Quantitative measurements and modeling of cargo–motor interactions during fast transport in the living axon

Author Posting. © IOP Publishing, 2012. This article is posted here by permission of IOP Publishing for personal use, not for redistribution. The definitive version was published in Physical Biology 9 (2012): 055005, doi:10.1088/1478-3975/9/5/055005.The kinesins have long been known to drive microtubule-based transport of sub-cellular components, yet the mechanisms of their attachment to cargo remain a mystery. Several different cargo-receptors have been proposed based on their in vitro binding affinities to kinesin-1. Only two of these—phosphatidyl inositol, a negatively charged lipid, and the carboxyl terminus of the amyloid precursor protein (APP-C), a trans-membrane protein—have been reported to mediate motility in living systems. A major question is how these many different cargo, receptors and motors interact to produce the complex choreography of vesicular transport within living cells. Here we describe an experimental assay that identifies cargo–motor receptors by their ability to recruit active motors and drive transport of exogenous cargo towards the synapse in living axons. Cargo is engineered by derivatizing the surface of polystyrene fluorescent nanospheres (100 nm diameter) with charged residues or with synthetic peptides derived from candidate motor receptor proteins, all designed to display a terminal COOH group. After injection into the squid giant axon, particle movements are imaged by laser-scanning confocal time-lapse microscopy. In this report we compare the motility of negatively charged beads with APP-C beads in the presence of glycine-conjugated non-motile beads using new strategies to measure bead movements. The ensuing quantitative analysis of time-lapse digital sequences reveals detailed information about bead movements: instantaneous and maximum velocities, run lengths, pause frequencies and pause durations. These measurements provide parameters for a mathematical model that predicts the spatiotemporal evolution of distribution of the two different types of bead cargo in the axon. The results reveal that negatively charged beads differ from APP-C beads in velocity and dispersion, and predict that at long time points APP-C will achieve greater progress towards the presynaptic terminal. The significance of this data and accompanying model pertains to the role transport plays in neuronal function, connectivity, and survival, and has implications in the pathogenesis of neurological disorders, such as Alzheimer's, Huntington and Parkinson's diseases.This work was supported in part by NINDS RO1 NS046810 and RO1 NS062184 (ELB), NIGMS RO1 GM47368 (ELB), the Physical Sciences in Oncology Center grant U54CA143837 (VC), NIGMS K12GM088021 (JP), and NSF IGERT DGE-0549500 (PES). ELB and VC also received pilot project funds from the UNM Center for Spatiotemporal modeling, funded by NIGMS, P50GM08273, which also supported AC.2013-09-2

Dynamic density functional theory of solid tumor growth: Preliminary models

Cancer is a disease that can be seen as a complex system whose dynamics and growth result from nonlinear processes coupled across wide ranges of spatio-temporal scales. The current mathematical modeling literature addresses issues at various scales but the development of theoretical methodologies capable of bridging gaps across scales needs further study. We present a new theoretical framework based on Dynamic Density Functional Theory (DDFT) extended, for the first time, to the dynamics of living tissues by accounting for cell density correlations, different cell types, phenotypes and cell birth/death processes, in order to provide a biophysically consistent description of processes across the scales. We present an application of this approach to tumor growth

A Geometrically-Constrained Mathematical Model of Mammary Gland Ductal Elongation Reveals Novel Cellular Dynamics within the Terminal End Bud

International audienceMathematics is often used to model biological systems. In mammary gland development, mathematical modeling has been limited to acinar and branching morphogenesis and breast cancer, without reference to normal duct formation. We present a model of ductal elongation that exploits the geometrically-constrained shape of the terminal end bud (TEB), the growing tip of the duct, and incorporates morphometrics, region-specific proliferation and apoptosis rates. Iterative model refinement and behavior analysis, compared with biological data, indicated that the traditional metric of nipple to the ductal front distance, or percent fat pad filled to evaluate ductal elongation rate can be misleading, as it disregards branching events that can reduce its magnitude. Further, model driven investigations of the fates of specific TEB cell types confirmed migration of cap cells into the body cell layer, but showed their subsequent preferential elimination by apoptosis, thus minimizing their contribution to the luminal lineage and the mature duct. Author Summary Our paper describes a mathematical model of mammary ductal elongation during pubertal development. We make several conclusions that will be of interest to scientists studying mammary gland biology, epithelial tube formation, and branching morphogenesis. First, our model indicates that a common measurement of developmental outgrowth ('percent fat pad filled') underestimates the total growth and leads to mischaracterization of mutant PLOS Computational Biology

Assessment of TEB path tortuosity.

<p>The angle of deflection caused by bifurcation, the frequency of bifurcation, and the disparity between displacement and path tracing measurements were measured. A) Representative image of a TEB bifurcation event with the original path of the TEB noted as a solid line, the new path of each TEB as a result of the bifurcation are noted as dotted lines and the angles measured noted. B) Quantification of the angle of deflection presented as mean (whiskers denote range)(n = 62). C) Representative image of TEB’s growth path with 2 bifurcation events noted and the length of duct between noted with a solid line. D) Quantification of the total length of duct between bifurcation events is presented as mean (whiskers denote range)(n = 23). E) Total length of duct measurements were compared to corresponding displacement measurements. Displacement measurements consistently underestimated the total length by 6.1% (±0.9) (p = .0001, paired ratios t-Test, n = 23).</p

Determination of proliferation rate and cell cycle dynamics.

<p>Proliferation rates were analyzed by performing a dual labeling experiment with thymidine analogs EdU and BrdU. Mice were given a pulse of EdU at time “0”, then pulsed with BrdU every 2 hours for 24 hours. Mice were harvested 2 hours after pulsing with BrdU. A) Representative images of TEBs from each time point stained for EdU and BrdU incorporation. B) Quantification of EdU and Brdu single and double-positive populations throughout the time course indicate an S phase duration of 6 hours and total cell cycle time of 16 hours (n = 3 mice, 12 glands, 10 TEBs). See also <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004839#pcbi.1004839.s003" target="_blank">S3 Fig</a>.</p

Experimental determination of TEB displacement rate.

<p>Quantification of the distance from the nipple to the ductal boundary in 5 (n = 18), 6 (n = 18), 7 (n = 18), and 8 (n = 8) week FVB mice. A) Representative inguinal glands from 5, 6, 7 and 8 week old FVB mice are pictured with a dashed line demarcating the ductal front. B) Quantification of the outgrowths at each time point are fitted with a best fit line (one-way ANOVA p<0.0001, R2 = .8274). On average during puberty, the duct grows at a rate of 0.54 mm per day.</p

Morphology characterization of the terminal end bud.

<p>Glands from 5 and 6 week old mice were embedded, sectioned and stained for epithelial markers and measurements were taken of both cells and the TEB structure. A) Regional measurements of the TEB are represented in a scaled schematic (n values: Regions 1, 2, 5, and 6 = 15 TEBs, Region 3 = 23 TEBs, Region 4 = 8 TEBs, Region 7 layer diameter = 24 TEBs, lumen = 15 TEBs, length = 29 TEBs, Region 8 = 8 ducts). B) Mean cellular dimensions of the cap and myoepithelial cells, Regions 1–4 (whiskers denote range, n values: Region 1 length = 15 TEBs/ 45 cells, Region 1 width = 10 TEBs/ 126 cells. Region 2 length = 15 TEBs/ 56 cells, Region 2 width = 10 TEBs/ 115 cells. Region 3 length = 23 TEBs/ 273 cells, Region 3 width = 9 TEBs/ 36 cells. Region 4 length = 8 TEBs/ 197 cells, Region 4 width = 8 TEBs/ 197 cells). C) Mean cellular dimensions of body and luminal cells, Regions 5–8 (whiskers denote range, n values: Region 5 width/length = 5 TEBs/ 221 cells. Region 6 width/length = 5 TEBs/ 316 cells. Region 7 length/width = 4 TEBs/ 204 cells. Region 8 length/width = 6 ducts/ 301 cells). See also Table A in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004839#pcbi.1004839.s001" target="_blank">S1 Text</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004839#pcbi.1004839.s002" target="_blank">S2 Fig</a>.</p