[Paper Review] Physics and modelling of intracellular diffusion

Svyatoslav Kondrat|arXiv (Cornell University)|Oct 12, 2018

Gene Regulatory Network AnalysisBiochemistry, Genetics and Molecular Biology3 citations

TL;DR

This paper presents a physics-based framework for modeling intracellular diffusion in crowded cellular environments, emphasizing steric and hydrodynamic effects using Brownian dynamics simulations. It demonstrates that macromolecular diffusion is strongly influenced by crowder composition and volume fraction, with anomalous subdiffusion prevalent at intermediate timescales, challenging the use of volume fraction alone as a crowding metric and highlighting the limitations of simplified in vitro models with artificial crowders.

ABSTRACT

Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of macromolecules under crowding conditions inside living cells. I describe briefly how to characterize, model and measure diffusion properties. The focus is on physics and simulations, with a particular emphasis on the effects important for crowded, biologically relevant systems.

Motivation & Objective

• To understand how macromolecular diffusion is altered in the crowded intracellular environment compared to dilute laboratory conditions.
• To evaluate the role of steric and hydrodynamic interactions in reducing diffusion coefficients in dense biological systems.
• To assess the limitations of using volume fraction as a unique measure of crowding, given its insensitivity to molecular composition.
• To investigate the discrepancy between experimental observations of anomalous subdiffusion and simulation time scales.
• To highlight the need for improved multiscale models that incorporate both diffusion and biochemical reactions in whole-cell simulations.

Proposed method

• Modeling diffusion using the Langevin and Ermak-McCammon equations to describe Brownian motion under friction and hydrodynamic interactions.
• Employing Brownian dynamics simulations with explicit macromolecules of varying sizes and compositions to simulate cytoplasmic environments.
• Using mean square displacement (MSD) analysis to quantify diffusion behavior, distinguishing short-time, anomalous, and long-time regimes.
• Comparing results from two-component systems with artificial crowders to a complex, multi-component model cytoplasm to assess crowding effects.
• Applying time-averaged and ensemble-averaged MSD to improve statistical reliability under ergodicity assumptions.
• Using the Ermak-McCammon algorithm to solve the overdamped Langevin equation with hydrodynamic interactions, enabling accurate simulation of particle motion in viscous, crowded media.

Experimental results

Research questions

• RQ1 How does macromolecular diffusion deviate from normal Fickian behavior in crowded intracellular environments?
• RQ2 To what extent do steric and hydrodynamic interactions govern the reduction of diffusion coefficients in dense cytoplasm?
• RQ3 Why do experimental observations of anomalous subdiffusion persist despite the limitations of current Brownian dynamics simulations in accessing long timescales?
• RQ4 How does the composition of macromolecular crowders affect diffusion, and why might monodisperse artificial crowders fail to replicate in vivo conditions?
• RQ5 Can volume fraction alone serve as a reliable proxy for crowding, or is molecular composition equally critical in determining diffusion rates?

Key findings

• The short-time diffusion coefficient $ D_s $ decreases with increasing macromolecular size and volume fraction, while the long-time coefficient $ D_l $ is significantly reduced in crowded environments.
• Anomalous subdiffusion emerges in the intermediate time regime $ \tau_s < t < \tau_l $, with crossover timescales dependent on inter-macromolecular distances and packing fraction.
• The crossover time $ \tau_s $ increases with particle size and decreases with volume fraction, vanishing at $ \eta_{\text{max}} = \pi/6 \approx 0.54 $, indicating a theoretical limit of maximum packing.
• Diffusion in a complex, multi-component cytoplasm model is faster than in a two-component system with the same volume fraction, demonstrating that composition critically influences diffusion beyond volume fraction alone.
• Artificial crowders such as dextran may inadequately mimic the in vivo environment, as diffusion in the cytoplasm is faster than in similarly crowded two-component systems despite higher overall volume fraction.
• The study reveals that volume fraction is not a sufficient measure of crowding, as systems with higher volume fractions can exhibit faster diffusion depending on macromolecular composition.