Search bioRxiv⌕ Search
Home/Archive/bioRxiv

bioRxiv · 10.1101/227090

Statistical methods for large ensemble of super-resolution stochastic single particle trajectories

Hoze, N.·holcman, d.
View original source ↗Export metadata ↓

Abstract

Following recent progresses in super-resolution microscopy obtained in the last decade, massive amount of redundant single stochastic trajectories are now available for statistical analysis. Flows of trajectories of molecules or proteins are sampling the cell membrane or its interior at a very high time and space resolution. Several statistical analysis were developed to extract information contained in these data, such as the biophysical parameters of the underlying stochastic motion to reveal the cellular organization. These trajectories can further reveal hidden subcellular organization. We present here the statistical analysis of these trajectories based on the classical Langevin equation, which serves as a model of trajectories. Parametric and non-parametric estimators are constructed by discretizing the stochastic equations and they allow recovering tethering forces, diffusion tensor or membrane organization from measured trajectories, that differ from physical ones by a localization noise. Modeling, data analysis and automatic detection algorithms serve extracting novel biophysical features such as potential wells and other sub-structures, such as rings at an unprecedented spatiotem-poral resolution. It is also possible to reconstruct the surface membrane of a biological cell from the statistics of projected random trajectories.

Source connections

Explore related subjects

biophysicsPreprint

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Hoze, N., holcman, d.. 2017-11-30. Statistical methods for large ensemble of super-resolution stochastic single particle trajectories. https://doi.org/10.1101/227090

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related preprints

bioRxiv2026

Single Molecule Diffusion Studies Reveal Rapid Translations Across Target Membrane Surfaces for both p40Phox PX domain and Class III PI3K VPS34 Complex 1, the Autophagy Lipid Kinase

Single molecule analyses are providing new insights into the molecular mechanisms by which peripheral membrane proteins approach and translate across a target bilayer surface before stable docking. Here we compare and contrast the translational movements of four diffusers on a representative supported lipid bilayer: (i) the fluorescent lipid LRB-(DO)PE, (ii) the G-protein Rab1A anchored to (DO)PE; (iii) the PI(3)P sensor p40Phox PX domain, and (iv) the autophagy lipid kinase VPS34 Complex 1. The latter enzyme is a Class III PI-3-Kinase and its unusual architecture exhibits two distinct membrane-docking "feet" unique to Class III PI3Ks. Notably, the membrane contact surfaces of the PX domain and autophagy lipid kinase each possess multiple positive charges suitable for electrostatic interactions with their anionic target membrane. The present single molecule tracking studies reveal that both the fluorescent lipid and the lipid-anchored G protein Rab1A exhibit 2-dimensional translation typical of simple lipid diffusion in the bilayer. Single molecule density measurements indicate both PX domain and autophagy lipid kinase exhibit significantly reduced membrane docking when the bilayer negative charge is decreased, confirming the importance of their protein-bilayer electrostatic interactions. Single molecule tracking studies reveal that both PX domain and autophagy lipid kinase exhibit hopping movements across the bilayer surface during their initial bilayer contacts, yielding a significantly higher frequency of long range displacements than allowed by lipid 2-D diffusion. After transitioning from hopping to a stable bilayer-docked state, both PX domain and autophagy lipid kinase exhibit 2-D diffusion slower than lipid diffusion indicating the appearance of increased frictional drag against the bilayer due to new protein-bilayer contacts. PX domain requires its target lipid for the transition from electrostatic hopping to stable bilayer docking, while autophagy lipid kinase can dock spontaneously to anionic lipid bilayers even in the absence of its substrate lipid. In principle, the slowly diffusing, bilayer-docked states of PX domain and autophagy lipid kinase could be interrupted by unbinding-hopping-rebinding events. However, such events are not detected for PX domain in the presence of target lipid (DO)PI(3)P nor for autophagy lipid kinase in the presence of substrate lipid (DO)PI. Instead, unbinding-hopping-rebinding events are only observed for autophagy lipid kinase in the absence of substrate lipid, indicating that the presence of a specific binding lipid reduces the frequency or spatial amplitude of such events. Overall, the findings provide evidence that p40Phox PX domain possesses a search mechanism involving electrostatic hopping that speeds its acquisition of target lipid, as previously observed for PH domains. The evidence indicates that the autophagy lipid kinase also exhibits electrostatic hopping/skating behavior that is proposed to play a functional role by speeding regulatory encounters with autophagy lipid kinase activators and effectors. Moreover, the ability of the lipid kinase to spontaneously dock to anionic membranes without a target lipid could facilitate its distribution across broad regions of the growing autophagosome. Finally, the autophagy lipid kinase exhibits multiple translational modes that we hypothesize are enabled by its two membrane docking feet.

biophysics↗
bioRxiv2026

Inferring scaling laws of branching networks from their geometry by global optimization

Optimality principles are widely used to understand branching networks, yet they are tested on individual branchings that cannot reliably distinguish competing scaling laws. We formulate the missing link between the laws and measurements by mapping each law to its predicted branch points through global optimization. Vascular branch points closely match weighted-length optima when each vessel is allowed its own fitted weight. Inferred scaling laws reveal type-specific geometric signatures hidden from local analysis. They beat all tested laws, including Murray's law in 1,679 of 1,744 held-out hepatic and pulmonary trees. For coronary arteries on the heart surface, an exact discrete optimization model extends the framework beyond convex geometry and supports area-preserving scaling. The framework also identifies distinct laws for airways and plant shoots while rejecting weighted-length optimality for neuronal axons. Global optimization turns network geometry into a quantitative test of the principles that govern branching networks.

biophysics↗
bioRxiv2026

Ultra-precision 3D Printed Sample Tubes of Complex Cross Section for Enhanced Electron Paramagnetic Resonance Sensitivity of AqueousSamples

This paper discusses the applications of ultra-precision 3D printing in developing EPR sample tubes for X-band measurements of aqueous samples. The seed idea of this work started from the flat cell idea discussed in Mett and Hyde et al.(2003), Sidabras et al. (2005), and Sidabras et al. (2017), where placing multiple aqueous flat cells perpendicular to the electric field in the microwave cavity reduce RF losses and improve EPR signal sensitivity. In this work, we present the 3D printed aquastar sample holders for dielectric resonators and the aquasun sample holders for cavity resonators. Even though the ultra-precision 3D printing enables the fabrication of complex cross-sections at 25um resolution, the photopolymer material has comparatively higher dielectric losses compared to the conventional materials like glass and PTFE. To reduce the RF losses due to the inherent dielectric properties, we introduced the latticing approach in reducing the amount of plastic without compromising the structural stability. In addition to this, we present the slicing and dielectric approximation approach in reducing the computation cost for these complex cross-sections. The novel sample tubes discussed here present signal improvements through both simulation and experiments, which were validated through power saturation experiments. The sample tube development methodology presented here provide a general framework for designing and implementing 3D printed EPR sample holders, based on resonator electromagnetic field distribution and dielectric properties of the photopolymer material.

biophysics↗