Nucleation Hypothesis Research Articles

Bubble Nucleation from a de Sitter–Planck Background with Quantum Boltzmann Statistics

Every physical theory involving quantum fields requires a model of quantum vacuum. The vacuum associated to quantum gravity must incorporate the prescriptions from both the theory of relativity and quantum physics. In this work, starting from the hypothesis of nucleation of sub-Planckian bubbles from a de Sitter vacuum, we study the necessary conditions to obtain baby universes, black holes and particles. The de Sitter-Planck background is described by an “infinite” Quantum Boltzmann statistics that generates fermions and bosons, and manifests itself as a deformation of the geometry that leads to a generalized uncertainty principle, a unified expression for the generalized Compton wavelength and event horizon size, drawing a connection between quantum black holes and elementary particles, seen as a collective organization of the bubbles of the vacuum described by the generalized Compton wavelength. The quantum thermodynamics of black holes is then outlined and the physical history of each bubble is found to depend on the cosmological constant described in terms of thermodynamic pressure. A treatment of the Casimir effect is provided in the de Sitter-Planck background, and finally wormholes are explored as bubble coalescence processes.

Metal cyamelurates: structural diversity caused by kinetic and thermodynamic controls

The kinetic control of chemical reactions makes it possible both to isolate metastable substances with properties different from those of thermodynamically stable phases and to obtain information useful for studying the crystal nucleation and further transformations of metastable phases into stable ones. Metal cyamelurates are suitable subjects for kinetic control in synthesis due to their easy crystallization and short reaction times. In this work, cobalt, manganese, magnesium, copper, aluminum, chromium, calcium, and lead cyamelurates were obtained and their crystal structures were determined. Most syntheses at room temperature take place under kinetic control, and this often leads to a mixture of phases. KM(C6N7O3)·5H2O (M = Co(II), Mn(II)) powders consisted of one crystalline compound. An increase in temperature leads to thermodynamic control, which is proved by registration of Mn(C6N7O3H)·5H2O and KMg(C6N7O3)·5H2O crystalline phases. It was possible to isolate Ca(C6N7O3H)·6H2O and Pb(C6N7O3H)·3H2O from the mixture by washing samples with a weak acid solution. As a result of the work, five different structural types were obtained, including KCu(C6N7O3)∙2H2O and KM(C6N7O3H)2·6H2O (M = Al, Cr(III)). Despite the diversity of salts obtained as a result of thermodynamic or kinetic control, practically the same building blocks form the crystal structure of cyamelurates. The hypothesis of nucleation in a colloidal micelle with electric double layer can be applied to the compounds listed above.

Is Ice Nucleation by Organic Crystals Nonclassical? An Assessment of the Monolayer Hypothesis of Ice Nucleation.

Potent ice nucleating organic crystals display an increase in nucleation efficiency with pressure and memory effect after pressurization that set them apart from inorganic nucleants. These characteristics were proposed to arise from an ordered water monolayer at the organic-water interface. It was interpreted that ordering of the monolayer is the limiting step for ice nucleation on organic crystals, rendering their mechanism of nucleation nonclassical. Despite the importance of organics in atmospheric ice nucleation, that explanation has never been investigated. Here we elucidate the structure of interfacial water and its role in ice nucleation at ambient pressure on phloroglucinol dihydrate, the paradigmatic example of outstanding ice nucleating organic crystal, using molecular simulations. The simulations confirm the existence of an interfacial monolayer that orders on cooling and becomes fully ordered upon ice formation. The monolayer does not resemble any ice face but seamlessly connects the distinct hydrogen-bonding orders of ice and the organic surface. Although large ordered patches develop in the monolayer before ice nucleates, we find that the critical step is the formation of the ice crystallite, indicating that the mechanism is classical. We predict that the fully ordered, crystalline monolayer nucleates ice above -2 °C and could be responsible for the exceptional ice nucleation by the organic crystal at high pressures. The lifetime of the fully ordered monolayer around 0 °C, however, is too short to account for the memory effect reported in the experiments. The latter could arise from an increase in the melting temperature of ice confined by strongly ice-binding surfaces.

Nucleation and Crystallization Kinetics of Barium Sulfate in the Hydrodynamic Boundary Layer: An Explanation of Mineral Deposition

The initialization of barite deposition is believed to be mineral nucleation. The induction times characterizing the kinetics of nucleation have been widely studied to investigate the precipitation kinetics of barium sulfate and to estimate the risk of mineral deposition in the flowing tube. It is generally accepted that if the solution’s supersaturated solution’s induction time is longer than the pipe’s traveling time, barium sulfate will not precipitate inside the pipe. However, recent research shows that barium sulfate still deposits inside the flowing tube even though the predicted induction time is longer than the travel time. The results correlate to the field observations that the mineral scale deposition is found in the production well even at the condition that is predicted to be kinetically stable. The contradiction suggests that there is a missing step of mineral deposition in the flow. In this work, a hypothesis of nucleation in the boundary layer is proposed to explain the contradiction: the barium sulfate can nucleate inside the boundary layer at the surface where the linear flow velocity approaches zero. This slow-flow region offers enough time for the crystals to form without being flushed away. A series of experiments were conducted in the flowing tube and the microfluidic channels to support the hypothesis. The amounts of deposited barium sulfate in the pipes were measured and compared with the induction time prediction. The result shows that with barite SI (supersaturation index) = 0.5–0.9 at 120 °C, the barium sulfate can deposit all along the tube even when the predicted induction times are longer than the traveling time (311 s). On the other hand, the observed nucleation time in the microfluidic channels matches the previously reported nucleation time in the kinetic turbidity tests in beakers. This implies that the barium sulfate can stay and nucleate in the boundary layer at the surface, which further supports the proposed mechanism. To conclude, we combine the ideas of induction times, boundary layer, and precipitation kinetics to describe a new mechanism of barium sulfate deposition. Once the solution in the boundary layer reaches its induction time, the deposition begins.

Determining the origin of inclusions in garnet: Challenges and new diagnostic criteria

ABSTRACT Permian metapegmatite garnets from the Koralpe region (Eastern Alps, Austria) contain abundant submicrometer- to micrometer-sized inclusions of rutile, corundum, Fe-Mn phosphate, ilmenite, xenotime, zircon, and apatite. Variations in inclusion abundance, phase assemblage, habit, and size define sector and concentric zones in the garnets, tracing low-indexed garnet facets. Zoning resulted from a process occurring at the garnet-melt interface, homogeneous along each facet, but sensitive to its crystallographic plane. Furthermore, inclusion and host lattices interacted, generating host-inclusion crystallographic orientation relationships (CORs). These phenomena exclude inclusion formation via overgrowth of pre-existing phases, infiltration of fluids/melts, or dissolution-reprecipitation. Magmatic garnet rims contain rutile needles up to 100 μm long, showing an interface-dependent shape-preferred orientation (SPO) that cannot be explained by exsolution models. Furthermore, the COR distribution for needles is unique, and implies large 3D lattice mismatches. These phenomena suggest that needles originated via oriented heterogeneous nucleation at the garnet interface and subsequent simultaneous growth of both phases. The origin of equant inclusions in core domains is less clear. With some assumptions, integrated compositions remain compatible with closed system exsolution or open system precipitation (OSP) involving divalent cation loss. Still, the oriented interface nucleation hypothesis seems to better explain the fact that the frequency of rutile-garnet CORs varies strongly not only between cores and rims but also between garnet core domains. Inclusion formation by oriented interface nucleation and simultaneous growth can explain many observations commonly attributed to exsolution, making distinguishing between these two mechanisms a challenge. We suggest interface-dependence of SPOs and COR frequencies as criteria for identifying inclusion formation via oriented nucleation at an interface and subsequent simultaneous growth.

Numerical Frameworks for Laser-Induced Cavitation: Is Interface Supersaturation a Plausible Primary Nucleation Mechanism?

Crystallization has been observed in laser-induced cavities in saturated solutions, but the mechanisms behind nucleation of crystals are not entirely clear. A hypothesis is that high solution supersaturation during the bubble growth period triggers the nucleation. Because of small spatiotemporal scales of the cavitation event, the supersaturation is very difficult to measure experimentally. To test the nucleation hypothesis, we perform a two-dimensional axisymmetric direct numerical simulation of an experimentally observed laser-induced cavitation event with crystallization. We demonstrate a significant degree of supersaturation and argue that the nucleation hypothesis is indeed plausible. To analyze factors that lead to a high supersaturation, we develop a comprehensive one-dimensional model for spherical laser-induced cavities. We conduct an extensive investigation on how the solute solubility, solute diffusivity, laser pulse energy, and superheated liquid volume affect the supersaturation. We show that high supersaturation is possible under a range of relevant conditions but not readily obtained for all solutions and laser setups. Guidelines are provided to identify if a specific solution or laser setup may attain high supersaturation. The insights obtained and the numerical methods formulated in this work can be applied to assess and design new laser-induced cavitation setups that allow for precise control of the duration and degree of the supersaturation

Advances in vapor dropwise condensation heat transfer

Vapor condensation on solid surface is widely observed in nature and employed in industry, among which, dropwise condensation (DWC) has attracted a lot of attentions due to its high performance in heat transfer and wide applications in industries. With remarkable advances in functional surface engineering, more and more progresses have been obtained in this field. Therefore, it is necessary to carry a review for those investigations obtained by different methods and on various aspects of DWC. An introduction of the wetting of droplets is firstly presented, and then this review article turns to theoretical modelling of heat transfer, followed by numerical and experimental works. No doubt that it is impossible to cover all the efforts since 1930, when DWC was observed for the first time. Thus, the present work is mainly devoted to delivering two issues, by summarizing several representative questions. One is the origin of classical heat transfer model and the other is a framework of DWC research. The wetting of both macro-droplets and nano-droplets matters significantly in the whole life of a condensed droplet. For the former, contact angle and wetting status are introduced, while for the latter, three hypotheses for nano-droplet formation are responded. “The hypothesis of film break-up” has been abandoned; the widely accepted “hypothesis of specific nucleation cites” is demonstrated here based on solid evidence from molecular dynamics (MD) simulations. To be honest, it is not easy to sufficiently abandon “the hypothesis of coexistence of droplet and film”, which may still be regarded as an open question. For heat transfer modelling, via a comparison with Nusselt’s theory of filmwise condensation, it is shown that heat transfer modelling for DWC, as a challenging topic, is remarkably different from those for convention heat transfer, or even filmwise condensation. The development of this topic presents a long story. The efforts in early stage are devoted to understanding basic mechanisms and improving measurement accuracy. With the advances in superhydrophobic surfaces, the enhancement of DWC is obtained by advanced manipulation of condensed droplets wetting, especially by efficient removal of condensed droplets. These works are divided into three types according to the differences in their motivations: For accurately modelling of solid-liquid interaction, for the effect of coalescence-induced droplet jumping, and for new-facing situations of industry applications. To optimize DWC, it is necessary to sufficiently understand its mechanism of droplet wetting, which is mainly performed by numerical simulations, especially by MD simulation method and lattice Boltzmann method (LBM). Before a summary of the latter one, the contribution of MD simulations is credited by presenting their exploration on the fundamental behaviours of condensed nano-droplets, especially the formation, wetting, growth, coalescence and self-driven departures. The efforts and advances above are actually inspired by, and will be applied to as well, experimental investigations. Firstly, a summary is given for the coating techniques for super-hydrophobic surfaces, with some comments. Then, the development of experimental work is presented by dividing its history into three stages: Initial pioneering for mechanism and measurement, coating-inspired DWC, and interdiscipline-boosted DWC. The advances of DWC with non-condensable gas are introduced as well, which is expected to help DWC be applied extensively. Finally, a summary of the progresses and possible challenges are given, followed by the advices on several specific questions. Our revisit to “the DWC museum” is concluded by an outlook full of promise, with the application of emerging technologies in this classical field.

Surface tension in bulk and bounded liquids

The paper is aimed at theoretical studying the following problems and its relation to the available experimental data: 1) the coefficient of surface tension and capillary constant in bulk and spatially bounded liquids in a wide range of thermodynamic parameters (temperature, density, pressure, etc.), including the critical region; 2) influence of size effects on surface tension and capillary constant in liquids with a varying spatial dimensionality, namely from the “surface” 2D-state to the “bulk” 3D-state, and then to regular 4D-state where the fluctuation effects may be neglected in liquids like water with the Ginzburg number, Gi < 1; 3) comparison the obtained results and empirical approach to the water surface tension in a wide intervals of thermodynamic variables, including confined supercooled water; 4) medical application of results for surface tension, using similarity between processes of carcinogenesis and nucleation.The theoretical formulas are proposed for dependence of surface tension and capillary constant in bulk and confined liquids on temperature, density, pressure, and size variables in a wide vicinity of the critical region. The agreement of theoretical and experimental data for the temperature dependence of surface tension and capillary constant appears to be quite satisfactory. The 2D↔3D dimensional crossover for surface tension and capillary constant is analyzed. The surface tension of liquids with a relatively small Ginzburg number, including bulk water, is studied with taking into account the dimensionality crossover from 3D-systems to 4D-systems, where the Landau mean-field theory is valid. The empirical formula for surface tension of pure water is discussed together with the Tolman correction and the fluctuation theory of phase transitions. The consequences of the similarity hypothesis of nucleation and carcinogenesis are discussed.

Overview: Nucleation of clathrate hydrates.

Molecular level knowledge of nucleation and growth of clathrate hydrates is of importance for advancing fundamental understanding on the nature of water and hydrophobic hydrate formers, and their interactions that result in the formation of ice-like solids at temperatures higher than the ice-point. The stochastic nature and the inability to probe the small length and time scales associated with the nucleation process make it very difficult to experimentally determine the molecular level changes that lead to the nucleation event. Conversely, for this reason, there have been increasing efforts to obtain this information using molecular simulations. Accurate knowledge of how and when hydrate structures nucleate will be tremendously beneficial for the development of sustainable hydrate management strategies in oil and gas flowlines, as well as for their application in energy storage and recovery, gas separation, carbon sequestration, seawater desalination, and refrigeration. This article reviews various aspects of hydrate nucleation. First, properties of supercooled water and ice nucleation are reviewed briefly due to their apparent similarity to hydrates. Hydrate nucleation is then reviewed starting from macroscopic observations as obtained from experiments in laboratories and operations in industries, followed by various hydrate nucleation hypotheses and hydrate nucleation driving force calculations based on the classical nucleation theory. Finally, molecular simulations on hydrate nucleation are discussed in detail followed by potential future research directions.

A first test of the hypothesis of biogenic magnetite-based heterogeneous ice-crystal nucleation in cryopreservation

An outstanding biophysical puzzle is focused on the apparent ability of weak, extremely low-frequency oscillating magnetic fields to enhance cryopreservation of many biological tissues. A recent theory holds that these weak magnetic fields could be inhibiting ice-crystal nucleation on the nanocrystals of biological magnetite (Fe3O4, an inverse cubic spinel) that are present in many plant and animal tissues by causing them to oscillate. In this theory, magnetically-induced mechanical oscillations disrupt the ability of water molecules to nucleate on the surface of the magnetite nanocrystals. However, the ability of the magnetite crystal lattice to serve as a template for heterogeneous ice crystal nucleation is as yet unknown, particularly for particles in the 10–100 nm size range. Here we report that the addition of trace-amounts of finely-dispersed magnetite into ultrapure water samples reduces strongly the incidence of supercooling, as measured in experiments conducted using a controlled freezing apparatus with multiple thermocouples. SQUID magnetometry was used to quantify nanogram levels of magnetite in the water samples. We also report a relationship between the volume change of ice, and the degree of supercooling, that may indicate lower degassing during the crystallization of supercooled water. In addition to supporting the role of ice-crystal nucleation by biogenic magnetite in many tissues, magnetite nanocrystals could provide inexpensive, non-toxic, and non-pathogenic ice nucleating agents needed in a variety of industrial processes, as well as influencing the dynamics of ice crystal nucleation in many natural environments.

A constitutive-based element-by-element crack propagation algorithm with local mesh refinement

In the context of multiple constitutive models, multiple finite element formulations and crack nucleation and propagation hypotheses, we propose a simple yet effective algorithm to initiate and propagate cracks in 2D models which is independent of the constitutive and element specific technology. Observed phenomena such as multiple crack growth and shielding emerge naturally, without specialized algorithms for calculating the crack growth direction. The algorithm consists of a sequence of mesh subdivision, mesh smoothing and element erosion steps. Element subdivision is based on the classical edge split operations using a given constitutive quantity (either damage or void fraction). Mesh smoothing makes use of edge contraction as function of a given constitutive quantity (such as void fraction or principal stress). To assess the robustness and accuracy of this algorithm, we use classical quasi-brittle benchmarks and ductile tests.

TEM Characterization of a Titanium Nitride (TiN) Inclusion in a Fe-Ni-Co Maraging Steel

A TEM observation of a TiN inclusion associated to a spinel (MgAl2O4) and calcium sulfide germs is reported. It shows an orientation relationship between these three phases, indicating an epitaxial growth of the TiN over the spinel and CaS. This observation strengthens the hypothesis of a heterogeneous nucleation of TiN particles during the solidification of a maraging steel.

Pasture succession in the Neotropics: extending the nucleation hypothesis into a matrix discontinuity hypothesis.

The nucleation hypothesis appears to explain widespread patterns of succession in tropical pastures, specifically the tendency for isolated trees to promote woody species recruitment. Still, the nucleation hypothesis has usually been tested explicitly for only short durations and in some cases isolated trees fail to promote woody recruitment. Moreover, at times, nucleation occurs in other key habitat patches. Thus, we propose an extension, the matrix discontinuity hypothesis: woody colonization will occur in focal patches that function to mitigate the herbaceous vegetation effects, thus providing safe sites or regeneration niches. We tested predictions of the classical nucleation hypothesis, the matrix discontinuity hypothesis, and a distance from forest edge hypothesis, in five abandoned pastures in Costa Rica, across the first 11 years of succession. Our findings confirmed the matrix discontinuity hypothesis: specifically, rotting logs and steep slopes significantly enhanced woody colonization. Surprisingly, isolated trees did not consistently significantly enhance recruitment; only larger trees did so. Finally, woody recruitment consistently decreased with distance from forest. Our results as well as results from others suggest that the nucleation hypothesis needs to be broadened beyond its historical focus on isolated trees or patches; the matrix discontinuity hypothesis focuses attention on a suite of key patch types or microsites that promote woody species recruitment. We argue that any habitat discontinuities that ameliorate the inhibition by dense graminoid layers will be foci for recruitment. Such patches could easily be manipulated to speed the transition of pastures to closed canopy forests.

Nucleation hypothesis to explain how mineralization of matrices occurs in vivo

Nucleation hypothesis to explain how mineralization of matrices occurs in vivo

Textures of rectangular extrusions and their effects on the mechanical properties of thermo-mechanically treated, lamellar microstructure, Ti–47Al–2Cr–2Nb–0.15B

Textures of α2 and γ phases in Ti–47Al–2Cr–2Nb–0.15B (at.%) rectangular billet, extruded below its α transus temperature, were evaluated and their relation to the mechanical properties of TMTL microstructure was investigated. Strong α2 phase texture {112¯0}<101¯0> was found after extrusion and it evolved into {101¯0}<112¯0> recrystallization texture via oriented growth during α solution treatment. The α/α2 phase texture changes α grain growth behavior at Tα, such that it is slow at first but becomes rapid when the solution time exceeds a critical value, creating a new method of obtaining fine-grained TMTL microstructure. Mechanical properties of the TMTL microstructure were shown to be closely related to the Kearns texture factor of the α2 phase along the loading direction. The center and edge of as-extruded billet have distinct γ phase textures, dominated by β fiber (center) and featuring multiple texture components (edge), respectively. In the highly strained edge region, the presence of C-twin, Y, and Z texture components suggests the occurrence of mechanical twinning and shear band deformation, while B/G auxiliary component was found to act as a transition band from deformation to cubic recrystallization texture, in support of the oriented nucleation hypothesis for the formation of cubic texture.

Structural typologies of salivary calculi

Several theories have been put forward regarding the aetiology and pathogenesis of salivary calculi, although a comprehensive understanding of the nucleation and growth mechanisms involved in the formation of these structures is still lacking.In general, sialoliths present one core partially or highly mineralized surrounded by concentric layers of organic and mineralized matter that alternate in succession following a chronologic sequence. The layers consist of fine mineralized strata intercalated with fine organic ones and threaded globular structures with variable degrees of mineralization.The exact mechanism involved in the genesis of sialoliths remains largely unknown, theories defending an initial organic nidus or an initial precipitation of minerals, with subsequent deposition of organic and inorganic layers, can be found in the literature. Nevertheless, it remains object of discussion the etiologic factors responsible for the formation of the first nidus or the initial precipitation, since infection, inflammation of the gland, viscous nature of the mucous secretions or naturally existing sialomicroliths have all have been implicated.Aiming at an exhaustive systematization of salivary calculi morphogenesis, their morphology has been studied by micro-computed tomography (bCT) and scanning electron microscopy (SEM). CCT studies were done on as-extracted dried samples using uCT SkyScan 1172 instrument with a 1.3 Megapixel camera, operated at the maximum available power of the source (10W). Radiographs acquisition was performed with a rotational step in the 0.70-1° range, until a maximum of 180º, with an exposure time in the 3.1-5 s range. Microscopy observations were carried out with backscattered electron (BSE) signals using a JEOL JSM 7001F operated at 15 kV, samples were previously prepared following metallographic procedures.The submandibular and parotid calculi investigated presented similar growth patterns, which can follow either concentric (Figure 1) or perturbed-growth typologies (Figure 2), although in most situations a gradation between them has been found. Nevertheless, a single well-defined core constituted by material with low mineralization was frequently present, supporting the nucleation hypothesis of an initial organic nidus.The combination of TCT with SEM enabled a comprehensive characterization of the sialoliths: (i) the former technique allowed for a precise localization of the core and other morphological features within the calculus volume, while (ii) investigation of details at higher resolution could be achieved with the latter method. However, due to the friable nature of the sialoliths, handling during sample preparation results often in material loss (compare (a) and (b) in both Figures).The work was carried out with financial support of the Portuguese Foundation for Science and Technology through PTDC/SAU-ENB/111941/2009 and PEst-OE/CTM-UI0084/2011 grants.

Solubility of Aqueous Methane under Metastable Conditions: Implications for Gas Hydrate Nucleation

To understand the prenucleation stage of methane hydrate formation, we measured methane solubility under metastable conditions using molecular dynamics simulations. Three factors that influence solubility are considered: temperature, pressure, and the strength of the modeled van der Waals attraction between methane and water. Moreover, the naturally formed water cages and methane clusters in the methane solutions are analyzed. We find that both lowering the temperature and increasing the pressure increase methane solubility, but lowering the temperature is more effective than increasing the pressure in promoting hydrate nucleation because the former induces more water cages to form while the latter makes them less prevalent. With an increase in methane solubility, the chance of forming large methane clusters increases, with the distribution of cluster sizes being exponential. The critical solubility, beyond which the metastable solutions spontaneously form hydrate, is estimated to be ~0.05 mole fraction in this work, corresponding to the concentration of 1.7 methane molecules/nm(3). This value agrees well with the cage adsorption hypothesis of hydrate nucleation.

The cages, dynamics, and structuring of incipient methane clathrate hydrates

Interest in describing clathrate hydrate formation mechanisms spans multiple fields of science and technical applications. Here, we report findings from multiple molecular dynamics simulations of spontaneous methane clathrate hydrate nucleation and growth from fully demixed and disordered two-phase fluid systems of methane and water. Across a range of thermodynamic conditions and simulation geometries and sizes, a set of seven cage types comprises approximately 95% of all cages formed in the nucleated solids. This set includes the ubiquitous 5(12) cage, the 5(12)6(n) subset (where n ranges from 2-4), and the 4(1)5(10)6(n) subset (where n also ranges from 2-4). Transformations among these cages occur via water pair insertions/removals and rotations, and may elucidate the mechanisms of solid-solid structural rearrangements observed experimentally. Some consistency is observed in the relative abundance of cages among all nucleation trajectories. 5(12) cages are always among the two most abundant cage types in the nucleated solids and are usually the most abundant cage type. In all simulations, the 5(12)6(n) cages outnumber their 4(1)5(10)6(n) counterparts with the same number of water molecules. Within these consistent features, some stochasticity is observed in certain cage ratios and in the long-range ordering of the nucleated solids. Even when comparing simulations performed at the same conditions, some trajectories yield swaths of multiple adjacent sI unit cells and long-range order over 5 nm, while others yield only isolated sI unit cells and little long-range order. The nucleated solids containing long-range order have higher 5(12)6(2)/5(12) and 5(12)6(3)/4(1)5(10)6(2) cage ratios when compared to systems that nucleate with little long-range order. The formation of multiple adjacent unit cells of sI hydrate at high driving forces suggests an alternative or addition to the prevailing hydrate nucleation hypotheses which involve formation through amorphous intermediates.

Mathematical Modeling of Endocytic Actin Patch Kinetics in Fission Yeast: Disassembly Requires Release of Actin Filament Fragments

We used the dendritic nucleation hypothesis to formulate a mathematical model of the assembly and disassembly of actin filaments at sites of clathrin-mediated endocytosis in fission yeast. We used the wave of active WASp recruitment at the site of the patch formation to drive assembly reactions after activation of Arp2/3 complex. Capping terminated actin filament elongation. Aging of the filaments by ATP hydrolysis and gamma-phosphate dissociation allowed actin filament severing by cofilin. The model could simulate the assembly and disassembly of actin and other actin patch proteins using measured cytoplasmic concentrations of the proteins. However, to account quantitatively for the numbers of proteins measured over time in the accompanying article (Sirotkin et al., 2010, MBoC 21: 2792-2802), two reactions must be faster in cells than in vitro. Conditions inside the cell allow capping protein to bind to the barbed ends of actin filaments and Arp2/3 complex to bind to the sides of filaments faster than the purified proteins in vitro. Simulations also show that depolymerization from pointed ends cannot account for rapid loss of actin filaments from patches in 10 s. An alternative mechanism consistent with the data is that severing produces short fragments that diffuse away from the patch.

Quantitative Analysis of the Mechanism of Endocytic Actin Patch Assembly and Disassembly in Fission Yeast

We used quantitative confocal microscopy to measure the numbers of 16 proteins tagged with fluorescent proteins during assembly and disassembly of endocytic actin patches in fission yeast. The peak numbers of each molecule that accumulate in patches varied <30-50% between individual patches. The pathway begins with accumulation of 30-40 clathrin molecules, sufficient to build a hemisphere at the tip of a plasma membrane invagination. Thereafter precisely timed waves of proteins reach characteristic peak numbers: endocytic adaptor proteins (approximately 120 End4p and approximately 230 Pan1p), activators of Arp2/3 complex (approximately 200 Wsp1p and approximately 340 Myo1p) and approximately 300 Arp2/3 complexes just ahead of a burst of actin assembly into short, capped and highly cross-linked filaments (approximately 7000 actins, approximately 200 capping proteins, and approximately 900 fimbrins). Coronin arrives last as all other components disperse upon patch internalization and movement over approximately 10 s. Patch internalization occurs without recruitment of dynamins. Mathematical modeling, described in the accompanying paper (Berro et al., 2010, MBoC 21: 2803-2813), shows that the dendritic nucleation hypothesis can account for the time course of actin assembly into a branched network of several hundred filaments 100-200 nm long and that patch disassembly requires actin filament fragmentation in addition to depolymerization from the ends.