-
Nature Communications Oct 2018Most biochemical reactions in living cells rely on diffusive search for target molecules or regions in a heterogeneous overcrowded cytoplasmic medium. Rapid...
Most biochemical reactions in living cells rely on diffusive search for target molecules or regions in a heterogeneous overcrowded cytoplasmic medium. Rapid rearrangements of the medium constantly change the effective diffusivity felt locally by a diffusing particle and thus impact the distribution of the first-passage time to a reaction event. Here, we investigate the effect of these dynamic spatiotemporal heterogeneities onto diffusion-limited reactions. We describe a general mathematical framework to translate many results for ordinary homogeneous Brownian motion to heterogeneous diffusion. In particular, we derive the probability density of the first-passage time to a reaction event and show how the dynamic disorder broadens the distribution and increases the likelihood of both short and long trajectories to reactive targets. While the disorder slows down reaction kinetics on average, its dynamic character is beneficial for a faster search and realization of an individual reaction event triggered by a single molecule.
Topics: Diffusion; Models, Theoretical; Time Factors
PubMed: 30353010
DOI: 10.1038/s41467-018-06610-6 -
Biophysical Journal Oct 2021Erk signaling regulates cellular decisions in many biological contexts. Recently, we have reported a series of Erk activity traveling waves that coordinate regeneration...
Erk signaling regulates cellular decisions in many biological contexts. Recently, we have reported a series of Erk activity traveling waves that coordinate regeneration of osteoblast tissue in zebrafish scales. These waves originate from a central source region, propagate as expanding rings, and impart cell growth, thus controlling tissue morphogenesis. Here, we present a minimal reaction-diffusion model for Erk activity waves. The model considers three components: Erk, a diffusible Erk activator, and an Erk inhibitor. Erk stimulates both its activator and inhibitor, forming a positive and negative feedback loop, respectively. Our model shows that this system can be excitable and propagate Erk activity waves. Waves originate from a pulsatile source that is modeled by adding a localized basal production of the activator, which turns the source region from an excitable to an oscillatory state. As Erk activity periodically rises in the source, it can trigger an excitable wave that travels across the entire tissue. Analysis of the model finds that positive feedback controls the properties of the traveling wavefront and that negative feedback controls the duration of Erk activity peak and the period of Erk activity waves. The geometrical properties of the waves facilitate constraints on the effective diffusivity of the activator, indicating that waves are an efficient mechanism to transfer growth factor signaling rapidly across a large tissue.
Topics: Animals; Diffusion; Models, Theoretical; Osteoblasts; Signal Transduction; Zebrafish
PubMed: 34022234
DOI: 10.1016/j.bpj.2021.05.004 -
Biophysical Journal Sep 2021Antibody-based therapeutics are the fastest-growing drug class on the market, used to treat aggressive forms of cancer, chronic autoimmune conditions, and numerous other...
Antibody-based therapeutics are the fastest-growing drug class on the market, used to treat aggressive forms of cancer, chronic autoimmune conditions, and numerous other disease states. Although the specificity, affinity, and versatility of therapeutic antibodies can provide an advantage over traditional small-molecule drugs, their development and optimization can be much more challenging and time-consuming. This is, in part, because the ideal formulation buffer systems used for in vitro characterization inadequately reflect the crowded biological environments (serum, endosomal lumen, etc.) that these drugs experience once administered to a patient. Such environments can perturb the binding of antibodies to their antigens and receptors, as well as homo- and hetero-aggregation, thereby altering therapeutic effect and disposition in ways that are incompletely understood. Although excluded volume effects are classically thought to favor binding, weak interactions with co-solutes in crowded conditions can inhibit binding. The second virial coefficient (B) parameter quantifies such weak interactions and can be determined by a variety of techniques in dilute solution, but analogous methods in complex biological fluids are not well established. Here, we demonstrate that fluorescence correlation spectroscopy is able to measure diffusive B-values directly in undiluted serum. Apparent second virial coefficient (B) measurements of antibodies in serum reveal that changes in the balance between attractive and repulsive interactions can dramatically impact global nonideality. Furthermore, our findings suggest that the approach of isolating specific components and completing independent cross-term virial coefficient measurements may not be an effective approach to characterizing nonideality in serum. The approach presented here could enrich our understanding of the effects of biological environments on proteins in general and advance the development of therapeutic antibodies and other protein-based therapeutics.
Topics: Diffusion; Humans; Proteins; Solutions
PubMed: 34384764
DOI: 10.1016/j.bpj.2021.08.007 -
Biophysical Journal Jun 2023Previous studies have documented the formation of a heterodimer between the two protein kinases PDK1 and PKCα on a lipid bilayer containing their target lipids. This...
Previous studies have documented the formation of a heterodimer between the two protein kinases PDK1 and PKCα on a lipid bilayer containing their target lipids. This work investigates the association-dissociation kinetics of this PDK1:PKCα heterodimer. The approach monitors the two-dimensional diffusion of single, membrane-associated PDK1 molecules for diffusivity changes as PKCα molecules bind and unbind. In the absence of PKCα, a membrane-associated PDK1 molecule exhibits high diffusivity (or large diffusion constant, D) because its membrane-contacting PH domain binds the target PIP lipid headgroup with little bilayer penetration, yielding minimal frictional drag against the bilayer. In contrast, membrane-associated PKCα contacts the bilayer via its C1A, C1B, and C2 domains, which each bind at least one target lipid with significant bilayer insertion, yielding a large frictional drag and low diffusivity. The present findings reveal that individual fluor-PDK1 molecules freely diffusing on the membrane surface undergo reversible switching between distinct high and low diffusivity states, corresponding to the PDK1 monomer and the PDK1:PKCα heterodimer, respectively. The observed single-molecule diffusion trajectories are converted to step length time courses, then subjected to two-state, hidden Markov modeling and dwell time analysis. The findings reveal that both the PDK1 monomer state and the PDK1:PKCα heterodimer state decay via simple exponential kinetics, yielding estimates of rate constants for state switching in both directions. Notably, the PDK1:PKCα heterodimer has been shown to competitively inhibit PDK1 phosphoactivation of AKT1, and is believed to play a tumor suppressor role by limiting excess activation of the highly oncogenic PDK1/AKT1/mTOR pathway. Thus, the present elucidation of the PDK1:PKCα association-dissociation kinetics has important biological and medical implications. More broadly, the findings illustrate the power of single-molecule diffusion measurements to reveal the kinetics of association-dissociation events in membrane signaling reactions that yield a large change in diffusive mobility.
Topics: Protein Kinase C-alpha; Lipid Bilayers; Signal Transduction; Protein Binding; Diffusion
PubMed: 36733254
DOI: 10.1016/j.bpj.2023.01.041 -
Proceedings of the National Academy of... Jun 2007Past work has shown that ions can pass through a membrane more readily in one direction than the other. We demonstrate here in a model and an experiment that for a... (Comparative Study)
Comparative Study
Past work has shown that ions can pass through a membrane more readily in one direction than the other. We demonstrate here in a model and an experiment that for a mixture of small and large particles such asymmetric diffusion can arise solely from an asymmetry in the geometry of the pores of the membrane. Our deterministic simulation considers a two-dimensional gas of elastic disks of two sizes diffusing through a membrane, and our laboratory experiment examines the diffusion of glass beads of two sizes through a metal membrane. In both experiment and simulation, the membrane is permeable only to the smaller particles, and the asymmetric pores lead to an asymmetry in the diffusion rates of these particles. The presence of even a small percentage of large particles can clog a membrane, preventing passage of the small particles in one direction while permitting free flow of the small particles in the other direction. The purely geometric kinetic constraints may play a role in common biological contexts such as membrane ion channels.
Topics: Computer Simulation; Diffusion; Kinetics; Membranes, Artificial; Models, Theoretical; Permeability
PubMed: 17522257
DOI: 10.1073/pnas.0703280104 -
Nano Letters Mar 2023Using single-molecule displacement/diffusivity mapping (SMM), an emerging super-resolution microscopy method, here we quantify, at nanoscale resolution, the diffusion of...
Using single-molecule displacement/diffusivity mapping (SMM), an emerging super-resolution microscopy method, here we quantify, at nanoscale resolution, the diffusion of a typical fluorescent protein (FP) in the endoplasmic reticulum (ER) and mitochondrion of living mammalian cells. We thus show that the diffusion coefficients in both organelles are ∼40% of that in the cytoplasm, with the latter exhibiting higher spatial inhomogeneities. Moreover, we unveil that diffusions in the ER lumen and the mitochondrial matrix are markedly impeded when the FP is given positive, but not negative, net charges. Calculation shows most intraorganellar proteins as negatively charged, hence a mechanism to impede the diffusion of positively charged proteins. However, we further identify the ER protein PPIB as an exception with a positive net charge and experimentally show that the removal of this positive charge elevates its intra-ER diffusivity. We thus unveil a sign-asymmetric protein charge effect on the nanoscale intraorganellar diffusion.
Topics: Animals; Proteins; Endoplasmic Reticulum; Diffusion; Mitochondria; Nanotechnology; Mammals
PubMed: 36802676
DOI: 10.1021/acs.nanolett.2c04379 -
Bone Nov 2009Solute transport through the bone lacunar-canalicular system (LCS) is essential for osteocyte survival and function, but quantitative data on the diffusivity of various...
Solute transport through the bone lacunar-canalicular system (LCS) is essential for osteocyte survival and function, but quantitative data on the diffusivity of various biological molecules in the LCS are scarce. Using our recently developed approach based on fluorescence recovery after photobleaching (FRAP), diffusion coefficients of five exogenous fluorescent tracers (sodium fluorescein, dextran-3k, dextran-10k, parvalbumin, and ovalbumin) were measured in murine tibiae in situ. These tracers were chosen to test the dependency of solute diffusion on molecular weight (376-43,000 Da) and shape (linear vs. globular). Among the five tracers, no fluorescence recovery (and thus mobility) was detected for dextran-10k and the diffusion coefficients (D(LCS)) of the other four tracers were 295+/-46, 128+/-32, 157+/-88, 65+/-21 microm(2) s(-1) in the LCS, respectively. Overall, the rate of solute diffusion in the bone LCS showed strong dependency on molecular size and shape. Diffusivity decreased with increasing molecular weight for both linear and globular molecules, with the linear molecules decreasing at a faster rate. Compared with free diffusion (D(free)) in aqueous solutions, the relative diffusivities (D(LCS)/D(free)) of the four tracers were not significantly different for sodium fluorescein, dextran-3k, parvalbumin, and ovalbumin (55.0+/-8.6%, 68.1+/-17.0%, 79.7+/-44.7%, 61.0+/-19.6%, respectively). This result did not agree with the homogenous molecular sieve model proposed for the osteocytic pericellular matrix structure. Instead, a heterogeneous porous model of the pericellular matrix may account for the observed solute transport in the LCS. In summary, the present study provides quantitative data on diffusion of various nutrients and signaling molecules in the LCS that are important for bone metabolism and mechanotransduction.
Topics: Animals; Bone and Bones; Diffusion; Fluorescence Recovery After Photobleaching; Mice; Mice, Inbred C57BL; Molecular Weight
PubMed: 19647808
DOI: 10.1016/j.bone.2009.07.076 -
Self-mixing in microtubule-kinesin active fluid from nonuniform to uniform distribution of activity.Nature Communications Nov 2022Active fluids have applications in micromixing, but little is known about the mixing kinematics of systems with spatiotemporally-varying activity. To investigate,...
Active fluids have applications in micromixing, but little is known about the mixing kinematics of systems with spatiotemporally-varying activity. To investigate, UV-activated caged ATP is used to activate controlled regions of microtubule-kinesin active fluid and the mixing process is observed with fluorescent tracers and molecular dyes. At low Péclet numbers (diffusive transport), the active-inactive interface progresses toward the inactive area in a diffusion-like manner that is described by a simple model combining diffusion with Michaelis-Menten kinetics. At high Péclet numbers (convective transport), the active-inactive interface progresses in a superdiffusion-like manner that is qualitatively captured by an active-fluid hydrodynamic model coupled to ATP transport. Results show that active fluid mixing involves complex coupling between distribution of active stress and active transport of ATP and reduces mixing time for suspended components with decreased impact of initial component distribution. This work will inform application of active fluids to promote micromixing in microfluidic devices.
Topics: Kinesins; Microtubules; Kinetics; Diffusion; Adenosine Triphosphate; Coloring Agents
PubMed: 36323696
DOI: 10.1038/s41467-022-34396-1 -
Cell Reports Apr 2017Previous autonomous pattern-formation models often assumed complex molecular and cellular networks. This theoretical study, however, shows that a system composed of one...
Previous autonomous pattern-formation models often assumed complex molecular and cellular networks. This theoretical study, however, shows that a system composed of one substrate with multisite phosphorylation and a pair of kinase and phosphatase can generate autonomous spatial information, including complex stripe patterns. All (de-)phosphorylation reactions are described with a generic Michaelis-Menten scheme, and all species freely diffuse without pre-existing gradients. Computational simulation upon >23,000,000 randomly generated parameter sets revealed the design motifs of cyclic reaction and enzyme sequestration by slow-diffusing substrates. These motifs constitute short-range positive and long-range negative feedback loops to induce Turing instability. The width and height of spatial patterns can be controlled independently by distinct reaction-diffusion processes. Therefore, multisite reversible post-translational modification can be a ubiquitous source for various patterns without requiring other complex regulations such as autocatalytic regulation of enzymes and is applicable to molecular mechanisms for inducing subcellular localization of proteins driven by post-translational modifications.
Topics: Diffusion; Enzymes; Kinesics; Models, Biological; Protein Processing, Post-Translational
PubMed: 28445735
DOI: 10.1016/j.celrep.2017.03.081 -
Biophysical Journal Mar 2019Using fluorescence correlation spectroscopy (FCS) to distinguish between different types of diffusion processes is often a perilous undertaking because the analysis of...
Using fluorescence correlation spectroscopy (FCS) to distinguish between different types of diffusion processes is often a perilous undertaking because the analysis of the resulting autocorrelation data is model dependant. Two recently introduced strategies, however, can help move toward a model-independent interpretation of FCS experiments: 1) the obtention of correlation data at different length scales and 2) their inversion to retrieve the mean-squared displacement associated with the process under study. We use computer simulations to examine the signature of several biologically relevant diffusion processes (simple diffusion, continuous-time random walk, caged diffusion, obstructed diffusion, two-state diffusion, and diffusing diffusivity) in variable-length-scale FCS. We show that, when used in concert, length-scale variation and data inversion permit us to identify non-Gaussian processes and, regardless of Gaussianity, to retrieve their mean-squared displacement over several orders of magnitude in time. This makes unbiased discrimination between different classes of diffusion models possible.
Topics: Diffusion; Models, Theoretical; Spectrometry, Fluorescence
PubMed: 30782396
DOI: 10.1016/j.bpj.2019.01.024