In addition, using recordings from gerbil, mouse, and bullfrog auditory organs, we find that the spatial coupling between Ca2+ influx and exocytosis changes from nanodomain in low-frequency tuned hair cells (∼<2 kHz) to progressively more microdomain in high-frequency cells (∼>2 kHz). Hair cell synapses have thus developed remarkable frequency-dependent tuning of exocytosis: accurate low-latency encoding of onset and offset of sound intensity in the cochlea's base and submillisecond encoding of membrane receptor potential fluctuations in the apex for precise phase-locking to sound signals. We also found that synaptic vesicle pool recovery from depletion was sensitive to high concentrations of EGTA, suggesting that intracellular Ca2+ buffers play an important role in vesicle recruitment in both low- and high-frequency hair cells. In conclusion, our results indicate that microdomain coupling is important for exocytosis in high-frequency hair cells, suggesting a novel hypothesis for why these cells are more susceptible to sound-induced damage than low-frequency cells; high-frequency inner hair cells must have a low Ca2+ buffer capacity to sustain exocytosis, thus making them more prone to Ca2+-induced cytotoxicity.The cochlea processes auditory signals over a wide range of frequencies and intensities. However, the transfer characteristics at hair cell ribbon synapses are still poorly understood at different frequency locations along the cochlea. Using recordings from mature gerbils, we report here a surprisingly strong block of exocytosis by the slow CaSIGNIFICANCE STATEMENT In the inner ear, sensory hair cells signal reception of sound. They do this by converting the sound-induced movement of their hair bundles present at the top of these cells, into an electrical current. This current depolarizes the hair cell and triggers the calcium-induced release of the neurotransmitter glutamate that activates the postsynaptic auditory fibers. The speed and precision of this process enables the brain to perceive the vital components of sound, such as frequency and intensity. We show that the coupling strength between calcium channels and the exocytosis calcium sensor at inner hair cell synapses changes along the mammalian cochlea such that the timing and/or intensity of sound is encoded with high precision. Hair cells have developed unique morphological, molecular, and biophysical features that allow them to distinguish a wide range of sound frequencies and intensities  while machannels , clusterchannels , and useocytosis . However2+ channels and docked vesicles improves release efficiency and is important for fast and high-fidelity neurotransmission, not only at functionally mature sensory synapses  (2+ channels and the exocytotic Ca2+ sensor (2+ influx and exocytosis is controlled by the cooperativity of many channels (Ca2+ microdomain), and it is the Ca2+ sensor that generates the efficient exocytosis in mature IHC ribbon synapses  , but alsof Held)  and mammof Held) . Calcium+ sensor  has also+ sensor . This ti+ sensor  and also+ sensor , which p+ sensor . Howeversynapses .2+ chelator BATPA on exocytosis and found it to be comparable in apical and basal gerbil IHCs  of ∼0.35, ∼2.5, and ∼30 kHz, respectively. Experiments were also performed on P19 to P26 mouse (of either sex) IHCs positioned in the apical coil of the cochlea with a mean CF of ∼3.0 kHz. All experiments in mice and gerbils were performed in accordance with Home Office regulations under the Animals (Scientific Procedures Act) 1986 and following approval by the University of Sheffield Ethical Review Committee.IHCs from young adult gerbils of either sex  were stu2, 0.9 MgCl2, 0.7 NaH2PO4, 5.6 d-glucose, 10 HEPES-NaOH. Sodium pyruvate (2 mM), amino acids, and vitamins were added from concentrates (Fisher Scientific). The pH was adjusted to 7.5 . The dissected cochlear coils were transferred to a microscope chamber containing extracellular solution and viewed using an upright microscope (Olympus BX51WI or Nikon FN1) with Nomarski DIC optics and a long working distance 60× water-immersion objective.Cochleae were dissected from gerbils and mice in normal extracellular solution (in mM) as follows: 135 NaCl, 5.8 KCl, 1.3 CaClmΩ) were coated with surf-wax (Mr Zoggs SexWax) and contained the following (in mM): 106 Cs-glutamate, 20 CsCl, 3 MgCl2, 1 EGTA-CsOH, 5 Na2ATP, 0.3 Na2GTP, 5 HEPES-CsOH, 10 Na2-phosphocreatine, pH 7.3 (294 mmol/kg). In the experiments in which 1 mM EGTA was replaced by different EGTA concentrations , Cs-glutamate was adjusted to keep the osmolality constant. In a few experiments, perforated patch was used, and the pipette-filling solution contained the following (in mM): 110 Cs-aspartate, 21 CsCl, 3 MgCl2, 5 Na2ATP, 1 BAPTA, 5 HEPES-CsOH, 10 Na2-phosphocreatine, pH 7.3 (295 mmol/kg). The antibiotic amphotericin B (Merck Millipore) was dissolved in dry DMSO before dilution in the above intracellular solution to 120 or 240 μg/ml (Gerbil and mouse recordings were performed at body temperature (34°C–37°C) using an Optopatch amplifier (Cairn Research). Patch pipettes (2–3 40 μg/ml .Cm) were measured as previously described (Cm requires a high and constant membrane resistance (Rm), which was 738 ± 61 mΩ (n = 87). In the experiments performed at the physiological membrane potentials , which could possibly lead to some facilitation of vesicle release (Cm was measured by averaging the Cm trace over a 200 ms period following the voltage step and subtracting the prepulse baseline. Data were acquired using pClamp software (RRID:SCR_011323) and a Digidata 1440A (Molecular Devices) and analyzed with Origin 2016 . Membrane potentials were corrected for the voltage drop across the series resistance  and a liquid junction potential of −11 mV, measured between electrode and bath solutions. The cell membrane capacitance (Cm) in whole cell was as follows: apical coil IHCs, 11.6 ± 0.2 pF, n = 60; middle, 11.3 ± 0.5 pF, n = 12; basal, 11.4 ± 0.4 mΩ, n = 45; Cm in perforated patch was as follows: apical coil IHCs, 10.8 ± 0.3 pF, n = 4; basal, 10.0 ± 0.5 mΩ, n = 5. The average voltage-clamp time constant (product of Rs and Cm) in whole cell was 56 ± 2 μs in apical, 55 ± 2 μs in middle, and 62 ± 4 μs in basal IHCs; in perforated patch, it was 55 ± 2 μs in apical and 48 ± 2 μs in basal IHCs. Experiments were performed in the presence of 30 mM TEA and 15 mM 4-AP in the extracellular solution  to block the BK current , and linopirdine (80 μm: Tocris Bioscience) to block IK,n  were carefully dissected as previously described . Oxygenated artificial perilymph was perfused continuously (2–3 ml/min) during the recordings, which were performed at room temperature.Following an Oregon Health and Science University  approved animal care protocol, amphibian papillae of adult female or male bullfrogs . The amount of Cs-gluconate was adjusted to match osmolarity of 230 mmol/kg for pipette solution containing 0.1 and 10 mM EGTA instead of 2 mM EGTA. For whole-cell recordings, patch pipettes of borosilicate glass were pulled to resistances of 6–7 mΩ for hair cells and 8–9 mΩ for afferent fibers. Hair cells were voltage-clamped with a resting membrane potential of either −60 mV or −90 mV, and afferent fibers were held at −90 mV (mΩ for hair cells (n = 93) and 26.5 ± 1.7 mΩ for afferent fibers (n = 17). ΔCm measurements were performed under voltage clamp with the “Sine + DC” method (Cm via a Patchmaster software emulator of a lock-in amplifier (An Olympus BX51WI microscope equipped with a 60× water-immersion objective lens (Olympus) and digital CCD camera (QImaging Scientific) were used to view the preparation, and electrophysiological recordings were performed in the middle area of amphibian papillae at an average CF of ∼0.4 kHz . All rect −90 mV . Membran” method  using anmplifier .t test and one-way ANOVA followed by the Bonferroni test. Data are expressed as mean ± SEM.Data analysis was performed with Igor Pro software  and Prism . Statistical significance was assessed with unpaired 2+-dependent exocytosis in hair cells at specific CFs of the mature gerbil, mouse, and bullfrog auditory organs. Although the mouse and the frog are the most common animal models used for hearing research, they are mainly tuned to high- (mouse hearing frequency range: ∼2–100 kHz) (Whole-cell patch-clamp recordings were used to investigate Ca100 kHz)  and low-100 kHz)  frequenc100 kHz) , more si100 kHz) , which s2+ concentration present in the perilymph surrounding the IHCs (1.3 mM)   . The phyocytosis . This is+ sensor . As suchn) e.g., .ICa) and corresponding ΔCm recordings from IHCs positioned along the gerbil cochlea are shown in 2+ at body temperature . This is consistent with previous findings showing that the size of ICa in apical and basal gerbil IHCs was unaffected by different concentrations of the intracellular Ca2+ buffer BAPTA . Although in apical IHCs 10 mM EGTA did not significantly affect ΔCm  compared with 0.1 mM EGTA  , the ability of the Ca2+ chelator EGTA to uncouple Ca2+ influx and exocytosis greatly increased toward the high-frequency region of the gerbil cochlea. In the presence of 0.1 mM intracellular EGTA, the size of the induced ΔCm in IHCs from the middle  and basal  cochlear regions were significantly larger  than the values obtained when EGTA was increased to 10 mM . In 10 mM EGTA, ΔCm was significantly (p < 0.001) smaller in basal and middle IHCs compared with apical cells. With 10 mM intracellular EGTA, the largely reduced or absent ΔCm in middle and basal IHCs, respectively, suggests the presence of a microdomain coupling between the Ca2+ channels and the Ca2+ sensor for vesicle fusion. This finding is also supported by the fact that, although the size of ΔCm in apical IHCs  is comparable to that previously reported using 1 mM intracellular EGTA (50 ms voltage step)  was in most cells larger despite the similar number of synaptic ribbons per cell in the two regions  is unlikely to result in a different ΔCm. However, the microdomain scenario in high-frequency IHCs would allow Ca2+ to travel further when reducing the concentration of EGTA from 1 to 0.1 mM, and most likely able to recruit a small part of the secondary releasable pool in some IHCs (see below).Calcium-dependent exocytosis was measured from IHCs (P20-P27) positioned in the apical (low-frequency: CF ∼0.35 kHz), middle (CF ∼2.5 kHz), and basal (high-frequency: CF ∼30 kHz) regions of the gerbil cochlea. Calcium currents  A,D, the ge step) , that me regions . Because regions  to 0.1 mCm in response to depolarizing voltage steps to −11 mV of varying duration , which is also in agreement with previous reports in mice , the size of the isolated RRP in 10 mM EGTA  was not significantly different from that obtained in 0.1 mM EGTA , as also shown in Figure 1D. The initial release rate was also similar between the two recording conditions . However, compared with 0.1 mM EGTA, 10 mM EGTA largely reduced the release from the RRP in middle-coil IHCs  and almost completely abolished it in basal cells . As for IHCs in the apical coil, the initial release rate in middle IHCs was also similar between the two recording conditions .To investigate whether the vesicle pool dynamics in high EGTA also varied as a function of frequency position, we measured the rate of neurotransmitter release in gerbil IHCs (P18-P31) by measuring Δsee also , 2010. Lls frog: . In 10 m in mice  and lowe in mice . However2+ buffering, we found that the pool sizes and release kinetics of the RRP and SRP were comparable between apical and basal cells in these physiological conditions (A–C). We have previously shown that the endogenous buffer concentration was similar between low- and high-frequency gerbil IHCs when expressed as an equivalent BAPTA concentration , they revealed a higher sensitivity to Ca2+ buffering in high-frequency IHCs (∼2.9 mM) compared with low-frequency cells (∼6.6 mM) (D). However, this is not an indication of the endogenous buffer in IHCs but provides further evidence for a different exocytotic Ca2+ coupling of the RRP between apical and basal cells.Using perforated-patch recordings that preserve the endogenous intracellular Canditions A–C. We hntration . However of EGTA D, they r∼6.6 mM) D. Howeve2+ influx and exocytosis observed in IHCs along the gerbil cochlea  in the presence of either low (0.1 and 1 mM) or high (5 and 10 mM) concentrations of intracellular EGTA, respectively. The apical coil of the mouse cochlea has a CF in the same range to that of the middle region of the gerbil cochlea (∼2.5 kHz: ICa recorded in IHCs (P15-P26) was not significantly different between low  and high EGTA . However, the induced ΔCm was significantly reduced  in the presence of 5 mM  or 10 mM EGTA  , compared with the lower concentrations .To confirm that the different coupling between Ca cochlea –3 was duCm in response to depolarizing voltage steps of increasing duration (E) as described for Cm that could be approximated with a single exponential (F). However, in the presence of 5 or 10 mM intracellular EGTA, the largely reduced size of the RRP was also associated with a significantly reduced initial release rate  compared with that measured in lower EGTA concentrations  (F). The SRP in high EGTA was almost absent (E). Considering that the total number of ribbons per IHC is ∼20 (2+ (5–10 mM) and room temperature.The rate of neurotransmitter release in mouse IHCs (P19-P26) was studied by measuring Δduration E as desconential F. Howevey ANOVA) F. The SRt absent E. ConsidC is ∼20 , the vesC is ∼20  but not C is ∼20  cells usICa and the corresponding ΔCm in single hair cells from a semi-intact adult bullfrog amphibian papilla preparation, which are tuned to a lower frequency range (∼400–500 Hz) . A depolarization to −30 mV elicits the peak ICa in bullfrog hair cells (Cm (A) . Depolarizing pulses <50 ms did not show any significant difference in ΔCm between 2 and 10 mM EGTA  . Our previous study shows that a pulse <50 ms from −90 mV to −30 mV only triggers the RRP of hair cells, which includes ∼700 vesicles per hair cell, or 12 vesicles per synaptic ribbon . The average ΔCm in response to a 20 ms pulse was not significantly different with 0.1 mM , 2 mM , and 10 mM EGTA . In contrast, different concentrations of intracellular EGTA significantly changed the average ΔCm in response to a 500 ms pulse : ΔCm with 0.1 mM , which was significantly different from that with 10 mM EGTA , although the ΔCm with 2 mM  was not significantly different from those with 0.1 and 10 mM EGTA (post-test). In summary, our data suggest that, in stark contrast to mouse high-frequency IHCs  , to examurations A. A depoir cells . As the ells (Cm A (Li et  (Cm (A) . We complar EGTA A,B. Depo < 0.05) . Howeverc ribbon . To confncy IHCs , the relCm recovery from gerbil IHCs (P18-P27) positioned in the apical and basal cochlear regions by applying a two-pulse protocol in which cells were depolarized to −11 mV for 50 ms, which recruited the RRP, while changing the interpulse interval (IPI) from 10 ms up to 1.0 s (A). Examples of ΔCm recorded from apical and basal IHCs using the two-pulse protocol and in the presence of either 0.1 mM EGTA or 10 mM EGTA are shown in Figure 6B and C, respectively. The average ΔCm ratio  from apical IHCs  was plotted against IPI, and the data were well approximated with a single exponential function . For basal IHCs, the average ΔCm ratio in 0.1 mM EGTA showed an initial depression at short intervals and then facilitation at ∼100 ms   .in vivo resting membrane potential (A). Hair cells were stimulated by a pair of 20 ms depolarizing pulses from −60 mV to −30 mV with various IPIs and EPSCs recorded from the connected postsynaptic afferent fibers . The average amplitude of the first EPSC was not significantly different with 2 mM  and 10 mM EGTA , showing that the RRP exocytosis released by 20 ms pulses is insensitive to the concentration of EGTA. These results using AMPA receptor-mediated EPSCs confirm our earlier results with ΔCm changes in hair cells held at −90 mV .To study whether the concentration of EGTA can affect short-term plasticity at low-frequency tuned hair cell synapses (tuned to ∼400–500 Hz), we performed paired recordings between adult bullfrog hair cells and their afferent fibers. We held presynaptic hair cells at −60 mV, which is close to their physiological otential  and measotential A. Hair ct fibers A,B. The 0 mV see A,C.A,B). For short IPIs, such as 20 ms, this synapse shows very strong paired-pulse depression; and as the IPIs get longer, paired-pulse depression recovers . This depression is not caused by AMPA receptor desensitization  and slow  time constants (C)  and slow  time constants. The median (weighted-mean) time constant increased significantly from 232 ms with 2 mM EGTA to 787 ms with 10 mM EGTA. These data thus indicate that recovery of paired-pulse depression is dependent on global intracellular Ca2+ levels within hair cells. This suggests again that the recruitment of vesicles from a reserve vesicle pool to the RRP is sensitive to the intracellular levels of EGTA and thus to the intracellular free Ca2+.We next studied the changes in PPR with 2 and 10 mM EGTA. While hair cells were held at −60 mV, the second EPSC was smaller than the first EPSC throughout various IPIs (from 3 ms to 4 s), showing a robust paired-pulse depression A,B. For recovers A,B. Thistization , and mortization . We examonstants C (Cho etants (C) . When wein vivo resting potential is likely to be ∼−50 mV for apical and −60 mV for basal IHCs (ICa has been shown to activate at ∼−60 mV (gerbils) . Therefore, we investigated gerbil IHC (P19-P28) exocytosis and the coupling between Ca2+ influx and the RRP using the more physiological resting membrane potentials  for both the RRP and SRP. This also allowed us to test the specific effect of the theoretical in vivo membrane potential on the release and replenishment of the RRP. Despite the different resting membrane potentials, the maximal ICa  and the corresponding ΔCm  was similar between apical and basal IHCs (A–D), as well as the size of the RRP (E). However, the rate of ΔCm recovery during paired pulses was significantly faster in basal  than in apical IHCs . This is in line with our findings in the bullfrog showing that faster recovery depends on the availability of global free intracellular Ca2+ present in a microdomain situation (C).The above experiments in mice and gerbils were performed using a holding potential of −81 mV, which is commonly used for exocytosis (capacitance measurements) studies from hair cell ribbon synapses mouse: . Becausesal IHCs , and ICagerbils) , cells wtentials . For theable ΔCm  as thoseable ΔCm E for botsal IHCs A–D, as w the RRP E. Howeveituation C.2+ level and body temperature, we show that the coupling between Ca2+ channels and the Ca2+ sensor for vesicle fusion changes as a function of the cell's frequency position. While low-frequency hair cells (∼<2 kHz), which phase-lock to sound, exhibit a nanodomain coupling between Ca2+ channels and Ca2+ sensor, high-frequency cells have a looser coupling, which becomes progressively more microdomain along the gerbil cochlea. We have also shown that the level of intracellular Ca2+ buffer affects the speed of recovery from paired-pulse synaptic depression. We propose that either nanodomain or microdomain coupling is present in mature auditory hair cells, the function of which is to preserve the precise temporal coding of sound in phase-locked low-frequency hair cells and stimulus intensity in high-frequency cells, respectively.Using physiological recording conditions, in terms of extracellular Ca2+ entry and vesicle fusion at IHC ribbon synapses is the change in the Ca2+ dependence of exocytosis from a high-order relation in immature cells to linear in mature post-hearing cells  (2+ channels are sufficient to govern the release of a nearby vesicle (2+ sensor(s) that affect the intrinsic Ca2+ dependence of the synaptic machinery. Although otoferlin is the major Ca2+ sensor in IHCs  . In this vesicle . However in IHCs , synaptopendence , which cA domain . In thisstulated . These tectively .2+ channels and exocytotic Ca2+ sensors at mature synapses. However, recent findings have shown that mature hippocampal synapses can also operate via a loose coupling . Although it has previously been reported that the RRP in mouse IHCs was insensitive to 5 mM EGTA  was largely reduced by 5 mM EGTA  and bull frog papilla (<1 kHz), were relatively insensitive to EGTA, whereas RRP release from IHCs responding above a few kHz was either largely reduced (∼2–3 kHz) or abolished (∼30 kHz). This indicates that the spatial coupling between Ca mM EGTA , perhaps mM EGTA .C). The enhanced fast recovery of EPSCs with lower Ca2+ buffering may be due to the greater spread of Ca2+ that speeds the replenishment of vesicles to the ribbon , but still within the limit for phase-locking, the reduced time for Ca2+ influx into IHCs is likely to be insufficient to trigger exocytosis; this could be overcome, in a nanodomain scenario, by the elementary Ca2+ tail currents, where the amplitude and speed of the current are maximized and constant. Indeed, when sinusoidal stimuli of a few hundred hertz were applied to rat IHCs or hair cells from the bullfrog papilla, afferent fibers responded with large EPSCs that occurred more frequently during the repolarizing phase of the cycles  has a predominantly phasic component that is phase-locked to the sound frequency and graded in size to the stimulation intensity . The locmplitude . At verye cycles , which cICa with sound intensity are now more relevant   exhibit a strong block of exocytosis by 10 mM EGTA, indicating that these cells cannot have a large endogenous Cantration . Indeed,encoding , suggestlbindin) , suggest2+-binding proteins, which will not block exocytosis but may confer neuroprotection against excessive Ca2+ influx during prolonged stimulation. By contrast, the low Ca2+ buffer capacity in high-frequency basal IHCs, which is required for their graded release, will make them more prone to Ca2+-induced cytotoxicity. A tonotopic gradient in Ca2+-binding protein expression has been reported in auditory hair cells (High-frequency hair cell synapses are also particularly vulnerable to damage during loud noises and aging, which has been shown to lead to the loss of both IHC synaptic ribbons  and low-ir cells , which mir cells .


Lonicera confusa, especially to karst calcium-rich environment, can provide important theoretical basis for repairing desertification by genetic engineering. In this study, the Ca2+ imaging in the leaves of L. confusa was explored by LSCM  and TEM (Transmission Electron Microscopy), which revealed that the calcium could be transported to gland, epidermal hair and stoma in the leaves of L. confusa in high-Ca2+ environment. In addition, we simulated the growth environment of L. confusa and identified DEGs  under different Ca2+ concentrations by RNA sequencing. Further analysis showed that these DEGs were assigned with some important biological processes. Furthermore, a complex protein-protein interaction network among DEGs in L. Confusa was constructed and some important regulatory genes and transcription factors were identified. Taken together, this study displayed the Ca2+ transport and the accumulation of Ca2+ channels and pools in L. Confusa with high-Ca2+ treatment. Moreover, RNA sequencing provided a global picture of differential gene expression patterns in L. Confusa with high-Ca2+ treatment, which will help to reveal the molecular mechanism of the adaptation of L. confusa to high-Ca2+ environment in the future.As a medicinal plant widely planted in southwest karst of China, the study of adaptation mechanisms of  As one of typical species in southwestern China, the study on the adaptation mechanisms of Lonicera confusa to karst environment, especially to karst calcium-rich environment, can provide important theoretical basis for repairing desertification environment by plant genetic engineering.Currently, ecological deterioration, soil erosion and desertification increase have seriously restricted the development of local economy in karst area of southwestern China. The use of genetic engineering to repair desertification is an important method in vegetation recovery2+), one of the most abundant metal elements, is available in most soils3. It is involved in the growth, development and the adaptation to the environment in plants. It is also one of the most important second messenger upon environmental stimulation4. Through the cytoplasmic concentration of Ca2+ cyclical change, plants response to outside stimulation and produce calcium signals. The calcium target protein, such as calmodulin (CaM), calcium dependence protein kinase (CDPKs) and calcineurin B (CBL), pass down the signal to regulate plant growth, development, photosynthesis and stress resistance7. On the other side, high concentration of Ca2+ in the cell can cause toxicity9. Excessive Ca2+ restricted the growth of many plants in calcareous soils10. For instance, high Ca2+ interfered with various crucial cell processes, including Ca2+ dependent signaling, phosphate-based energy metabolism and microskeletal dynamics12. Previous studies indicated that plant cells have evolved to possess fine mechanism to adjust free Ca2+ concentration in the cytoplasm in response to environmental changes, which mainly through the body Ca2+ transport system, including Ca2+-ATPase and Ca2+ channels18. For example, some plant cells can actively transport Ca2+ from the cytosol into the vacuole, endoplasmic reticulum, mitochondria, plastids and cell walls21, and other plants could accumulate crystalline Ca oxalate and deposit it in the storage parenchyma, bundle sheath cell, epidermal trichomes or chlorenchyma24.Calcium ions . Moreover, differentially expressed genes (DEGs) are identified under different Ca2+concentrations by employing RNA-seq technology and GeneFishing PCR. The results showed that multiple DEGs were related to Ca2+ transport and accumulation in L. confusa. Furthermore, protein-protein interaction network among DEGs identified some important regulatory genes and transcription factors. In summary, the present results provided the groundwork for revealing the molecular mechanism for the adaptation to calcium-rich environment in L. confusa.In this study, the ultrastructure of mature leaves treated with high or low CaL. confusa planted in Nongla Karst Experimental Site  was performed for microwave digestion and flame atomic absorption spectrometry. The results revealed that the average calcium content was about 5.93 mg · g−1, which was much higher than that planted in sandstone soil36. In order to identify the distribution law of calcium in the leaves of L. confusa, the 0, 25, 50, 75, 100 and 125 mg/L gradient concentration of calcium chloride were used for pouring the plant materials, respectively. The leaves with different concentration of external Ca2+ treatment were labeled with Fluo-3/AM ester and examined under LSCM.The mature leaves of 2+ concentration37. The LSCM results in this study revealed that the fluorescent intensity improved with increased external Ca2+ treatment  for 24 hours and 30 days were used for DEG analysis. Two biological replicates of RNA-seq of L. confusa leaf tissues treated with different level of Ca2+ were performed. The two sets of the corresponding sequencing samples were combined, which generated 57393938, 69001767 and 60782634 clean reads, respectively. The obtained clean reads were then mapped to the assembled transcriptome of L. confusa38. The results showed that 35584241, 44851148 and 38596972 clean reads can be mapped to the assembled unigenes38, respectively. Among the mapped reads, 24908968, 32292826 and 28171538 clean reads were uniquely mapped to the unigenes, respectively. 10675273, 12558322 and 10425434 clean reads were mapped to multiple locations of unigenes, respectively. After mapping, 94607, 90574 and 86396 expressed unigenes for 0 h, 24-hour and 30-day Ca2+-treatment were obtained, respectively. To identify the DEGs between control and calcium-treated L. Confusa, we set the expression level of unigenes of control as a control and investigated the up- or down-regulated unigenes of calcium-treated L. confusa. The analysis showed that 322,69 unigenes were differentially expressed between control and 24-hour calcium-treatment L. confusa, and 43,148 unigenes were differentially expressed between control and 30-day calcium-treatment L. confusa. Also, we observed that a total of 34,155 unigenes were differentially expressed between 24-hour and 30-day calcium-treatment L. confusa samples, which indicated that short-term (24-hour) and long-term (30-day) Ca2+ treatment to L. confusa may induce different physiological status of L. confusa. As shown in Supplementary Fig. L. Confusa were further annotated with GO terms. Furthermore, the GO-enriched DEGs between control and calcium-treated L. Confusa were displayed by heatmap analysis  for 30 days were used for GeneFishing analysis. In all, 24 DEGs were identified between control and high Ca2+-treated L. confusa . As shown in Fig. 2+ induction DEGs generated 300 and 404 nodes, respectively. These nodes were classified into different categories. The common terms between short-term (24 hours)  Fig.  and longrs) Fig.  Ca2+ ind2+ treatment) and 30-day Ca2+ treatment L. Confusa were further assigned for KEGG pathway analysis. As shown in Supplementary Dataset −7), “Phenylpropanoid biosynthesis” , “Methane metabolism” (P = 2.39 × e−6), “Cyanoamino acid metabolism”  and “Phenylalanine metabolism” . Furthermore, we extracted the Ca2+ metabolism-related pathways for analysis. As shown in Supplementary Fig. 2+ metabolism-related pathways were classified into five categories including Cellular Processes, Environmental Information Processing, Genetic Information Processing, Metabolism and Organismal Systems. Among them, Cellular Processes category enriched 142 genes in which 32 genes are involved in the pathway of “Transport and catabolism”. More importantly, we observed that a lot of (265) genes are involved in “Signal transduction” pathway in Environmental Information Processing category. These results indicated long-term Ca2+ treatment on L. Confusa may induce Ca2+ transport and related signal transduction processes.To reveal biological functions of the identified genes, the DEGs between control  and Ca2+-ATPases (ACA)21. CAX1 has a primary role in Ca2+ accumulation in the leaf mesophyll and it is important in controlling apoplastic Ca2+, stomatal aperture, and growth42. In this study, we also observed high-Ca2+ treatment induced the transport of Ca2+ to trichomes, glands, and stoma in the leaves of L. Confusa. Moreover, more calcium channels and calcium pool are accumulated in the leaves of L. confusa in high calcium environment. Although the signaling role of Ca2+ in organisms has developed rapidly21, fundamental information regarding the mechanisms that regulate Ca2+ transport and storage in plants still remains elusive43.Various studies have revealed that CaL. Confusa. Bioinformatics analysis showed that 322,69 unigenes were differentially expressed between control and 24-hour calcium-treatment L. confusa, and 43,148 unigenes were differentially expressed between control and 30-day calcium-treatment L. confusa. Importantly, the different gene expression level between 0-hour and 24-hour or 30-day Ca2+-treated L. confusa might be induced not only by the Ca2+ treatment but also by own natural growth of L. confusa. Therefore, we could not fully exclude the effect of 24-hour or 30-day natural growth of L. confusa on the gene expression level. Nevertheless, the samples used for RNA-seq were mature leaves of L. confuse. We supposed that the gene expression level in the mature leaves is very stable in 24 hours or 30 days, and the different gene expression level between 0-hour and 24-hour or 30-day Ca2+-treated L. confusa were mainly induced by Ca2+ treatment. Furthermore, the identified DEGs were validated by GeneFishing PCR. For example, Tua3, CaM, CDPKs, CBL and some other important genes were identified. Tua3 is one of the important cytoskeleton components. Our network analysis showed that Tua3 interacts with 9 target genes, in which all target genes are associated with the formation of microtubule. Taken together, these results indicate that Tua3 and target genes may regulate cell morphology and intercellular transportation by a complex gene interaction network in L. confusa. In the meanwhile, it has been reported that CaM, CDPKs and CBL are involved in cytoskeleton formation and movement, osmotic stress resistance45. Calcium, as the second messenger upon environmental stimulation in plant, plays critical roles in response to outside signals and activates the expression of related genes. For Ca2+ transport into the vacuole in plant cells, both Ca2+-ATPases (ACA) and Ca2+/H+ antiporters (CAX) play important roles46. Therefore, transcript abundance of transporters could be up-regulated under conditions of adequate Ca supply. Also, proteins that modify activity of transporters, such as CAM or CXIP, could also be regulated in a similar fashion48. For instance, compared with epidermal cells, mesophyll cells of Arabidopsis have the higher capacity to store Ca2+ in their vacuoles by virtue of the higher expression of the Ca2+/H+ antiporter on the tonoplast membrane41. Our DEGs analysis in this study showed that CaM and CAX were upregulated in long-term Ca2+ treated L. Confusa, which might reflect the adaptive changes of L. Confusa to high-Ca2+ environment. In addition, EnrichmentMap analysis showed that multiple DEGs were involved in “Cellular cation homeostais” and “Transport” processes. The results suggested that Ca2+ treatment induced the activation of relative Ca2+ transport pathways and L. confusa gradually adapted to high-Ca2+ environment and kept a new cation balance after long-term Ca2+ treatment, which is very consistent with our LSCM and TEM results. Collectively, identification of these important DEGs will help us to explore the possible regulatory mechanism of the adaptation to high-Ca2+ environment in L. confusa.RNA-seq technology is an effective transcriptome analysis tool, which can detect novel and rare RNA transcripts and accurately quantify gene expression level. In this study, we identified multiple DEGs  between control and calcium-treated L. confusa cultivars were taken from typical Nongla Karst Experimental Site  as previously described34. The L. confusa cultivars were planted in the soils transported from Nongla Karst Experimental Site. In order to remove the calcium ions in the soils, the soils were washed with pure water for several times. Furthermore, 24 basin of L. confusa materials were divided into six groups and treated with different concentrations of Ca2+, respectively.2+ images in the leaves of L. confusa were detected as previously described49. The L. confusa leaves growing in soils with different level Ca2+ were soaked in Fluo-3/AM ester solution at 4 °C for 2 h. These L. confusa leaves were then washed with PBS solutions and observed under Olympus FV1000 LSCM .The CaL. confusa was performed as previously described50 except for small modification. First, 5 independent leaf samples of L. confusa with different level Ca2+ treatment were isolated, washed with phosphate buffer solution and cut into 0.2 cm × 0.2 cm slices. Furthermore, these samples were fixed and dehydrated through graded ethanol concentrations once for 10 min and soaked in 100% acetone twice for 30 min. Subsequently, the samples were treated with 2% potassium pyroantimonate and dehydrated. Finally, the samples were embedded with Spurr epoxy resin and sectioned with superfine section machine. The obtained sections were dyed and examined using TEM .TEM analysis of the leaves of L. confusa leaves treated with different level of Ca2+ was performed as previously described51. GeneFishing kit  was used for differential display PCR analysis. GeneFishingTM PCR were done with dT-ACP2 and 20 pairs of random primers, the PCR products were run on 2% agarose gel and the cDNA bands ranged from 100 and 1.5 kb were used for cloning and sequencing  and sequenced. Further Semi-quantitative RT- PCR experiments were utilized for the validation of the GeneFishing results. The Primers used for GeneFishing PCR and Semi-quantitative RT- PCR were shown in Supplementary Tables The total RNA isolation of the L. confusa leaves treated with different level of Ca2+ were constructed using TruSeqTM RNA Sample Preparation Kit . Shortly, oligo (dT) magnetic beads (NEB) were used to capture poly-A mRNAs from the isolated total RNA. The captured mRNAs were fragmented into 200–500 bp for cDNA synthesis and adaptor ligations. The synthesized cDNAs were PCR-amplified, quantified and sequenced on Illumina HiSeq 2000 using 2 × 100 bp pair-end sequencing protocol. The generated clean reads were deposited in NCBI Sequence Read Archive (SRA) Sequence Database (Accession number: SRR6024635). Bioinformatics analysis of differentially expressed genes of RNA-seq samples was performed as described37. Briefly, gene expression level of each RNA-seq sample was measured by RPKM (Reads Per kb per Million reads). The genes with RPKM ≥1 were regarded to be expressed in the RNA-seq analysis. The edgeR software was then used to identify the differentially expressed genes. The differentially expressed genes among L. confusa leaves treated with different level of Ca2+ were selected using a log FC (log-fold expression change) >2 or <−2, a false discovery rate (FDR < 0.001) and p-value < 0.005 as the threshold value.The RNA-seq cDNA libraries of http://www.genome.jp/tools/blast). Cytoscape_2_6_3 (http://www.cytoscape.org/plugins/index.php) was used to analyze the protein-protein interaction among DEGs.The functions of the DEGs were analyzed by using Kyoto Encyclopedia of Genes and Genomes (KEGG) database (RNA sequencing data have been deposited in NCBI Sequence Read Archive (SRA) Sequence Database with accession number SRR6024635.Supplementary informationDataset 1


At the organ level, the PMCA1cko hearts became more susceptible to atrial arrhythmias under rapid programmed electrical stimulation compared with the PMCA1loxP/loxP hearts, and such arrhythmic events became more severe under Ca2+ overload conditions. At the cellular level, the occurrence of irregular‐type action potentials of PMCA1cko atrial myocytes increased significantly under Ca2+ overload conditions and/or at higher frequency of stimulation. The decay of Na+/Ca2+ exchanger current that followed a stimulation protocol was significantly prolonged in PMCA1cko atrial myocytes under basal conditions, with Ca2+ overload leading to even greater prolongation. In conclusion, PMCA1 is required for maintaining Ca2+ homeostasis and electrical stability in the atrium. This is particularly critical during fast removal of Ca2+ from the cytosol, which is required under stress conditions.To determine the role of plasma membrane Ca 2+‐ATPase 1 (PMCA1) in Ca2+ homeostasis and electrical stability in atrial tissue has been investigated at both organ and cellular levels in mice with cardiomyocyte‐specific deletion of PMCA1 (PMCA1cko)The role of plasma membrane Cacko hearts became more susceptible to atrial arrhythmic stress conditions than PMCA1loxP/loxP hearts.The PMCA12+ homeostasis under both baseline and stress conditions.PMCA1 deficiency alters cellular Ca2+ homeostasis and electrical stability in murine atria under stress conditions.PMCA1 is required for maintaining cellular Ca AFatrial fibrillationAPaction potential90APDaction potential duration at 90%ATatrial tachycardiaBCLbasal cycle lengthDADdelayed after‐depolarizationEADearly after‐depolarizationERPeffective refractory periodHRheart rateLTCC2+ channelL‐type CaMAPmonophasic action potentialNCX+/Ca2+ exchangerNaPESprogrammed electrical stimulationPMCA2+‐ATPaseplasma membrane CaRyRryanodine receptorSRsarcoplasmic reticulum2+ is involved in cardiac electrophysiological activity, excitation–contraction coupling, contractile function, energy balance, cell death and gene transcription. During each action potential (AP) of cardiac myocytes, Ca2+ fluxes into the cell through voltage gated L‐type Ca2+ channels (LTCCs), which are activated by AP‐induced membrane depolarization. The primary role of this Ca2+ influx is to trigger sarcoplasmic reticulum (SR) Ca2+ release, through the process of Ca2+‐induced Ca2+ release. The Ca2+ released from the SR Ca2+ store then causes myocytes to contract. When contraction ends the Ca2+ ions are taken up by SERCA2a back into the SR, with the remainder being extruded by two outward transport mechanisms in the sarcolemma that are responsible for calcium extrusion: (i) the plasma‐membrane Ca2+‐ATPase (PMCA), which ejects calcium to the extracellular compartment using energy derived from ATP hydrolysis and is dependent on calmodulin , which counter‐transports 1 molecule of calcium in exchange for 3 molecules of sodium utilizing the sodium gradient across the plasma membrane as an energy source  encoded by separate genes have been identified in mammals. Among them, PMCA1 is predominantly expressed in cardiac tissues. It has been suggested that PMCA1 pumps only make a minor contribution to CaPMCA1 gene expression specifically in cardiac tissue to generate a mouse cardiomyocyte‐specific knockout model of PMCA1 (PMCA1cko). Using this unique model we clarified the role of PMCA1 in maintaining atrial Ca2+ homeostasis and electrophysiological stability in the atria. The study was carried out in several steps. Firstly, the expression of PMCA1 in the atrial tissue was studied by immunostaining tissue sections, and the deletion efficiency of PMCA1 in the atrium of PMCA1cko mice was examined. Then, the in vivo and ex vivo electrophysiological cardiac phenotypes of PMCA1cko mice and their control littermates, PMCA1loxP/loxP mice, were investigated by ECG and monophasic action potential (MAP) recordings under 1 mm [Ca2+]o and 2 mm [Ca2+]o (Ca2+ overload) conditions with and without programmed electrical stimulation (PES). Finally a series of single cell studies were conducted on atrial myocytes isolated from PMCA1cko and PMCA1loxP/loxP mice using patch clamping, epifluorescence Ca2+ measurements and confocal Ca2+ imaging.As the global deletion of PMCA1 is embryonic lethal, we used the Cre‐loxP system to disrupt The Journal’s policy and regulations  in accordance with the UK Animals (Scientific Procedures) Act 1986, were approved by the University of Manchester ethical committee and were conducted in accordance with the national guidelines under which the institution operates. All mice used in this study were maintained in a pathogen‐free facility at the University of Manchester. The authors confirm that they have taken all steps to minimize the animals’ pain and suffering. Our work complies with  Grundy, .loxP technology. PMCA1 floxed mice in which loxP sites were inserted to flank exon 2, containing the ATG start codon of the PMCA1 gene, were generated as described in Ryan et al.  male PMCA1n et al. . PMCA1ck−1) under general anaesthetic for 5 min by injecting the anaesthetic agent Avertin  before Schedule 1 killing. Animals were killed by cervical dislocation, and the heart was removed immediately and placed in ice‐cold Krebs–Ringer solution (concentration (mm): 120 NaCl, 4 KCl, 1.3 MgSO4·7H2O, 1.2 NaH2PO4·2H2O, 25.2 NaHCO3, 5.8 glucose, oxygenated with 95% oxygen and 5% carbon dioxide) during transport for ex vivo, single cell and molecular studies.For atrial single cell isolation, in order to prevent blood clot formation, animals were injected with 0.2 ml heparin . The onset of the QT interval was taken to correspond either to the Q wave deflection or, if this was absent, the base of the R wave. The end of the QT interval was taken as the time point after the T wave peak when the first derivative of the voltage trace (dV/dt) became zero. When undershoots were present, the end of the QT interval was estimated from the minimum value of the undershoot. The QT interval was also corrected for heart rate (HR) using the following formula: QTc = QT/(RR/100)1/2, where QTc is the corrected QT interval and RR is the R–R interval  were placed on the atrial septum and the PES, controlled by Spike2 software  was applied. Propensity to atrial arrhythmias in Langendorff‐perfused hearts was assessed by PES. Pacing trains of eight stimuli (S1) delivered at a basic cycle length of 100 ms were followed by a single premature extra stimulus (S2) introduced at S1–S2 intervals progressively shortened with successive stimulus cycles repeated until arrhythmia was induced or the atrial refractory period was reached. A burst‐pacing protocol applied atrial pacing in trains of 20 S1 stimuli at progressively shorter intervals from an initial cycle length of 100 ms until an arrhythmia was induced or a cycle length of 30 ms was reached. Arrhythmia was defined as three or more consecutive premature atrial waveforms. Tachycardia showing regular waveforms was defined as atrial tachycardia (AT), whereas irregular fibrillating waveforms were considered to represent atrial fibrillation (AF).m): 115 NaCl, 10 Hepes‐acid, 11.1 glucose, 1.2 NaH2PO4, 1.2 MgSO4, 4 KCl, 50 taurine, pH 7.34 with NaOH) to flush away any remaining blood. Then the heart was perfused with the enzyme solution, which contained 0.5 mg ml−1 collagenase Type‐2  and 0.05 mg ml−1 protease  dissolved in isolation solution  for approximately 5–6 min. When the heart became flaccid, the ventricles were chopped up into small pieces and washed in taurine solution to prevent over‐digestion by the remaining enzyme solution; myocytes were isolated from ventricular tissue by gently suspending, and further digestion was applied when the tissue was under‐digested.Mice were killed by a Schedule 1 procedure. The heart was removed and then immediately cannulated and Langendorff‐perfused  dissolved in isolation solution in a 37°C water bath for another approximately 5 min. When the atrium became soft and flabby, the tissue was gently torn up and suspended allowing isolation of atrial myocytes. Further incubations were applied as necessary.The atrial myocytes were isolated by a two‐step procedure. After the heart was perfused with the first enzyme for approximately 5–6 min, the left and right atria were dissected from the heart and incubated in second enzyme solution containing 3 mg mlm): 134 NaCl, 4 KCl, 1 CaCl2, 1.2 MgCl2, 11.1 glucose, 10 Hepes, pH 7.4 with NaOH) at room temperature.The isolated cardiomyocytes were washed in 0.1% (w/v) BSA in taurine solution to remove any excessive enzyme and stop further digestion, and stored in normal Tyrode solution  ester form, cell permeant, I‐1223, Thermo Fisher Scientific, Paisley, UK) powder was dissolved in 50 μl 25% Pluronic acid (Sigma‐Aldrich) in dimethyl sulfoxide ; 1 mg of Pluronic acid powder was dissolved in 4 μl DMSO to make 25% (w/v); vortexing with heating was applied during the process of dissolving. The 25% Pluronic acid DMSO stock solution was used to dissolve the Ca2+ indicator Fluo‐4, Fluo4‐AM  to provide a wide range of sensitivity to changes of [Ca2+]i. Fluo‐4 powder was dissolved in DMSO containing 25% Pluronic acid (Sigma‐Aldrich) at a concentration of 1 μg μl−1. Myocytes were then incubated with Fluo‐4 Ca2+ indicator solution for 15 min followed by 45 min in normal Tyrode solution to permit the Ca2+ indicator to de‐esterify. Measured fluorescence was normalized to resting levels (F/F0).Cells were loaded with the AM form of the Cam): 120 CsCl, 12 NaCl, 10 Hepes, 20 tetraethyl ammonium chloride, 0.1 EGTA, 5 MgCl2 and 5 K2ATP, titrated to pH 7.2 with CsOH. The cells were continuously perfused with normal Tyrode solution, which contained (in mm) 134 NaCl, 11.1 glucose, 1 CaCl2, 10 Hepes, 1.2 MgCl2, 4 KCl, 5 4‐aminopyridine, 0.1 BaCl2, titrated to pH 7.4 with NaOH. 4‐Aminopyridine and BaCl2 were used to block the potassium current. Experiments were performed at room temperature (20–22°C). Whole cell membrane current and membrane voltage were recorded using an Axopatch 200B Amplifier  and data requisition and analysis performed by the pCLAMP 10 programme (Molecular Devices). Cells were stimulated with depolarizing pulses (100 ms duration from −40 to 0 mV) at different stimulating frequencies.Patch electrodes were pulled from borosilicate glass  on a gravity vertical puller . The fire‐polished electrodes had a resistance of 2.5–3 MΩ when filled with patch electrode internal solutions, which contained  and Ca2+ efflux associated with the Ca2+ transient by integration of NCX tail current (INCX) immediately after repolarization. For these calculations, the current value corresponding to the minimum [Ca2+]i reached after systole was used as the baseline current level.Ca2+ content was assessed following trains of action potentials by rapidly switching to voltage clamp control at a holding potential of −80 mV and applying 10 mm caffeine to deplete the SR Ca2+ store. The resultant NCX current was integrated and corrected for Ca2+ removal by non‐electrogenic mechanisms.SR Ca2+ indicator Fluo‐4 (Thermo Fisher Scientific) at a final concentration of 3 μm. The Ca2+ spark images were recorded using a Nikon Aviovert 200 inverted microscope with an Andor iQ confocal system attached with a Nipkow spinning disk confocal set‐up . Laser excitation of Fluo‐4 was at 488 nm by diode laser  and the emitted light was collected using a 515 nm long pass filter using an Andor iXON897 EM‐CCD camera (Andor Technology) at a frame rate of 50 Hz. Ca2+ spark images were recorded and analysed using Andor iQ software.Mouse atrial myocytes were isolated and loaded with the fluorescent CaThe linescan images of mouse atrial myocytes were recorded with the Leica DMIRB inverted confocal microscope system attached with a Leica TCS NT scanning head under line scan mode at a rate of 2.6 ms per line. Myocytes were visualized with a ×100 oil immersion objective lens. Excitation light of 488 nm was provided by an argon ion laser system  and emitted light was collected at 515 nm wavelength by using a long pass filter. The images were recorded using Leica TCS NT software and analysed using ImageJ software.The atrium tissue was cut off immediately after killing the mice, and was embedded and frozen completely in Optimal Cutting Temperature compound  by liquid nitrogen and isopentane (Sigma‐Aldrich). The frozen tissue was sliced by the Leica CM 3050S cryostat (Leica Microsystems (UK) Ltd) on Superfrost Plus histological slides . Slides were incubated with 4% formaldehyde (Sigma‐Aldrich) at room temperature for 30 min followed by three washes of 10 min each with PBS (Sigma‐Aldrich), then permeablized with 0.1% Triton X‐100 (Sigma‐Aldrich) for 30 min. After three washes of 10 min each wash with PBS the sections were incubated with 3% (w/v) BSA in PBS at room temperature for 30 min. The targeting proteins were labelled by primary antibody diluted in 3% (w/v) BSA in PBS at 4°C overnight, and then washed three times of 10 min each with PBS. The primary antibody was then tagged with corresponding secondary antibody, either fluorescein isothiocyanate or Cy3 dye diluted in 3% (w/v) BSA in PBS at room temperature for 2.5 h in a dark room. The tissues section was then washed and mounted with Vectashield mounting medium  and sealed with nail varnish.m: 20 Tris–HCL, pH 7.4, 137 NaCl, 2 EDTA, 25 β‐glycerophosphate, 1 orthovanadate, 1 phenylsulphfonyl fluoride, 1% Triton X‐100, 10% glycerol, 10 μg ml−1 leupeptin, 10 μg ml−1 aprotinin). Immunoblot analyses of protein extracts (50 μg) with antibody against PMCA1  and α‐tubulin  were repeated three times on three individual animals. Immunocomplexes were detected by enhanced chemiluminescence with the corresponding secondary antibody; anti‐rabbit IgG horseradish peroxidase , or anti‐goat IgG coupled to horseradish peroxidase .Protein from atrial tissue was extracted in Triton lysis buffer (m−1) was reverse transcribed into cDNA using the High Capacity RNA‐to‐cDNA kit (Thermo Fisher Scientific).RNA was extracted from ventricle samples using the Trizol method (Thermo Fisher Scientific). Due to the small size of atria (≤30 mg), RNA was isolated from atrial samples using the RNeasy fibrous tissue mini kit , following the manufacturer's protocol. RNA concentration was quantified using a NanoDrop 1000 spectrophotometer (Thermo Fisher Scientific) and RNA  according to manufacturer's instructions.Gene expression was assessed using qPCR. TaqMan primers and probes were used to measure mRNA expression levels of PMCA4 in the atria and ventricle of PMCA1−1 body weight day−1 for up to 7 days at an infusion rate of 0.25 μl h−1. Pumps were filled with either isoprenaline solution or 0.9% NaCl (vehicle control) before being implanted in mice under anaesthesia (isoflurane). The analgesic buprenorphine (0.1 mg kg−1 body weight) was injected subcutaneously immediately prior to surgery. Post‐surgery the mice were continuously monitored until awake and were then transferred to a 37°C warming cabinet for 2 h. The mice continued to be regularly monitored in the days post‐surgery. In vivo ECG recordings were measured before and 7 days following isoprenaline stimulation.Osmotic mini‐pumps  were implanted subcutaneously into mice. Isoprenaline (Sigma‐Aldrich) was dissolved in 0.9 % NaCl at a concentration calculated to deliver 10 μg g−1. Mice received a single intraperitoneal injection of dobutamine at a dose of 1.5 ug g−1 body weight or an equivalent volume 0.9% NaCl (vehicle). In vivo ECG recordings were measured before and periodically throughout the experiment until peak heart rate response was achieved and the heart rate began to return to normal.Dobutamine hydrochloride (Sigma‐Aldrich) was diluted in 0.09% NaCl to a concentration of 0.1 μg μlIn vivo ECG was carried out on 3‐month‐old mice. Recording were conducted under general anaesthetic induced by isoflurane. Subcutaneous electrodes were inserted and three‐lead ECG recordings  were made. LabChart Pro (ADInstruments) was used to pace and analyse in vivo ECG recordings. Heart rate and the following intervals were measured: RR, PR, QRS, QT and JT. Corrected QT duration for heart rate (QTc) was calculated using the Bazett formula (QTc = QT/√(60/HR)). The mice were killed by cervical dislocation after the ECG recording was completed and the hearts were harvested for molecular or immunohistological studies.B and H, and n experiments, and the observations were thought to be sufficiently close to a ‘normal’ distribution, as judged by Kolmogorov–Smirnov normality, to permit the use of parametric tests. Student's paired or unpaired t test was used as appropriate. Comparisons of more than one factor or between multiple groups utilized two‐way ANOVA, corrected by a Bonferonni post hoc t test if necessary. The analysis of categorical data  employed Fisher's exact test. In the statistical tests significance was taken to correspond to a probability ≤0.05. All P‐values are two‐sided, AND the statistical software used to generate the results was SPSS  and Prism  software.In the analysis of the continuous experimental data  and PMCA1cko hearts (n = 8). The role of PMCA1 in maintaining atrial electrical stability was then investigated under baseline conditions (1 mm [Ca2+]o Krebs solution); when subjected to Ca2+ overload produced by increasing the extracellular Ca2+ concentration ([Ca2+]o) to 2 mm [Ca2+]o in the Krebs solution; and when hearts were subjected to PES.For the ECG characteristics, atrial MAPs were recorded in Langendorff perfused PMCA1ex vivo ECG and MAP characteristics between PMCA1loxP/loxP and PMCA1cko hearts . However, when the hearts were subject to PES, either S1S1 burst pacing and S1S2 extra‐stimulus pacing, PMCA1cko but not PMCA1loxP/loxP had high incidences of atrial tachyarrhythmia including AT and AF . The occurrence of AT/AF was particularly high following S1S1 burst pacing frequencies  <50 ms) . Only 1 out of 7 PMCA1loxP/loxP hearts exhibited a short AF at 30 ms pacing interval accounting for only 0.8% of the total pacing duration under the S1S1 burst pacing protocol at 30 ms BCL, whereas short AT/AF were triggered in 8 out 8 PMCA1cko hearts by S1S1 burst pacing, accounting for 11.8% of the total pacing duration.Under basal conditions of sinus rhythm, there was no significant difference in rts Fig. A. Howevm [Ca2+]o Krebs solution under sinus rhythm, ectopic beats and AP alternans were noticed in 1 out of 6 PMCA1cko hearts. The PMCA1loxP/loxP hearts remained under normal heart rhythm during and after both S1S2 and S1S1 pacing protocols. However, frequent, short episodes of AT were induced by S1S2 protocol pacing in PMCA1cko hearts, and much longer durations of AT were induced by S1S1 pacing, particularly at higher S1S1 burst pacing frequencies (BCL < 50 ms). These short episodes of AF or AT were triggered by S1S2 pacing in 5 out of 6 PMCA1cko hearts but none were recorded in PMCA1loxP/loxP hearts. S1S1 burst pacing at high frequencies triggered severe and longer AT or AF in all PMCA1cko hearts . It was clear that most of the arrhythmic events were evoked at high frequencies (cycle length ∼30–50 ms) in PMCA1cko hearts, and that more severe AT/AF was seen in PMCA1cko hearts under 2 mm [Ca2+]o Krebs solution  than under baseline conditions.However, when perfused with 2 mrts Fig. B and C.loxP/loxP and PMCA1cko atrial myocytes demonstrated significant differences in Ca2+ homeostasis and stability in membrane potentials. Figure A and B compares APs and Ca2+ transients from PMCA1loxP/loxP and PMCA1cko myocytes following stimulation at 1 and 3 Hz field and perfusion with 1 mm [Ca2+]o  or 2 mm [Ca2+]o  Tyrode solutions. PMCA1cko myocytes showed higher occurrences of arrhythmia‐like APs and Ca2+ events (delayed after‐depolarization (DADs) and irregular, alternating Ca2+ transients and/or Ca2+ waves) with increased stimulation frequencies than PMCA1loxP/loxP myocytes .Isolated PMCA1+]o Fig. A or 2 m+]o Fig. B Tyrodetes Fig. C.2+ sparks in the cytosol as measured by linescan. Thus increased Ca2+ sparks in PMCA1cko myocytes occurred under both baseline  and 2 mm [Ca2+]o  conditions compared to PMCA1loxP/loxP myocytes under both baseline  and 2 mm [Ca2+]o  conditions. The increased number of Ca2+ sparks was also demonstrated in PMCA1cko myocytes measured by spinning‐disc microscopy compared to PMCA1loxP/loxP myocytes under both baseline  and 2 mm [Ca2]o  conditions. Under 1 mm [Ca2+]o conditions, the number of Ca2+ sparks per second in PMCA1loxP/loxP atrial myocytes (n = 5) was 1.17 ± 0.16 s−1, which was similar to that seen in PMCA1cko atrial myocytes (1.16 ± 0.10 s−1) (n = 11). In PMCA1cko atrial myocytes (n = 11), but not PMCA1loxP/loxP atrial myocytes , the number of Ca2+ sparks was significantly increased to 2.40 ± 0.17 s−1 under 2 mm [Ca2+]o .These instabilities correlated with differences in evoked Caine Fig. D right +]o Fig. E right ine Fig. D left a+]o Fig. E left c2+ responses and NCX  and PMCA1cko myocytes (grey traces) under either baseline  or 2 mm [Ca2]o .(i)2+]i was estimated from the differences between peaks and baselines of systolic Ca2+ transients obtained during regular stimulations. This was indistinguishable between PMCA1loxP/loxP myocytes (n = 26) and PMCA1cko myocytes (n = 25) under either baseline or 2 mm [Ca2]o conditions.Peak systolic [Ca(ii)2+content measured by integration of INCX was indistinguishable between PMCA1loxP/loxP (n = 7) and PMCA1cko (n = 15) myocytes under either baseline [Ca2]o or 2 mm [Ca2]o conditions .SR Cacko n = 1 myocytes(iii)2+ transients provided estimates of rates of Ca2+ removal by NCX from the cytosol. The time decay of INCX in PMCA1cko myocytes (n = 7) was prolonged significantly compared to PMCA1loxP/loxP myocytes (n = 15) under both baseline and 2 mm [Ca2]o conditions .Decay of caffeine‐induced Cates n = 1 under bo(iv)INCX and corresponding Ca2+ transient amplitude showed no significant difference between PMCA1loxP/loxP and PMCA1cko myocytes under baseline  and 2 mm [Ca2]o  conditions.The density of ine Fig. Ae–h and2]o Fig. Be–h con(v)ILTCC was measured under voltage clamp of PMCA1loxP/loxP myocytes (n = 23) and PMCA1cko myocytes (n = 19). There was no significant difference in the density of ILTCC between PMCA1loxP/loxP myocytes (8.7 ± 0.49 pA pF−1) and PMCA1cko myocytes (6.13 ± 0.77 pA pF−1) .Finally the These instabilities correlated with differences in evoked cytosolic and SR CaNCX Fig.  among PMine Fig. A or 2 m2]o Fig. B.(i)Pe2+ homeostasis under baseline conditions and when subjected to Ca2+ overload (2 mm [Ca2]o) stress.Together these findings demonstrate that PMCA1 deficiency alters cellular Caet al. et al. 2+ homeostasis by studying a cardiomyocyte‐specific deletion of PMCA1 in a mouse model.Whilst it is evident from several recent genome‐wide association studies that PMCA1 has a strong association with hypertension and blood pressure variance in humans  and effective refractory period (ERP) between PMCA1loxP/loxP and PMCA1cko hearts. Bayer et al. studied the changes in amplitude and duration of ion currents against pacing frequency with a dynamic pacing protocol, and showed that 88–94% of the current amplitude in LTCCs was reduced at high pacing frequency compared to low pacing frequency , suggests that Ca2+ influx to trigger the SR Ca2+ release was similar in PMCA1loxP/loxP and PMCA1cko myocytes. To maintain Ca2+ homeostasis in the myocyte, the amount of Ca2+ that enters the myocyte via LTCCs is approximately equivalent to the amount of Ca2+ to be removed by NCX and PMCA ‐ or DAD‐type and spontaneous APs. Our findings are thus consistent with the results from Eisner's groups, as they found that increased [Ca2+]o leads to increased frequency of spontaneous Ca2+ release associated with increased SR content, and more frequent oscillation of the myocytes.However, as shown in Fig. loxP/loxP myocytes; however, in PMCA1cko myocytes, frequent EAD‐ or DAD‐type APs with corresponding spontaneous Ca2+ transients occurred, particularly when Ca2+ overload conditions were combined with high frequencies (3 and 5 Hz). These results coincide with the ex vivo heart studies  clusters. They found that in mouse atrial myocytes, axial tubule structures triggered Ca2+ release from the SR approximately two times faster at the centre of the atrial myocyte than at the surface. Rapid Ca2+ release correlated with colocalization of highly phosphorylated RyR2 clusters at axial tubule–SR junctions and earlier, more rapid shortening of central sarcomeres. This may suggest different local control of excitation–contraction coupling in atrial myocytes compared to ventricular myocytes. The development of local control theories in cardiac excitation–contraction coupling solved a major problem in the Ca2+‐induced Ca2+ release hypothesis. Local control explained how regeneration, inherent in the Ca2+‐induced Ca2+ release mechanism, might be limited spatially to enable graded Ca2+ release (and force production). The key lies in the stochastic recruitment of individual Ca2+ release units (or couplons) where adjacent Ca2+ release units are partially uncoupled by the distance between them. In the Ca2+ release unit, individual groups of sarcoplasmic reticulum Ca2+ release channels (RyRs) are very close to the surface membrane where Ca2+ influx, controlled by membrane depolarization, leads to high local Ca2+ levels that enable a high speed response from RyRs that have a very low probability of opening at resting Ca2+ levels  PMCA1 becomes more important not only for its contribution in Ca2+ extrusion but also for its role in eletrophysiological stability, and is thus critical for maintaining atrial Ca2+ homeostasis. This is particularly critical during fast removal of Ca2+ from the cytosol which is required under stress conditions.In conclusion, our study shows that as a fast Ca2+ events, such as its role in regional spontaneous Ca2+ spark activity, was not investigated. It will be an interesting area to examine in the future. Previous studies indicated that cells lacking t‐tubules such as atrial myocytes and neonatal myocytes show variable spontaneous Ca2+ spark activity , BHF , BHF CRE at Oxford (M.L.) grants.


It is found that the vibration frequency is an eigenvalue of the delaminated lamina determined only by the geometry of the delamination. Authentication of the multiscale study is fulfilled by comparing the analytical solutions with the FEA results.This paper presents a multiscale approach to study the nonlinear vibration of fiber reinforced composite laminates containing an embedded, through-width delamination dividing the laminate into four sub-laminates. The equations of motion are established from macroscopic nonlinear mechanics for plates and shells and micro-mechanics of composite material to allow for the influences of large amplitude, membrane stretching in the neutral plane, and the interactions of the sublaminates. Analytical solutions obtained in this paper reveal that the interaction penalty at the interfaces plays a coupling effect between sublaminates, which eventually alters the vibration characters of the four-sublaminate lamina in macroscopic and microscopic mechanism. From a macro perspective, sub-laminates above and below the delamination vibrate in exactly the same mode in spite of their different stiffness and the four-sublaminate lamina has a consistent global vibration mode. In accompanying with the macro vibration, micro buckles occur on the interfaces of the delamination with amplitude about 10 Carbon-fiber-reinforced composite materials consist of two parts: matrices and reinforcements. The reinforcements are usually carbon fibers which provide the strength and rigidity for the composite materials, measured by the stress and the elastic modulus respectively. The matrix is usually a polymer resin, such as epoxy, to bind the reinforcements together. Unlike isotropic materials, such as steel and aluminum, carbon-fiber-reinforced composite has directional strength and properties. The properties of carbon-fiber-reinforced composite depend on the layouts of the carbon fiber and the proportion of the carbon fibers in the polymer.1. Therefore, researchers have launched various studies to investigate the effects of contact on the mechanical responses of the delaminated composite structures.During manufacturing process, fiber breakage, matrix cracking, and fiber/matrix interface debonding may exist in the composite materials and, as a result, develop delamination in the composite materials. Delamination is one of the primary failure types in composite laminates and will cause the stiffness degradation and strength loss of the entire laminate, consequentially the premature failure of the composite materials. The failure of fiber reinforced composite structures containing buried delamination is much complex due to presence of various mechanisms. The analysis of the response of the delaminated composite structures under the external loadings needs to account for various factors, e.g., large deformation, nonlinear constitutive behavior, failure, delamination, and interaction penalty effects, etc. Ignoring the interaction penalty effects may result in the underestimation of the load carrying capacity and the penetration of the deflection between the sublaminates above and below the interfaces of delaminationet al.2 may be one of the first to carry out the study of the delaminated composite laminates. By simplifying the composite plate as a beam-plate, they proposed a one dimensional analytical model to assess the compressive strength of a delaminated composites plate. Cranford3 investigated the mechanical stability of graphene-based nanoscale multi-layers and derived the critical length scale and required adhesion energy to prevent delamination under buckling conditions. Oyewole et al.4 presented the results of experimental and theoretical/computational micro-wrinkles and buckling on the surfaces of stretchable poly-dimethylsiloxane (PDMS) coated with nano-scale Gold (Au) layers. The interfacial delamination occurred along with the buckling was also studied using finite element simulations of the interfacial crack growth. Ovesy et al.5 suggested a novel layerwise theory to evaluate the buckling and post-buckling behavior of delaminated composite plates with multiple through-the-width delaminations based on the first order shear deformation theory (FSDT). Giannakopoulos et al.6 and Whitcomb7 investigated the stability by considering the nonlinearity associated with the contact problem. The results reveal that the effects of the contact conditions are significant, especially with regard to the propagation of the debonded region. Hu et al.8 introduced artificial springs to compute the fictitious contact forces occurred in the buckling of laminates with an embedded delamination based on the Mindlin plate theory. The other research topics include simulation of the multi-failure responses, see Ho et al.9; multiscale method to compute the elastic deformations for general bilayer, see Kumar et al.10; contact of interfacial debonding front region and face matrix cracking, etc. in face/core interface debonded composite sandwich plates, see Chen and Bai11; the non-linear behaviors of delaminated sandwich panels with a compressible core, see Frostig and Thomsen12; fatigue delamination growth for piezoelectric laminated cylindrical shells, see Zhu et al.13; analysis of the mixed mode delamination in composite laminates from point view of fracture mechanics and contact mechanics, see Bruno et al.14; experimental studies on laminated plates with strip-type delamination under pure bending, see Yet et al.16.Numerous approaches as well as different results have been reported in many literatures. Chai et al.17. They modeled a beam with one through-width delamination by simply using four Timoshenko beams connected at delamination edges. Wang et al.18 improved the analytical solution by including the coupling between flexural and axial vibrations of the delaminated beams which were modeled as split regions. Recurrence equations relating integration constants for adjacent split regions were established by satisfying continuity conditions at junctions of sub-regions. Ramkumar et al.’s and Wang et al.’s models were essentially one-dimensional models. Dynamic responses of laminates with two-dimensional embedded delamination were studied by Dey and Karmakar19 to examine free vibration of multiple delaminated angle-ply composite conical shells using Mindlin’s theory and the multi-point constraint algorithm and by Noh and Lee20 to analyze the dynamic stability of laminated skew plates by developing a finite element formulation based on HSDT. Such models are called “free model”. As pointed out in present published paper21, the “free model” result in interpenetration of the delaminated sub-regions, which is physical impossible. To overcome this defect a piecewise linear spring model inserted in the delaminated region was introduced. Several researchers conducted their studies based on this model. Luo and Hanagud22 carried out the dynamic response analysis of a delaminated beam by taking into account of shear effect, rotary inertia terms and bending-extension coupling. Kargarnovin et al.23 examined a delaminated Timoshenko beam under the motion of a constant amplitude point force traveling with uniform velocity by accounting for the Poisson’s effect, shear deformation and rotary inertia. Chen et al.25 presented a formula of element stiffness and mass matrices for the composite laminates using the first-order shear deformation theory combined with the selecting numerical integration scheme. A virtual interface linear spring element was employed to avoid the overlap and penetration phenomenon between the upper and lower sublaminates at the delamination region. Chattopadhyay et al.26 presented an FE model using the first-order zig–zag theory for delaminated composites and smart composite plates. The linear spring model needs to specify the spring constant before solving the problem, which is basically equivalent to specifying whether the sublaminates are in contact or not beforehand, this model therefore does not reflect the essential feature of the contact problem, that is, the contact region and the degree of interpenetration are all unknown a priori. Oh et al.27 and Kwon and Aygunes28 developed finite element models adopting the approach given by Hughes et al.29 for correcting the velocity, acceleration and contact force values during release-to-contact condition. Their models were able to achieve nonpenetration of interlaminates but the results they present can still be argued upon for its physical correctness, as both the top and bottom laminates experience a kind of total separation. In reality, they must collide more than once during the vibration as both of the sub-laminates are shown to be vibrating by themselves at higher frequencies than the contact occurrence. Recently, Wang and Tong30 suggested a nonlinear interpenetration constraint model to handle the contact problem. In this nonlinear model, the contact force was considered to be proportional to the relative deflections of the mid-planes of subregions above and below the delamination interfaces. Schwarts-Givli et al.31 further put forward a step function in the nonlinear constrain model to incorporate “with and without contact” conditions in the governing equations, which reflects the nonlinear nature of the contact behavior.Except the static analysis, the dynamic responses of composite laminate with delamination are also the focus of a number of studies. One of the earliest models for vibration analysis of composite beams with delaminations was proposed by Ramkumar 34. The bending analysis of the delaminated plates is an interdiscipline and multiscale problem. The research involves two mechanical mechanisms: theories of plates and interaction mechanics. The multiscale composition of the composite lamina causes it to undergo macro deformation as well as micro buckling. The problem becomes even more intricate due to the obscurity of the interaction properties, such as the locations and sizes of the contact area, the intensity of the contact force, etc. For this reason, almost all the analyses and results in above mentioned literatures are accomplished in virtue of computer techniques. Such analyses may lead to an argument that the contact properties, such as the locations and the sizes of the contact area, are unpredictable.Although, a vast literature exists on the effects of delamination on the dynamic response of composite structures, they have mostly ignored large deformation effects. When delaminated laminates undergo large deflection, the large deflection induces geometric nonlinearity in the delaminated region and leads to the couple effect between the membrane stretching and transverse bending and the occurrence of the contact phenomenon at the delaminated region. As a result, non-uniform interaction constrains are produced along the interfaces in-between the upper and lower sublaminates. They restrict the two sublaminates to deform penetrating with each other by causing a local compressive stress and a vertical deformation along the interfaces of the delaminationIn this article, we develop a general framework to analyze the nonlinear vibration of fiber-reinforced composite laminate with embedded delamination using a multi-scale modeling approach and infer possible consequences of delamination geometry on vibration properties. While the interaction forces at the interfaces of the delamination is investigated from the point view of micro-mechanics, governing equations for the delaminated laminates undergoing nonlinear vibration are derived based on von Karman nonlinear mechanics for plates and shells to include nonlinear geometry deformation and membrane stretching and are solved via Galerkin approach. To demonstrate the validity of our method, we analyze the nonlinear free vibration of a simply supported, symmetrically cross-plied laminate with a though-width delamination. We obtain close-form analytical solutions and provide the macroscopic and microscopic explanation for the outcome of the consistent macro vibration mode and the micro buckles on the interfaces of the delamination. We have compared the vibration frequency as well as the vibration mode predicted by our multi-scale approach with the dynamics simulations from ABAQUS, obtained an excellent agreement between these two approaches.This article mainly focuses on investigating the nonlinear vibration of a delaminated composite laminate. The study includes investigation of the overall dynamic responses of the composite laminate and determination of the local transverse deformation of sub-laminates above and below the delamination due to the interaction forces between them. The overall dynamic responses of the composite laminate are mainly achieved by virtue of shell theories in which the in-plane material properties is of much more significance.E11 and E22, Poisson’s ratio μ21 and Shear modulus G12Em, μm, Gm and vm are the Young’s modulus, Poisson’s ratio, Shear modulus and volume fraction of the matrix, and Ef, μf, Gf and vf are the corresponding properties of the fiber. The laminate is manufactured by stacking the fiber reinforced composite plies in an orientation sequence, as shown in Fig. θ be the angle of the orientation of m-th ply with respect to the horizontal axis in the global coordinate systems, the stiffness coefficient matrix of the m-th ply 35c = cosθ, s = sinθ, andFigure a, width b, and height h. The composite lamina consists of K layers of fiber-reinforced composite ply with a through-width delamination located at depth h2 from its top surface. The delamination divides the spatial region of the laminate into four sub-laminates of length li and height hi, separately referred to as sub-laminate Ωi), as shown in Fig. Ai)( and the bending stiffness Di)( of sub-laminate Ωi) are given by the following formula35hm and hm−1 are the location of the m-th ply with respect to the neutral axis of sub-laminate Ωi) and the bending moment M(i) of sub-laminate Ωi)( are related to the in-plane strain components ε(i) and the change of curvatures κ(i), respectively, through the following constitutive relations:In this article, we are interested in analytical investigation on the interaction mechanism between the sub-laminates and its influence on the nonlinear vibration properties. Such analysis requires solving eight nonlinear partial differential equations and thirty-two auxiliary conditions. To clearly present our analytical approach without hindered by tedious calculation, we consider that all the four sub-laminates εz is ignored. For this reason, the material property in the transverse direction of the composite laminate E33 is not required in shell theories. Such approximation won’t produce obvious error in analyzing the overall responses of the composite laminate. Nevertheless, to scrutinize the nonlinear vibration of the delaminated composite laminate, our discussion is on the conduct of local interaction effects between the sub-laminates.Because of much small thickness dimension comparing to the in-plane dimensions, the transverse displacement at any point in the laminate is represented by the deflection at the corresponding point on the middle plane in the shell theories, i.e., the unit elongation in the transverse direction of the composite laminate x - or y - axis. Therefore, the vertical stacking of the composite plies does not affect the material properties in transverse direction. In other words, the material properties in transverse direction are sensitive to the material properties and the volume frictions of the matrix and the fiber but are insusceptible to the orientation sequence. Following this observation, we draw a very important conclusion that regardless of the stacking sequence and the number of plies, the equivalent Young’s modulus in transverse direction of the four sub-laminates are identical and equal to that of the single ply provided that the composition for each single ply remains unchanged, i.e.Prior to the commencement of local deformation, we need to ascertain the material properties of the four sub-laminates in transverse direction. As shown in Fig. Ω(2). Sub-laminate Ω(2) continues to deflect by pushing sub-laminate Ω(3) to deform downwards simultaneously until both Sub-laminates Ω(2) and Ω(3) reach their equilibrium states. During this process, a reaction force q*, called interaction force, is produced between Sub-laminates Ω(2) and Ω(3).When the laminate undergoes vibration, it experiences transverse deflection. Once the laminate deviates from its equilibrium position, it starts to bend first at the center of sub-laminate Ωi)( experiences a particular deflection wi) . Depending on the amplitudes of w(2) and w(3), contact regions (where w(2) ≥ w(3)) and voids (where w(2) < w(3)) may form alternately along the interfaces of the delamination between Sub-laminates Ω(2) and Ω(3). Although the contact effects, such as the positions where the contact may occur, the size of the contact areas and the magnitude of the contact force, are still unknown, it does not prevent us from further analyzing. It sounds quite rational to consider that the contact may occur at several regions along the interface of sub-laminates Ω(2) and Ω(3). Denoting the coordinates of one of such regions as R ∈ , a contact force q* is produced at this place since the deflection of sub-laminates Ω(2) is larger than that of Ω(3), as shown in Fig. q* developed at the contact regions produces thickness reductions by amounts of δ(2) and δ(3) for Sub-laminates Ω(2) and Ω(3), respectivelyh2 and h3 are original thickness of Ω(2) and Ω(3), and Ω(2) and Ω(3) in the z-direction. The relative movement of the mid-plane of sub-laminates Ω(2) and Ω(3) is approximatelyw(2)–w(3) of Sub-laminates Ω(2) and Ω(3) and their interaction forces q* is found to bek is the interaction factor given by:The vibration modes represent the overall response of the delaminated laminate to the external load, thus the amplitudes and the patterns of the external forces, the supporting conditions at the boundary and the geometries of the laminate determine the modes of the vibration. However, the general modes are not the prior to determine the interaction constraint. On the contrary, they depend on the interaction constraint. At any particular moment of the vibration, each of the sub-laminate The interaction brace plays a pivotal role in our problem. It determines both the general response (macro behavior) and the local buckling (micro behavior) of the laminate subjected to the action of the external load.We consider the composite laminate under the action of an external excitation. The external excitation is resolved into two components: a horizontal one acting in the middle plane of the composite laminate and a transverse one normal to the middle plane. The horizontal component causes the laminate to undergo in-plane or membrane deformation and the transverse component induces out-of-plane deflection or bending in the composite laminate. Therefore, the deformation mechanisms of the composite laminate are analyzed via both membrane and flexural mechanisms of plates. When the in-plane deformations and the flexural deflection of the laminate are small, the membrane and the flexural shell models are analyzed independently. Under such circumstance, we say that the problem is linear. On the contrary, the membrane and the flexural analyses are coupled with each other. We refer to such case as nonlinear problem. In this section, we derive a theory of nonlinear vibration for delaminated composite laminate.Ωi)( are obtained from theory of elasticity as follows:ψi) such thatWe begin with the nonlinear membrane kinematics. When the delaminated composite laminate is subjected to high levels of acoustic pressure, it undergoes large amplitude vibrations. The large amplitude produces in-plane membrane stretching in the composite laminate which is considered as in-plane force resultants applied to the middle planes of each of the sub-laminate and parallel to their middle planes. In these conditions, the problems are reduced to plane stress problems. Ignoring the body forces and the in-plane inertial forces, the differential equations of equilibrium for membrane deformation of sub-laminate Ωi)( as ui) and vi). The in-plane strain components εi) are related to the in-plane displacements and the transverse deflection through von Karman nonlinear geometric kinematics as follows37:ui)( and vi)( from Eq. (Ai)*( is the inverse of the membranous stiffness Ai)(. Equation (Ωi)( in terms of the stress function ψi)( and the transverse deflection wi)(.Define the in-plane displacements in the middle plane of sub-laminate from Eq.  and 13)Ω(i) as Ωi)( take the following forms37:Qji) is the transverse shear forces of sub-laminate Ωi) is the distributed load in transverse direction applied to Sub-laminates Ωi) are given byNext, we examine the nonlinear flexural mechanism of the composite laminate. From the point view of shell theory, the nonlinear problem differs from the linear problem mainly on the treatment of the membrane forces. In linear problem, the membrane forces in the middle plane of the laminate are fixed, while in nonlinear problem they change with the increasing of the amplitude of the deflection and the influence of the membrane forces on the force equilibrium in transverse direction cannot be ignored. For this reason, the differential equation of equilibrium in transverse direction and the moment equilibrium for nonlinear bending of sub-laminate o of Eq. , 13) an anΩ(i) mi) between sub-laminates, the distributed load acting on each sub-laminate qi) is not the same. The interaction forces transmit the external force from sub-laminate Ω(2) to Ω(3), causing a reallocation of the external force q between sub-laminates Ω(2) and Ω(3): that is a net force of q - q* on sub-laminates Ω(2) and q* on Ω(3). With the available interaction forces q* given in Eqs (qi)( is reapportioned as follows:Ωi)q*( and Ω3), the shear force Qxi), the in-plane displacements ui) and vi) are related to the transverse deflection wi)( and the stress function ψi)In Eqs  and 21)x = l1 +quations , 18–22)–22x = lE11 = 140 GPa, the transverse modulus E22 = 10 GPa, the shear modulus G12 = 5 GPa, and the Poisson’s ratios μ12 = 0.3. It contains a though-width delamination symmetrically located at its center and is referred to a global coordinate system  centered at the left corner of the middle surface of the sublaminate, in which x and y are in the longitudinal and breadth directions and z is in the direction of the inward normal to the middle surface.As an application of the proposed theory, we analyze the free vibration of a delaminated composite laminate simply supported at its four edges. The laminate is made of graphite/epoxy composite plies with equivalent material properties of the longitudinal modulus ω is the frequency of free vibration of the composite lamina. The free vibration of the composite laminate is an eigenvalue problem, thus the frequency of the free vibration ω is a characteristic value of the composite laminate and unaffected by external forces, such as the transverse load q on the surfaces or in-plane forces Nij at the edges. Under this circumstance, the membrane forces induced by the transverse deflection do not need to be considered, i.e. Equation ( and Lji)( and λL are found from the governing equation as follows (See section Method for detail):ai, bi and ci are constants determined by the geometric parameters and material properties of Sublaminate Ωi)( as follows:Ω2)( and Ω3) > w(3) and the voids where w(2) < w(3).In a real problem, mechanical behaviors depend on the dimensions of the physical quantities. To establish a general model with performances insusceptible to the dimensions of the physical quantities, we introduce the following non-dimensional parameters:Equation  is not rfrom Eqs  and 19)23\documes in Eqs  and 21)23\documeΩ2)( and Ω3)33) manifΩ1)( and Ω4) = A(4), D(1) = D(4). We have mentioned at the beginning of this section that the composite laminate has a symmetrically located delamination at its center, in geometrical expressions l1 = l4, l2 = l3. Under such circumstance we have λG1)( = λG4)( from Eqs (Ω1)( and Ω4)( are the same. So do those for Sub-laminates Ω(2) and Ω(3), as shown in Eq. (Ω2)( and Ω3)( and Sub-laminate Ω3)( and Sub-laminate Ω4)Ω(1) andn in Eq. . We now t of Eq. . All theλGi)4 in which Ki is the number of composite ply of Sub-laminate Ωi)( ∝ bi/ai and λL ∝ (a2)1/4, respectively. Considering that ai, bi, ci ∝ Ki2(h0/li)4 and a2, it is easy to see that λL ≫ λGi)(. Our further investigations indicate (except very limit conditions when li < 0.05a) thatBased on above observation, we estimate the approximate values of i in Eq.  are estiL in Eq.  are appr3 times of those of local buckling, that is to say, the global vibration is macroscopic and the local buckling is microscopic. In addition, it can be seen from Eqs (λGi) an an\documg to Eqs , it is fs in Eqs –29 and ts in Eqs  from whiρ = 2150 kg/m3 stacked in a sequence of [0°/90°/0°]20 with each single-layer thickness h0 = 0.002 m. The equivalent material properties of each composite ply are still the same as those in Nonlinear dynamic stability analysis, i.e. E11 = 140 GPa, E22 = 10 GPa, G12 = 5 GPa, and μ12 = 0.3.In order to study the performance of the nonlinear vibration of the delaminated laminates, we conduct numerical analysis. Based on the results presented above, we develop MATLAB programs to perform numerical calculations. In the implementations, the laminate has a geometry size of 2 m × 2 m × 0.12 m and is composed of 60 plies made of T300/QY8911 carbon fiber reinforced composite material with the density x = a/2 is shown in Fig. η = l2/l = 0.5 and the non-dimensional delamination depth τ = h2/h = 0.3. As a comparison, we also perform finite element simulation using ABAQUS software. Unlike the shell theory in theoretical analysis, we use solid elements and General Contact Interaction Module in ABAQUS analysis in order to incorporate the anti-penetration penalty at the interfaces of sublaminates Ω(2) and Ω(3)–above and below the delamination–to prevent them from penetrating with each other during vibration. Figure η and τ used in Fig. The data obtained enable us to clearly reveal the nature of the free vibration of composite laminates containing a buried delamination. The profile of the vibration modes of the delaminated laminate at the cross section of x-direction at cross section y = 1 m for both Sublaminates Ω(2) and Ω(3). Distinct from their consistent global vibrations, their local buckling modes of Sublaminates Ω(2) and Ω(3) are not identical—not only the buckling amplitude of Sublaminates Ω(2) is much larger than that of Sublaminate Ω(3) due to its weaker stiffness, but also their amplitudes are completely reversal with each other. It is also found from Fig. Ω(2) and lower Sublaminate Ω(3) buckles upwards and downwards respectively. Between the voids the two sublaminates buckle in the opposite directions. Interaction forces are produced in these regions. With these characteristics, voids and interaction areas are developed alternately at the interfaces of the delamination, as illustrated in Fig. −3 of the magnitudes of the vibration modes, so the voids are microscopic, invisible to the naked eyes.We have discussed that except the consistent global vibration the nonlinear vibration of the delaminated composite laminate includes a local buckling. Figure For a more comprehensive understanding of the situation, we further investigate cases of different length of delamination with/without the interaction penalty. Figure η are given in Fig. η. It is a common sense that the smaller the stiffness of a laminate, the larger its amplitude and the lower its frequency. The delaminated laminate is actually a single whole with reduced stiffness due to the existence of the delamination. As the length of the delamination enlarges, the stiffness of the laminate continues deteriorating, thus leading to the decreasing of the frequency.We further carry out a parametric study to investigate the influence of the delamination properties on the vibration frequency. Variation of the nondimensional frequency η = 0.6 and η = 0.8 for both analytical solutions and ABAQUS results. Likewise, the nondimensional frequency Ω(1) and Ω(4) are invariable. Under such circumstance, the stiffness of the delaminated laminate is determined either by Sublaminate Ω(2) or Sublaminate Ω(3), whichever has a larger stiffness. As the delamination moves from the surface to the middle of the laminate, the stiffness of Sublaminate Ω(3) continues to decrease but still exceeds that of Sublaminate Ω(2), thus the stiffness of the delaminated laminate is continuously reduced. At the middle plane, Sublaminates Ω(2) and Ω(3) possess equal stiffness and the delaminated laminate has the lowest stiffness. Once the delamination is in the lower part of the laminate, the stiffness of the delaminated laminate is mainly controlled by Sublaminates Ω(2) instead of Ω(3) and increases with the delamination depth.We also plot variation of the nondimensional frequency η from the two approaches are somewhat different, as shown in Fig. Ω(2) and Ω(3) in ABAQUS simulation, hard contact property is defined in interaction module to impose constrains on the bottom of Ω(2) and on the top of Ω(3). However such application is practicable only to solid model in which shear modulus in transverse direction are necessary. As the shear deformation in transverse direction is omitted in theoretical analysis, inevitably, there are deviations between the theoretical and finite element results. Nevertheless, the comparisons are still adequate in validating our theoretical predictions.Comparison of the nondimensional frequency −3 times smaller than those of the vibration mode. By developing numerical MATLAB program, we investigate the effects of the delamination on the intrinsic behaviors of composite laminate over a wide range of the delamination length and the delamination depth. The free vibration frequency is shown to monotonic decrease upon increasing of the delamination length and to decrease then increase as the delamination depth increases. We perform finite element simulations for the free vibration of delaminated laminates with/without interaction penalty enforced at the interfaces of the delamination, which suggest that the interaction penalty influence not only the vibration frequency but also the vibration mode. For laminates of the same geometry and delamination parameters, the one without the interaction penalty has much lower vibration frequency than that with the interaction penalty. The difference is reflected on the vibration mode in which sublaminate above and below the delamination penetrate with each other when the interaction penalty are not enforced. The characteristic behaviors of the delaminated laminate are consistent in both theoretical solutions and finite element results, thereby demonstrating the effective of the analysis.In summary, we present an analysis of the nonlinear vibration of composite laminates containing a buried delamination through the newly developed multiscale framework. The delaminated laminate is treated as four independent sublaminates with granted restrains of forces and deformations at the delamination fronts to reunite them as single whole. By incorporating the anti-penetrating interaction kinematics at the interfaces of the delamination into the nonlinear theory for vibration of composite laminate, the nonlinear vibration of delaminated composite laminates is explored. We consider the multiscale compositions of the laminate and identify two failure modes of global vibration and local buckling. The modes of the global vibration are macroscopic and compatible among the four sublaminates with exactly the same frequency. In particular, sublaminates above and below the delamination undergoes a fully consistency vibration. On the other hand, the local buckling is microscopic, occurring only between sublaminates above and below the delamination with completely reverse amplitudes that are about 10Ωi)( and must satisfy the boundary conditions of Sublaminate Ωi)(. Noticing that each of Sublaminate Ωi)ai, bi λ(1) and λ(4) in Eq. (Ω(2) and Ω(3) are quite clear and are given in Eq.  in Eq.  for Subln in Eq. . As for n in Eq. , they ar4 in Eq.  have appai, bi, ci and ξ2, ξ3, ξ4 > 104 ≫ ξ1 < 2. With such coefficient properties, Eq.  are given in Eq. (λ(2), we can formulate the vibration mode in x directionΩ(2)Considering the magnitudes of ies, Eq.  must havpose Eq.  into thepand Eq. . The coen in Eq. . With thλ(3) = λ(2) (see Eq. (G(3) ≈ G(2) and L(3) = −ιL(3)  and G((see Eqs  and 38)\documentΩ(2) and Sublaminate Ω(3) which is expressed as a concise formula in Eq. (Replacing into Eq.  and theninto Eq. , we obtaa in Eq. .