Abstract:Molecular motion of biopolymers in vivo is known to be strongly influenced by the high concentration of organic matter inside cells, usually referred to as crowding conditions. To elucidate the effect of intermolecular interactions on Brownian motion of proteins, we performed (1)H pulsed-field gradient NMR and fluorescence correlation spectroscopy (FCS) experiments combined with small-angle X-ray scattering (SAXS) and viscosity measurements for three proteins, αB-crystalline (αBc), bovine serum albumin, and he… Show more
“…We find that, in general, rotational diffusion follows the same trend as for translational diffusion, including a very similar dependency on local crowding (Figure 5—figure supplement 1). A similar reduction of translational and rotational diffusion upon crowding on shorter, sub-microsecond time scales found here is consistent with experimental data from quasi-elastic neutron backscattering and NMR relaxometry (Roosen-Runge et al, 2011; Roos et al, 2016). However, our simulations are too short to probe the suggested protein species dependent decoupling of rotational and translational diffusion on longer time scales based on pulsed field gradient NMR measurements of dense protein solutions (Roos et al, 2016).…”
Section: Resultssupporting
confidence: 90%
“…A similar reduction of translational and rotational diffusion upon crowding on shorter, sub-microsecond time scales found here is consistent with experimental data from quasi-elastic neutron backscattering and NMR relaxometry (Roosen-Runge et al, 2011; Roos et al, 2016). However, our simulations are too short to probe the suggested protein species dependent decoupling of rotational and translational diffusion on longer time scales based on pulsed field gradient NMR measurements of dense protein solutions (Roos et al, 2016). 10.7554/eLife.19274.021Figure 5.Rotational diffusion of macromolecules.( A ) Averaged angular velocity ( ω ) of macromolecules in MG m1 as a function of their Stokes radii ( R s ) (gray squares with IF1, ATRN, PDHD, PDHA, and PGK highlighted in purple, red, blue, yellow, and green, respectively) ( B ) Rotational correlation functions ( θ ) of macromolecules (IF1, ATRN, PDHD, PDHA, and PGK colored in purple, red, blue, yellow, and green, respectively).…”
Biological macromolecules function in highly crowded cellular environments. The structure and dynamics of proteins and nucleic acids are well characterized in vitro, but in vivo crowding effects remain unclear. Using molecular dynamics simulations of a comprehensive atomistic model cytoplasm we found that protein-protein interactions may destabilize native protein structures, whereas metabolite interactions may induce more compact states due to electrostatic screening. Protein-protein interactions also resulted in significant variations in reduced macromolecular diffusion under crowded conditions, while metabolites exhibited significant two-dimensional surface diffusion and altered protein-ligand binding that may reduce the effective concentration of metabolites and ligands in vivo. Metabolic enzymes showed weak non-specific association in cellular environments attributed to solvation and entropic effects. These effects are expected to have broad implications for the in vivo functioning of biomolecules. This work is a first step towards physically realistic in silico whole-cell models that connect molecular with cellular biology.DOI:
http://dx.doi.org/10.7554/eLife.19274.001
“…We find that, in general, rotational diffusion follows the same trend as for translational diffusion, including a very similar dependency on local crowding (Figure 5—figure supplement 1). A similar reduction of translational and rotational diffusion upon crowding on shorter, sub-microsecond time scales found here is consistent with experimental data from quasi-elastic neutron backscattering and NMR relaxometry (Roosen-Runge et al, 2011; Roos et al, 2016). However, our simulations are too short to probe the suggested protein species dependent decoupling of rotational and translational diffusion on longer time scales based on pulsed field gradient NMR measurements of dense protein solutions (Roos et al, 2016).…”
Section: Resultssupporting
confidence: 90%
“…A similar reduction of translational and rotational diffusion upon crowding on shorter, sub-microsecond time scales found here is consistent with experimental data from quasi-elastic neutron backscattering and NMR relaxometry (Roosen-Runge et al, 2011; Roos et al, 2016). However, our simulations are too short to probe the suggested protein species dependent decoupling of rotational and translational diffusion on longer time scales based on pulsed field gradient NMR measurements of dense protein solutions (Roos et al, 2016). 10.7554/eLife.19274.021Figure 5.Rotational diffusion of macromolecules.( A ) Averaged angular velocity ( ω ) of macromolecules in MG m1 as a function of their Stokes radii ( R s ) (gray squares with IF1, ATRN, PDHD, PDHA, and PGK highlighted in purple, red, blue, yellow, and green, respectively) ( B ) Rotational correlation functions ( θ ) of macromolecules (IF1, ATRN, PDHD, PDHA, and PGK colored in purple, red, blue, yellow, and green, respectively).…”
Biological macromolecules function in highly crowded cellular environments. The structure and dynamics of proteins and nucleic acids are well characterized in vitro, but in vivo crowding effects remain unclear. Using molecular dynamics simulations of a comprehensive atomistic model cytoplasm we found that protein-protein interactions may destabilize native protein structures, whereas metabolite interactions may induce more compact states due to electrostatic screening. Protein-protein interactions also resulted in significant variations in reduced macromolecular diffusion under crowded conditions, while metabolites exhibited significant two-dimensional surface diffusion and altered protein-ligand binding that may reduce the effective concentration of metabolites and ligands in vivo. Metabolic enzymes showed weak non-specific association in cellular environments attributed to solvation and entropic effects. These effects are expected to have broad implications for the in vivo functioning of biomolecules. This work is a first step towards physically realistic in silico whole-cell models that connect molecular with cellular biology.DOI:
http://dx.doi.org/10.7554/eLife.19274.001
“…9 and do not require a PBC correction. 67
where l =2 and the overall rotational correlation time τ is obtained from the fast and slow correlation times as follows:
Additionally, averages of the inverse tumbling times were also calculated as they are more relevant for comparison with many experiments such as dynamic light scattering 68 :
The correlation functions obtained at the highest concentrations were additionally fitted to a triple-exponential function since a double-exponential fit did not fully describe the data:
where τ Rf , τ Rm , and τ Rs are fast, medium and slow correlation times with the corresponding S Rm 2 and S Rs 2 weights.…”
For a long time the effect of crowded cellular environment on protein dynamics has been largely ignored. Recent experiments indicate that proteins diffuse much slower in a living cell than in a diluted solution and further studies suggest that the diffusion depends on the local surrounding. Here, detailed insight into how diffusion depends on protein-protein contacts is presented based on extensive all-atom molecular dynamics simulations of concentrated villin head piece solutions. After force field adjustments in the form of increased protein-water interactions to reproduce experimental data, translational and rotational diffusion was analyzed in detail. While internal protein dynamics remained largely unaltered, rotational diffusion was found to slow down more significantly than translational diffusion as the protein concentration increased. The decrease in diffusion is interpreted in terms of a transient formation of protein clusters. These clusters persist on sub-microsecond time scales and follow distributions that increasingly shift toward larger cluster size with increasing protein concentrations. Weighting diffusion coefficients estimated for different clusters extracted from the simulations with the distribution of clusters largely reproduces the overall observed diffusion rates, suggesting that transient cluster formation is a primary cause for a slow-down in diffusion upon crowding with other proteins.
“…According to the above expression, k D is determined by both translational and rotational diffusion. Note that recent experimental studies for diffusion of molecular probes in complex polymer solutions, reveal a very novel decoupling phenomenon between the translational and rotational diffusion [19,20]. Namely, it was found experimentally that, for diffusion of proteins in polymer solutions, the SE relation for the translational diffusion remains well satisfied, while rotational diffusion exhibits large deviations from the traditional SED relation given by D r = k B T /8πη macro r 3 h .…”
Abstract.In the present paper, we establish a theoretical formalism to study the protein-protein association rate in the framework of diffusion-limited theory. To account for the crowding effect due to the presence of polymer, we particularly take into account the deviation of rotational diffusion of proteins from the Stokes-Einstein-Debye relation. Based on fluid mechanics and depletion theory, a new scaling relation for the retardation factor of the rotational diffusion was proposed. Besides, the crowding-induced interaction energy between the proteins has been also properly introduced into the association rate theory. We apply our theory to calculate the association rate constant of proteins β-lactamase and β-lactamase inhibitor protein in poly(ethylene glycol) solutions. Particular attention is paid to the dependence of the association rate constant on the polymer concentration and polymer molecular weight. The deviation from the simple relation based on Stokes-Einstein approximation is well addressed. We find that our theoretical results show good agreements with the experimental data in the whole concentration region, which demonstrates the validity of our theory.
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