Translational Diffusion Constants Research Articles

Persistence of an active asymmetric rigid Brownian particle in two dimensions.

We have studied the persistence probability p(t) of an active Brownian particle with shape asymmetry in two dimensions. The persistence probability is defined as the probability of a stochastic variable that has not changed its signin a given fixed time interval. We have investigated two cases: (1) diffusion of a free active particle and (2) that of a harmonically trapped particle. In our earlier work, by Ghosh et al. [J. Chem. Phys. 152, 174901 (2020)], we had shown that p(t) can be used to determine the translational and rotational diffusion constant of an asymmetrically shaped particle. The method has the advantage that the measurement of the rotational motion of the anisotropic particle is not required. In this paper, we extend the study to an active anisotropic particle and show how the persistence probability of an anisotropic particle is modified in the presence of a propulsion velocity. Furthermore, we validate our analytical expression against the measured persistence probability from the numerical simulations of single particle Langevin dynamics and test whether the method proposed in our earlier work can help distinguish between active and passive anisotropic particles.

Theory and Applications of Nitroxide-based Paramagnetic Cosolutes for Probing Intermolecular and Electrostatic Interactions on Protein Surfaces.

Solvent paramagnetic relaxation enhancement (sPRE) arising from nitroxide-based cosolutes has recently been used to provide an atomic view of cosolute-induced protein denaturation and to characterize residue-specific effective near-surface electrostatic potentials (ϕENS). Here, we explore distinct properties of the sPRE arising from nitroxide-based cosolutes and provide new insights into the interpretation of the sPRE and sPRE-derived ϕENS. We show that: (a) the longitudinal sPRE rate Γ1 is heavily dependent on spectrometer field and viscosity, while the transverse sPRE rate Γ2 is much less so; (b) the spectral density J(0) is proportional to the inverse of the relative translational diffusion constant and is related to the quantity ⟨r-4⟩norm, a concentration-normalized equilibrium average of the electron-proton interspin separation; and (c) attractive intermolecular interactions result in a shortening of the residue-specific effective correlation time for the electron-proton vector. We discuss four different approaches for evaluating ϕENS based on Γ2, J(0), Γ1, or ⟨r-6⟩norm. The latter is evaluated from the magnetic field dependence of Γ1 in conjunction with Γ2. Long-range interactions dominate J(0) and Γ2, while, at high magnetic fields, the contribution of short-range interactions becomes significant for J(ω) and hence Γ1; the four ϕENS quantities enable one to probe both long- and short-range electrostatic interactions. The experimental ϕENS potentials were evaluated using three model protein systems, two folded (ubiquitin and native drkN SH3) and one intrinsically disordered (unfolded state of drkN SH3), in relation to theoretical ϕENS potentials calculated from atomic coordinates using the Poisson-Boltzmann theory with either a r-6 or r-4 dependence.

Diffusion of Squalene in Nonaqueous Solvents.

Capillary flow techniques have been used to determine the translational diffusion constant, D, of squalene in seven alkanes and five cyclohexanes. The alkanes are n-hexane, n-octane, n-decane, n-dodecane, n-tetradecane, 2,2,4,4,6,8,8-heptamethylnonane (isocetane), and 2,6,10,14-tetramethylpentadecane (pristane). The cyclohexanes are cyclohexane, n-butylcyclohexane, n-hexylcyclohexane, n-octylcyclohexane, and n-dodecylcyclohexane. When combined with published data in CD2Cl2, ethyl acetate, n-hexadecane, squalane, n-octane–squalane mixtures, and supercritical CO2, the 35 diffusion constants and viscosities, η, vary by factors of ∼230 and ∼500, respectively. A fit to the modified Stokes–Einstein equation (MSE, D/T = ASE/ηp) gives an average absolute percentage difference (AAPD) of 7.72% between the experimental and calculated D values where p and ASE are constants, T is the absolute temperature, and the AAPD is the average value of (102) (|Dcalcd – Dexptl|/Dexptl). Two other MSE fits using subsets of the 35 diffusion constants may be useful for (a) estimating the viscosity of the hydrophobic core of lipid droplets, where squalene is a naturally occurring component, and (b) providing estimates of the D values needed to design extraction processes by which squalene is obtained from plant oils. The Wilke–Chang equation also was considered and found to give larger AAPDs than the corresponding MSE fits.

Diffusion of chiral active particles in a Poiseuille flow.

We study the diffusive behavior of chiral active (self-propelled) Brownian particles in a two-dimensional microchannel with a Poiseuille flow. Using numerical simulations, we show that the behavior of the transport coefficients of particles, for example, the average velocity v and the effective diffusion coefficient D_{eff}, strongly depends on flow strength u_{0}, translational diffusion constant D_{0}, rotational diffusion rate D_{θ}, and chirality of the active particles Ω. It is demonstrated that the particles can exhibit upstream drift, resulting in a negative v, for the optimal parameter values of u_{0}, D_{θ}, and Ω. Interestingly, the direction of v can be controlled by tuning these parameters. We observe that for some optimal values of u_{0} and Ω, the chiral particles aggregate near a channel wall and the corresponding D_{eff} are enhanced. However, for the nonchiral particles (Ω=0), D_{eff} is suppressed by the presence of Poiseuille flow. It is expected that these findings have a great potential for developing microfluidic and lab-on-a-chip devices for separating the active particles.

Spinnoise gradient echoes.

Nuclear spinnoise spectroscopy in the absence of radio frequency pulses was studied under the influence of pulsed field gradients (PFGs) on pure and mixed liquids. Under conditions where the radiation-damping-induced line broadening is smaller than the gradient-dependent inhomogeneous broadening, echo responses can be observed in difference spectra between experiments employing pulsed field gradient pairs of the same and opposite signs. These observed spinnoise gradient echoes (SNGEs) were analyzed through a simple model to describe the effects of transient phenomena. Experiments performed on high-resolution nuclear magnetic resonance (NMR) probes demonstrate how refocused spin noise behaves and how it can be exploited to determine sample properties. In bulk liquids and their mixtures, transverse relaxation times and translational diffusion constants can be determined from SNGE spectra recorded following tailored sequences of magnetic field gradient pulses.

Effects of ethanol and n-butanol on the fluidity of supported lipid bilayers

The interactions of molecules such as short-chain alcohols with the mammalian plasma membrane are thought to play a role in anesthetic effects. We have examined the concentration-dependent effects of ethanol and n-butanol on the fluidity of planar model lipid bilayer structures supported on mica. The supported model bilayer was composed of 1,2-dioleoyl-sn-phosphatidylcholine (DOPC), cholesterol, and sphingomyelin, and the bilayers were formed by vesicle fusion from extruded unilamellar vesicles (133 nm diameter, polydispersity index of 0.17). Controlled amounts of ethanol and n-butanol were added during vesicle deposition. Translational diffusion constants were obtained utilizing fluorescence recovery after photobleaching (FRAP) measurements on the micrometer scale with perylene as the fluorophore. The translational diffusion constants increased and then decreased with increasing ethanol concentration, with the bilayer structure degrading at ca. 0.8 M ethanol. A similar trend was observed for n-butanol at lower alcohol concentrations owing to greater interactions with phospholipid bilayer constituents. For n-butanol, the integrity of the planar bilayer structure deteriorated at ca. 0.4 M n-butanol. The results are consistent with bilayer interdigitation.

Ceramide-mediation of diffusion in supported lipid bilayers

The fluidity and compositional heterogeneity of the mammalian plasma membrane play deterministic roles in a variety of membrane functions. Designing model bilayer systems allows for compositional control over these properties. Ceramide is a phospholipid capable of extensive headgroup-region hydrogen bonding, and we report here on the role of ceramide in planar model bilayers. We use fluorescence recovery after photobleaching (FRAP) to obtain translational diffusion constants of two chromophores in supported model bilayers composed of cholesterol, 1,2-dioleoyl-sn-phosphatidylcholine (DOPC), sphingomyelin, and ceramide. FRAP data for perylene report on the acyl chain region of the model bilayer and FRAP data for 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-(lissamine rhodamine B sulfonyl) sense diffusional dynamics in the bilayer headgroup region. Dynamics in the headgroup region exhibit anomalous diffusion behavior that is characteristic of spatially heterogeneous media.

Dynamic range and background filtering in raster image correlation spectroscopy.

Raster-scan image correlation spectroscopy (RICS) enables researchers to measure molecular translational diffusion constants and concentrations from standard confocal laser scanning microscope images and is suitable for measuring a wide range of mobility, especially fast-diffusing molecules. However, as RICS analysis is based on the spatial autocorrelation function of fluorescence images, it is sensitive to the presence of fluorescent structures within the image. In this study, we investigate methods to filter out immobile or slow moving background structures and their impact on RICS results. Both the conventional moving-average subtraction-based method and cross-correlation subtraction-based method are rationalized and quantified. Simulated data and experimental measurements in living cells stress the importance of optimizing the temporal resolution of background filtering for reliable RICS measurements. Finally, the capacity of RICS analysis to separate two species isstudied.

Diffusive dynamics of elongated particles in active colloidal suspensions of motile algae

Swimming microorganisms can influence the diffusion of passive particles. The effect of this swimmer-particle interaction depends on different properties, such as the hydrodynamic field of the swimmer and the relative sizes of microorganisms and particles. We investigated an enhancement of the diffusion of silica doublets in a suspension of microalgae Chlamydomonas reinhardtii in a flat capillary. Depending on the concentration of microswimmers, the translational and rotational diffusion constants increase by several orders of magnitude in the presence of the swimming algae. For low concentrations of algae, the doublets exhibit Brownian motion in a fluctuating flow field generated by multiple swimmers. One can observe strong, diffusive transport caused by occasional large displacements. At high swimmer concentration, the algae form dense clusters, where the rotational motion of the doublets shows a subdiffusive behaviour while the translational motion remains diffusive.

Diffusion of Polymethylene Chain Molecules in Nonpolar Solvents.

The translational diffusion constants, D, for solutes with polymethylene chains are compared with the predictions of a hydrodynamic bead model based on Kirkwood-Riseman theory. The solute-solvent combinations include (a) n-alkanes in n-alkanes; (b) n-alkanes in benzene, toluene, tetralin, decalin, and CCl4; (c) 1-alkenes in n-alkanes; (d) 1-phenylalkanes in n-alkanes; and (e) 1-phenylalkanes in isocetane (2,2,4,4,6,8,8-heptamethylnonane), pristane (2,6,10,14-tetramethylpentadecane), and squalane (2,6,10,15,19,23-hexamethyltetracosane). The bead model gives good overall agreement with an average difference of less than 3% between 207 experimental and calculated diffusion constants that include published data as well as new D values determined for 1-alkenes and 1-phenylalkanes using capillary flow techniques. The calculated values are obtained using chain element (bead) radii that decrease as the solvent viscosity increases. The bead model's results are comparable to those obtained using cylinder and lollipop diffusion for many of the same solute-solvent systems; the three models are compared and discussed. The results for the 1-alkenes and n-alkanes in the n-alkanes are the first from a Kirkwood-Riseman analysis in a homologous series of solvents.

Raster Image Correlation Spectroscopy Performance Evaluation

Raster image correlation spectroscopy (RICS) is a fluorescence image analysis method for extracting the mobility, concentration, and stoichiometry of diffusing fluorescent molecules from confocal image stacks. The method works by calculating a spatial correlation function for each image and analyzing the average of those by model fitting. Rules of thumb exist for RICS image acquisitioning, yet a rigorous theoretical approach to predict the accuracy and precision of the recovered parameters has been lacking. We outline explicit expressions to reveal the dependence of RICS results on experimental parameters. In terms of imaging settings, we observed that a twofold decrease of the pixel size, e.g., from 100 to 50 nm, decreases the error on the translational diffusion constant (D) between three- and fivefold. For D = 1 μm2 s−1, a typical value for intracellular measurements, ∼25-fold lower mean-squared relative error was obtained when the optimal scan speed was used, although more drastic improvements were observed for other values of D. We proposed a slightly modified RICS calculation that allows correcting for the significant bias of the autocorrelation function at small (≪50 × 50 pixels) sizes of the region of interest. In terms of sample properties, at molecular brightness E = 100 kHz and higher, RICS data quality was sufficient using as little as 20 images, whereas the optimal number of frames for lower E scaled pro rata. RICS data quality was constant over the nM–μM concentration range. We developed a bootstrap-based confidence interval of D that outperformed the classical least-squares approach in terms of coverage probability of the true value of D. We validated the theory via in vitro experiments of enhanced green fluorescent protein at different buffer viscosities. Finally, we outline robust practical guidelines and provide free software to simulate the parameter effects on recovery of the diffusion coefficient.

Kinetics of interaction between antimicrobial peptide nisin and Langmuir monolayers of DPPC and DPPG molecules.

We have studied the kinetics of the interaction between antimicrobial peptide nisin and Langmuir monolayers of phospholipids DPPC and DPPG at the air-water interface using the surface manometry technique. The charge on the nisin and the lipid molecules is controlled by varying the pH of the subphase, and the interactions between them are studied by measuring the surface pressure of the lipid monolayer as a function of time after injecting the nisin in the subphase. A model based on the diffusion of particles under the influence of a constant force is developed to obtain an analytical expression for surface pressure as a function of time. The expression was found to fit well with the experimental data. The average hydrodynamic radius and the translational diffusion constant of the nisin molecules are calculated from the fit parameters for the different subphase pH solutions.

Classification of mobile- and immobile-molecule timescales for the Stokes–Einstein and Stokes–Einstein–Debye relations in supercooled water

Molecular dynamics simulations have been performed on TIP4P/2005 supercooled water to investigate the molecular diffusion and shear viscosity at various timescales and assess the Stokes–Einstein (SE) and Stokes–Einstein–Debye (SED) relations. For this purpose, we calculated various time correlation functions, such as the mean-squared displacement, stress relaxation function, density correlation function, hydrogen-bond correlation function, rotational correlation function of molecular orientation, non-Gaussian parameter, and four-point correlation function. Our study of the SE and SED relations indicates that the transport coefficients and timescales obtained using these time correlation functions may be classified into two distinct classes: those governed by either mobile or immobile molecules, due to dynamical heterogeneity. In particular, we show that the stress relaxation time, hydrogen-bond lifetime, and large-angle rotational relaxation time are coupled with translational diffusion, and are characterized by mobile molecules. In contrast, the structural -relaxation time, small-angle rotational relaxation time, and characteristic timescales of four-point correlation functions are decoupled with translational diffusion, and are governed by immobile molecules. This decoupling results in a violation of the SE relation. These results indicate that the identification of timescales that appropriately characterize transport coefficients, such as translational diffusion constant and shear viscosity, provides a deep insight into the violation of the SE and SED relations in glass-forming liquids.

Spurious violation of the Stokes\u2013Einstein\u2013Debye relation in supercooled water

The theories of Brownian motion, the Debye rotational diffusion model, and hydrodynamics together provide us with the Stokes–Einstein–Debye (SED) relation between the rotational relaxation time of the {boldsymbol{ell }}-th degree Legendre polynomials {{boldsymbol{tau }}}_{{boldsymbol{ell }}}, and viscosity divided by temperature, η/T. Experiments on supercooled liquids are frequently performed to measure the SED relations, {{boldsymbol{tau }}}_{{boldsymbol{ell }}}kBT/η and Dt{{boldsymbol{tau }}}_{{boldsymbol{ell }}}, where Dt is the translational diffusion constant. However, the SED relations break down, and its molecular origin remains elusive. Here, we assess the validity of the SED relations in TIP4P/2005 supercooled water using molecular dynamics simulations. Specifically, we demonstrate that the higher-order {{boldsymbol{tau }}}_{{boldsymbol{ell }}} values exhibit a temperature dependence similar to that of η/T, whereas the lowest-order {{boldsymbol{tau }}}_{{boldsymbol{ell }}} values are decoupled with η/T, but are coupled with the translational diffusion constant Dt. We reveal that the SED relations are so spurious that they significantly depend on the degree of Legendre polynomials.

Diffusion-Limited Cluster Aggregation: Impact of Rotational Diffusion

Diffusion-limited cluster aggregation (DLCA) is a well established model for the formation of highly porous low-density non-equilibrium structures. One of the main conclusions of the previous studies considering this model is that the rotational diffusion of aggregating clusters does not change their structure characterized by a universal fractal dimension of $d_f=1.7-1.8$. In contradiction to this assumption, we demonstrate that the rotation movement of clusters significantly changes the structure of forming aggregates. The fractal dimension of rotating clusters is lower than the one found in the standard DLCA model and decreases with the increasing ratio of rotational and translational diffusion constants $D_r/D_t$, which offers a possibility to tune the structures of the aggregates below the conventional DLCA fractal dimension limit.

Measuring Diffusion Constants of Invisible Protein Conformers by Triple-Quantum 1 H CPMG Relaxation Dispersion.

Proteins are not locked in a single structure but often interconvert with other conformers that are critical for function. When such conformers are sparsely populated and transiently formed they become invisible to routine biophysical methods, however they can be studied in detail by NMR spin-relaxation experiments. Few experiments are available in the NMR toolkit, however, for characterizing the hydrodynamic properties of invisible states. Herein we describe a CPMG-based experiment for measuring translational diffusion constants of invisible states using a pulsed-field gradient approach that exploits methyl 1 H triple-quantum coherences. An example, involving diffusion of a sparsely populated and hence invisible unfolded protein ensemble is presented, without the need for the addition of denaturants that tend to destroy weak interactions that can be involved in stabilizing residual structure in the unfolded state.

Measuring Diffusion Constants of Invisible Protein Conformers by Triple‐Quantum 1H CPMG Relaxation Dispersion

AbstractProteins are not locked in a single structure but often interconvert with other conformers that are critical for function. When such conformers are sparsely populated and transiently formed they become invisible to routine biophysical methods, however they can be studied in detail by NMR spin‐relaxation experiments. Few experiments are available in the NMR toolkit, however, for characterizing the hydrodynamic properties of invisible states. Herein we describe a CPMG‐based experiment for measuring translational diffusion constants of invisible states using a pulsed‐field gradient approach that exploits methyl 1H triple‐quantum coherences. An example, involving diffusion of a sparsely populated and hence invisible unfolded protein ensemble is presented, without the need for the addition of denaturants that tend to destroy weak interactions that can be involved in stabilizing residual structure in the unfolded state.

The influence of polarizability and charge transfer on specific ion effects in the dynamics of aqueous salt solutions.

The diffusion rates for water molecules in salt solutions depend on the identity of the ions, as well as their concentration. Among the alkali metal ions, cesium and potassium increase and sodium strongly decreases the diffusion constant of water. The origin of the difference can be understood by examining the simulation results using different potential models. In this work, aqueous solutions of salts are simulated with a variety of models. Commonly used non-polarizable models, which otherwise reproduce many experimental properties, do not capture the trend in the diffusion constant, while models which include polarization and/or charge transfer interactions do. For the non-polarizable models, the diffusion constant decreases too strongly with salt concentration. The changes in the water diffusion constant with increasing salt concentration match the diffusion constant of the ion. The ion diffusion constant is dependent on the residence time for water in the ion solvation shell. The non-polarizable models over-estimate the residence time, relative to the translational diffusion constant and so tend to under-estimate the ion and water diffusion constants.

Diffusion of Benzene and Alkylbenzenes in Nonpolar Solvents.

The translational diffusion constants, D, of benzene and a series of alkylbenzenes have been determined in n-pentadecane, 2,6,10,14-tetramethylpentadecane (pristane), 2,2,4,4,6,8,8-heptamethylnonane (isocetane), and 2,6,10,15,19,23-hexamethyltetracosane (squalane) using capillary flow techniques. The solutes' D values are compared with the predictions of a cylinder diffusion model as are those for (a) benzene and alkylbenzenes in n-nonane, n-decane, n-dodecane, and supercritical CO2 and (b) n-alkanes and 1-alkenes in n-hexane, n-heptane, n-octane, benzene, and toluene. The D values for benzene and the alkylbenzenes also are compared with the predictions of lollipop diffusion for which the phenyl ring is the candy and the alkyl chain is the handle. Both models give an average difference of less than 4% between experimental and calculated diffusion constants in solvents whose viscosities vary by a factor of more than 600 when benzene and toluene (as solutes) are omitted; the comparisons include 150 and 85 D values for the cylinder and lollipop models, respectively. The differences increase when benzene and toluene are included and are most likely because of their shapes and the shapes assumed by the models. The agreement with the models indicates that the chains of the alkylbenzenes and 1-alkenes, like those of the n-alkanes, are relatively extended. The D values for several of the solutes also are fitted to a modification of the Stokes-Einstein relation that varies their dependence on viscosity instead of chain dimensions.

Identifying time scales for violation/preservation of Stokes-Einstein relation in supercooled water.

The violation of the Stokes-Einstein (SE) relation D ~ (η/T)-1 between the shear viscosity η and the translational diffusion constant D at temperature T is of great importance for characterizing anomalous dynamics of supercooled water. Determining which time scales play key roles in the SE violation remains elusive without the measurement of η. We provide comprehensive simulation results of the dynamic properties involving η and D in the TIP4P/2005 supercooled water. This enabled the thorough identification of the appropriate time scales for the SE relation Dη/T. In particular, it is demonstrated that the temperature dependence of various time scales associated with structural relaxation, hydrogen bond breakage, stress relaxation, and dynamic heterogeneities can be definitely classified into only two classes. That is, we propose the generalized SE relations that exhibit "violation" or "preservation." The classification depends on the examined time scales that are coupled or decoupled with the diffusion. On the basis of the classification, we explain the physical origins of the violation in terms of the increase in the plateau modulus and the nonexponentiality of stress relaxation. This implies that the mechanism of SE violation is attributed to the attained solidity upon supercooling, which is in accord with the growth of non-Gaussianity and spatially heterogeneous dynamics.