What is it about?
During an infection, adenoviruses inside a target cell must navigate through the cytoplasm to deliver their genetic material to the cell nucleus. To do this, they rely on the cell's internal transport network, binding to motor proteins like kinesin that walk along structural filaments known as microtubules. Within the cell, these viral particles alternate between diffusing freely in the fluid cytoplasm and hitching rides on molecular motors, which move directionally while also undergoing random thermal motion. Modeling this transport process in spherical cells usually requires complex numerical simulations that can suffer from computational instability or unphysical oscillations. In this paper, we formulated the transient transport equations in a three-dimensional spherical coordinate system and developed an exact analytical solution using a generalized Fourier series method. By utilizing two distinct sets of orthogonal eigenfunctions, our approach calculates the changing concentrations of both free and motor-bound viral particles over time as they move between the cell membrane and nucleus.
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Why is it important?
Previous mathematical models often simplified cellular geometry by assuming cylindrical shapes for elongated cells or ignored the random, stochastic component of motor-assisted movement. Our model advances the field by capturing realistic spherical cell geometry and incorporating a diffusion term that accounts for thermal fluctuations experienced by motor-bound viruses, which effectively removes numerical oscillations from the solution. Beyond its theoretical contribution, our generalized Fourier series solution converges rapidly, matching high-accuracy numerical simulations with just a few terms. This provides biophysicists, mechanical engineers, and medical researchers with an efficient mathematical tool to analyze intracellular viral kinetics, optimize gene therapy vectors, and understand early infection stages without requiring high-performance computing resources.
Perspectives
Working on this paper alongside my collaborator A.A. Avramenko was a fantastic opportunity to bridge classical transport phenomena with cell biology. Applying mathematical methods like separation of variables and generalized Fourier series—tools routinely used in heat and mass transfer engineering—to model intracellular viral kinetics allowed us to uncover elegant, closed-form solutions to complex biological problems. I hope this paper illustrates how engineering physics and applied mathematics can shed light on fundamental biological processes like viral trafficking and targeted nanomedicine. I am also deeply grateful for the support of the NATO Collaborative Linkage Grant, which facilitated our international research collaboration and helped lay the groundwork for further bio-transport studies.
Andrey V Kuznetsov
North Carolina State University
Read the Original
This page is a summary of: Generalized Fourier series solution of equations governing molecular-motor-assisted transport of adenoviral vectors in a spherical cell, International Communications in Heat and Mass Transfer, April 2008, Elsevier,
DOI: 10.1016/j.icheatmasstransfer.2007.08.003.
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