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Register a new userPhysics and modelling of intracellular diffusion
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Svyatoslav Kondrat
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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.
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Many experiments in recent years have reported that, when exposed to their corresponding substrate, catalytic enzymes undergo enhanced diffusion as well as chemotaxis (biased motion in the direction of a substrate gradient). Among other possible mechanisms, in a number of recent works we have explored several passive mechanisms for enhanced diffusion and chemotaxis, in the sense that they require only binding and unbinding of the enzyme to the substrate rather than the catalytic reaction itself. These mechanisms rely on conformational changes of the enzyme due to binding, as well as on phoresis due to non-contact interactions between enzyme and substrate. Here, after reviewing and generalizing our previous findings, we extend them in two different ways. In the case of enhanced diffusion, we show that an exact result for the long-time diffusion coefficient of the enzyme can be obtained using generalized Taylor dispersion theory, which results in much simpler and transparent analytical expressions for the diffusion enhancement. In the case of chemotaxis, we show that the competition between phoresis and binding-induced changes in diffusion results in non-trivial steady state distributions for the enzyme, which can either accumulate in or be depleted from regions with a specific substrate concentration.
Tracer particles immersed in suspensions of biological microswimmers such as E. coli or Chlamydomonas display phenomena unseen in conventional equilibrium systems, including strongly enhanced diffusivity relative to the Brownian value and non-Gaussian displacement statistics. In dilute, 3-dimensional suspensions, these phenomena have typically been explained by the hydrodynamic advection of point tracers by isolated microswimmers, while, at higher concentrations, correlations between pusher microswimmers such as E. coli can increase the effective diffusivity even further. Anisotropic tracers in active suspensions can be expected to exhibit even more complex behaviour than spherical ones, due to the presence of a nontrivial translation-rotation coupling. Using large-scale lattice Boltzmann simulations of model microswimmers described by extended force dipoles, we study the motion of ellipsoidal point tracers immersed in 3-dimensional microswimmer suspensions. We find that the rotational diffusivity of tracers is much less affected by swimmer-swimmer correlations than the translational diffusivity. We furthermore study the anisotropic translational diffusion in the particle frame and find that, in pusher suspensions, the diffusivity along the ellipsoid major axis is higher than in the direction perpendicular to it, albeit with a smaller ratio than for Brownian diffusion. Thus, we find that far field hydrodynamics cannot account for the anomalous coupling between translation and rotation observed in experiments, as was recently proposed. Finally, we study the probability distributions (PDFs) of translational and rotational displacements. In accordance with experimental observations, for short observation times we observe strongly non-Gaussian PDFs that collapse when rescaled with their variance, which we attribute to the ballistic nature of tracer motion at short times.
In living cells, proteins combine 3D bulk diffusion and 1D sliding along the DNA to reach a target faster. This process is known as facilitated diffusion, and we investigate its dynamics in the physiologically relevant case of confined DNA. The confining geometry and DNA elasticity are key parameters: we find that facilitated diffusion is most efficient inside an isotropic volume, and on a flexible polymer. By considering the typical copy numbers of proteins in vivo, we show that the speedup due to sliding becomes insensitive to fine tuning of parameters, rendering facilitated diffusion a robust mechanism to speed up intracellular diffusion-limited reactions. The parameter range we focus on is relevant for in vitro systems and for facilitated diffusion on yeast chromatin.
Bacterial biofilms, surface-attached communities of cells, are in some respects similar to colloidal solids; both are densely packed with non-zero yield stresses. However, unlike non-living materials, bacteria reproduce and die, breaking mechanical equilibrium and inducing collective dynamic responses. We report experiments and theory investigating the motion of immotile Vibrio cholerae, which can kill each other and reproduce in biofilms. We vary viscosity by using bacterial variants that secrete different amounts of extracellular matrix polymers, but are otherwise identical. Unlike thermally-driven diffusion, in which diffusivity decreases with increased viscosity, we find that cellular motion mediated by death and reproduction is independent of viscosity over timescales relevant to bacterial reproduction. To understand this surprising result, we use two separate modeling approaches. First we perform explicitly mechanical simulations of one-dimensional chains of Voigt-Kelvin elements that can die and reproduce. Next, we perform an independent statistical approach, modeling Brownian motion with the classic Langevin equation under an effective temperature that depends on cellular division rate. The diffusion of cells in both approaches agrees quite well, supporting a kinetic interpretation for the effective temperature used here and developed in previous work. As the viscoelastic behavior of biofilms is believed to play a large role in their anomalous biological properties, such as antibiotic resistance, the independence of cellular diffusive motion --- important for biofilm growth and remodeling --- on viscoelastic properties likely holds ecological, medical, and industrial relevance.
Nanophotonic objects like plasmonic nanoparticles and colloidal quantum dots can complement the functionality of molecular dyes in biomedical optics. However, their operation is usually governed by spontaneous processes, which results in broad spectral features and limited signal-to-noise ratio, thus restricting opportunities for spectral multiplexing and sensing. Lasers provide the ultimate spectral definition and background suppression, and their integration with cells has recently been demonstrated. However, laser size and threshold remain problematic. Here, we report on the design, high-throughput fabrication and intracellular integration of semiconductor nanodisk lasers. By exploiting the large optical gain and high refractive index of GaInP/AlGaInP quantum wells, we obtain lasers with volumes 1000-fold smaller than the eukaryotic nucleus ($V_{laser}$<0.1 $mu$m$^3$), lasing thresholds 500-fold below the pulse energies typically used in two-photon microscopy ($E_{th} approx $0.13 pJ), and excellent spectral stability (<50 pm wavelength shift). Multiplexed labelling with these lasers allows cells-tracking through micro-pores, thus providing a powerful tool to study cell migration and cancer invasion.
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