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Journal of Visualized Experiments : JoVE Jan 2011Using the three-dimensional structure of biological macromolecules to infer how they function is one of the most important fields of modern biology. The availability of...
Using the three-dimensional structure of biological macromolecules to infer how they function is one of the most important fields of modern biology. The availability of atomic resolution structures provides a deep and unique understanding of protein function, and helps to unravel the inner workings of the living cell. To date, 86% of the Protein Data Bank (rcsb-PDB) entries are macromolecular structures that were determined using X-ray crystallography. To obtain crystals suitable for crystallographic studies, the macromolecule (e.g. protein, nucleic acid, protein-protein complex or protein-nucleic acid complex) must be purified to homogeneity, or as close as possible to homogeneity. The homogeneity of the preparation is a key factor in obtaining crystals that diffract to high resolution (Bergfors, 1999; McPherson, 1999). Crystallization requires bringing the macromolecule to supersaturation. The sample should therefore be concentrated to the highest possible concentration without causing aggregation or precipitation of the macromolecule (usually 2-50 mg/mL). Introducing the sample to precipitating agent can promote the nucleation of protein crystals in the solution, which can result in large three-dimensional crystals growing from the solution. There are two main techniques to obtain crystals: vapor diffusion and batch crystallization. In vapor diffusion, a drop containing a mixture of precipitant and protein solutions is sealed in a chamber with pure precipitant. Water vapor then diffuses out of the drop until the osmolarity of the drop and the precipitant are equal (Figure 1A). The dehydration of the drop causes a slow concentration of both protein and precipitant until equilibrium is achieved, ideally in the crystal nucleation zone of the phase diagram. The batch method relies on bringing the protein directly into the nucleation zone by mixing protein with the appropriate amount of precipitant (Figure 1B). This method is usually performed under a paraffin/mineral oil mixture to prevent the diffusion of water out of the drop. Here we will demonstrate two kinds of experimental setup for vapor diffusion, hanging drop and sitting drop, in addition to batch crystallization under oil.
Topics: Crystallization; Crystallography, X-Ray; Diffusion; Proteins
PubMed: 21304455
DOI: 10.3791/2285 -
Advances in Experimental Medicine and... 2020Diffusion within bacteria is often thought of as a "simple" random process by which molecules collide and interact with each other. New research however shows that this... (Review)
Review
Diffusion within bacteria is often thought of as a "simple" random process by which molecules collide and interact with each other. New research however shows that this is far from the truth. Here we shed light on the complexity and importance of diffusion in bacteria, illustrating the similarities and differences of diffusive behaviors of molecules within different compartments of bacterial cells. We first describe common methodologies used to probe diffusion and the associated models and analyses. We then discuss distinct diffusive behaviors of molecules within different bacterial cellular compartments, highlighting the influence of metabolism, size, crowding, charge, binding, and more. We also explicitly discuss where further research and a united understanding of what dictates diffusive behaviors across the different compartments of the cell are required, pointing out new research avenues to pursue.
Topics: Bacteria; Biophysical Phenomena; Diffusion
PubMed: 32894475
DOI: 10.1007/978-3-030-46886-6_2 -
Biophysical Journal Apr 2022Biochemical specificity is critical in enzyme function, evolution, and engineering. Here we employ an established kinetic model to dissect the effects of reactant...
Biochemical specificity is critical in enzyme function, evolution, and engineering. Here we employ an established kinetic model to dissect the effects of reactant geometry and diffusion on product formation speed and accuracy in the presence of cognate (correct) and near-cognate (incorrect) substrates. Using this steady-state model for spherical geometries, we find that, for distinct kinetic regimes, the speed and accuracy of the reactions are optimized on different regions of the geometric landscape. From this model we deduce that accuracy can be strongly dependent on reactant geometric properties even for chemically limited reactions. Notably, substrates with a specific geometry and reactivity can be discriminated by the enzyme with higher efficacy than others through purely diffusive effects. For similar cognate and near-cognate substrate geometries (as is the case for polymerases or the ribosome), we observe that speed and accuracy are maximized in opposing regions of the geometric landscape. We also show that, in relevant environments, diffusive effects on accuracy can be substantial even far from extreme kinetic conditions. Finally, we find how reactant chemical discrimination and diffusion can be related to simultaneously optimize steady-state flux and accuracy. These results highlight how diffusion and geometry can be employed to enhance reaction speed and discrimination, and similarly how they impose fundamental restraints on these quantities.
Topics: Diffusion; Kinetics; Ribosomes
PubMed: 35278424
DOI: 10.1016/j.bpj.2022.03.005 -
Annual Review of Biophysics May 2023Diffusion is a pervasive process present in a broad spectrum of cellular reactions. Its mathematical description has existed for nearly two centuries and permits the... (Review)
Review
Diffusion is a pervasive process present in a broad spectrum of cellular reactions. Its mathematical description has existed for nearly two centuries and permits the construction of simple rules for evaluating the characteristic timescales of diffusive processes and some of their determinants. Although the term diffusion originally referred to random motions in three-dimensional (3D) media, several biological diffusion processes in lower dimensions have been reported. One-dimensional (1D) diffusions have been reported, for example, for translocations of various proteins along DNA or protein (e.g., microtubule) lattices and translation of helical peptides along the coiled-coil interface. Two-dimensional (2D) diffusion has been shown for dynamics of proteins along membranes. The microscopic mechanisms of these 1-3D diffusions may vary significantly depending on the nature of the diffusing molecules, the substrate, and the interactions between them. In this review, we highlight some key examples of 1-3D biomolecular diffusion processes and illustrate the roles that electrostatic interactions and intrinsic disorder may play in modulating these processes.
Topics: Static Electricity; DNA; Diffusion; Microtubules; Motion
PubMed: 36750250
DOI: 10.1146/annurev-biophys-111622-091220 -
Journal of Biological Physics Sep 2023We present an analysis of an epidemic spreading process on an Apollonian network that can describe an epidemic spreading in a non-sedentary population. We studied the...
We present an analysis of an epidemic spreading process on an Apollonian network that can describe an epidemic spreading in a non-sedentary population. We studied the modified diffusive epidemic process using the Monte Carlo method by computational analysis. Our model may be helpful for modeling systems closer to reality consisting of two classes of individuals: susceptible (A) and infected (B). The individuals can diffuse in a network according to constant diffusion rates [Formula: see text] and [Formula: see text], for the classes A and B, respectively, and obeying three diffusive regimes, i.e., [Formula: see text], [Formula: see text], and [Formula: see text]. Into the same site i, the reaction occurs according to the dynamical rule based on Gillespie's algorithm. Finite-size scaling analysis has shown that our model exhibits continuous phase transition to an absorbing state with a set of critical exponents given by [Formula: see text], [Formula: see text], and [Formula: see text] familiar to every investigated regime. In summary, the continuous phase transition, characterized by this set of critical exponents, does not have the same exponents of the mean-field universality class in both regular lattices and complex networks.
Topics: Humans; Computer Simulation; Algorithms; Epidemics; Models, Biological; Diffusion
PubMed: 37118345
DOI: 10.1007/s10867-023-09634-2 -
Proceedings of the National Academy of... Aug 2023Real-world networks are neither regular nor random, a fact elegantly explained by mechanisms such as the Watts-Strogatz or the Barabási-Albert models, among others....
Real-world networks are neither regular nor random, a fact elegantly explained by mechanisms such as the Watts-Strogatz or the Barabási-Albert models, among others. Both mechanisms naturally create shortcuts and hubs, which while enhancing the network's connectivity, also might yield several undesired navigational effects: They tend to be overused during geodesic navigational processes-making the networks fragile-and provide suboptimal routes for diffusive-like navigation. Why, then, networks with complex topologies are ubiquitous? Here, we unveil that these models also entropically generate network bypasses: alternative routes to shortest paths which are topologically longer but easier to navigate. We develop a mathematical theory that elucidates the emergence and consolidation of network bypasses and measure their navigability gain. We apply our theory to a wide range of real-world networks and find that they sustain complexity by different amounts of network bypasses. At the top of this complexity ranking we found the human brain, which points out the importance of these results to understand the plasticity of complex systems.
Topics: Humans; Brain; Diffusion
PubMed: 37490534
DOI: 10.1073/pnas.2305001120 -
The Journal of General Physiology Oct 2023Osmosis is an important force in all living organisms, yet the molecular basis of osmosis is widely misunderstood as arising from diffusion of water across a membrane...
Osmosis is an important force in all living organisms, yet the molecular basis of osmosis is widely misunderstood as arising from diffusion of water across a membrane separating solutions of differing osmolarities, and hence different water concentrations. In 1923, Peter Debye proposed a physical model for a semipermeable membrane emphasizing the repulsive forces between solute molecules and membrane that prevent the solute from entering the membrane. His work was hardly noticed at the time and slipped out of view. We show that Debye's analysis of van 't Hoff's law for osmotic equilibrium also provides a consistent and plausible mechanism for osmotic flow. A difference in osmolyte concentrations in solutions separated by a semipermeable membrane leads to different pressures at the two water-membrane interfaces because the total repulsive force between solute molecules and the membrane is different at the two interfaces. Water is therefore driven through the membrane for exactly the same reason that pure water flows in response to an imposed hydrostatic pressure difference. In this paper, we present the Debye model in both equilibrium and flow conditions. We point out its applicability regardless of the nature of the membrane with examples ranging from the predominantly convective flow of water through synthetic membranes and capillary walls to the purely diffusive flow of independent water molecules through a lipid bilayer and the flow of a single-file column of water molecules in narrow protein channels.
Topics: Diffusion; Lipid Bilayers; Osmosis; Pressure; Water
PubMed: 37624228
DOI: 10.1085/jgp.202313332 -
Journal of the Royal Society, Interface Nov 2022Budding allows virus replication and macromolecular secretion in cells through the formation of a membrane protrusion (bud) that evolves into an envelope. The largest...
Budding allows virus replication and macromolecular secretion in cells through the formation of a membrane protrusion (bud) that evolves into an envelope. The largest energetic barrier to bud formation is membrane deflection and is trespassed primarily thanks to nucleocapsid-membrane adhesion. Transmembrane proteins (TPs), which later form the virus ligands, are the main promotors of adhesion and can accommodate membrane bending thanks to an induced spontaneous curvature. Adhesive TPs must diffuse across the membrane from remote regions to gather on the bud surface, thus, diffusivity controls the kinetics. This paper proposes a simple model to describe diffusion-mediated budding unravelling important size limitations and size-dependent kinetics. The predicted optimal virion radius, giving the fastest budding, is validated against experiments for coronavirus, HIV, flu and hepatitis. Assuming exponential replication of virions and hereditary size, the model can predict the size distribution of a virus population. This is verified against experiments for SARS-CoV-2. All the above comparisons rely on the premise that budding poses the tightest size constraint. This is true in most cases, as demonstrated in this paper, where the proposed model is extended to describe virus infection via receptor- and clathrin-mediated endocytosis, and via membrane fusion.
Topics: Humans; SARS-CoV-2; COVID-19; Virus Replication; Virion; Diffusion
PubMed: 36321373
DOI: 10.1098/rsif.2022.0525 -
Magnetic Resonance in Medicine Jul 2022Relationships between diffusion-weighted MRI signals and hepatocyte microstructure were investigated to inform liver diffusion MRI modeling, focusing on the following...
PURPOSE
Relationships between diffusion-weighted MRI signals and hepatocyte microstructure were investigated to inform liver diffusion MRI modeling, focusing on the following question: Can cell size and diffusivity be estimated at fixed diffusion time, realistic SNR, and negligible contribution from extracellular/extravascular water and exchange?
METHODS
Monte Carlo simulations were performed within synthetic hepatocytes for varying cell size/diffusivity / , and clinical protocols (single diffusion encoding; maximum b-value: {1000, 1500, 2000} s/mm ; 5 unique gradient duration/separation pairs; SNR = { , 100, 80, 40, 20}), accounting for heterogeneity in and perfusion contamination. Diffusion ( ) and kurtosis ( ) coefficients were calculated, and relationships between and were visualized. Functions mapping to were computed to predict unseen values, tested for their ability to classify discrete cell-size contrasts, and deployed on 9.4T ex vivo MRI-histology data of fixed mouse livers RESULTS: Relationships between and are complex and depend on the diffusion encoding. Functions mapping to captures salient characteristics of and dependencies. Mappings are not always accurate, but they enable just under 70% accuracy in a three-class cell-size classification task (for SNR = 20, = 1500 s/mm , = 20 ms, and = 75 ms). MRI detects cell-size contrasts in the mouse livers that are confirmed by histology, but overestimates the largest cell sizes.
CONCLUSION
Salient information about liver cell size and diffusivity may be retrieved from minimal diffusion encodings at fixed diffusion time, in experimental conditions and pathological scenarios for which extracellular, extravascular water and exchange are negligible.
Topics: Animals; Contrast Media; Diffusion; Diffusion Magnetic Resonance Imaging; Hepatocytes; Magnetic Resonance Imaging; Mice; Water
PubMed: 35181943
DOI: 10.1002/mrm.29174 -
Magnetic Resonance in Medical Sciences... Apr 2024Diffusion MRI is a physical measurement method that quantitatively indicates the displacement of water molecules diffusing in voxels. However, there are insufficient...
PURPOSE
Diffusion MRI is a physical measurement method that quantitatively indicates the displacement of water molecules diffusing in voxels. However, there are insufficient data to characterize the diffusion process physically in a uniform structure such as a phantom. This study investigated the transitional relationship between structure scale, temperature, and diffusion time for simple restricted diffusion using a capillary phantom.
METHODS
We performed diffusion-weighted pulsed-gradient stimulated-echo acquisition mode (STEAM) MRI with a 9.4 Tesla MRI system (Bruker BioSpin, Ettlingen, Germany) and a quadrature coil with an inner diameter of 86 mm (Bruker BioSpin). We measured the diffusion coefficients (radial diffusivity [RD]) of capillary plates (pore sizes 6, 12, 25, 50, and 100 μm) with uniformly restricted structures at various temperatures (10ºC, 20ºC, 30ºC, and 40ºC) and multiple diffusion times (12-800 ms). We evaluated the characteristics of scale, temperature, and diffusion time for restricted diffusion.
RESULTS
The RD decayed and became constant depending on the structural scale. Diffusion coefficient fluctuations with temperature occurred mostly under conditions of a large structural scale and short diffusion time. We obtained data suggesting that temperature-dependent changes in the diffusion coefficients follow physical laws.
CONCLUSION
No water molecules were observed outside the glass tubes in the capillary plates, and the capillary plates only reflected a restricted diffusion process within the structure.We experimentally evaluated the characteristics of simple restricted diffusion to reveal the transitional relationship of the diffusion coefficient with diffusion time, structure scale, and temperature through composite measurement.
Topics: Temperature; Magnetic Resonance Imaging; Diffusion Magnetic Resonance Imaging; Diffusion; Biological Transport; Phantoms, Imaging; Water
PubMed: 36754420
DOI: 10.2463/mrms.mp.2022-0103