Over hundreds of millions of years, evolution has optimized brain design to maximize its functionality while minimizing costs associated with building and maintenance. This observation suggests that one can use optimization theory to rationalize various features of brain design. Here, we attempt to explain the dimensions and branching structure of dendritic arbors by minimizing dendritic cost for given potential synaptic connectivity. Assuming only that dendritic cost increases with total dendritic length and path length from synapses to soma, we find that branching, planar, and compact dendritic arbors, such as those belonging to Purkinje cells in the cerebellum, are optimal. The theory predicts that adjacent Purkinje dendritic arbors should spatially segregate. In addition, we propose two explicit cost function expressions, falsifiable by measuring dendritic caliber near bifurcations.

The activity of the ERK has complex spatial and temporal dynamics that are important for the specificity of downstream effects. However, current biochemical techniques do not allow for the measurement of ERK signaling with fine spatiotemporal resolution. We developed a genetically encoded, FRET-based sensor of ERK activity (the extracellular signal-regulated kinase activity reporter, EKAR), optimized for signal-to-noise ratio and fluorescence lifetime imaging. EKAR selectively and reversibly reported ERK activation in HEK293 cells after epidermal growth factor stimulation. EKAR signals were correlated with ERK phosphorylation, required ERK activity, and did not report the activities of JNK or p38. EKAR reported ERK activation in the dendrites and nucleus of hippocampal pyramidal neurons in brain slices after theta-burst stimuli or trains of back-propagating action potentials. EKAR therefore permits the measurement of spatiotemporal ERK signaling dynamics in living cells, including in neuronal compartments in intact tissues.

Sequence database searches require accurate estimation of the statistical significance of scores. Optimal local sequence alignment scores follow Gumbel distributions, but determining an important parameter of the distribution (lambda) requires time-consuming computational simulation. Moreover, optimal alignment scores are less powerful than probabilistic scores that integrate over alignment uncertainty ("Forward" scores), but the expected distribution of Forward scores remains unknown. Here, I conjecture that both expected score distributions have simple, predictable forms when full probabilistic modeling methods are used. For a probabilistic model of local sequence alignment, optimal alignment bit scores ("Viterbi" scores) are Gumbel-distributed with constant lambda = log 2, and the high scoring tail of Forward scores is exponential with the same constant lambda. Simulation studies support these conjectures over a wide range of profile/sequence comparisons, using 9,318 profile-hidden Markov models from the Pfam database. This enables efficient and accurate determination of expectation values (E-values) for both Viterbi and Forward scores for probabilistic local alignments.

We present a Bayesian framework for action recognition through ballistic dynamics. Psycho-kinesiological studies indicate that ballistic movements form the natural units for human movement planning. The framework leads to an efficient and robust algorithm for temporally segmenting videos into atomic movements. Individual movements are annotated with person-centric morphological labels called ballistic verbs. This is tested on a dataset of interactive movements, achieving high recognition rates. The approach is also applied on a gesture recognition task, improving a previously reported recognition rate from 84% to 92%. Consideration of ballistic dynamics enhances the performance of the popular Motion History Image feature. We also illustrate the approach’s general utility on real-world videos. Experiments indicate that the method is robust to view, style and appearance variations.

Neurobiological processes occur on spatiotemporal scales spanning many orders of magnitude. Greater understanding of these processes therefore demands improvements in the tools used in their study. Here we review recent efforts to enhance the speed and resolution of one such tool, fluorescence microscopy, with an eye toward its application to neurobiological problems. On the speed front, improvements in beam scanning technology, signal generation rates, and photodamage mediation are bringing us closer to the goal of real-time functional imaging of extended neural networks. With regard to resolution, emerging methods of adaptive optics may lead to diffraction-limited imaging or much deeper imaging in optically inhomogeneous tissues, and super-resolution techniques may prove a powerful adjunct to electron microscopic methods for nanometric neural circuit reconstruction.

Neurobiological processes occur on spatiotemporal scales spanning many orders of magnitude. Greater understanding of these processes therefore demands improvements in the tools used in their study. Here we review recent efforts to enhance the speed and resolution of one such tool, fluorescence microscopy, with an eye toward its application to neurobiological problems. On the speed front, improvements in beam scanning technology, signal generation rates, and photodamage mediation are bringing us closer to the goal of real-time functional imaging of extended neural networks. With regard to resolution, emerging methods of adaptive optics may lead to diffraction-limited imaging or much deeper imaging in optically inhomogeneous tissues, and super-resolution techniques may prove a powerful adjunct to electron microscopic methods for nanometric neural circuit reconstruction.

Commentary: A brief review of recent trends in microscopy. The section “Caveats regarding the application of superresolution microscopy” was written in an effort to inject a dose of reality and caution into the unquestioning enthusiasm in the academic community for all things superresolution, covering the topics of labeling density and specificity, sample preparation artifacts, speed vs. resolution vs. photodamage, and the implications of signal-to-background for Nyquist vs. Rayleigh definitions of resolution.

Back-propagating action potentials (bAPs) travelling from the soma to the dendrites of neurons are involved in various aspects of synaptic plasticity. The distance-dependent increase in Kv4.2-mediated A-type K(+) current along the apical dendrites of CA1 pyramidal cells (CA1 PCs) is responsible for the attenuation of bAP amplitude with distance from the soma. Genetic deletion of Kv4.2 reduced dendritic A-type K(+) current and increased the bAP amplitude in distal dendrites. Our previous studies revealed that the amplitude of unitary Schaffer collateral inputs increases with distance from the soma along the apical dendrites of CA1 PCs. We tested the hypothesis that the weight of distal synapses is dependent on dendritic Kv4.2 channels. We compared the amplitude and kinetics of mEPSCs at different locations on the main apical trunk of CA1 PCs from wild-type (WT) and Kv4.2 knockout (KO) mice. While wild-type mice showed normal distance-dependent scaling, it was missing in the Kv4.2 KO mice. We also tested whether there was an increase in inhibition in the Kv4.2 knockout, induced in an attempt to compensate for a non-specific increase in neuronal excitability (after-polarization duration and burst firing probability were increased in KO). Indeed, we found that the magnitude of the tonic GABA current increased in Kv4.2 KO mice by 53% and the amplitude of mIPSCs increased by 25%, as recorded at the soma. Our results suggest important roles for the dendritic K(+) channels in distance-dependent adjustment of synaptic strength as well as a primary role for tonic inhibition in the regulation of global synaptic strength and membrane excitability.

The development of high-resolution microscopy makes possible the high-throughput screening of cellular information, such as gene expression at single cell resolution. One of the critical enabling techniques yet to be developed is the automatic recognition or annotation of specific cells in a 3D image stack. In this paper, we present a novel graph-based algorithm, ARC, that determines cell identities in a 3D confocal image of C. elegans based on their highly stereotyped arrangement. This is an essential step in our work on gene expression analysis of C. elegans at the resolution of single cells. Our ARC method integrates both the absolute and relative spatial locations of cells in a C. elegans body. It uses a marker-guided, spatially-constrained, two-stage bipartite matching to find the optimal match between cells in a subject image and cells in 15 template images that have been manually annotated and vetted. We applied ARC to the recognition of cells in 3D confocal images of the first larval stage (L1) of C. elegans hermaphrodites, and achieved an average accuracy of 94.91%.

We present an algorithm for automatic segmentation of the human pelvic bones from CT datasets that is based on the application of a statistical shape model. The proposed method is divided into three steps: 1) The averaged shape of the pelvis model is initially placed within the CT data using the Generalized Hough Transform, 2) the statistical shape model is then adapted to the image data by a transformation and variation of its shape modes, and 3) a final free-form deformation step based on optimal graph searching is applied to overcome the restrictive character of the statistical shape representation. We thoroughly evaluated the method on 50 manually segmented CT datasets by performing a leave-one-out study. The Generalized Hough Transform proved to be a reliable method for an automatic initial placement of the shape model within the CT data. Compared to the manual gold standard segmentations, our automatic segmentation approach produced an average surface distance of 1.2 ± 0.3mm after the adaptation of the statistical shape model, which could be reduced to 0.7±0.3mm using a final free-form deformation step. Together with an average segmentation time of less than 5 minutes, the results of our study indicate that our method meets the requirements of clinical routine.