Anomalous, non-Gaussian, viscoelastic, and age-dependent dynamics of histonelike nucleoid-structuring proteins in live Escherichia coli

Editors' Suggestion

Anomalous, non-Gaussian, viscoelastic, and age-dependent dynamics of histonelike nucleoid-structuring proteins in live Escherichia coli

Asmaa A. Sadoon and Yong Wang

Phys. Rev. E 98, 042411 – Published 19 October 2018

Abstract

We report our measurements of the dynamics of histonelike nucleoid-structuring (H-NS) proteins, which interact with both proteins and DNA simultaneously, in live Escherichia coli bacteria. The dynamics turn out to differ significantly from other molecules reported previously. A power-law distribution was observed for the diffusion coefficients of individual H-NS proteins. In addition, we observed a distribution of displacements which does not follow the Gaussian, Cauchy, or Laplace distributions but the Pearson Type VII distribution. Furthermore, we experimentally measured the time and frequency dependence of the complex modulus of the bacterial cytoplasm, which deviates from the viscoelasticity of homogeneous protein solutions and shows a glass-liquid transition. Last, we observed that the dynamics of H-NS proteins is cell length and cell age dependent. The findings are expected to fundamentally change the current views on bacterial cytoplasm and diffusional dynamics of molecules in bacteria.

Received 19 June 2018

DOI:https://doi.org/10.1103/PhysRevE.98.042411

Physics Subject Headings (PhySH)

Anomalous diffusion Viscoelasticity

Physics of Living SystemsInterdisciplinary PhysicsFluid DynamicsPolymers & Soft Matter

Authors & Affiliations

Asmaa A. Sadoon and Yong Wang^*

Department of Physics, Microelectronics-Photonics Graduate Program, Cell and Molecular Biology Program, University of Arkansas, Fayetteville, Arkansas 72701, USA

^*yongwang@uark.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 98, Iss. 4 — October 2018

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Illustration of H-NS proteins' key activities. The H-NS protein is a DNA-binding protein, consisting of a DNA-binding domain, a linker, and an oligomerization domain, which allows H-NS proteins to form polymers and DNA bridging. (b) SptPALM for tracking H-NS proteins in live E. coli. (c) An example of superresolved images of H-NS proteins in individual E. coli. (d) Examples of trajectories of H-NS proteins in the same area of panel (c). (e) Examples of individual trajectories.
Reuse & Permissions
Figure 2
(a) Ensemble-averaged MSD ( $\circ$ ) from 38 796 trajectories (error bar: SEM). Fitting the data via $MSD = 4 D τ^{α}$ gives $D = (8.0 \pm 0.3) \times 10^{3} {nm}^{2} / s$ and $α = 0.57 \pm 0.02$ (red dashed line). Inset: log-log plot of the same data. (b) MSD of 2000 individual trajectories (gray lines) in log-log scale, overlapped with the fitted ensemble-average (red dashed line). (c) Distribution of the anomalous scaling exponent $α$ . (d) Distribution of the generalized apparent diffusion coefficients fitted with $P (D) \propto D^{- (β + 1)}$ (red dashed line, $β = 0.97 \pm 0.07$ ). Left-bottom inset: distribution of the short-time apparent diffusion coefficients, $P (D_{s})$ . Right-top inset: distribution of the number of proteins per cluster fitted with $P (n) \propto p^{n}$ (red dashed line, $p = 0.952 \pm 0.004$ ).
Reuse & Permissions
Figure 3
(a) Examples of long MSD curves ( $> 20$ frames) showing superdiffusive motions (i.e., steeper than the slope of one, which is shown as a black dashed line). The colored portions of the curves were used for fittings to obtain the generalized diffusion coefficient and the anomalous scaling exponent, $MSD = 4 D τ^{α}$ . Inset: The same MSD curves in linear scales. (b) Ensemble-averaged MSD curves for bacteria in the exponential growth phase (or log phase, LOG) and bacteria treated with formaldehyde (HCHO). (c) Distributions of the anomalous scaling exponent $α$ for untreated bacteria in the exponential growth phase (LOG) and treated bacteria with formaldehyde (HCHO).
Reuse & Permissions
Figure 4
(a, b) Distributions of displacements (A: $Δ x$ , B: $Δ y$ ). The experimental data (black circles) cannot be fitted with the Gaussian (red dot-dashed line), Cauchy (magenta dashed line), or Laplace (brown dotted line) distributions. Instead, the Pearson Type VII distribution (green solid line) fits the data very well. (c) Fitting errors $δ$ from the fittings of the data using the Gaussian (G), Cauchy (C), Laplace (L), and Pearson Type VII (P) distributions. Inset: $χ^{2}$ of the fittings. (d) Distribution of displacements from Monte Carlo simulations (blue triangles) overlapping with the experimental measurements (black circles, same data as in panel a). Inset: the Monte Carlo simulations assume that the molecules can switch between a bound state (B, slow diffusion) and an unbound state (U, fast diffusion) with rates of $p_{u b}$ (U to B) and $p_{b u}$ (B to U).
Reuse & Permissions
Figure 5
(a) Velocity autocorrelation of H-NS proteins is negative at short timescales. (b) Frequency dependence of the magnitude of the complex modulus $| G (ω) |$ of bacterial cytoplasm. Inset: the ensemble-averaged MSD curve with longer $τ$ . (c) Frequency dependence of the storage (red circles) and loss (blue squares) modulii, $G^{'} (ω)$ and $G^{''} (ω)$ . (d) Frequency dependence of $tan ϕ = G^{''} / G^{'}$ .
Reuse & Permissions
Figure 6
(a) Ensemble-averaged MSD curves for bacteria with different lengths ( $< 1.2 μ m$ : red circles, $2.8 - 3.0 μ m$ : magenta squares, $> 5 μ m$ : blue triangles). Error bars = SEM. (b) Radius of gyration $R_{g}$ of trajectories for the cells from the three groups. (c) Fitted diffusion coefficients $D$ from panel (a). (d) Fitted exponents $α$ from panel (a). Error bars in panels (c) and (d) represent fitting errors. (e) Comparison of the magnitude of the complex modulus $| G (ω) |$ of bacterial cytoplasm between bacteria with different lengths. (f) Comparison of the storage modulus $G^{'} (ω)$ of bacterial cytoplasm between bacteria with different lengths. (g) Comparison of the loss modulus $G^{''} (ω)$ of bacterial cytoplasm between bacteria with different lengths.
Reuse & Permissions

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics