Differential interference with actin-binding protein function by acute Cytochalasin B.

Dynamic actin filament remodeling is crucial for a plethora of fundamental cell biological processes, ranging from cell division and migration to cell communication, intracellular trafficking or tissue development. Cytochalasin B and -D are fungal secondary metabolites frequently used for interference with such processes. Although generally assumed to block actin filament polymerization at their rapidly growing barbed ends and compete with regulators at these sites, our molecular understanding of their precise effects in dynamic actin structures is scarce. Here we combine live cell imaging and analysis of fluorescent actin-binding protein dynamics with acute treatment of lamellipodia in migrating cells with cytochalasin B. Our results show that in spite of an abrupt halt of lamellipodium protrusion, cytochalasin B affects various actin filament barbed end-binding proteins in a differential fashion. Cytochalasin B enhances instead of diminishes the accumulation of prominent barbed end-binding factors such as Ena/VASP family proteins and heterodimeric capping protein (CP) in the lamellipodium. Similar results were obtained with cytochalasin D. All these effects are highly specific, as cytochalasin-induced VASP accumulation requires the presence of CP, but not vice versa , and coincides with abrogation of both actin and VASP turnover. Cytochalasin B can also increase apparent barbed end interactions with the actin-binding ß-tentacle of CP and partially mimic its Arp2/3 complex-promoting activity in the lamellipodium. In conclusion, our results reveal a new spectrum of cytochalasin activities on barbed end-binding factors, with important implications for the interpretation of their effects on dynamic actin structures.

Hem1 is essential for ruffled border formation in osteoclasts and efficient bone resorption.

Bone resorption is highly dependent on the dynamic rearrangement of the osteoclast actin cytoskeleton to allow formation of actin rings and a functional ruffled border. Hem1 is a hematopoietic-specific subunit of the WAVE-complex which regulates actin polymerization and is crucial for lamellipodia formation in hematopoietic cell types. However, its role in osteoclast differentiation and function is still unknown. Here, we show that although the absence of Hem1 promotes osteoclastogenesis, the ability of Hem1-/- osteoclasts to degrade bone was severely impaired. Global as well as osteoclast-specific deletion of Hem1 in vivo revealed increased femoral trabecular bone mass despite elevated numbers of osteoclasts in vivo. We found that the resorption defect derived from the morphological distortion of the actin-rich sealing zone and ruffled border deformation in Hem1-deficient osteoclasts leading to impaired vesicle transport and increased intracellular acidification. Collectively, our data identify Hem1 as a yet unknown key player in bone remodeling by regulating ruffled border formation and consequently the resorptive capacity of osteoclasts.

The distinct localization of CDC42 isoforms is responsible for their specific functions during migration.

The small G-protein CDC42 is an evolutionary conserved polarity protein and a key regulator of polarized cell functions, including directed cell migration. In vertebrates, alternative splicing gives rise to two CDC42 proteins: the ubiquitously expressed isoform (CDC42u) and the brain isoform (CDC42b), which only differ in their carboxy-terminal sequence, including the CAAX motif essential for their association with membranes. We show that these divergent sequences do not directly affect the range of CDC42's potential binding partners but indirectly influence CDC42-driven signaling by controlling the subcellular localization of the two isoforms. In astrocytes and neural precursors, which naturally express both variants, CDC42u associates with the leading-edge plasma membrane of migrating cells, where it recruits the Par6-PKCζ complex to fulfill its polarity function. In contrast, CDC42b mainly localizes to intracellular membrane compartments, where it regulates N-WASP-mediated endocytosis. Both CDC42 isoforms contribute their specific functions to promote the chemotaxis of neural precursors, demonstrating that their expression pattern is decisive for tissue-specific cell behavior.

Neurite Outgrowth-Inducing Drimane-Type Sesquiterpenoids Isolated from Cultures of the Polypore Abundisporus violaceus MUCL 56355.

Abundisporin A (1), together with seven previously undescribed drimane sesquiterpenes named abundisporins B-H (2-8), were isolated from a polypore, Abundisporus violaceus MUCL 56355 (Polyporaceae), collected in Kenya. Chemical structures of the isolated compounds were elucidated based on exhaustive 1D and 2D NMR spectroscopic measurements and supported by HRESIMS data. The absolute configurations of the isolated compounds were determined by using Mosher's method for 1-4 and TDDFT-ECD calculations for 4 and 5-8. None of the isolated compounds exhibited significant activities in either antimicrobial or cytotoxicity assays. Notably, all of the tested compounds demonstrated neurotrophic effects, with 1 and 6 significantly increasing outgrowth of neurites when treated with 5 ng/mL NGF.

Biologically active drimane derivatives isolated from submerged cultures of the wood-inhabiting basidiomycete Dentipellis fragilis.

Four previously undescribed drimane sesquiterpenoids were isolated from submerged cultures of the wood-inhabiting basidiomycete Dentipellis fragilis along with two compounds that were previously reported as synthetic or biotransformation compounds but not as natural products. The constitution and relative configuration of these compounds was determined based on high-resolution electrospray ionization mass spectrometry as well as by 1D and 2D nuclear magnetic resonance spectroscopy. The absolute configurations were established based on exemplary calculation of circular dichroism spectra and comparison with measured data as well as on biogenetic considerations. The biological activities of the isolated compounds were assessed in antimicrobial, cytotoxicity and neurotrophic assays. 10-Methoxycarbonyl-10-norisodrimenin (3) exhibited weak activity against the Gram-positive bacterium Staphylococcus aureus and the zygomycete Mucor hiemalis with minimal inhibitory concentrations of 66.7 µg mL-1. In addition, compound 3 showed weak inhibition of the mammalian cell line KB3.1 (human endocervical adenocarcinoma) with a half maximal inhibitory concentration of 21.2 µM. The neurotrophic activities of 15-hydroxyisodrimenin (1) and 10-carboxy-10-norisodrimenin (5) were assed in neurite outgrowth and real-time quantitative reverse transcription polymerase chain reaction (RT-qPCR) assays. When supplemented with 5 ng mL-1 nerve growth factor (NGF), the drimanes 1 and 5 induced neurite outgrowth in PC-12 (rat pheochromocytoma) cells compared to cells solely treated with NGF. As evaluated by RT-qPCR, compounds 1 and 5 also increased NGF and brain-derived neurotrophic factor expression levels in 1321N1 astrocytoma cells. Interestingly, the current study only represents the second report on neurotrophic activities of this widespread class of terpenoids. The only other available study deals with Cyathus africanus, another basidiomycete that can produce drimanes and cyathanes, but is only distantly related to Dentipellis and the Hericiaceae.

RhoB promotes Salmonella survival by regulating autophagy.

Salmonella enterica serovar Typhimurium manipulates cellular Rho GTPases for host cell invasion by effector protein translocation via the Type III Secretion System (T3SS). The two Guanine nucleotide exchange (GEF) mimicking factors SopE and -E2 and the inositol phosphate phosphatase (PiPase) SopB activate the Rho GTPases Rac1, Cdc42 and RhoA, thereby mediating bacterial invasion. S. Typhimurium lacking these three effector proteins are largely invasion-defective. Type III secretion is crucial for both early and later phases of the intracellular life of S. Typhimurium. Here we investigated whether and how the small GTPase RhoB, known to localize on endomembrane vesicles and at the invasion site of S. Typhimurium, contributes to bacterial invasion and to subsequent steps relevant for S. Typhimurium lifestyle. We show that RhoB is significantly upregulated within hours of Salmonella infection. This effect depends on the presence of the bacterial effector SopB, but does not require its phosphatase activity. Our data reveal that SopB and RhoB bind to each other, and that RhoB localizes on early phagosomes of intracellular S. Typhimurium. Whereas both SopB and RhoB promote intracellular survival of Salmonella, RhoB is specifically required for Salmonella-induced upregulation of autophagy. Finally, in the absence of RhoB, vacuolar escape and cytosolic hyper-replication of S. Typhimurium is diminished. Our findings thus uncover a role for RhoB in Salmonella-induced autophagy, which supports intracellular survival of the bacterium and is promoted through a positive feedback loop by the Salmonella effector SopB.

Cytochalasans and Their Impact on Actin Filament Remodeling.

The eukaryotic actin cytoskeleton comprises the protein itself in its monomeric and filamentous forms, G- and F-actin, as well as multiple interaction partners (actin-binding proteins, ABPs). This gives rise to a temporally and spatially controlled, dynamic network, eliciting a plethora of motility-associated processes. To interfere with the complex inter- and intracellular interactions the actin cytoskeleton confers, small molecular inhibitors have been used, foremost of all to study the relevance of actin filaments and their turnover for various cellular processes. The most prominent inhibitors act by, e.g., sequestering monomers or by interfering with the polymerization of new filaments and the elongation of existing filaments. Among these inhibitors used as tool compounds are the cytochalasans, fungal secondary metabolites known for decades and exploited for their F-actin polymerization inhibitory capabilities. In spite of their application as tool compounds for decades, comprehensive data are lacking that explain (i) how the structural deviances of the more than 400 cytochalasans described to date influence their bioactivity mechanistically and (ii) how the intricate network of ABPs reacts (or adapts) to cytochalasan binding. This review thus aims to summarize the information available concerning the structural features of cytochalasans and their influence on the described activities on cell morphology and actin cytoskeleton organization in eukaryotic cells.

Hericioic Acids A-G and Hericiofuranoic Acid; Neurotrophic Agents from Cultures of the European Mushroom Hericium flagellum.

Neurodegenerative diseases are currently posing huge social, economic, and healthcare burdens among the aged populations worldwide with few and only palliative treatment alternatives available. Natural products continue to be a source of a vast array of potent neurotrophic molecules that could be considered as drug design starting points. The present study reports eight new isoindolinone and benzofuranone derivatives, for which we propose the trivial names, hericioic acids A-G (1-7) and hericiofuranoic acid (8), which were isolated from a solid culture (using rice as substrate) of the rare European edible mushroom Hericium flagellum. The chemical structures of these compounds were determined based on extensive 1D and 2D NMR spectroscopy along with HRESIMS analyses. The isolated compounds were assessed for their neurotrophic activity in rat pheochromocytoma cells (PC-12) to promote neurite outgrowth on 5 ng NGF supplementation; all the compounds increased neurite outgrowths, with compounds 3, 4, and 8 exhibiting the strongest effects.

Cytochalasans produced by Xylaria karyophthora and their biological activities.

The recent description of the putative fungal pathogen of greenheart trees, Xylaria karyophthora (Xylariaceae, Ascomycota), prompted a study of its secondary metabolism to access its ability to produce cytochalasans in culture. Solid-state fermentation of the ex-type strain on rice medium resulted in the isolation of a series of 19,20-epoxidated cytochalasins by means of preparative high-performance liquid chromatography (HPLC). Nine out of 10 compounds could be assigned to previously described structures, with one compound being new to science after structural assignment via nuclear magnetic resonance (NMR) assisted by high-resolution mass spectrometry (HRMS). We propose the trivial name "karyochalasin" for the unprecedented metabolite. The compounds were used in our ongoing screening campaign to study the structure-activity relationship of this family of compounds. This was done by examining their cytotoxicity against eukaryotic cells and impact on the organization of networks built by their main target, actin-a protein indispensable for processes mediating cellular shape changes and movement. Moreover, the cytochalasins' ability to inhibit the biofilm formation of Candida albicans and Staphylococcus aureus was examined.

Baculovirus Actin Rearrangement-Inducing Factor 1 Can Remodel the Mammalian Actin Cytoskeleton.

The actin rearrangement-inducing factor 1 (Arif-1) of Autographa californica multiple nucleopolyhedrovirus (AcMNPV) is an early viral protein that manipulates the actin cytoskeleton of host insect cells. Arif-1 is conserved among alphabaculoviruses and is responsible for the accumulation of F-actin at the plasma membrane during the early phase of infection. However, the molecular mechanism underlying Arif-1-induced cortical actin accumulation is still open. Recent studies have demonstrated the formation of invadosome-like structures induced by Arif-1, suggesting a function in systemic virus spread. Here, we addressed whether Arif-1 is able to manipulate the actin cytoskeleton of mammalian cells comparably to insect cells. Strikingly, transient overexpression of Arif-1 in B16-F1 mouse melanoma cells revealed pronounced F-actin remodeling. Actin assembly was increased, and intense membrane ruffling occurred at the expense of substrate-associated lamellipodia. Deletion mutagenesis studies of Arif-1 confirmed that the C-terminal cytoplasmic region was not sufficient to induce F-actin remodeling, supporting that the transmembrane region for Arif-1 function is also required in mammalian cells. The similarities between Arif-1-induced actin remodeling in insect and mammalian cells indicate that Arif-1 function relies on conserved cellular interaction partners and signal transduction pathways, thus providing an experimental tool to elucidate the underlying mechanism. IMPORTANCE Virus-induced changes of the host cell cytoskeleton play a pivotal role in the pathogenesis of viral infections. The baculovirus Autographa californica multiple nucleopolyhedrovirus (AcMNPV) is known for intervening with the regulation of the host actin cytoskeleton in a wide manner throughout the infection cycle. The actin rearrangement-inducing factor 1 (Arif-1) is a viral protein that causes actin rearrangement during the early phase of AcMNPV infection. Here, we performed overexpression studies of Arif-1 in mammalian cells to establish an experimental tool that allows elucidation of the mechanism underlying the Arif-1-induced remodeling of actin dynamics in a well-characterized and genetically accessible system.

Neurotrophic and Immunomodulatory Lanostane Triterpenoids from Wood-Inhabiting Basidiomycota.

Neurotrophins such as nerve growth factor (ngf) and brain-derived neurotrophic factor (bdnf) play important roles in the central nervous system. They are potential therapeutic drugs for the treatment of neurodegenerative diseases, including Alzheimer's disease and Parkinson's disease. In this study, we investigated the neurotrophic properties of triterpenes isolated from fruiting bodies of Laetiporus sulphureus and a mycelial culture of Antrodia sp. MUCL 56049. The structures of the isolated compounds were elucidated based on nuclear magnetic resonance (NMR) spectroscopy in combination with high-resolution electrospray mass spectrometry (HR-ESIMS). The secondary metabolites were tested for neurotrophin (ngf and bdnf) expression levels on human astrocytoma 1321N1 cells. Neurite outgrowth activity using rat pheochromocytoma (PC-12) cells was also determined. Twelve triterpenoids were isolated, of which several potently stimulated the expression of neurotrophic factors, namely, ngf (sulphurenic acid, 15α-dehydroxytrametenolic acid, fomefficinic acid D, and 16α-hydroxyeburicoic acid) and bdnf (sulphurenic acid and 15α-dehydroxytrametenolic acid), respectively. The triterpenes also potentiated ngf-induced neurite outgrowth in PC-12 cells. This is, to the best of our knowledge, the first report on the compound class of lanostanes in direct relation to bdnf and ngf enhancement. These compounds are widespread in medicinal mushrooms; hence, they appear promising as a starting point for the development of drugs and mycopharmaceuticals to combat neurodegenerative diseases. Interestingly, they do not show any pronounced cytotoxicity and may, therefore, be better suited for therapy than many other neurotrophic compounds that were previously reported.

Novel insights into mouse models of ectopic proplatelet release.

Mature bone marrow (BM) megakaryocytes (MKs) produce platelets by extending proplatelets into sinusoidal blood vessels. Defects in this process can lead to thrombocytopenia and increased risk of bleeding. Mice lacking the actin-regulatory proteins Profilin 1 (PFN1), Wiskott-Aldrich Syndrome protein (WASp), Actin Related Protein 2/3 complex (Arp2/3), or adhesion and degranulation-promoting adapter protein (ADAP) display thrombocytopenia and ectopic release of (pro)platelet-like particles into the BM compartment, pointing to an important axis of actin-mediated directional proplatelet formation. The mechanism underlying ectopic release in these mice is still not completely understood. However, we hypothesized that similar functional defects account for this observation. We analyzed WASp-, ADAP-, PFN1-, and ARPC2-knockout mice to determine the role of actin reorganization and integrin activation in directional proplatelet formation. ADAP-, ARPC2-, and PFN1-deficient MKs displayed reduced adhesion to collagen, defective F-actin organization, and diminished ß1-integrin activation. WASp-deficient MKs showed the strongest reduction in the adhesion assay of collagen and altered F-actin organization with reduced podosome formation. Our results indicate that ADAP, PFN1, WASp, and ARP2/3 are part of the same pathway that regulates polarization processes in MKs and directional proplatelet formation into BM sinusoids.

The autophagy inducer SMER28 attenuates microtubule dynamics mediating neuroprotection.

SMER28 originated from a screen for small molecules that act as modulators of autophagy. SMER28 enhanced the clearance of autophagic substrates such as mutant huntingtin, which was additive to rapamycin-induced autophagy. Thus, SMER28 was established as a positive regulator of autophagy acting independently of the mTOR pathway, increasing autophagosome biosynthesis and attenuating mutant huntingtin-fragment toxicity in cellular- and fruit fly disease models, suggesting therapeutic potential. Despite many previous studies, molecular mechanisms mediating SMER28 activities and its direct targets have remained elusive. Here we analyzed the effects of SMER28 on cells and found that aside from autophagy induction, it significantly stabilizes microtubules and decelerates microtubule dynamics. Moreover, we report that SMER28 displays neurotrophic and neuroprotective effects at the cellular level by inducing neurite outgrowth and protecting from excitotoxin-induced axon degeneration. Finally, we compare the effects of SMER28 with other autophagy-inducing or microtubule-stabilizing drugs: whereas SMER28 and rapamycin both induce autophagy, the latter does not stabilize microtubules, and whereas both SMER28 and epothilone B stabilize microtubules, epothilone B does not stimulate autophagy. Thus, the effect of SMER28 on cells in general and neurons in particular is based on its unique spectrum of bioactivities distinct from other known microtubule-stabilizing or autophagy-inducing drugs.

Lamellipodia-like actin networks in cells lacking WAVE regulatory complex.

Cell migration frequently involves the formation of lamellipodia induced by Rac GTPases activating WAVE regulatory complex (WRC) to drive Arp2/3 complex-dependent actin assembly. Previous genome editing studies in B16-F1 melanoma cells solidified the view of an essential, linear pathway employing the aforementioned components. Here, disruption of the WRC subunit Nap1 (encoded by Nckap1) and its paralog Hem1 (encoded by Nckap1l) followed by serum and growth factor stimulation, or active GTPase expression, revealed a pathway to formation of Arp2/3 complex-dependent lamellipodia-like structures (LLS) that requires both Rac and Cdc42 GTPases, but not WRC. These phenotypes were independent of the WRC subunit eliminated and coincided with the lack of recruitment of Ena/VASP family actin polymerases. Moreover, aside from Ena/VASP proteins, LLS contained all lamellipodial regulators tested, including cortactin (also known as CTTN), the Ena/VASP ligand lamellipodin (also known as RAPH1) and FMNL subfamily formins. Rac-dependent but WRC-independent actin remodeling could also be triggered in NIH 3T3 fibroblasts by growth factor (HGF) treatment or by gram-positive Listeria monocytogenes usurping HGF receptor signaling for host cell invasion. Taken together, our studies thus establish the existence of a signaling axis to Arp2/3 complex-dependent actin remodeling at the cell periphery that operates without WRC and Ena/VASP.

Antiproliferative and Cytotoxic Cytochalasins from Sparticola triseptata Inhibit Actin Polymerization and Aggregation.

Laying the groundwork on preliminary structure-activity relationship study relating to the disruptive activity of cytochalasan derivatives on mammalian cell actin cytoskeleton, we furthered our study on the cytochalasans of the Dothideomycetes fungus, Sparticola triseptata. A new cytochalasan analog triseptatin (1), along with the previously described cytochalasans deoxaphomin B (2) and cytochalasin B (3), and polyketide derivatives cis-4-hydroxy-6-deoxyscytalone (4) and 6-hydroxymellein (5) were isolated from the rice culture of S. triseptata. The structure of 1 was elucidated through NMR spectroscopic analysis and high-resolution mass spectrometry (HR-ESI-MS). The relative and absolute configurations were established through analysis of NOESY spectroscopic data and later correlated with experimental electronic circular dichroism and time-dependent density functional theory (ECD-TDDFT) computational analysis. Compounds 1 and 2 showed cytotoxic activities against seven mammalian cell lines (L929, KB3.1, MCF-7, A549, PC-3, SKOV-3, and A431) and antiproliferative effects against the myeloid leukemia K-562 cancer cell line. Both 1 and 2 were shown to possess properties inhibiting the F-actin network, prompting further hypotheses that should to be tested in the future to enable a well-resolved concept of the structural implications determining the bioactivity of the cytochalasin backbone against F-actin.

SMER28 Attenuates PI3K/mTOR Signaling by Direct Inhibition of PI3K p110 Delta.

SMER28 (Small molecule enhancer of Rapamycin 28) is an autophagy-inducing compound functioning by a hitherto unknown mechanism. Here, we confirm its autophagy-inducing effect by assessing classical autophagy-related parameters. Interestingly, we also discovered several additional effects of SMER28, including growth retardation and reduced G1 to S phase progression. Most strikingly, SMER28 treatment led to a complete arrest of receptor tyrosine kinase signaling, and, consequently, growth factor-induced cell scattering and dorsal ruffle formation. This coincided with a dramatic reduction in phosphorylation patterns of PI3K downstream effectors. Consistently, SMER28 directly inhibited PI3Kδ and to a lesser extent p110γ. The biological relevance of our observations was underscored by SMER28 interfering with InlB-mediated host cell entry of Listeria monocytogenes, which requires signaling through the prominent receptor tyrosine kinase c-Met. This effect was signaling-specific, since entry of unrelated, gram-negative Salmonella Typhimurium was not inhibited. Lastly, in B cell lymphoma cells, which predominantly depend on tonic signaling through PI3Kδ, apoptosis upon SMER28 treatment is profound in comparison to non-hematopoietic cells. This indicates SMER28 as a possible drug candidate for the treatment of diseases that derive from aberrant PI3Kδ activity.

Parallel kinase pathways stimulate actin polymerization at depolarized mitochondria.

Mitochondrial damage (MtD) represents a dramatic change in cellular homeostasis, necessitating metabolic changes and stimulating mitophagy. One rapid response to MtD is a rapid peri-mitochondrial actin polymerization termed ADA (acute damage-induced actin). The activation mechanism for ADA is unknown. Here, we use mitochondrial depolarization or the complex I inhibitor metformin to induce ADA. We show that two parallel signaling pathways are required for ADA. In one pathway, increased cytosolic calcium in turn activates PKC-ß, Rac, WAVE regulatory complex, and Arp2/3 complex. In the other pathway, a drop in cellular ATP in turn activates AMPK (through LKB1), Cdc42, and FMNL formins. We also identify putative guanine nucleotide exchange factors for Rac and Cdc42, Trio and Fgd1, respectively, whose phosphorylation states increase upon mitochondrial depolarization and whose suppression inhibits ADA. The depolarization-induced calcium increase is dependent on the mitochondrial sodium-calcium exchanger NCLX, suggesting initial mitochondrial calcium efflux. We also show that ADA inhibition results in enhanced mitochondrial shape changes upon mitochondrial depolarization, suggesting that ADA inhibits these shape changes. These depolarization-induced shape changes are not fragmentation but a circularization of the inner mitochondrial membrane, which is dependent on the inner mitochondrial membrane protease Oma1. ADA inhibition increases the proteolytic processing of an Oma1 substrate, the dynamin GTPase Opa1. These results show that ADA requires the combined action of the Arp2/3 complex and formin proteins to polymerize a network of actin filaments around mitochondria and that the ADA network inhibits the rapid mitochondrial shape changes that occur upon mitochondrial depolarization.

WASP stings into matrix to lead immune cell migration.

WASP is a remodeler of the actin cytoskeleton, but its mechanistic contribution to neutrophil migration is unclear. In this issue, Brunetti et al. (2021. J. Cell Biol.https://doi.org/10.1083/jcb.202104046) show that WASP is recruited to substrate-induced membrane deformations near the cell front, where it induces Arp2/3 complex-mediated local actin assembly to direct migration.

WAVE regulatory complex.

Dynamic rearrangement of the actin cytoskeleton drives a myriad of processes in eukaryotic cells, such as cell migration and vesicle trafficking, and its dysregulation is deeply associated with various diseases, including cancer, immune deficiency, and neurological disorders. Members of the Wiskott-Aldrich syndrome protein (WASP) family, including WASP, N-WASP, WAVE, WASH, WHAMM, JMY, and the recently identified WHIMP, are ubiquitous regulators of actin dynamics. Although each WASP-family protein uses a different regulatory mechanism and participates in distinct cellular processes, they all act by integrating various upstream signals and transmitting them to their carboxy-terminal WCA (WH2-central-acidic, where WH2 stands for WASP homology 2) domain. This domain stimulates the actin nucleation activity of the Arp2/3 complex to promote the formation of new filaments from existing ones, creating branched actin networks that are crucial for dynamic deformations of membranes.