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Biophysical Journal May 2019Rebinding kinetics of molecular ligands plays a key role in the operation of biomachinery, from regulatory networks to protein transcription, and is also a key factor in...
Rebinding kinetics of molecular ligands plays a key role in the operation of biomachinery, from regulatory networks to protein transcription, and is also a key factor in design of drugs and high-precision biosensors. In this study, we investigate initial release and rebinding of ligands to their binding sites grafted on a planar surface, a situation commonly observed in single-molecule experiments and that occurs in vivo, e.g., during exocytosis. Via scaling arguments and molecular dynamic simulations, we analyze the dependence of nonequilibrium rebinding kinetics on two intrinsic length scales: the average separation distance between the binding sites and the total diffusible volume (i.e., height of the experimental reservoir in which diffusion takes place or average distance between receptor-bearing surfaces). We obtain time-dependent scaling laws for on rates and for the cumulative number of rebinding events. For diffusion-limited binding, the (rebinding) on rate decreases with time via multiple power-law regimes before the terminal steady-state (constant on-rate) regime. At intermediate times, when particle density has not yet become uniform throughout the diffusible volume, the cumulative number of rebindings exhibits a novel, to our knowledge, plateau behavior because of the three-dimensional escape process of ligands from binding sites. The duration of the plateau regime depends on the average separation distance between binding sites. After the three-dimensional diffusive escape process, a one-dimensional diffusive regime describes on rates. In the reaction-limited scenario, ligands with higher affinity to their binding sites (e.g., longer residence times) delay entry to the power-law regimes. Our results will be useful for extracting hidden timescales in experiments such as kinetic rate measurements for ligand-receptor interactions in microchannels, as well as for cell signaling via diffusing molecules.
Topics: Binding Sites; Diffusion; Kinetics; Ligands; Molecular Dynamics Simulation; Protein Binding; Protein Conformation; Proteins
PubMed: 31029377
DOI: 10.1016/j.bpj.2019.02.033 -
The Journal of Cell Biology May 2023Single-particle tracking microscopy is a powerful technique to investigate how proteins dynamically interact with their environment in live cells. However, the analysis...
Single-particle tracking microscopy is a powerful technique to investigate how proteins dynamically interact with their environment in live cells. However, the analysis of tracks is confounded by noisy molecule localization, short tracks, and rapid transitions between different motion states, notably between immobile and diffusive states. Here, we propose a probabilistic method termed ExTrack that uses the full spatio-temporal information of tracks to extract global model parameters, to calculate state probabilities at every time point, to reveal distributions of state durations, and to refine the positions of bound molecules. ExTrack works for a wide range of diffusion coefficients and transition rates, even if experimental data deviate from model assumptions. We demonstrate its capacity by applying it to slowly diffusing and rapidly transitioning bacterial envelope proteins. ExTrack greatly increases the regime of computationally analyzable noisy single-particle tracks. The ExTrack package is available in ImageJ and Python.
Topics: Bacterial Proteins; Diffusion; Kinetics; Microscopy
PubMed: 36880553
DOI: 10.1083/jcb.202208059 -
The European Respiratory Journal Jul 2022
Topics: Carbon Monoxide; Diffusion; Humans; Pulmonary Diffusing Capacity
PubMed: 35902101
DOI: 10.1183/13993003.00789-2022 -
Medical Physics May 2022The goal of this work is to provide temperature and concentration calibration of water diffusivity in polyvinylpyrrolidone (PVP) solutions used in phantoms to assess...
OBJECTIVE
The goal of this work is to provide temperature and concentration calibration of water diffusivity in polyvinylpyrrolidone (PVP) solutions used in phantoms to assess system bias and linearity in apparent diffusion coefficient (ADC) measurements.
METHOD
ADC measurements were performed for 40 kDa (K40) PVP of six concentrations (0%, 10%, 20%, 30%, 40%, and 50% by weight) at three temperatures (19.5°C, 22.5°C, and 26.4°C), with internal phantom temperature monitored by optical thermometer (±0.2°C). To achieve ADC measurement and fit accuracy of better than 0.5%, three orthogonal diffusion gradients were calibrated using known water diffusivity at 0°C and system gradient nonlinearity maps. Noise-floor fit bias was also controlled by limiting the maximum b-value used for ADC calculation of each sample. The ADC temperature dependence was modeled by Arrhenius functions of each PVP concentration. The concentration dependence was modeled by quadratic function for ADC normalized by the theoretical water diffusion values. Calibration coefficients were obtained from linear regression model fits.
RESULTS
Measured phantom ADC values increased with temperature and decreasing PVP concentration, [PVP]. The derived Arrhenius model parameters for [PVP] between 0% and 50%, are reported and can be used for K40 ADC temperature calibration with absolute ADC error within ±0.016 μm /ms. Arrhenius model fit parameters normalized to water value scaled with [PVP] between 10% and 40%, and proportional change in activation energy increased faster than collision frequency. ADC normalization by water diffusivity, D , from the Speedy-Angell relation accounted for the bulk of temperature dependence (±0.035 μm /ms) and yielded quadratic calibration for ADC /D = (12.5 ± 0.7) ·10 ·[PVP] - (23.2 ± 0.3)·10 ·[PVP]+1, nearly independent of PVP molecular weight and temperature.
CONCLUSION
The study provides ground-truth ADC values for K40 PVP solutions commonly used in diffusion phantoms for scanning at ambient room temperature. The described procedures and the reported calibration can be used for quality control and standardization of measured ADC values of PVP at different concentrations and temperatures.
Topics: Diffusion; Diffusion Magnetic Resonance Imaging; Phantoms, Imaging; Povidone; Temperature; Water
PubMed: 35184316
DOI: 10.1002/mp.15556 -
Journal of Theoretical Biology Jan 2021A new method to derive an essential integral kernel from any given reaction-diffusion network is proposed. Any network describing metabolites or signals with arbitrary...
A new method to derive an essential integral kernel from any given reaction-diffusion network is proposed. Any network describing metabolites or signals with arbitrary many factors can be reduced to a single or a simpler system of integro-differential equations called "effective equation" including the reduced integral kernel (called "effective kernel") in the convolution type. As one typical example, the Mexican hat shaped kernel is theoretically derived from two component activator-inhibitor systems. It is also shown that a three component system with quite different appearance from activator-inhibitor systems is reduced to an effective equation with the Mexican hat shaped kernel. It means that the two different systems have essentially the same effective equations and that they exhibit essentially the same spatial and temporal patterns. Thus, we can identify two different systems with the understanding in unified concept through the reduced effective kernels. Other two applications of this method are also given: Applications to pigment patterns on skins (two factors network with long range interaction) and waves of differentiation (called proneural waves) in visual systems on brains (four factors network with long range interaction). In the applications, we observe the reproduction of the same spatial and temporal patterns as those appearing in pre-existing models through the numerical simulations of the effective equations.
Topics: Computer Simulation; Diffusion; Models, Biological
PubMed: 33007272
DOI: 10.1016/j.jtbi.2020.110496 -
Journal of the Royal Society, Interface Dec 2021Diffusion of water into plant materials is known to decrease their mechanical strength and stiffness but improve formability. Here, we characterize water diffusion...
Diffusion of water into plant materials is known to decrease their mechanical strength and stiffness but improve formability. Here, we characterize water diffusion through areca palm leaf-sheath-a model plant material, with hierarchical structure, used in eco-friendly foodware. The diffusion process is studied using mass gain measurements and imaging of water transport. By treating the areca sheath as homogeneous ensemble, and incorporating effects of material swelling due- to water absorption, a factor typically neglected in prior studies, the diffusion coefficient for water is estimated as (6.5 ± 2.2) × 10 mm s. It is shown that neglecting the swelling results in gross underestimation of . Microstructural effects (e.g. fibre, matrix) on the diffusion are characterized using imaging of the water transport at high resolution. The observations show that the water diffuses an order of magnitude faster in the matrix (8.63 × 10 mm s) than in the fibres (7.19 × 10 mm s). This non-uniformity is also reflected in the swelling-induced strain in the leaf, mapped by image correlation. Lastly, we vary salt concentration by controlled additions of NaCl and note a non-monotonic dependence of the diffusion on concentration. Implications of the results for improving foodware manufacturing processes and product life are discussed.
Topics: Biological Transport; Diffusion; Plant Leaves; Sodium Chloride; Water
PubMed: 34847794
DOI: 10.1098/rsif.2021.0483 -
Biochimica Et Biophysica Acta.... Oct 2018We compare the way that relationships for diffusion constants scale with the size of diffusing membrane domains and the geometry of their environments. Then, we review... (Review)
Review
We compare the way that relationships for diffusion constants scale with the size of diffusing membrane domains and the geometry of their environments. Then, we review our experimental work on the dynamics of dissolution/growth of membrane domains in crowding induced mixing, phase separation, and Ostwald ripening in a highly confined environment. Overall, the scaling relationships applied to diffusion constants obtained by fits to our dynamic data indicate that dissolution and growth is influenced by the diffusion of clusters or small domains of lipids, in addition to kinetic processes and geometrical constraints.
Topics: Diffusion; Lipids; Membranes; Models, Biological; Solubility
PubMed: 29501605
DOI: 10.1016/j.bbamem.2018.02.028 -
Journal of the Royal Society, Interface Mar 2022Patterns in nature are fascinating both aesthetically and scientifically. Alan Turing's celebrated reaction-diffusion model of pattern formation from the 1950s has been...
Patterns in nature are fascinating both aesthetically and scientifically. Alan Turing's celebrated reaction-diffusion model of pattern formation from the 1950s has been extended to an astounding diversity of applications: from cancer medicine, via nanoparticle fabrication, to computer architecture. Recently, several authors have studied pattern formation in underlying networks, but thus far, controlling a reaction-diffusion system in a network to obtain a particular pattern has remained elusive. We present a solution to this problem in the form of an analytical framework and numerical algorithm for optimal control of Turing patterns in networks. We demonstrate our method's effectiveness and discuss factors that affect its performance. We also pave the way for multidisciplinary applications of our framework beyond reaction-diffusion models.
Topics: Algorithms; Diffusion; Models, Biological
PubMed: 35259961
DOI: 10.1098/rsif.2021.0739 -
Proceedings of the National Academy of... Mar 2020Protein mobility at solid-liquid interfaces can affect the performance of applications such as bioseparations and biosensors by facilitating reorganization of adsorbed...
Protein mobility at solid-liquid interfaces can affect the performance of applications such as bioseparations and biosensors by facilitating reorganization of adsorbed protein, accelerating molecular recognition, and informing the fundamentals of adsorption. In the case of ion-exchange chromatographic beads with small, tortuous pores, where the existence of surface diffusion is often not recognized, slow mass transfer can result in lower resin capacity utilization. We demonstrate that accounting for and exploiting protein surface diffusion can alleviate the mass-transfer limitations on multiple significant length scales. Although the surface diffusivity has previously been shown to correlate with ionic strength (IS) and binding affinity, we show that the dependence is solely on the binding affinity, irrespective of pH, IS, and resin ligand density. Different surface diffusivities give rise to different protein distributions within the resin, as characterized using confocal microscopy and small-angle neutron scattering (length scales of micrometer and nanometer, respectively). The binding dependence of surface diffusion inspired a protein-loading approach in which the binding affinity, and hence the surface diffusivity, is modulated by varying IS. Such gradient loading increased the protein uptake efficiency by up to 43%, corroborating the importance of protein surface diffusion in protein transport in ion-exchange chromatography.
Topics: Diffusion; Ion Exchange Resins; Models, Chemical; Proteins
PubMed: 32179691
DOI: 10.1073/pnas.1921499117 -
Magnetic Resonance in Medicine Nov 2022While diffusion and T relaxation are intertwined, little or no correlation exists between diffusion and T relaxation of intracellular metabolites in the rodent brain, as...
PURPOSE
While diffusion and T relaxation are intertwined, little or no correlation exists between diffusion and T relaxation of intracellular metabolites in the rodent brain, as measured by diffusion-weighted MRS at different TEs. However, situation might be different for lactate, since it is present in both extracellular and intracellular spaces, which exhibit different diffusion properties and may also exhibit different T . Such a TE dependence would be crucial to account for when interpreting or modeling lactate diffusion. Here we propose to take advantage of a new diffusion sequence, where J-modulation of lactate is canceled even at long TE, thus retaining excellent signal, to assess potential T dependence on diffusion of lactate in the mouse brain.
METHODS
Using a frequency-selective diffusion-weighted spin-echo sequence that removes J-modulation at 1.3 ppm, thus preserving lactate signal even at long TE, we investigate the effect of TE between 50.9 and 110.9 ms (while keeping diffusion time constant) on apparent diffusivity and kurtosis in the mouse brain.
RESULTS
Regardless of the metabolites, no difference appears for the diffusion-weighted signal attenuation with increasing TE. For lactate, apparent diffusivity and kurtosis remain unchanged as TE increases.
CONCLUSION
No significant TE dependence of diffusivity and kurtosis is measured for lactate in the 50-110 ms TE range, confirming that potential T effects can be ignored when interpreting or modeling lactate diffusion.
Topics: Animals; Brain; Diffusion; Diffusion Magnetic Resonance Imaging; Lactic Acid; Mice
PubMed: 35906915
DOI: 10.1002/mrm.29395