Vesicle Fluctuation Spectroscopy · IISER Mohali

Membrane
Mechanics
from Thermal Fluctuations

An interactive analysis site for Giant Unilamellar Vesicles (GUVs). Compute angular auto-correlations, extract bending rigidity κ and effective surface tension Σ via Helfrich / Brochard–Lennon theory.

→ Start Analysis
Core Equation \[ \langle |u_{lm}|^2 \rangle = \frac{k_B T}{\kappa(l-1)(l+2)\left[l(l+1)+\Sigma\right]} \]
Analysis Modules
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Angular Auto-Correlation
Visualise \(\xi(\gamma)=\sum_l b_l P_l(\cos\gamma)\) for any combination of modes. Explore how each mode l contributes.
→ \(\xi(\gamma)\) · \(P_l(\cos\gamma)\)
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Legendre Spectrum
Plot mode amplitudes bl vs mode number l. See how bending rigidity and tension suppress higher modes.
→ bl vs l
κ
κ / Σ Extraction
Input experimental Bl ± σl data and run χ² minimisation to extract bending rigidity with error estimates.
→ χ² fitting · covariance
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Computational Workflow
Learn the complete computational pipeline from the paper: random quasi-spherical vesicle generation, angular auto-correlation, Legendre decomposition, and χ² fitting for κ and Σ.
→ End-to-end tutorial
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Theory Reference
Full derivation: Helfrich energy, spherical harmonics, Legendre expansion, equipartition theorem, χ² fitting procedure.
→ Full Derivation
Based on Kumar et al., Chem. Phys. Lipids 259, 105374 (2024) Avneesh Singh & Ridima Singh · SMBL IISERM Biophysics/lab.html