peak-to-peak distance was observed in the upper laminae in 13/15 (87%) gyri and in the lower laminae in 8/ 12 (67%) gyri, suggesting a regularly repeating pattern of NFT clusters along the cortex. The regularly distributed clusters of NFT were between 500 and 800 μm in size, the estimated size of the cells of origin of the FF and FB cortico-cortical projections, in the upper laminae of 6/13 (46%) gyri and in the lower laminae of 2/8 (25%) gyri. Clusters of NFT in the upper laminae were spatially correlated (in phase) with those in the lower laminae in 5/16 (31%) gyri. The clustering patterns of the NFT are consistent with their formation in relation to the FF and FB cortico-cortical pathways. In most gyri, NFT clusters appeared to develop independently in the upper and lower laminae.

Spatial patterns of the pathological changes in the temporal lobe of patients with neuronal intermediate filament inclusion disease

Neuronal intermediate filament inclusion disease (NIFID) is a new neurodegenerative disease characterized histologically by the presence of neuronal cytoplasmic inclusions (NI) immunopositive for intermediate filament proteins, neuronal loss, swollen achromatic neurons (SN), and gliosis. We studied the spatial patterns of these pathological changes parallel to the pia mater in gyri of the temporal lobe in four cases of NIFID. Both the NI and SN occurred in clusters that were regularly distributed parallel to the pia mater, the cluster sizes of the SN being significantly greater than those of the NI. In a significant proportion of areas studied, there was a spatial correlation between the clusters of NI and those of the SN and with the density of the surviving neurons. In addition, the clusters of surviving neurons were negatively correlated (out of phase) with the clusters of glial cell nuclei. The pattern of clustering of these histological features suggests that there is degeneration of the cortico-cortical projections in NIFID leading to the formation of NI and SN within the same vertical columns of cells. The glial cell reaction may be a response to the loss of neurons rather than to the appearance of the NI or SN.

Spatial patterns of the pathological changes in the cerebellar cortex in sporadic Creutzfeldt-Jakob disease (sCJD)

The spatial patterns of the vacuolation ("spongiform change"), surviving cells, and prion protein (PrP) deposition were studied in the various cell laminae of the cerebellar cortex in 11 cases of sporadic Creutzfeldt-Jakob disease (sCJD). Clustering of the histological features, with the clusters regularly distributed along the folia, was evident in all cell laminae. In the molecular layer, clusters of vacuoles coincided with the surviving Purkinje cells. In the granule cell layer, however, the spatial relationship between the vacuoles and surviving cells was more complex and varied between cases. PrP deposition was not spatially correlated with either the vacuoles or the surviving cells in any of the cerebellar laminae in the majority of cases. In some cases, there were spatial relationships between th histological features in the molecular and granule cell layers. The data suggest that degeneration of the cerebellar cortex in sCJD may occur in a topographic pattern consistent with the spread of prion pathology along anatomical pathways. The development of the vacuolation may be an early stage of the pathology in the cerebellum preceding the appearance of the PrP deposits. In addition, there is evidence that the pathological changes may spread across the different laminae of the cerebellar cortex.