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Definition and estimation of resolution in single-particle reconstructions.

ABSTRACT: In this paper, we review current practices for establishing the resolution in single-particle reconstructions. The classical Raleigh criterion for the resolution is not applicable in this case, and the resolution is commonly defined by a consistency test, whereby the data set is randomly split in half and the two resulting reconstructions are then compared. Such a procedure, however, may introduce statistical dependence between the two half-sets, which leads to a too optimistic resolution estimate. On the other hand, this overestimation is counteracted by the diminished statistical properties of a mere half of the data set. The "true" resolution of the whole data set can be estimated when the functional relationship between the data size and the resolution is known. We are able to estimate this functional by taking into account the B-factor and the geometry of data collection. Finally, the drawbacks of resolution estimation are entirely avoided by computing the correlation of neighboring voxels in the Fourier domain.

SUBMITTER: Liao HY

PROVIDER: S-EPMC2923553 | biostudies-literature | 2010 Jul

REPOSITORIES: biostudies-literature

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Definition and estimation of resolution in single-particle reconstructions.

Liao Hstau Y HY Frank Joachim J

Structure (London, England : 1993) 20100701 7

In this paper, we review current practices for establishing the resolution in single-particle reconstructions. The classical Raleigh criterion for the resolution is not applicable in this case, and the resolution is commonly defined by a consistency test, whereby the data set is randomly split in half and the two resulting reconstructions are then compared. Such a procedure, however, may introduce statistical dependence between the two half-sets, which leads to a too optimistic resolution estima ...[more]

PMID: 20637413

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Project description:Neuronal information processing in cortical networks critically depends on the organization of synaptic connectivity. Synaptic connections can form when axons and dendrites come in close proximity of each other. The spatial innervation of neuronal arborizations can be described by their axonal and dendritic density fields. Recently we showed that potential locations of synapses between neurons can be estimated from their overlapping axonal and dendritic density fields. However, deriving density fields from single-slice neuronal reconstructions is hampered by incompleteness because of cut branches. Here, we describe a method for recovering the lost axonal and dendritic mass. This so-called completion method is based on an estimation of the mass inside the slice and an extrapolation to the space outside the slice, assuming axial symmetry in the mass distribution. We validated the method using a set of neurons generated with our NETMORPH simulator. The model-generated neurons were artificially sliced and subsequently recovered by the completion method. Depending on slice thickness and arbor extent, branches that have lost their outside parents (orphan branches) may occur inside the slice. Not connected anymore to the contiguous structure of the sliced neuron, orphan branches result in an underestimation of neurite mass. For 300 ?m thick slices, however, the validation showed a full recovery of dendritic and an almost full recovery of axonal mass. The completion method was applied to three experimental data sets of reconstructed rat cortical L2/3 pyramidal neurons. The results showed that in 300 ?m thick slices intracortical axons lost about 50% and dendrites about 16% of their mass. The completion method can be applied to single-slice reconstructions as long as axial symmetry can be assumed in the mass distribution. This opens up the possibility of using incomplete neuronal reconstructions from open-access data bases to determine population mean mass density fields.

Dataset Information

Definition and estimation of resolution in single-particle reconstructions.

Publications

Definition and estimation of resolution in single-particle reconstructions.

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