A key question in understanding microtubule dynamics is how GTP hydrolysis leads to catastrophe, the switch from slow growth to rapid shrinkage. We first provide a review of the experimental and modeling literature, and then present a new model of microtubule dynamics. We demonstrate that vectorial, random, and coupled hydrolysis mechanisms are not consistent with the dependence of catastrophe on tubulin concentration and show that, although single-protofilament models can explain many features of dynamics, they do not describe catastrophe as a multistep process. Finally, we present a new combined (coupled plus random hydrolysis) multiple-protofilament model that is a simple, analytically solvable generalization of a single-protofilament model. This model accounts for the observed lifetimes of growing microtubules, the delay to catastrophe following dilution and describes catastrophe as a multistep process.

Recent studies have found that microtubule-associated proteins (MAPs) can regulate the dynamical properties of microtubules in unexpected ways. For most MAPs, there is an inverse relationship between their effects on the speed of growth and the frequency of catastrophe, the conversion of a growing microtubule to a shrinking one. Such a negative correlation is predicted by the standard GTP-cap model, which posits that catastrophe is due to loss of a stabilizing cap of GTP-tubulin at the end of a growing microtubule. However, many other MAPs, notably Kinesin-4 and combinations of EB1 with XMAP215, contradict this general rule. In this review, we show that a more nuanced, but still simple, GTP-cap model, can account for the diverse regulatory activities of MAPs.

Biological filaments, such as actin filaments, microtubules, and cilia, are often imaged using different light-microscopy techniques. Reconstructing the filament curve from the acquired images constitutes the filament segmentation problem. Since filaments have lower dimensionality than the image itself, there is an inherent trade-off between tracing the filament with sub-pixel accuracy and avoiding noise artifacts. Here, we present a globally optimal filament segmentation method based on B-spline vector level-sets and a generalized linear model for the pixel intensity statistics. We show that the resulting optimization problem is convex and can hence be solved with global optimality. We introduce a simple and efficient algorithm to compute such optimal filament segmentations, and provide an open-source implementation as an ImageJ/Fiji plugin. We further derive an information-theoretic lower bound on the filament segmentation error, quantifying how well an algorithm could possibly do given the information in the image. We show that our algorithm asymptotically reaches this bound in the spline coefficients. We validate our method in comprehensive benchmarks, compare with other methods, and show applications from fluorescence, phase-contrast, and dark-field microscopy.

Alternative splicing results in the inclusion or exclusion of exons in an RNA, thereby allowing a single gene to code for multiple RNA isoforms. Genes are often composed of many exons, allowing combinatorial choice to significantly expand the coding potential of the genome. How much coding potential is gained by alternative splicing and what is the main contributor: alternative-splicing-depth or exon-count? Here we develop a splice-site-centric quantification method, allowing us to characterize transcriptome-wide alternative splicing with a simple probabilistic model, enabling species-wide comparison. We use information theory to quantify the coding potential gain and show that an increase in alternative splicing probability contributes more to transcriptome expansion than exon-count. Our results suggest that dominant isoforms are co-expressed alongside many minor isoforms. We propose that this solves two problems simultaneously, that is, expression of functional isoforms and expansion of the transcriptome landscape potentially without a direct function, but available for evolution. GlossaryTranscriptome: Set of all RNA molecules in a sample (e.g. cell, tissue, organism). Transcriptome expansion: Increase of coding expansion of the genome. Gene annotation: Meta information added to the raw DNA sequence, such as exon-intron structure. Gene architecture: Exon-intron structure of genes. RNA Splicing: RNA maturation event leading to removal of introns and joining of exons. Intron: Sequence removed by splicing, often non-coding for proteins. Exon: Sequence retained by splicing, often coding. Splice site: Exon-intron (5' splice site) or intron-exon boundary (3' splice site). Constitutive splicing: The process that results in the joining of two splice-sites in all observed situation. Alternative splicing: The process that results that one splice site can be joined to distinct partner splice sites. RNA-seq experiment: Qualitative and quantitative profile of transcriptome by deep sequencing. Extent: A parameter used to characterize the amount of alternative splicing in any given transcriptome; technically, the extent = ! ! , where is the exponent in the power law distribution that describes the amount of alternative splicing in the transcriptome. Splice site expression: Number of RNA-Seq observations per splice site. Shannon Entropy: Metric of the expected information content. True Diversity: An ecological concept which measures both the number of distinct species (richness) and how uniformly they are distributed in a sample (evenness). Machine Learning: Computational algorithms which learn rules (model) to predict an output from an input. Random Forest: A non-linear machine learning model based on an ensemble of decision trees with random feature subset selection at each decision node. Lasso Regression: Linear regression regularized by absolute value of the sum of all regression coefficients (L1 norm). Bootstrapping: Resampling technique to infer the confidence in a population measurement. Probability density function (p...

Dendrites are branched neuronal processes that receive input signals from other neurons or the outside world [1]. To maintain connectivity as the organism grows, dendrites must also continue to grow. For example, the dendrites in the peripheral nervous system continue to grow and branch to maintain proper coverage of their receptor fields [2,3,4,5]. One such neuron is the Drosophila melanogaster class IV dendritic arborization neuron [6]. The dendritic arbors of these neurons tile the larval surface [7], where they detect localized noxious stimuli, such as jabs from parasitic wasps [8]. In the present study, we used a novel measure, the hitting probability, to show that the class IV neuron forms a tight mesh that covers the larval surface. Furthermore, we found that the mesh size remains largely unchanged during the larval stages, despite a dramatic increase in overall size of the neuron and the larva. We also found that the class IV dendrites are dense (assayed with the fractal dimension) and uniform (assayed with the lacunarity) throughout the larval stages. To understand how the class IV neuron maintains its morphology during larval development, we constructed a mathematical model based on random branching and self-avoidance. We found that if the branching rate is uniform in space and time and that if all contacting branches are deleted, we can reproduce the branch length distribution, mesh size and density of the class IV dendrites throughout the larval stages. Thus, a simple set of statistical rules can generate and maintain a complex branching morphology during growth.