Diffusion Of Proteins Research Articles

Composite Numerical Methods and Scalable Tile Algorithms

Numerical modeling is an important tool when studying various natural processes and phenomena. Fractional diffusion can be used for modeling many processes in biology, for example in silico experiments in molecular biology and medicine design, protein diffusion within cells, complex media geometry, etc. The problem is usually reduced to a system of linear algebraic equations and in many cases this system has a dense coefficient matrix. Numerically solving such problems with the traditional LU factorization is a computationally expensive endeavour - $O(n^3)$. In this paper we explore the use of a hierarchical compression method based on Hierarchical Semi-Separable compression and ULV-like factorization from the STRUctured Matrices PACKage (STRUMPACK) software library for a flow around airfoils problem discretized with Boundary Element Method and fractional diffusion problem discretized with the Finite Element Method. The HSS based method promises better overall computational complexity of $O(r^2n)$ for problems with suitable structure - low rank off-diagonal blocks. Here $r$ is the maximum rank of the off-diagonal blocks. We present analysis of the performance and accuracy of the HSS based method and compare it with the state of the art direct LU factorization solvers. This paper is based on the PhD thesis Composite Numerical Methods and Scalable Tile Algorithms of the author defended on 17.05.2022 in the Institute of Information and Communication Technologies at the Bulgarian Academy of Sciences.

Anther development in Arabidopsis thaliana involves symplastic isolation and apoplastic gating of the tapetum-middle layer interface.

During flowering plant reproduction, anthers produce pollen grains, the development of which is supported by the tapetum, a nourishing maternal tissue that also contributes non-cell-autonomously to the pollen wall, the resistant external layer on the pollen surface. How the anther restricts movement of the tapetum-derived pollen wall components, while allowing metabolites such as sugars and amino acids to reach the developing pollen, remains unknown. Here, we show experimentally that in arabidopsis thaliana the tapetum and developing pollen are symplastically isolated from each other, and from other sporophytic tissues, from meiosis onwards. We show that the peritapetal strip, an apoplastic structure, separates the tapetum and the pollen grains from other anther cell layers and can prevent the apoplastic diffusion of fluorescent proteins, again from meiosis onwards. The formation and selective barrier functions of the peritapetal strip require two NADPH oxidases, RBOHE and RBOHC, which play a key role in pollen formation. Our results suggest that, together with symplastic isolation, gating of the apoplast around the tapetum may help generate metabolically distinct anther compartments.

Transport between im/mobile fractions shapes the speed and profile of cargo distribution in neurons

Neuronal function requires continuous distribution of ion channels and other proteins throughout large cell morphologies. Protein distribution is complicated by immobilization of freely diffusing subunits such as on lipid rafts or in postsynaptic densities. Here, we infer rates of immobilization for the voltage-gated potassium channel Kv4.2. Fluorescence recovery after photobleaching quantifies protein diffusion kinetics, typically reported as a recovery rate and mobile fraction. We show that, implicit in the fluorescence recovery, are rates of particle transfer between mobile and immobile fractions (im/mobilization). We performed photobleaching of fluorescein-tagged ion channel Kv4.2-sGFP2 in over 450 dendrites of rat hippocampal cells. Using mass-action models, we infer rates of Kv4.2-sGFP2 im/mobilization. Using a realistic neuron morphology, we show how these rates shape the speed and profile of subunit distribution. The experimental protocol and model inference introduced here is widely applicable to other cargo and experimental systems.

"Shutter" Effects Enhance Protein Diffusion in Dynamic and Rigid Molecular Networks.

Hydrogels have been widely applied to understand the fundamental functions and mechanism of a natural extracellular matrix (ECM). However, revealing the high permeability of ECM through synthetic hydrogels is still challenged by constructing analogue networks with rigid and dynamic properties. Here, in this study, taking advantage of the rigidity and dynamic binding of DNA building blocks, we have designed a model hydrogel system with structural similarity to ECM, leading to enhanced diffusion for proteins compared with a synthetic polyacrylamide (PAAm) hydrogel. The molecular diffusion behaviors in such a rigid and dynamic network have been investigated both in experiments and simulations, and the dependence of diffusion coefficients with respect to molecular size exhibits a unique transition from a power law to an exponential function. A "shutter" model based on the rigid and dynamic molecular network has been proposed, which has successfully revealed how the rigidity and dynamic bond exchange determine the diffusion mechanism, potentially providing a novel perspective to understand the possible mechanism of enhanced diffusion behaviors in ECM.

Docking-based long timescale simulation of cell-size protein systems at atomic resolution

Computational methodologies are increasingly addressing modeling of the whole cell at the molecular level. Proteins and their interactions are the key component of cellular processes. Techniques for modeling protein interactions, thus far, have included protein docking and molecular simulation. The latter approaches account for the dynamics of the interactions but are relatively slow, if carried out at all-atom resolution, or are significantly coarse grained. Protein docking algorithms are far more efficient in sampling spatial coordinates. However, they do not account for the kinetics of the association (i.e., they do not involve the time coordinate). Our proof-of-concept study bridges the two modeling approaches, developing an approach that can reach unprecedented simulation timescales at all-atom resolution. The global intermolecular energy landscape of a large system of proteins was mapped by the pairwise fast Fourier transform docking and sampled in space and time by Monte Carlo simulations. The simulation protocol was parametrized on existing data and validated on a number of observations from experiments and molecular dynamics simulations. The simulation protocol performed consistently across very different systems of proteins at different protein concentrations. It recapitulated data on the previously observed protein diffusion rates and aggregation. The speed of calculation allows reaching second-long trajectories of protein systems that approach the size of the cells, at atomic resolution.

Locally correlated kinetics of post-replication DNA methylation reveals processivity and region specificity in DNA methylation maintenance.

DNA methylation occurs predominantly on cytosine-phosphate-guanine (CpG) dinucleotides in the mammalian genome, and the methylation landscape is maintained over mitotic cell division. It has been posited that coupling of maintenance methylation activity among neighbouring CpGs is critical to stability over cellular generations; however, the mechanism is unclear. We used mathematical models and stochastic simulation to analyse data from experiments that probe genome-wide methylation of nascent DNA post-replication in cells. We find that DNA methylation maintenance rates on individual CpGs are locally correlated, and the degree of this correlation varies by genomic regional context. By using theory of protein diffusion along DNA, we show that exponential decay of methylation rate correlation with genomic distance is consistent with enzyme processivity. Our results provide quantitative evidence of genome-wide methyltransferase processivity in vivo. We further developed a method to disentangle different mechanistic sources of kinetic correlations. From the experimental data, we estimate that an individual methyltransferase methylates neighbour CpGs processively if they are 36 basepairs apart, on average. But other mechanisms of coupling dominate for longer inter-CpG distances. Our study demonstrates that quantitative insights into enzymatic mechanisms can be obtained from replication-associated, cell-based genome-wide measurements, by combining data-driven statistical analyses with hypothesis-driven mathematical modelling.

Cytoplasmic organization promotes protein diffusion in Xenopus extracts

The cytoplasm is highly organized. However, the extent to which this organization influences the dynamics of cytoplasmic proteins is not well understood. Here, we use Xenopus laevis egg extracts as a model system to study diffusion dynamics in organized versus disorganized cytoplasm. Such extracts are initially homogenized and disorganized, and self-organize into cell-like units over the course of tens of minutes. Using fluorescence correlation spectroscopy, we observe that as the cytoplasm organizes, protein diffusion speeds up by about a factor of two over a length scale of a few hundred nanometers, eventually approaching the diffusion time measured in organelle-depleted cytosol. Even though the ordered cytoplasm contained organelles and cytoskeletal elements that might interfere with diffusion, the convergence of protein diffusion in the cytoplasm toward that in organelle-depleted cytosol suggests that subcellular organization maximizes protein diffusivity. The effect of organization on diffusion varies with molecular size, with the effects being largest for protein-sized molecules, and with the time scale of the measurement. These results show that cytoplasmic organization promotes the efficient diffusion of protein molecules in a densely packed environment.

Protein adsorption on core-shell resins for flow-through purifications: Effect of protein molecular size, shape, and salt concentration.

This work addresses the functional properties of the core-shell resins Capto Core 400 and 700 for a broad range of proteins spanning 66.5 to 660 kDa in molecular mass, including bovine serum albumin (BSA) in monomer and dimer form, fibronectin, thyroglobulin, and BSA conjugates with 10 and 30 kDa poly(ethylene glycol) chains. Negatively charged latex nanoparticles (NPs) with nominal diameters of 20, 40, and 100 nm are also studied as surrogates for bioparticles. Protein binding and its trends with respect to salt concentration depend on the protein size and are different for the two agarose-based multimodal resins. For the smaller proteins, the amount of protein bound over practical time scales is limited by the resin surface area and is larger for Capto Core 400 compared with Capto Core 700. For the larger proteins, diffusion is severely restricted in Capto Core 400, resulting in lower binding capacities than those observed for Capto Core 700 despite the larger surface area. Adding 500 mM NaCl reduces the local bound protein concentration and diffusional hindrance resulting in higher binding capacities for the large proteins in Capto Core 400 compared with low ionic strength conditions. The NPs are essentially completely excluded from the Capto Core 400 pores. However, 20 and 40 nm NPs bind significantly to Capto Core 700, further hindering protein diffusion. A model is provided to predict the dynamic binding capacities as a function of residence time.

Resolving molecular diffusion and aggregation of antibody proteins with megahertz X-ray free-electron laser pulses

X-ray free-electron lasers (XFELs) with megahertz repetition rate can provide novel insights into structural dynamics of biological macromolecule solutions. However, very high dose rates can lead to beam-induced dynamics and structural changes due to radiation damage. Here, we probe the dynamics of dense antibody protein (Ig-PEG) solutions using megahertz X-ray photon correlation spectroscopy (MHz-XPCS) at the European XFEL. By varying the total dose and dose rate, we identify a regime for measuring the motion of proteins in their first coordination shell, quantify XFEL-induced effects such as driven motion, and map out the extent of agglomeration dynamics. The results indicate that for average dose rates below 1.06 kGy μs−1 in a time window up to 10 μs, it is possible to capture the protein dynamics before the onset of beam induced aggregation. We refer to this approach as correlation before aggregation and demonstrate that MHz-XPCS bridges an important spatio-temporal gap in measurement techniques for biological samples.

Global pore blockage - cake filtration model including pressure effects on protein fouling in virus filtration

Virus removal filtration is a key step in the manufacture of monoclonal antibodies and serum-derived products. There is significant interest in developing continuous biomanufacturing processes for these products, requiring operation at much lower operating pressures/fluxes than those used in batch operations. The objective of this study was to examine the effect of low operating transmembrane pressure (TMP between 0.2 and 5 psi) on the fouling rate and fouling mechanisms during filtration of human serum Immunoglobulin G (hIgG) through the Viresolve® Pro membrane. At equal throughput, the extent of flux decline increased with increasing pressure, with the greatest flux decline observed at TMP ≈ 5 psi, before decreasing at higher pressures. A flux decline model based on fouling by intermediate pore blockage followed by cake formation was developed and shown to be in good agreement with the experimental data. The data at low pressures were combined with previously published results at high TMP (10–60 psi) to develop a global fouling model that was valid at all TMP. The rate of pore blockage decreased with increasing TMP, whereas the cake filtration parameter increased with increasing TMP, with the latter likely reflecting the compressibility of the fouling deposit. The observed transition between intermediate and complete pore blocking occurred around a Péclet number equal to one, corresponding to TMP between 5 and 10 psi, suggesting the importance of protein diffusion on membrane fouling. These results provide important insights into the effects of pressure on both the rate and mechanisms controlling protein fouling during virus removal filtration.

Viscosity and macromolecular crowding in the mitochondrial matrix: Impact on protein diffusion and structure

Viscosity and macromolecular crowding in the mitochondrial matrix: Impact on protein diffusion and structure

Effect of Protein–Protein Interactions on Translational Diffusion of Spheroidal Proteins

One of the commonly accepted approaches to estimate protein–protein interactions (PPI) in aqueous solutions is the analysis of their translational diffusion. The present review article observes a phenomenological approach to analyze PPI effects via concentration dependencies of self- and collective translational diffusion coefficient for several spheroidal proteins derived from the pulsed field gradient NMR (PFG NMR) and dynamic light scattering (DLS), respectively. These proteins are rigid globular α-chymotrypsin (ChTr) and human serum albumin (HSA), and partly disordered α-casein (α-CN) and β-lactoglobulin (β-Lg). The PPI analysis enabled us to reveal the dominance of intermolecular repulsion at low ionic strength of solution (0.003–0.01 M) for all studied proteins. The increase in the ionic strength to 0.1–1.0 M leads to the screening of protein charges, resulting in the decrease of the protein electrostatic potential. The increase of the van der Waals potential for ChTr and α-CN characterizes their propensity towards unstable weak attractive interactions. The decrease of van der Waals interactions for β-Lg is probably associated with the formation of stable oligomers by this protein. The PPI, estimated with the help of interaction potential and idealized spherical molecular geometry, are in good agreement with experimental data.

Nanoscale Polyelectrolyte Complex Vesicles from Bioinspired Peptidomimetic Homopolymers with Zwitterionic Property and Extreme Stability

The complexation of polyelectrolytes ranging from biomacromolecules to synthetic polymers offers a great opportunity to construct a new generation of hierarchical materials. Here, we report a new type of nanoscale peptidomimetic polyelectrolyte complex vesicles (PCVs), with excellent aqueous stability over time and a wide range of pH, assembled from a pair of oppositely charged bioinspired homopolypeptoids and homopoly(2-oxazoline)s. This is distinct from the traditional homopolyelectrolytes that typically form microscale-sized liquid coacervates or solids. Through a systematic study, we demonstrated that the appropriate strength of hydrogen-bonding effects arising from the polar tertiary amide groups is significantly important for the formation of the vesicle. The prepared PCVs bearing water inner lumen are capable of encapsulating hydrophilic cargo molecules with good selectivity and tunable permeability, which can facilitate the diffusion of water-soluble therapeutic molecules, proteins, and enzymes. Due to the simultaneous surface display of positive and negative charges, the vesicles show excellent stability in physiological protein solutions and low toxicity, similar to known zwitterionic polymers. These superior properties combined with the facile preparation strategy suggest that the binary PCVs could be excellent drug delivery candidates for biomedical and engineering applications.

Protein diffusion in Escherichia coli cytoplasm scales with the mass of the complexes and is location dependent.

We analyze the structure of the cytoplasm by performing single-molecule displacement mapping on a diverse set of native cytoplasmic proteins in exponentially growing Escherichia coli. We evaluate the method for application in small compartments and find that confining effects of the cell membrane affect the diffusion maps. Our analysis reveals that protein diffusion at the poles is consistently slower than in the center of the cell, i.e., to an extent greater than the confining effect of the cell membrane. We also show that the diffusion coefficient scales with the mass of the used probes, taking into account the oligomeric state of the proteins, while parameters such as native protein abundance or the number of protein-protein interactions do not correlate with the mobility of the proteins. We argue that our data paint the prokaryotic cytoplasm as a compartment with subdomains in which the diffusion of macromolecules changes with the perceived viscosity.

Quantitative Interpretation of Protein Diffusion Coefficients in Mixed Protiated-Deuteriated Aqueous Solvents.

Diffusion-ordered nuclear magnetic resonance (NMR) spectroscopy is widely used for the analysis of mixtures, dispersing the signals of different species in a two-dimensional spectrum according to their diffusion coefficients. However, interpretation of these diffusion coefficients is typically purely qualitative, for example, to deduce which species are bigger or smaller. In studies of proteins in solution, important questions concern the molecular weight of the proteins, the presence or absence of aggregation, and the degree of folding. The Stokes–Einstein Gierer–Wirtz estimation (SEGWE) method has been previously developed to simplify the complex relationship between diffusion coefficient and molecular mass, allowing the prediction of a species’ diffusion coefficient in a pure solvent based on its molecular weight. Here, we show that SEGWE can be extended to successfully predict both peptide and protein diffusion coefficients in mixed protiated–deuteriated water samples and, hence, distinguish effectively between globular and disordered proteins.

441 Super-resolution imaging for nuclear pore quantification in human keratinocyte differentiation

Nuclear Pore Complexes (NPCs) serve as essential gateways between the nucleus and cytoplasm. Dysregulation of NPC function is associated with aging and cancer, yet how NPC is implicated in epidermal homeostasis and skin disorders remains largely unexplored. Here, we show that the 74% of genes encoding nucleoporins (NUPs), the building blocks constituting the NPC, are significantly downregulated (p<0.05) in primary human keratinocyte differentiation. NUP93, an essential NUP for determining the protein diffusion size limit across the nuclear pores, is among the most drastically downregulated NUPs.

Revisiting the Temperature Dependence of Protein Diffusion inside Bacteria: Validity of the Stokes-Einstein Equation.

Although the transport and mixing of proteins and other molecules inside bacteria rely on the diffusion of molecules, many aspects of the molecular diffusion in bacterial cytoplasm remain unclear or controversial, including how the diffusion-temperature relation follows the Stokes-Einstein equation. In this study, we applied single-particle tracking photoactivated localization microscopy to investigate the diffusion of histonelike nucleoid structuring (HNS) proteins and free dyes in bacterial cytoplasm at different temperatures. Although the diffusion of HNS proteins in both live and dead bacteria increased at higher temperatures and appeared to follow the Arrhenius equation, the diffusion of free dyes decreased at higher temperatures, questioning the previously proposed theories based on superthermal fluctuations. To understand the measured diffusion-temperature relations, we developed an alternative model, in which the bacterial cytoplasm is considered as a polymeric network or mesh. In our model, the Stokes-Einstein equation remains valid, while the polymeric network contributes a significant term to the viscosity experienced by the molecules diffusing in bacterial cytoplasm. Our model was successful in predicting the diffusion-temperature relations for both HNS proteins and free dyes in bacteria. In addition, we systematically examined the predicted diffusion-temperature relations with different parameters in the model, and predicted the possible existence of phase transitions.

Modeling Receptor Motility along Advecting Lipid Membranes.

This work aims to overview multiphysics mechanobiological computational models for receptor dynamics along advecting cell membranes. Continuum and statistical models of receptor motility are the two main modeling methodologies identified in reviewing the state of the art. Within the former modeling class, a further subdivision based on different biological purposes and processes of proteins’ motion is recognized; cell adhesion, cell contractility, endocytosis, and receptor relocations on advecting membranes are the most relevant biological processes identified in which receptor motility is pivotal. Numerical and/or experimental methods and approaches are highlighted in the exposure of the reviewed works provided by the literature, pertinent to the topic of the present manuscript. With a main focus on the continuum models of receptor motility, we discuss appropriate multiphyisics laws to model the mass flux of receptor proteins in the reproduction of receptor relocation and recruitment along cell membranes to describe receptor–ligand chemical interactions, and the cell’s structural response. The mass flux of receptor modeling is further supported by a discussion on the methodology utilized to evaluate the protein diffusion coefficient developed over the years.

Torsional behaviour of supercoiled DNA regulates recognition of architectural protein Fis on minicircle DNA

Three-dimensional genome organization is indispensable for regulating its functions. Experimental techniques based on the proximity ligation principle have identified spatially segregated domains at a sub-megabase level. The transcriptional activity of these domains is strongly coupled with the supercoiled DNA topology. The underlying molecular principle however remains unknown. By developing a computational framework, we investigate the differential kinetics of an architectural protein Fis on supercoiled DNA. We find that DNA supercoiling favours formation of juxtaposition sites where proteins can perform intersegmental transfer between the spatially close sites. The juxtaposition sites in positively supercoiled DNA are torsionally pinned that results in a slow protein diffusion on it, whereas the torsional behaviour of negatively supercoiled DNA ensures rapid protein-DNA communication and overall fast recognition of the cognate site by proteins. The result is robust for other proteins irrespective of their molecular features. Furthermore, our study suggests that variation in protein diffusivity on different supercoiled DNA also influences the shape of the latter. By unravelling the underlying molecular picture, our results unravel a plausible link between the degree of DNA supercoiling and the regulation of gene transcription that significantly advances the current understanding of the function and organization of chromatin inside cells.

Dynamic Mode Decomposition of Fluorescence Loss in Photobleaching Microscopy Data for Model-Free Analysis of Protein Transport and Aggregation in Living Cells.

The phase separation and aggregation of proteins are hallmarks of many neurodegenerative diseases. These processes can be studied in living cells using fluorescent protein constructs and quantitative live-cell imaging techniques, such as fluorescence recovery after photobleaching (FRAP) or the related fluorescence loss in photobleaching (FLIP). While the acquisition of FLIP images is straightforward on most commercial confocal microscope systems, the analysis and computational modeling of such data is challenging. Here, a novel model-free method is presented, which resolves complex spatiotemporal fluorescence-loss kinetics based on dynamic-mode decomposition (DMD) of FLIP live-cell image sequences. It is shown that the DMD of synthetic and experimental FLIP image series (DMD-FLIP) allows for the unequivocal discrimination of subcellular compartments, such as nuclei, cytoplasm, and protein condensates based on their differing transport and therefore fluorescence loss kinetics. By decomposing fluorescence-loss kinetics into distinct dynamic modes, DMD-FLIP will enable researchers to study protein dynamics at each time scale individually. Furthermore, it is shown that DMD-FLIP is very efficient in denoising confocal time series data. Thus, DMD-FLIP is an easy-to-use method for the model-free detection of barriers to protein diffusion, of phase-separated protein assemblies, and of insoluble protein aggregates. It should, therefore, find wide application in the analysis of protein transport and aggregation, in particular in relation to neurodegenerative diseases and the formation of protein condensates in living cells.