In comparison with brain vessels undergoing EC migration-associated pruning, EC apoptosis-accompanied pruned vessels were longer and showed higher probability that the nuclei of neighboring vessels’ ECs occupied their both ends. Furthermore, we found that microglia were responsible for the clearance of apoptotic ECs accompanying vessel pruning, though microglia themselves were dispensable for the occurrence of vessel pruning. Thus, our study demonstrates that EC apoptosis contributes to vessel pruning in the brain during development in a microglial cell-independent manner.During development, immature blood vessel networks remodel to form a simplified and efficient vasculature to meet the demand for oxygen and nutrients, and this remodeling process is mainly achieved via the pruning of existing vessels. It has already known that the migration of vascular endothelial cells (ECs) is one of the mechanisms underlying vessel pruning. However, the role of EC apoptosis in vessel pruning remains under debate, especially in the brain. Here, we reported that EC apoptosis makes a significant contribution to vessel pruning in the brain of larval zebrafish. Using  During development, highly ramified immature blood vascular networks undergo extensive remodeling, including refined vessel pruning of selected vessel branches and complete regression of vascular networks, to form an efficient mature vasculature to meet their physiological functions , are specialized macrophages that play crucial roles in mediating immune-related functions  were maintained in an automatic fish housing system at 28°C following standard protocols s843 um13 y7 hkz011t . The 0.003% 1-phenyl-2-thiourea  was added into the Hanks’ solution to prevent pigment formation of zebrafish embryos. The zebrafish chorion was removed at 1 day post-fertilization (dpf) with the treatment of 2 mg/ml pronase , which was diluted in the Hanks’ solution. All animal use and handling procedures were approved by the Institute of Neuroscience, Chinese Academy of Sciences.Adult zebrafish . Larvae were embedded in 1% low-melting agarose (Sigma) for imaging without anesthetics. Imaging was carried out under a 40× water immersion objective  with an Olympus Fluoview 1000 confocal microscope . The Tg(coro1a:DsRedEx) microinjected with control or pu.1 MO. The microglial engulfment of apoptotic ECs was defined as a process that the microglia migrated to and engulfed the apoptotic ECs and then the apoptotic ECs faded away.All the images were analyzed by ImageJ (NIH). The pruned vessels were quantified in the whole zebrafish brain. For the quantification of vessel pruning, the vessel segment which initially displayed lumen morphology but with a collapsed shape and disappeared completely later was counted as a pruned vessel. For the quantification of EC apoptosis, the ECs exhibiting typical apoptotic features, such as plasma membrane blebbing and formation of apoptotic bodies, were counted as apoptotic ECs. For the quantification of microglial density, we counted the number of microglia in the whole brain region of the microglial transgenic zebrafish pu.1 MO (5′-GATATACTGATACTCCATTGGTGGT-3′) or equivalent control MO (5′-CCTCTTACCTCAGTTACAATTTATA-3′) were microinjected into one-cell-stage zebrafish embryos.Morpholino oligonucleotides (MOs) were purchased from Gene Tools . Lyophilized MOs were dissolved in nuclease-free water. The 4 ng Tg(kdrl:EGFP) larvae through the common cardinal vein. Immediately after the injection, time-lapse imaging was performed to trace pruned vessels with apoptotic ECs.The DAPI  was microinjected into the blood circulation system of 3-dpf Whole zebrafish embryos at 3 dpf were fixed in 4% paraformaldehyde for 2 h at room temperature, washed twice in PBS, and then incubated in a blocking solution  overnight at 4°C. The embryos were then incubated in the blocking solution with a rabbit anti-Caspase-3 primary antibody  for 72 h at 4°C. After washing with PBS 0.2% Triton, the embryos were incubated in the blocking solution with a secondary antibody (1:500) and DAPI (1:1000) for 48 h at 4°C. After washing with PBS 0.2% Triton, images were taken with an Olympus Fluoview 1000 confocal microscope . The dying ECs showing overlapped anti-Caspase-3 staining and DAPI staining are considered as the apoptotic ECs.t-test. Data were represented as mean ± SEM, and p < 0.05 was considered to be statistically significant.Statistical analyses were performed by using GraphPad Prism v6.0 software. The significance of the difference between two groups was determined by using two-tailed unpaired Student’s Tg(fli1a:nEGFP);Tg(fli1a.ep:DsRedEx), in which the nucleus and cellular morphology of ECs were labeled by enhanced green fluorescent protein (EGFP) and DsRed, respectively  larvae to label the nucleus of ECs, we found that the nucleus of apoptotic ECs condensed and fragmented during vessel pruning . These results suggest that the vessel segments with longer length and occupied by the nuclei of neighboring vessels’ ECs at their both ends are more likely to be pruned via EC apoptosis rather than EC migration.Compared with pruned vessels with EC lateral migration, we found that EC apoptosis-accompanied pruned vessels showed a higher probability that the nuclei of neighboring vessels’ ECs located near the both ends of the pruned vessels ;Tg(kdrl:EGFP) zebrafish larvae, in which DsRed and EGFP were expressed in microglia and ECs, respectively. Interestingly, we found that after the EC on the pruning vessel went into apoptosis, a microglial cell always migrated to and engulfed the apoptotic EC, followed by the completion of vessel pruning ;Tg(kdrl:EGFP) larvae, microglia were largely diminished . However, in accordance with in normal larvae (see Figure To further examine whether microglia are essential for EC apoptosis-accompanied vessel pruning, we downregulated the expression of the in vivo time-lapse imaging on larval zebrafish, in this study we identified, to our knowledge, for the first time that EC apoptosis makes a significant contribution to brain vessel pruning during development in a microglial cell-independent manner. Although unnecessary for EC apoptosis-accompanied vessel pruning, microglia can engulf and clear apoptotic ECs, a behavior that may be important for protecting the brain microenvironment from inflammation.Taking advantage of A previous study showed that the pruning of a defined blood vessel CrDI, which locates along the anterior margin of the eye in zebrafish and contains 3–4 ECs, was accompanied by the death of 1–2 ECs (Kochhan et al., In our previous study, we found that vessel pruning in the brain of larval zebrafish occurs preferentially at loop-forming vessels, which usually show inefficient blood flow and are functionally redundant (Chen et al., BX, YZ, JD and XD conceived the project and designed the experiments. BX and YZ carried out the experiments and analyzed the data with QC’s and YY’s help. BX, YZ, JD and XD wrote the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


The development of a highly oriented fiber morphology by effect of tensile deformation of stereodefective isotactic polypropylene (iPP) samples, starting from the unoriented γ form, is studied by following the transformation in real time during stretching through wide angle X-ray scattering (WAXS) measurements. In the stretching process, after yielding, the initial γ form transforms into the mesomorphic form of iPP through mechanical melting and re-crystallization. The analysis of the scattering invariant measured in the WAXS region highlights that the size of the mesomorphic domains included in the well oriented fiber morphology obtained at high deformations increases through a process which involves the coalescence of the small fragments formed by effect of tensile stress during lamellar destruction with the domain of higher dimensions. The structural and morphological transformations of isotactic polypropylene (iPP) by effect of stretching have been widely studied ,18,19,20rr triads, at concentrations in the range 0.5–11 mol % , t, t47], tAc) and the total area of the diffraction profile (Atot) does not apparently change , given by the term <f2> − <f>2, which represent the difference between the average square (<f2>) and the square of average (<f>2) of f [f> because of the presence of disorder, the higher the fluctuations, and the higher the diffuse scattering. By effect of coalescence of the small sub-domains into the large domains, the diffuse scattering decreases and the interference term (Bragg-like contribution) increases. The WAXS invariant increases, because the diffuse scattering term is always lower than the Bragg term.On the other hand, the fact that the crystallinity index measured from the radially averaged WAXS profiles as the ratio between the area of the crystalline phase  of f . Therefoq values at 900% deformation, indicating that the average correlation distance between the chain axes within the mesomorphic domains decreases, producing increase of electron density. Therefore, the increase of the scattering invariant is not only due to coarsening, but also to increase of electron density (densification).In order to probe the effective increase of the size of the mesomorphic domains by effect of stretching, we compare in The structural transformations occurring by effect of stretching in stereo-irregular isotactic polypropylene samples are studied in situ during deformation by collecting WAXS patterns. The metallocene-made iPP samples selected in this study show high ductility, allowing achieving high deformations before breaking. start) the γ form starts transforming into the mesomorphic form of iPP, and at 400–500% deformation (εend), the transformation is almost complete. The stress induced phase transition of the γ form into the mesophase occurs after the beginning of lamellar fragmentation, concomitant with destruction of the crystalline blocks  and re-crystallization in fibrillary entities containing mesomorphic aggregates. At the end of transformation into mesophase, a fibrillary morphology develops with a high degree of orientational order of the chain axes parallel to the stretching direction. We show that the chains extracted from the original crystals re-crystallize forming aggregates of mesomorphic domains responsible for the coherent elastic scattering (Bragg-like contribution) which include at the boundaries isolated chains or groups of 2–3 chains, which contribute to diffuse scattering. The coalescence process of these chains with the larger mesomorphic domains, increases the volume of coherence of the mesomorphic domains. Since the number of coherent domains does not decrease, the WAXS scattering invariant increases by effect of coalescence during deformation, even if the sampled q region is narrow. Coalescence starts concomitant with the process of lamellar destruction, and beginning of transformation of the initial γ form into the mesophase and, after complete transformation into the mesomorphic form, continues facilitated by the mechanical stress field.WAXS analysis reveals that the crystals of γ form tend to assume a nearly perpendicular chain axis orientation instead than parallel to the stretching direction at low deformations. At ≈200% deformation (ε


Informally, a domain is a spatially contiguous region that somehow participates in the same dynamic effect or function. The latter will result in highly correlated temporal activity between grid cells of the same domain. δ-MAPS first identifies the epicenters of activity of a domain. Next, it identifies a domain as the maximum possible set of spatially contiguous grid cells that include the detected epicenters and satisfy a homogeneity constraint. After identifying the domains, δ-MAPS infers a functional network between them. The proposed network inference method examines the statistical significance of each lagged correlation between two domains, applies a multiple-testing process to control the rate of false positives, infers a range of potential lag values for each edge, and assigns a weight to each edge reflecting the magnitude of interaction between two domains. δ-MAPS is related to clustering, multivariate statistical techniques and network community detection. However, as we discuss and also show with synthetic data, it is also significantly different, avoiding many of the known limitations of these methods.In real physical systems the underlying spatial components might not have crisp boundaries and their interactions might not be instantaneous. To this end, we propose δ-MAPS on data from two domains: climate science and neuroscience. First, the sea-surface temperature climate network identifies some well-known teleconnections (such as the lagged connection between the El NinWe illustrate the application of  Spatio-temporal data become increasingly prevalent and important for both science  and enterprises . The spatial scale of the available data is often determined by an arbitrary grid, which is typically larger than the true dimensionality of the underlying system. One major task is to identify the distinct semi-autonomous components of this system and to infer their  interconnections from the available spatio-temporal data. Traditional dimensionality reduction methods, such as principal component analysis (PCA), independent component analysis (ICA) or clustering, have been successfully used for many years but they have known limitations when the objective is to infer the functional network between all spatial components of the system.δ-MAPS, an inference method that first identifies these spatial components, referred to as “domains”, and then the connections between them  is a spatially contiguous region that somehow participates in the same dynamic effect or function. The exact mechanism that creates this effect or function varies across application domains; however, the key idea is that the functional relation between the grid cells of domain results in highly correlated temporal activity. If we accept this premise, it follows that we should be able to identify the “epicenter” or core of a domain as a point (or subregion) at which the local homogeneity is maximum across the entire domain. Instead of searching for the discrete boundary of a domain, which may not exist in reality, we compute a domain as the maximum possible set of spatially contiguous cells that include the detected core, and that satisfy a homogeneity constraint, expressed in terms of the average pairwise cross-correlation across all cells in the domain. Domains may be spatially overlapping. Also, some cells may not belong to any domain.We propose δ-MAPS infers a functional network between them. Different domains may have correlated activity, potentially at a lag, because of direct or indirect interactions. The proposed edge inference method examines the statistical significance of each lagged cross-correlation between two domains, applies a multiple-testing process to control the rate of false positives, infers a range of potential lag values for each edge, and assigns a weight to each edge based on the covariance of the corresponding two domains.After we identify all domains, δ-MAPS is related to clustering, parcellation , network community detection, multivariate statistical methods for dimensionality reduction such as PCA and ICA, as well as functional network and lag inference methods. However, as we discuss in “δ-MAPS is also significantly different than all these methods. δ-MAPS does not require the number of domains as an input parameter, the resulting domains are spatially contiguous and potentially overlapping, and the inferred connections between domains can be lagged and positively or negatively weighted. Further, the distinction between grid cells that are correlated within the same domain and grid cells that are correlated across two distinct domains allows δ-MAPS to separate between local diffusion (or dispersion) phenomena and remote interactions that may be due to underlying structural connections .δ-MAPS on data from two domains: climate science  or ICA techniques. For instance, in climate science, PCA  analysis) has been used to identify teleconnections between distinct climate regions . The ortδ-MAPS involves only four hyperparamteters and it is simpler compared to , spectrpared to .An approach of increasing popularity is to first construct a correlation-based network between individual grid cells, after pruning cross-correlations that are not statistically significant – see . Then, sspatial fieldX(t) sampled on an arbitrary gridG. This grid can be modeled as a planar graph G, where each vertex in V is a grid cell and each edge in E represents the spatial adjacency between two neighboring cells. A set of cells A⊆V is spatially contiguous, denoted by IG(A)=1, if it forms a connected component in G.The input data is generated from a K-neighborhood of a cell i, denoted by ΓK(i), includes i and the set of K nearest neighbors to i according to an appropriate spatial distance metric . The K-neighborhood of a cell is always spatially contiguous.The i is associated with a time series xi(t) of length T . We assume that xi(t) is sampled from a stationary signal and denote by i and j is measured with Pearson’s cross-correlation at zero-lag, Each grid cell Other similarity metrics could be used instead.local homogeneity at cell i is defined as the average pairwise cross-correlation between the K+1 cells in ΓK(i), The homogeneity of a set of cells A as the average pairwise cross-correlation between all distinct cells in A, Similarly, we define the domainA is a spatially contiguous set of cells that somehow participate in the same dynamic effect or function. The exact mechanism that creates this effect or function varies across application domains; however, the key premise is that the functional relation between the cells of domain A results in highly correlated temporal activity (at zero-lag), and thus high values of the homogeneity metric homogeneity threshold δ examines if the homogeneity of A is sufficiently high, i.e., a domain A must have δ is discussed later in this section).Intuitively, a core of a domain A as a cell i∈A at which the local homogeneity A (and certainly larger than δ). In general, the core of a domain may not be a unique cell.If we accept this premise, it follows that we should be able to identify the “epicenter” or c is in the core of a domain. The domain A rooted at c has to satisfy the following three properties: it should include cell c, be spatially contiguous, and have higher homogeneity than δ: More formally now, suppose that we know that cell largest possible set of cells that satisfies the previous three constraints.The boundaries of the underlying spatial components of a system are, in practice, unknown and may gradually “fade” into other regions dominated by noise. Instead of trying to identify such “fuzzy boundaries” however, we prefer for simplicity to compute a domain as the Domain identification problem: Given the field X(t) on the spatial gridG, a core cellc, and the thresholdδ, the domainA(c) is a maximum-sized set of cells that satisfies the three constraints of (aints of . In AppeX(t) may include several domains. The number of identified domains, denoted by N, depends on the threshold δ. Domains may be spatially overlapping; this is the case when the cells of a region are significantly correlated with two or more distinct domain cores. Also, some cells of the grid may not belong to any domain, meaning that their signal can be thought of as mostly noise . Decreasing δ will typically result in a larger number of detected domain cores. Further, as δ decreases, the spatial extent of each domain will typically increase, resulting in larger overlaps between nearby domains.A given spatial field δ can simply be a user-specified parameter for the minimum required average cross-correlation within a domain. Another way is to calculate δ based on a statistical test for the significance of the observed zero-lag cross-correlations as follows.i,j we compute the Pearson correlation ri,j at zero lag. To assess the significance of each correlation we use Bartlett’s formula  is the autocorrelation of the time series of grid cell i at lag τk. The scaled values α (set to 10−2 unless specified otherwise).here δ is set as the average of all significant correlations. A domain is a set of spatially contiguous grid cells, thus we require that the mean pairwise correlation for the cells belonging to the same domain to be higher than the mean pair-wise correlation of randomly picked pairs of grid cells. δ depends on the choice of the significance level α, on the autocorrelation structure of the underlying time series and on the correlation distribution of the field.The threshold seeds; each seed is a candidate core for a domain. In the second phase, each seed is initially considered as a distinct domain. Then, an iterative and greedy algorithm attempts to identify the largest possible domains that satisfy the three constraints of  is available online at https://github.com/deltaMAPS/deltaMAPS_fMRI.Given the NP-Hardness of the previous problem, we propose a greedy algorithm that runs in two phases. In the first phase, we identify a set of cells, referred to as aints of  through Seed selection Recall that the core of a domain is a cell of maximum local homogeneity across all cells of that domain. So, one way to detect potential core cells, while the domains are still unknown, is to identify points at which the homogeneity field i is a seed if j∈ΓK(i). Let S be the set of all identified seeds.δ. Further, additional seeds can appear in regions where domains overlap. Consequently, it is necessary to include a merging operation in which two or more seeds are eventually merged into the same domain.In general, a single domain may produce more than one seed because the local homogeneity field can be noisy and so it may include multiple local maxima, greater than K decreases, the local homogeneity field becomes more noisy and so we may detect more seeds in the same domain. On the other hand, larger values of the neighborhood size K can oversmooth the homogeneity field, removing seeds and potentially hiding entire domains. The latter is more likely if the spatial extent of a domain is smaller than K+1 cells. This observation implies that the spatial resolution of the given grid sets a lower bound on the size of the functional domains that can be detected.Note that as Domain-merging operation Two candidate domains A and B can be merged if they are spatially contiguous and if the homogeneity of their union is sufficiently high, i.e., S. It is also performed after each domain-expansion operation, whenever it is possible to do so.The merging operation is performed initially on the set of seeds Domain-expansion operation A domain A is expanded by considering all cells that are adjacent to A, and selecting the cell i that maximizes The expansion operation is repeated in rounds. At the start of each round, domains are sorted in decreasing order of homogeneity. Then, each domain is expanded by one cell at a time, as previously described, in that order. After every expansion operation, we check whether one or more merging operations are possible. A round is complete when we have attempted to expand each domain once.δ or if there are no other adjacent cells that can be added into the domain. The domain identification algorithm terminates when no further expansion or merging operations are possible.A domain can no longer expand if that would violate the homogeneity constraint N identified domains Vδ={A1,…AN}, the next step is to construct a network Gδ between domains. Different domains may have correlated activity because of direct or indirect interactions. We refer to Gδ as a functional network to emphasize that the edges between domains are based on functional activity and correlations instead of structural or physical connections  or causal interactions (“effective network”).Given the domain-level signalXA(t) with each domain A. The definition of this signal depends on the specific application field. For instance, when we analyze climate anomaly time series, the domain-level signal is defined as the cumulative anomaly across all cells of that domain, where the contribution of each signal is weighted by the relative size of that cell (it depends on the cell’s latitude). For fMRI data, the domain-level signal is defined as the average BOLD signal across the cells of that domain.We associate a τ. For this reason, we examine if there is a significant cross-correlation between different domains over a range of lags (−τmax≤τ≤τmax). The sample cross-correlation between domains A and B at a lag τ can be estimated as: Two different domains may be located at some distance, and so they may be correlated at a non-zero lag τmax should be large enough to include the typical signal propagation delays in the underlying system but at the same time it should be much lower than T. The 2τmax+1 cross-correlations for a pair of domains can be represented with a correlogram; an example based on climate sea-surface temperature data , for a fixed value of τ and under the assumption that A and B are two jointly stationary signals with independent, identically distributed normal errors. Under the null-hypothesis that the domain-level signals of A and B are uncorrelated, The next step is to examine the statistical significance of the measured cross-correlation between two domains  formula , which irA,A(τk) is the autocorrelation of the time series of domain A at lag τk.where rA,B(τ) is zero and the following statistic approximately follows the standard normal distribution N: Under the previous null-hypothesis, the expected value of rA,B(τ) is bounded between . So, we can now perform hypothesis testing for every pair of domains, computing a corresponding p-value based on z.The approximation is due to the fact that Gδ, we need to control the number of false positive edges that may result from the multiple testing problem. We do so using the False Discovery Rate (FDR) method of Benjamini and Hochberg , the Benjamini-Hochberg procedure ranks the Mp-values  and only keeps the first m<M tests (edges), where pm is the highest p-value such that pm<qm/M. Given that there may be several domains in Hochberg . Specifibased on . Given amentclass2pt{minimLag inference and edge directionality We infer the domain-level network Gδ as follows. Two domains A,B∈Vδ are connected if there is at least one lag value at which the cross-correlation rA,B(τ) has passed the FDR test. The standard approach in lag inference is to consider the lag value τ∗ that maximizes the absolute cross-correlation, The corresponding correlation is denoted as entclass1pt{minimaFocusing on Gδ may be associated with a range of lag values.A and B, denoted as Rτ, is defined as the range of lags that produce significant cross-correlations, within one standard deviation from Rτ includes τ=0, the edge is represented as undirected. If Rτ includes only positive lags, the edge is directed from A to B meaning that A’s signal precedes B’s by the given lag range; otherwise, we associate the opposite direction with that edge. We emphasize that the directionality of the edges does not imply causality; it only refers to temporal ordering.Instead, we follow a more robust approach in which an edge of the domain-level network Edge weight and domain strength How to assign a weight to each domain-level edge in Gδ? A common approach is to consider the (signed) magnitude of the cross-correlation Rτ instead. The weight of an edge can be positive or negative depending on the sign of the corresponding cross-correlation.The cross-correlation is computed at lag Finally, the strength of a network node (domain) is defined as the sum of the absolute weights of all edges of that node .δ-MAPS method works, and to contrast the results of the latter with commonly used methods such as PCA, ICA, spatial clustering, and overlapping community detection. We rely on synthetic data so that the ground-truth is known.The two objectives of this section are to illustrate how the Synthetic data description We construct five domains on a 50 ×70 spatial grid. Each domain i is associated with a “mother” time series yi(t), (i=1 …5). To make the experiment more realistic in terms of autocorrelation structure and marginal distribution, each yi(t) is a real fMRI time series with length T=1200 (see “yi(t) are uncorrelated , and they are normalized to zero-mean, unit-variance. To create correlations between domains , we construct five new time series xi(t) based on linear combinations of two or more mother time series. For instance, if we set xi(t)=(1−α)yi(t)+αyj(t+τ) with 0<α<1 and xj(t)=yj(t), domains i and j become positively correlated at a lag τ; the correlation increases with α. The time series xi are again normalized to zero-mean, unit-variance. We then scale the time series of domain i by a factor xi(t)]=si).200 see “” sectionrp. A domain has a “core region” with the same center and radius rc<rp; the core is supposed to be the epicenter of that domain. Every point in the core has the same signal xi(t) (before we add random noise). Outside the core, the signal attenuates at a distance d from the center of the domain as follows: For simplicity, each domain is a circle with radius Finally, we superimpose white Gaussian noise of zero-mean, unit-variance on the entire grid.The parameters of the five synthetic domains are shown in Table δ-MAPS results The parameters of δ-MAPS are set as follows: K=4 cells (up-down-left-right), and δ=0.55 (corresponds to significance level 10−2). In the edge inference step, the FDR threshold is q=10% and τmax=20.Fig. entclass1pt{minimaδ threshold). More quantitatively, the inferred domains include about 80%-90% of the ground-truth cells in each domain. In non-overlapping regions this fraction is higher (85%-95% of the cells), while in overlapping regions it drops to 45%-80%. The extent of overlapping regions is harder to correctly identify especially when a domain  overlaps with a stronger domain ; the stronger domain effectively masks the signal of the weaker domain. The average pairwise cross-correlation of the cells in each domain varies between 55%-70% in the ground-truth data, while the inferred domains have slightly higher average cross-correlation (65%-75%) due to their smaller expanse.Each domain is a subset of the domain’s true expanse. The reason is that some cells close to the periphery of each domain have very low signal-to-noise ratio . The lag ranges always include the correct value . Also, the three edges are correctly ordered in terms of absolute cross-correlation magnitude:  followed by , followed by .Finally, Fig. PCA/EOF results PCA assumes that the dominant patterns are orthogonal in space and time  but reqrue, see ).We apply EOF analysis using Matlab’s PCA toolbox. Figure ICA results We apply ICA on the synthetic data using Matlab’s FastICA toolbox. To help ICA perform better, we specified the right number of independent components, which is two . The two independent components are shown in Fig. Clustering results We apply the most well-known clustering method, k-means, on our synthetic data. As commonly done with correlation-based clustering, the distance between two cells i and j is determined by the maximum absolute correlation across all considered lags, as k=5 (the number of synthetic domains) and 6, respectively. For k=5, domains 1 and 3 form a single cluster because of their strong anti-correlation; the same happens with domains 4 and 5. The connection between domains 3 and 5 is missed, as well as the overlap between domain 2 with domains 1 and 3. Further, two of the five clusters (green and brown) cover just noise. The situation changes completely when we request k=6 clusters. In that case, the overlapping regions in domain 2 form a single cluster, while domains 1 and 3 are separated in different clusters. Another clustering algorithm, resulting in spatially contiguous clusters  field from the HadISST dataset , and transform the signal to zero-mean at each grid point.We first apply ver them . Here, w dataset , coverinδ-MAPS is applied as follows. We set the local neighborhood to the K=4 nearest cells so that we can identify the smallest possible domains at the given spatial resolution. Grid cells that cover mostly land do not have an SST signal and so they do not participate in the local neighborhood ΓK(i) of any sea-covered grid cell i. Second, the homogeneity threshold δ is set to 0.37 (corresponds to a significance level of 10−2). In the edge inference stage, the lag range is τmax=12 months , and the FDR threshold is set to q=3% .E) corresponds to the El NiF (part of the “horseshoe-pattern” surrounding ENSO), domain J (Indian ocean) and domain Q . The strength of the edges associated with ENSO are shown in Fig. Figure see Fig. b. Other Figure τ=0. The network consists of five weakly-connected components. If we analyze the largest component (which includes ENSO) as a signed network  we see that it is structurally balanced (The color code represents the (signed) cross-correlation for each edge. The lag range associated with each edge is shown in Fig. balanced . A graphQ seems to play a unique role, as it temporally precedes all other domains in the inferred network. Specifically, its activity precedes that of domains D, E and F by about 5-10 months. The lead of south tropical Atlantic SSTs (domain Q) on ENSO has recently received significant attention in climate science , we may also see a indirect correlation between B and C at a lag τA,B−τA,C. Or, it may be that A has a causal effect on B at lag τA,B and B has a causal effect on C at lag τB,C; in that case we may observe an indirect correlation between A and C at lag τA,B+τB,C. Or, it may be of course that the observed correlation between two nodes A and B is due to more than one causal paths that originate at A and terminate at B through one or more nodes.As expected, some of the edges we detect in the network of Fig. lag-consistent if there is at least one value in the lag range associated with each edge that would place the three nodes in a consistent temporal distance with respect to each other. For instance, in the case of the first triangle of Fig. Q to F has a lag of 8 months and the edge between E and F has lag -2 months (meaning that the direction would be from F to E); several other values would make this triangle lag-consistent. We have verified the lag-consistency of every triangle in the climate network. One exception is the triangle between domains , shown at the bottom of Fig. C to G can be explained with the triangle between domains , which is lag-consistent. We emphasize that the temporal ordering that results from these lag relations should not be misinterpreted as causality; we expect that several of the edges we identify are only due to indirect correlations, not associated with a causal interaction between the corresponding two nodes.Switching to lag inference, we say that a triangle is Q and E, respectively), are missed.For comparison purposes, Fig. Figure δ we use in δ-MAPS. That method ensures that every cluster (referred to as “area”) is spatially contiguous but it also requires that there is no overlap between areas and it attempts to assign each grid cell to an area. Consequently, it results in more areas (compared to the number of domains), some of which are just artifacts of the spatial parcellation process. Further, the spatial expanse of an area constrains the computation of subsequent areas because no overlaps are allowed.Finally, Fig. δ-MAPS on cortical resting-state fMRI data from a single subject  from the WU-Minn Human Connectome Project (HCP). Our goal is to illustrate that δ-MAPS is able to identify well-known resting-state networks even from single subject data, without having to rely on group-level averages. The data acquisition parameters are described in . We emphasize that major differences across different scanning sessions of the same subject are common in fMRI; for this reason, most studies of functional brain networks often only report group-level averages. The entire cortical volume is projected to a surface mesh (Conte69 32K) resulting in about 65K gray-ordinate points (as opposed to volumetric voxels). Each point of this mesh is adjacent to six other points; for this reason, we set K=6. The homogeneity threshold is set to δ=0.37 .In this paper, we analyze two scanning runs of the same subject (“scan-1” and “scan-2”). Each scan lasts about 14 minutes and results in a time series of length posed in ). The maδ-MAPS results in a network with about 850 domains in scan-1 (1120 domains in scan-2). 80% of the domains are smaller than 30-40 voxels (depending on the scan) and 5% of the domains are larger than 250 voxels  is 0.70 for scan-1 and 0.66 for scan-2). Further, the network is assortative meaning that domains tend to connect to other domains of similar degree (assortativity coefficient about 0.7 in both scans).The application of δ-MAPS networks are consistent with what neuroscientists currently know about resting-state activity in the brain. During rest, certain cortical regions that are collectively referred to as the Default-Mode Network (or DMN) are persistently active across age and gender , and it removes iteratively all nodes of degree k or less in each round so that after the extraction of the k’th core all remaining nodes have degree larger than k. The density of the remaining network, as shown in Fig. k=14 cores from the scan-1 network (k=16 cores in scan-2) shows a sudden increase by a factor of two. This suggests that the network includes a densely inter-connected backbone. The size of this backbone is small relative to the entire network: 130 domains in scan-1 (90 in scan-2).To further investigate the structure of those higher degree  domains, we perform position . The k-cSimilar observations about resting-state functional brain networks have been previously reported based on a rich-club network analysis method . Fig. 6cδ-MAPS can identify meaningful functional components and infer their connectivity.We conclude the analysis comparing our results to those obtained by ICA. ICA, in contrast to the proposed method, aims to identify temporally coherent components . Here, we use MELODIC ICA  to identδ-MAPS range from quantifying uncertainties in climate projections to diagnosing changes in teleconnections in response to anthropogenic perturbations. Furthermore δ-MAPS can be successfully applied towards quantifying differences across datasets and models, evaluating model performances, and investigating model biases and their propagation across different fields of the climate system. A more in-depth discussion of these aspects and applications can be found in . However, in many cases  feedback loops exist, thus such a framework is not a realistic model for the system’s dynamics. Alternative approaches to establish causal inference could be based on Granger causality or controlled interventions  where the local homogeneity is maximum across the entire domain. Instead of searching for the discrete boundary of a domain, which may not exist in reality, we compute a domain as the maximum possible set of spatially contiguous cells that include the detected core, and that satisfy a homogeneity constraint δ.In this paper we present δ-MAPS infers a functional network between domains. Different domains may have correlated activity, potentially at a lag, because of direct or indirect interactions. The proposed network inference method examines the statistical significance of each lagged cross-correlation between two domains, applies a multiple-testing process to control the rate of false positives, infers a range of potential lag values for each edge, and assigns a weight to each edge based on the covariance of the corresponding two domains.At a second step, δ-MAPS we analyzed the temporal relationships between different functional components of the climate system in the sea surface temperature field. We found that the proposed method successfully uncovered many well-known climate teleconnections and the lag associated with them. In the context of neuroscience, we performed a single subject analysis focusing on resting state fMRI data. We found that the proposed method was able to uncover many of the well-known resting state networks. We also show how the method identifies a small number of strongly interconnected areas forming the backbone of the resting state network. Finally, using synthetic data we also show how δ-MAPS overcomes limitations of traditional dimensionality reduction techniques such as PCA/ICA, clustering and overlapping community detection.Using X(t) on a grid G, a pairwise similarity metric between pairs of grid cells and a threshold δ. Starting from a grid cell c, the goal is to find the largest subset of grid cells that form a single spatially connected component, and whose average similarity exceeds the threshold δ. The spatial grid can be represented as a planar graph G where each grid cell is a node and edges connect adjacent grid cells. Formally we have the following graph optimization problem:We are given a spatio-temporal field Definition 1. Rooted Largest Connected δ-Dense Subgraph Problem (rooted LC δDS). Given a regular (grid) graph G, a weight function w=0 and symmetric), a threshold δ, and a node c∈V, find a maximum cardinality set of nodes A⊆V such that c∈A, the induced subgraph is connected (IG(A)=1) and δDS is NP-hard we first consider a variant of the problem in which the induced subgraph A has to satisfy two conditions; it has to be a connected subgraph of G, and the average weight of the edges in A has to exceed δ. More formally:To show that rooted LC δ-Dense Subgraph Problem (LC δDS). Given a regular (grid) graph G, a weight function w=0 and symmetric), and a threshold δ, find a maximum cardinality set of nodes A⊆V such that IG(A)=1 and Definition 2. Largest Connected δDS is NP-hard we use a reduction of the densest connected k subgraph problem.To show that LC k-Subgraph Problem (DCkS). Decision version: Given a graph G, and positive integers k and j, does there exist an induced subgraph on k vertices such that this subgraph has at least j edges and is connected?Definition 3. Densest Connected kS is polynomially time solvable for subclasses of planar graphs of bounded tree width  has been shown to be NP-complete on general graphs , as wellee width . Grid gree width ). It is δDS problem is NP-complete on planar graphs.LEMMA 1. The decision version of the LC kS. We reduce an instance <G,k,j> of the DCkS to an LC δDS instance by using the same graph G, setting w=I∈E  is 1 if and only if the pair of nodes is connected by an edge), and δ=j/k(k−1).PROOF. This can be shown via a reduction from the DCδDS is also NP-hard. If a poly-time algorithm existed for the rooted LC δDS, then by calling it |V| times with each of the nodes of the graph, we would obtain in poly-time a solution to the NP-hard LC δDS.Now it is easy to show that rooted LC


Our laboratory identified ADGRL4/ELTD1, an orphan GPCR belonging to the adhesion GPCR (aGPCR) family, as a novel regulator of angiogenesis and a potential anti-cancer therapeutic target. Little is known about how ADGRL4/ELTD1  function, a problem compounded by a lack of known ligands or means of activation. With this in mind, we turned to computational evolutionary biology with the aim of better understanding ADGRL4/ELTD1.ADGRL4/ELTD1 as a highly conserved early angiogenic gene which emerged in the first true vertebrates (bony fish) approximately 435 million years ago (mya), evolving alongside key angiogenic genes VEGFR2 and DLL4. We identified 3 evolutionary ADGRL4/ELTD1 variants based on EGF domain deletions with variant 2 first emerging 101 mya (95% CI 96–105) in Afrotheria and 82 mya (95% CI 76–89) in Primates. Additionally, conservation mapping across all orthologues reveals highest level conservation in EGF Ca binding domain 1, suggesting that this motif plays an essential role, as well as specific regions of the GAIN domain, GPS motif and 7TM domain, suggesting possible activation mechanisms and ligand binding positions. Additionally, we found that ADGRL4/ELTD1 (a member aGPCR family 1) is possibly ancestral to members of aGPCR family 2.We identified This work establishes ADGRL4/ELTD1’s evolution, sheds light on its possible activation and ligand binding zones, and establishes the first temporal references for the emergence of ADGRL4/ELTD1 variants during vertebrate evolution. Our approach is applicable to the greater aGPCR family and opens up new avenues for future experimental work.The online version of this article (10.1186/s12862-019-1445-9) contains supplementary material, which is available to authorized users. Recently, all aGPRCs underwent a nomenclature change . F. F11]. F2+ binding domain 2 are evolutionarily expendable and that losing them has been evolutionarily beneficial for newer species as no ADGRL4/ELTD1 orthologue regains these domains once a common ancestor has lost them. As the EGF Ca binding domain 1 is present in every examined ADGRL4/ELTD1 orthologue, it can be hypothesised that this is most functionally important of ADGRL4/ELTD1’s EGF domains and should be targeted in future ADGRL4/ELTD1 functional experiments. It is also worth noting that there have been no other domain deletions or major additions apart from the EGF domain to ADGRL4/ELTD1’s sequence during vertebrate evolution. Exactly why the number of EGF domains has decreased as vertebrates have evolved remains open to speculation. A possible hypothesis includes the consideration that this has occurred in response to an evolutionary modification of ADGRL4/ELTD1’s yet unsolved ligand(s) or through evolutionary pruning of excess or redundant domains. A minority of vertebrates were predicted to express more than one ADGRL4/ELTD1 variant, suggesting that these receptors are in the midst of evolutionary change. Interestingly, only two vertebrate genomes in our dataset were predicted to express ADGRL4/ELTD1 variant 3 only: the platypus  Percentage similarity to human orthologue across all 61 orthologues reveals that ADGRL4/ELTD1 is as highly conserved as VEGFR2 and DLL4 as well as the majority of highly evolutionarily important DNA damage repair and receptor tyrosine kinase genes, whilst a minority are less conserved than ADGRL4/ELTD1 and a smaller minority are more conserved. Comparisons with ADGRL4/ELTD1 using unpaired Student’s t-test, significance denoted as: * p ≤ 0.05, ** p ≤ 0.01, *** p ≤ 0.001, **** p ≤ 0.0001. B) Percentage similarity to human orthologue across 11 fish genomes reveals that adgrl4/eltd1 is conserved to a far greater extent than the conservation of the fish exome with the same being true for core angiogenic genes and the majority of unrelated evolutionarily important DNA repair and receptor tyrosine kinase genes. Comparisons to exome similarity, using unpaired Student’s t-test, significance denoted as: * p ≤ 0.05, ** p ≤ 0.01, *** p ≤ 0.001, **** p ≤ 0.0001. Abbreviations: ns = non-significant. Figure S2 A) Human ADGRL4/ELTD1 amino acid residue diagram highlighting areas of high conservation across ELTD1 orthologues. Domains with the highest conservation comprise the EGF Ca2+ domain, the N-terminal half of the GAIN domain, the majority of the GPS motif, and the first five transmembrane loops of the 7TM, the external portion of which possible ligand binding or receptor activation occurs. ADGRL4/ELTD1’s signal peptide sequence as well as all domains are colour coded and are detailed in the legend. B) Phylogenetic tree depicting amino acid similarity and evolutionary distance between ADGRL4/ELTD1 orthologues in 59 vertebrate species; schematic drawn to scale. Figure S3 A) Phylogenetic tree displaying the genetic difference between all murine aGPCRS showing that aGPCR family 1 (which contains ADGRL4/ELTD1) shares its common ancestor with family 2. B) Phylogenetic comparisons between EGF domains belonging to members of aGPCR Family 1, Family 2 and Family 5 reveals that ADGRL4/ELTD1’s EGF domains are most closely related to ADGRE3/EMR3’s EGF domains. Table S1. ADGRL4/ELTD1 orthologues and their predicted protein sequences, extracted from NCBI RefSeq and Ensembl databases. Colour coding relates to ADGRL4/ELTD1 variant expression: Red shading = ADGRL4/ELTD1 variant 1; Blue shading = ADGRL4/ELTD1 variant 2; Grey shading = ADGRL4/ELTD1 variant 3; Green shading = species expressing splice variants of both ADGRL4/ELTD1 variant 1 and 2. (DOCX 1110 kb)


Phosphated tetraphenylethylene was involved as the classical aggregation-induced emission dye. Sulfonated acedan representing one example of two-photon fluorescent probes, was also investigated. A ruthenium(II) complex with carboxylated bipyridyl ligands was included as a representative candidate of luminescent transition-metal complexes. We determined the association constants of the GC5A–dye complexes by fluorescence titration and discuss the complexation-induced photophysical changes. In addition, a comparison of the complexation behavior of GC5A with that of other macrocycles and potential applications according to the diverse photophysical responses are provided.We herein describe the comprehensive investigation of the complexation behavior of a guanidinium-modified calix[5]arene pentaisohexyl ether (GC5A) with a variety of typical luminescent dyes. Fluorescein, eosin Y, rose bengal, tetraphenylporphine sulfonate and sulfonated aluminum phthalocyanine were employed as classical aggregation-induced quenching dyes. 2-( Fluorescence sensing represents a powerful detection methodology due to its low cost, ease of use and high sensitivity, and has been widely used in fields of chemistry, biomedicine, environment, and so on . GeneralMacrocyclic hosts constitute a family of well-studied artificial receptors with a discrete cavity that is selective for complementary binding to certain guests . Modulato-positions of phenolic hydroxy groups  and 1.8-ANS  were established, respectively, by plotting the maximum emission wavenumbers of 2,6-TNS/1,8-ANS in a set of solvents as a function of solvent polarity ET(30) (ET(30) values for the involved solvents  and the maximum emission wavenumbers of 2,6-TNS/1,8-ANS were extracted from references arenes  with ammonium-modified TPE derivatives reported previously by us 2+  complex could be quenched by the phenol moieties of a covalent linked calixarene via proton-coupled electron transfer [3), where SC4A serves as a PET quencher [3 into the hydrophobic cavity of SC8A led to a considerable luminescence enhancement [3 complex forms indeed, but the corresponding luminescence remains nearly unaltered. On one hand, Ru(dcbpy)3 is too large to be included into the cavity of GC5A, so the luminescence alternation by a hydrophobic effect could be excluded. On the other hand, Ru(dcbpy)3 locates at the upper rim of GC5A via salt bridge interactions, so the distance between the host and guest is too long for PET to occur. As well-known, Ru(II) complexes have been widely used in constructing dye-sensitized TiO2 solar cells [3 provides an alternative way to non-covalently anchoring TiO2 and Ru(dcbpy)3, especially with the photophysical property unaltered. Moreover, the interface modification of TiO2 by calixarene derivatives can produce an interface energy barrier that could suppress back-electron transportation and/or charge recombination between the photoanode and the photosensitizer and thus improve the photovoltaic conversion efficiency [Luminescent transition-metal complexes, especially those with ruthenium (Ru), are of great importance owing to their well-documented chemical stability, abundant excited-state photophysics, redox behavior and utilizable luminescence properties –61. Thessolution . The abssolution . We ther complex . The dat 107 M−1 , Table 1transfer . Kitamurquencher . Shinkaiancement . That isar cells . The strficiency .6–108 M−1) to all dyes employed 3 strongly, but does not give rise to appreciable emission alternation.In summary, we have investigated the complexation behavior of GC5A with several classical luminescent dyes and analyzed their complexation-induced photophysical changes. GC5A affords strong binding naphthalene-6-sulfonic acid  were purchased from Tokyo Chemical Industry. Ru(dcbpy)3 was purchased from Yuanye Bio-Technology Co., Ltd , GC5A [All reagents and solvents were commercially available and used as received unless otherwise specified. Fluorescein (Fl) was purchased from Sigma-Aldrich, 1-anilinonaphthalene-8-sulfonic acid  and 2-(a), GC5A , P-TPE [a), GC5A  and TPS a), GC5A  were preThe HEPES buffer solution of pH 7.4 was prepared by dissolving 2.38 g of 4-(2-hydroxyethyl)piperazine-1-ethanesulfonic acid (HEPES) in approximate 900 mL double-distilled water. After titration to pH 7.4 at 25 °C with NaOH the volume of the solution was brought to 1000 mL with double-distilled water. The pH value of the buffer solution was then verified on a pH-meter calibrated with three standard buffer solutions. All fluorescence and UV–vis titrations were measured in HEPES buffer  at 25 °C.Steady-state fluorescence measurements were recorded in a conventional quartz cuvette (light path 10 mm) on a Cary Eclipse equipped with a Cary single-cuvette peltier accessory. UV–vis spectra were recorded in a quartz cuvette (light path 10 mm) on a Shimadzu UV–vis spectrophotometer (UV-2450) equipped with a dual cuvette peltier accessory and a temperature controller (TCC-240A).All fittings were performed in a nonlinear manner . All mea


The maximum instantaneous absorption efficiency of the nanoporous alumina sheet with 30 nm pore diameter was found at 0.92 when the radiation intensity was 100 W/m2. The testing results indicated that the nanoporous alumina sheet with the 30 nm pore diameter performed the best compared with the other two aluminum sheets. By error propagation analysis, the relative error of the average amount of heat absorption and the average absorptivity were acceptable.In order to improve the absorption performance of the aluminum sheet for solar application, the nanoporous alumina sheets with the pore diameters of 30 nm and 400 nm were prepared by the anodic oxidation method. The absorption properties of the nanoporous alumina sheets under different solar radiation intensity were studied and compared with the conventional polished aluminum sheet. The results showed that the average absorptivity of the aluminum sheets decreased with the increase of the radiation intensity. When the radiation intensity was 100 W/m The development of the renewable energy to replace the traditional energy is imminent. Renewable energy sources  can satisfy the energy demands with minor environmental impact compared with the traditional energy sources ,2,3. Of × 1020 J . Therefo2O3 on the stainless steel substrate by the magnetron sputtering method, which performed with the absorptivity of 0.92 and emissivity of 0.13 at 82 °C. Zou et al. [As far as today, vacuum deposition, magnetron sputtering and electro-deposition were the major methods to produce the selective absorber coatings for solar systems ,8,9,10. u et al.  reportedu et al. ,16. 2 nanocomposite films by the photopolymerization-induced phase-separation method, and these films show high solar absorptance (α = 0.766–0.863), low thermal emittance (ε = 0.06–0.12). However, nanoporous coatings still had some shortcomings, such as a long manufacturing process and poor controllability of the multi-step process [In order to resolve the above-mentioned problems of selective absorber coatings, nanoporous materials have been introduced, which can effectively reduce the reflection and scattering of sunlight. Wang et al.  obtained process .2. When prepared nanoporous alumina sheets with surface pore diameter of less than 30 nm, the oxidation current was small, and it was difficult to prepare nanopores with uniform distribution; when prepared nanoporous alumina sheets with surface pore diameter larger than 400 nm, the oxidation current was too large, and it was easy to break down the aluminum sheets. Therefore, the largest diameter nanoporous alumina sheet and the smallest diameter nanoporous alumina sheet were selected. The preparation method would be further improved. In order to investigate the solar absorption property of the proposed nanoporous alumina sheets, they would be compared with the conventional polished aluminum sheet under the different simulated radiations. The instantaneous solar absorptivity, average amount of absorbed heat, and average solar absorptivity would be analyzed, and the correlation of the solar absorptivity with the irradiation would be established. This research would present the advantages of the prepared nanoporous material and indicate the potential application in the solar market.In this paper, the nanoporous alumina sheets with the pore diameters of 30 nm and 400 nm and pore depth of 100 μm would be prepared by using the anodic oxidation method with the characteristics of stable performance, simple manufacturing, low cost, and high solar absorptivity. Nanoporous alumina sheets with different pore diameter could be obtained by changing the current magnitude. Current density range was 0.4–4.4 A/dmThe purpose of this work is not to develop new materials, nor to optimize the absorption and emissivity. Porous alumina layers with inclusion of transition metals like Fe, Co, Ni, Cu, Au, Ag, Mo, Cr and W have been widely studied . These sAs shown in The preparation of the nanoporous alumina sheet could be summarized into two steps: (1) Pretreatment of the aluminum sheet to make it smooth, clean and flat; and (2) anodic oxidation process to form the nanopores on the surface of the aluminum sheet. The pretreatment process of the aluminum sheet was shown in The detailed processes could be summarized as follows. Firstly, the aluminum sheets with a purity of 99.99% purchased from Guantai Metal Materials Co., Ltd.  was flattened by using the flattening machine . Then the aluminum sheet placed in the ethanol/acetone solution was cleaned for 10 min in the ultrasonic cleaner  to eliminate the oil. After that, the aluminum sheet was placed in the 1 mol/L sodium hydroxide solution  for five minutes to further remove the dirt and completely remove the natural oxide film on the surface to reveal the pure metal matrix, which was to ensure the uniformity of the surface. At last, the aluminum sheet would be polished in the 400 mL perchloric acid/ethanol solution  mixed in the ratio of 1:9 by using the aluminum as the anode and graphite  as the cathode, and stirring using the magnetic rod  for two minutes. The schematic of the anodic oxidation process of the aluminum sheet was shown in The scanning electron microscope  would be used to inspect whether the micro-pores distributed uniformly on the surface of the aluminum sheet, and In order to investigate the solar absorption performance of the nanoporous alumina sheet, the aluminum sheets with the pore diameters of 30 nm and 400 nm were prepared using the anodic oxidation method mentioned above and compared with the conventional polished aluminum sheet. It should be mentioned that due to the limits of the budget and experimental conditions, these two typical types of the nanoporous alumina sheet would only be made. Further tests will be conducted for the wide range of the pore diameters of the aluminum sheet.As shown in 2 to 800 W/m2 through regulating the input voltage of the lamp, and the simulated radiations were recorded by the pyranometer. The solar radiation intensity has been tested around the surface of the container, and their deviations were less than 5%. The testing would be operated in three hours, and the temperatures of the system components, e.g., aluminum sheet and water, were recorded every 20 min. The thermocouple wires transmitted the signal from the temperature measuring points to the temperature monitor. The characteristics of the devices used in the experiments were presented in One xenon lamp was used to simulate the sunlight with the different radiations from 100 W/mThe three parameters determining the solar absorption property of the aluminum sheets, i.e., instantaneous absorptivity, average amount of heat absorption and average absorptivity, would be analyzed and discussed. Q′t was the total amount of heat absorbed by the aluminum sheet and water every 20 min, which could be calculated by the change of water temperature and aluminum sheet temperature, due to their mass and specific heat capacity were known.The instantaneous absorptivity of the system could be calculated according to Equation (1) , and pre2, the maximum instantaneous absorptivity of the three testing rigs reached 0.92, 0.82 and 0.49 respectively. From above The thermal energy absorbed by the testing rig was composed of the amount of the heat absorbed by the aluminum sheet and cold water inside the water container, which were expressed from Equation (2) to Equation (4) , and theFrom the above 2, the heat absorption of the three testing rigs, i.e., the nanoporous alumina sheets with 30 nm and 400 nm pore diameters, and polished aluminum sheet, reached the maximum at 17,003 J, 13,974 J and 12,887 J respectively. This meant that the nanoporous alumina sheet performed better than the conventional polished aluminum sheet on the solar absorption characteristics, and the nanopore size of the aluminum sheet influenced its performance that the aluminum sheet with 30 nm nanopore diameter worked better than the sheet with 400 nm nanopore diameter.It could also be found that for the testing rigs operated under different working conditions, the amount of absorbed heat increased with the increase of the simulated solar radiation. When the simulated solar radiation was at 800 W/mQt could be calculated by Equation (2). Δt was the radiation time.The average absorptivity was defined as the ratio of the total absorbed radiation by the testing rigs to the total radiation emitted from the solar simulator as in Equation (5), and the testing results were calculated and presented in 2, which was 18% higher than that of the nanoporous alumina sheet with 400 nm pore diameter (0.33) and 50% higher than that of the polished aluminum sheet (0.26). When the simulated radiation was at 800 W/m2, the minimum average absorptivity of the three testing rigs was at 0.14, 0.10 and 0.08 respectively. The average absorptivity of the three aluminum sheets was also found to be decreased exponentially with time, and the nanoporous alumina sheets decreased significantly compared with the polished one due to the higher surface temperature of the nanoporous alumina sheets, leading to more radiant heat losses to the surroundings, as shown in the above From the above figures and table, the surface absorptivity was found to be decreased with the increase of the radiation intensity, and the average absorptivity of the nanoporous alumina sheet with 30 nm pore diameter reached the maximum at 0.39 when the simulated radiation was at 100 W/mBased on the above test results, the correlation of the absorptivity of the aluminum sheet with the radiation intensity was established in the exponential function.Assuming the boundary conditions, when:When:Equation (6) can be rewritten as:Then, the calculation results of the absorptivity of the three types of aluminum sheets were shown in Affected by the accuracy class of the testing devices, the uncertainty range of the major measure quantities containing temperature and solar radiation would be considered. From 2 for example (due that the maximum error would appear at this condition), the relative error of the heat absorbed and absorptivity could be calculated [Taking the polished aluminum sheet at the radiation intensity was 100 W/mlculated .The relative error of all the testing condition about heat absorbed would be less than 10.6%.The relative error of all the testing condition about absorptivity would be less than 14.6%.The relative error of the absorptivity for the other two sheets and at the other testing radiation intensity could be calculated by using the same method, the results were show in Therefore, the error with this experimental could be acceptable from In this paper, the nanoporous alumina sheets with the pore diameters of 30 nm and 400 nm were prepared by anodic oxidation method, and the SEM indicated that the nanopores evenly distributed on the surface of the aluminum sheets, which will be helpful in enhancing the stability of the aluminum surface and improving the solar absorption capability. In order to investigate the property of the nanoporous alumina sheet, the prepared aluminum sheets were compared with the conventional polished aluminum sheet and analyzed in the aspects of the instantaneous absorptivity, average absorbed heat and average absorptivity. The exponential correlation between the average absorptivity and the radiation intensity for the three testing rigs was also established. 2. The absorbed heat by the testing rigs increased with the increase of the radiation, while the average absorptivity decreased with the increase of the radiation. When the radiation intensity was 100 W/m2, the nanoporous alumina sheet with the 30 nm pore diameter had the highest average solar absorptivity of 0.39, which was 18% higher than that of the nanoporous alumina sheet with 400 nm pore diameter, and 50% higher than that of the polished aluminum sheet. The results indicated that the nanoporous alumina sheet performed better than the conventional polished aluminum sheet in the solar absorption property, and the pore size significantly influenced the solar absorptivity of the aluminum sheet. By error propagation analysis, the relative error of the average amount of heat absorption and the average absorptivity were acceptable.The results showed that the maximum instantaneous absorption efficiency of the nanoporous alumina sheet with 30 nm pore diameter was found at 0.92 when the radiation intensity was at 100 W/m


PLCγ contains the regulatory γ-specific array (γSA) comprising a tandem Src homology 2 (SH2) pair, an SH3 domain, and a split pleckstrin homology domain. Binding of an activated growth factor receptor to γSA leads to Tyr783 phosphorylation and consequent PLCγ activation. Several disease-relevant mutations in γSA have been identified; all lead to elevated phospholipase activity. In this work, we describe an allosteric mechanism that connects the Tyr783 phosphorylation site to the nSH2-cSH2 junction and involves dynamic interactions between the cSH2-SH3 linker and cSH2. Molecular dynamics simulations of the tandem SH2 protein suggest that Tyr783 phosphorylation is communicated to the nSH2-cSH2 junction by modulating cSH2 binding to sections of the cSH2-SH3 linker. NMR chemical shift perturbation analyses for designed tandem SH2 constructs reveal combined fast and slow dynamic processes that can be attributed to allosteric communication involving these regions of the protein, establishing an example in which complex N-site exchange can be directly inferred from 1H,15N-HSQC spectra. Furthermore, in tandem SH2 and γSA constructs, molecular dynamics and NMR results show that the Arg687Trp mutant in PLCγ1  perturbs the dynamic allosteric pathway. This combined experimental and computational study reveals a rare example of multistate kinetics involved in a dynamic allosteric process that is modulated in the context of a disease-relevant mutation. The allosteric influences and the weakened binding of the cSH2-SH3 linker to cSH2 should be taken into account in any more holistic investigation of PLCγ regulation.Phosphatidylinositol phospholipase C The polypeptide domain arrangement N-spPH–nSH2–cSH2–SH3–C-spPH, in which the N- and C-terminal portions of the split PH domain come together to form a globular domain (γSA.Phosphatidylinositol phospholipases (PLCs) are a family of enzymes that hydrolyze substrate membrane PI4,5)P inositol,4,5P3  results in phosphorylation of Tyr766 in the unstructured C-terminal tail of the receptor and leads to recruitment of PLC2 domain . We and 2 domain , 11. Binin alone .γs have been detected in a variety of disease conditions through DNA sequence analysis, and these mutations can occur throughout the length of the protein  or in cSH2 . Differential expression patterns of PLCγ1 and PLCγ2 have a great influence on the resulting pathology. For instance, Ser707Tyr (PLCγ2), which has been linked to autoimmune disease, was found to disrupt the autoinhibitory cSH2 interface with the enzyme core (γ1) has been linked to secondary angiosarcoma and is suspected to disrupt the cSH2 domain structure and thereby release autoinhibition (γ2) occurs in the context of resistance to the Bruton’s tyrosine kinase inhibitor ibrutinib used in chronic lymphocytic leukemia (γ2)/Arg687Trp (PLCγ1) mutation is currently available.Mutations in PLC protein . All patnd PLCγ2 . For exayme core , 13. Arghibition . The cSHleukemia . No struγ resting state, the extent to which the cSH2 domain is “available” for contact with the enzyme core and upstream agonists is unclear. In this context, the binding status of the cSH2 C-terminus, which is equivalent to the cSH2-SH3 linker and harbors the Tyr771, Tyr775, and Tyr783 phosphorylation sites, plays a particular role; recent studies proposed that Tyr783 phosphorylation by ITK kinase and Tyr771 phosphorylation by FGFR2 kinase would occur because of an enhancement of C-terminus availability  simulation and heteronuclear NMR spectroscopy. Unexpectedly, the NMR results reveal a complex signature, the examination of which suggests partial dynamic interaction between the C-terminus and the cSH2 domain. In line with the results yielded from MD simulations, we interpret the NMR data to indicate dynamic allosteric communication between the Tyr783 phosphorylation site and the inter-SH2 domain junction, which operates via the C-terminus and residues preceding the C-terminus. Though examples of dynamic allostery have been presented before, here we introduce a case in which the combination of fast- and slow-exchange phenomena results in complex but interpretable NMR crosspeak patterns. We also characterize the effect of the PLCγ1 Arg687Trp mutation—homologous to the cancer therapy resistance Arg665Trp substitution in PLCγ2—on the characteristics of the tandem SH2 domain.Here, we report the results of an investigation of the tandem nSH2-cSH2 segment of PLCMaterials and methods used during the course of this study are provided in γ1 nSH2 and cSH2 domains. The following will discuss in detail the structure and dynamics of different PLCγ1 tandem SH2 proteins (γ1 nSH2 domain comprises residues 545–662 and the cSH2 domain residues 663–756. The junction between the two SH2 domains (“nSH2-cSH2 junction”) is here defined as the residue region 658–668. The region of the polypeptide that encompasses residues to the C-terminus of the cSH2 domain can be described as comprising three segments: the “pre-C-terminus” (residues 757–770), the “C-terminal linker” (residues 771–778), and the “Tyr783-peptide region” (residues 779–790). Together, the C-terminal linker and the Tyr783 peptide region constitute the “C-terminus”; the combination of all three segments is referred to here as the “extended C-terminus.”Our principal aim was to probe the impact of Tyr783 phosphorylation on the structural and dynamical properties of both the PLCproteins . Accordi4FBN and 4EY0, respectively)  and 774–781 (4EY0), mainly corresponding to the C-terminal linker region, is missing, suggesting that this segment is dynamic in nature. In 4EY0, electron density corresponding to the phosphorylated Tyr783 peptide region is observed in the typical SH2 peptide-binding groove, indicating binding in cis. In the case of 4FBN, similar but much weaker density is observed, suggesting that at least partial binding can occur in the absence of Tyr783 phosphorylation. We sought to explore the effect of Tyr783 phosphorylation on the PLCγ1 tandem SH2 domain protein in solution using MD and heteronuclear NMR spectroscopy.Three crystal structures (Protein Data Bank (PDB): 3GQI, 4FBN, 4EY0) are available for the tandem nSH2-cSH2 protein. The structures reported by Bunney et al. comprise a “long” unmodified construct  and a similar construct that was phosphorylated on the Tyr783 side chain (PDB: ctively) . The thr783 using starting models derived from the crystal structures with PDB: 4FBN and 4EY0, respectively .MD simulations were used to generate hypotheses about the structural consequences of Tyr783 phosphorylation and to guide subsequent experiments. We performed six atomistic 100 ns MD simulations of NSH2CSH2 and four atomistic 100 ns simulations of NSH2CSH2-pY783 trajectories.We evaluated convergence for local motions in the cSH2 domain by comparing contact and eigenvalue ranges for different MD trajectories using identical eigenvector  sets from a principal component analysis (PCA). The trajectories were not of sufficient duration to satisfactorily predict the full range of protein motion, interdomain flexibility, and orientation that might be present in solution; special approaches that enhance sampling of the conformational space would be required to accurately address questions regarding interdomain properties of the tandem SH2 constructs. Nevertheless, we identified differences within the cSH2 domain between NSH2CSH2 and NSH2CSH2-pYa; 783 and NSH2CSH2 trajectories in NSH2CSH2 eigenvector 2 (b). Specifically, a high root mean-square fluctuation (RMSF) of the C-terminal linker and the pre-C-terminus in this eigenvector (a) suggests that the dynamics of this region differs between NSH2CSH2 and NSH2CSH2-pY783.PCA in Cartesian space for backbone atoms of the cSH2 domain and the nSH2-cSH2 junction was performed to provide a quantitative analysis of motion represented in the trajectories a; . Eigenvevector 2 b. Specienvector a suggesa). For these protein regions, we use the secondary structure nomenclature that has been widely employed in previous descriptions of SH2 domains (αA-helix (Arg675-Arg684) forms a rather exposed part of the cSH2 domain; the shorter αB-helix (Asp634-Gln641) is close in space to the nSH2-cSH2 junction (Glu650-Trp668). The results of the contact analysis are shown in c and d and a for the extended C-terminus, and in a for the αB-helix/nSH2-cSH2 junction. Here, we focus on the most significant differences in contact probability between the NSH2CSH2 and NSH2CSH2-pY783 trajectories related to the pre-C-terminus and the C-terminus. As expected, the contact between pTyr783 and the cSH2 domain was essentially permanent in the NSH2CSH2-pY783 trajectories but less stable in the NSH2CSH2 trajectories (b). The contact between the following interface pairs was more frequent in the phosphorylated constructs: (p)Tyr783 and cSH2 domain core (670–750), C-terminal linker and cSH2 domain αA-helix, pre-C-terminal region Asn757-Lys759 and cSH2 domain core, and pre-C-terminal region Asn757-Lys759 and nSH2-cSH2 junction residue Glu667 (a). Thus, the MD simulations suggest that Tyr783 phosphorylation modulates the interactions between the pre-C-terminus and the nSH2-cSH2 junction and leads to stronger interactions of the extended C-terminus with the cSH2 domain.To further explore this finding, we performed contact analyses of the trajectories. We specifically focused on contacts between the extended C-terminus and the nSH2-cSH2 junction on one hand and other regions of the protein on the other hand a. For t domains . Of partectories b. The ce Glu667  and S2ab). Particularly strong mutual information was found in the pre-C-terminus, the C terminus, and cSH2 core, which are likely to be in direct contact with these elements. Importantly, significant differences in mutual information were detected between NSH2CSH2 and NSH2CSH2-pY783. The mutual information between pre-C-terminus residues Asn757 and Glu759 on one hand and residues in the 1) C-terminal linker and 2) cSH2 domain—specifically the αA-helix—on the other hand is higher in the NSH2CSH2-pY783 simulations (b). Conversely, the mutual information between various residues in the C-terminus, cSH2 residue Arg694, and junction residues Thr660 and His663 is lower for the NSH2CSH2 trajectories. There was also a lower level of mutual information between Arg694 and the nSH2-cSH2 junction on one hand and on the other hand several nSH2 residues (b), only some of which are spatially close to the nSH2-cSH2 junction (Asn547-Arg567), whereas others are more distant . Our data suggest an allosteric connection between the Tyr783 phosphorylation site and the nSH2-cSH2 junction , which primarily involves sections of the extended C-terminus and the cSH2 domain residues with which they interact. Together, the MD PCA, contact, and MutInf analysis results suggest the potential presence of dynamic interplay between the extended C-terminus and the cSH2 domain.We used the tool MutInf  to prediulations b. Converesidues b, only b. Similar to the proteins in the crystal structures, we prepared unmodified (non-phospho) “NSH2CSH2” (residues 545–790) and Tyr783-phosphorylated “NSH2CSH2-pY783” . We also prepared a construct comprising solely the cSH2 domain and the appended C-terminal region , a shortened form of the tandem lacking the C-terminal residues 545–770 denoted “NSH2CSH2ΔCT,” and a complex of NSH2CSH2ΔCT with a pTyr783 phosphopeptide (residues 779–790) denoted “NSH2CSH2ΔCT-CTpY”; for the last sample, the CTpY peptide was added to 1.2 equivalents (CTpY binding to cSH2 has been described in a previous study (KD < 15 μM) to the cSH2 domain to be saturating under the NMR measurement conditions (783”), and single residue Ala mutants of CSH2 at Pro686, Pro745, Pro755, and Pro769.For NMR experiments, we prepared a variety of tandem-SH2 proteins; key constructs are illustrated schematically in us study ). From t1H,15N-heteronuclear single quantum coherence HSQC spectra of the tandem nSH2-cSH2 proteins constructs were generally well dispersed  and least complete for NSH2CSH2ΔCT (53%). Some crosspeaks for the cSH2 domain, in the nSH2-cSH2 junction, and in the extended C-terminus could not be located, suggesting intermediate exchange broadening. Multiple crosspeaks were observed for several residues in mostly, but not exclusively, CSH2, E664G-NSH2CSH2, and E664K-NSH2CSH2, indicating the presence of slow exchange. Spectra of nonphospho constructs generally displayed weaker intensity than their phospho counterparts. Although pronounced line broadening in the cSH2 domain is often a result of the aforementioned exchange phenomena, the generally lower signal/noise observed for all residues  is likely attributable to a propensity to weak self-association. We have characterized this behavior with 15N nuclear relaxation and small angle x-ray scattering data obtained for NSH2CSH2 and NSH2CSH2-pY783  between the “open” and “closed” forms were not confined to the putative binding contact zones in the cSH2 domain and pTyr783 region but were also observed for sites in the pre-C-terminus (distant from the pY783 binding site), the C-terminal linker, and throughout the cSH2 domain.Interactions between an SH2 domain and a cognate phosphopeptide ligand typically exhibit slow-exchange characteristics, which is consistent with relatively high affinity binding and a slow off-rate . On thisifferent . For theΔCT (“open” state) or NSH2CSH2-pY783 (“closed” state). The crosspeaks for a given residue lie on or close to the vector that joins the corresponding crosspeaks for the “open” and “closed” states. Importantly, this behavior was detected over a whole series of different constructs, several of which were not prepared with this specific phenomenon in mind but for other purposes, and so, this was an adventitious observation. For example, residues Gly777 and Gly789 from the C-terminus and residues Gly689, Ala690, and Gly710, which are located on the cSH2 protein surface, exhibit this behavior (a). This pattern suggests an underlying fast-exchange phenomenon; importantly, the population of “closed” and “open” states for any given construct and residue can be directly inferred by comparing the corresponding peak position to those for the reference “open” and “closed” states, similar to the procedure employed in chemical shift projection analysis (CHESPA)  . Given tc, whereas peak patterns are displayed in a, b), indicating that the dynamic situation in NSH2CSH2 cannot be properly described by a single two-state fast-exchange model applicable to the whole protein construct. Rather, the pattern suggests a heterogeneous dynamic interaction between the cSH2 domain and different parts of the C-terminal tail. For this reason, it is not possible to determine a single KD or kex parameter to describe globally the equilibrium between “open” and “closed” forms.Multiple NSH2CSH2 crosspeak patterns evidencing fast exchange were identified; the corresponding locations are projected onto a 3D structural representation in ΔCT-CTpY display evidence of heterogeneous “open” ⇌ “closed” dynamics, corresponding to a partially bound pre-C-terminus  toward the “closed” state is observed only when the C-terminal linker (residues 771–778) is present (a); the interaction between the cSH2 domain and the pre-C-terminus is dependent upon an intact tether between the pre-C-terminus and the C-terminal tail.Similar to the situation with NSH2CSH2, a subset of cSH2 residues of NSH2CSH2minus a; . However present a; the iΔCT-CTpY and to a greater degree for NSH2CSH2-pY783 . As the separation between Thr660 and the C-terminus is substantial (the distance between Thr660 and Tyr783 Cα atoms is ∼23.9 Å), the shift pattern suggests that Tyr783 phosphorylation is communicated to Thr660 in the nSH2-cSH2 junction, at least in part, via the tethering C-terminal linker. In line with this observation, substantial chemical shift differences between NSH2CSH2-pY783 and NSH2CSH2ΔCT-CTpY were observed throughout the cSH2 domain and the pre-C-terminus . One can rationalize these chemical shift patterns on the basis of a dynamic allosteric connection between the Tyr783 binding site and the nSH2-cSH2 junction.The peak position for nSH2-cSH2 junction residue Thr660 is perturbed by phosphorylation of Tyr783 both for NSH2CSH2minus c; b. One c783 , suggesting that the pre-C-terminus and the C-terminus populate the “closed” form more than in NSH2CSH2. Mutations within the nSH2-cSH2 junction, which in effect communicates the presence of the nSH2 domain, or removal of the nSH2 domain results in a stronger association of the pre-C-terminus and C-terminal linker with the cSH2 domain. As well as these C-terminal residues, Ala690 in the globular part of the cSH2 domain and in spatial proximity of the C-terminus displays a crosspeak in NSH2CSH2 at a position corresponding to dynamic fast exchange between “open” and “closed” states (b), whereas the equivalent crosspeak for the CSH2 construct is shifted toward position in the “closed” NSH2CSH2-pY783. This difference suggests that the attached nSH2 domain influences not only the extended C-terminus but also the cSH2 residues with which the C-terminus interacts. MD simulations and NMR reveal an unstable contact between Asn757-Glu759 and the nSH2-cSH2 junction in NSH2CSH2-pY783, which is further loosened in NSH2CSH2 by virtue of contact between the nSH2-cSH2 junction and the pre-C-terminus  and nSH2-cSH2-junction mutants E664G-NSH2CSH2 and E664K-NSH2CSH2 provide an opportunity to trace which cSH2 residues are influenced by the presence of the nSH2 domain and/or an intact nSH2-cSH2 junction. Relative to the wild-type tandem domain constructs, these proteins can be characterized as “junction-disrupted.” Moreover, along with the wild-type (WT) proteins, the spectra of these mutants are helpful in dissecting the influence of the C-terminus on the nSH2-cSH2 junction. The crosspeaks of residues Leu761, Lys763, Gly765, Glu776, Gly777, and Asn787 in the extended C-terminus for CSH2 as well as for E664G-NSH2CSH2 and E664K-NSH2CSH2 are often not coincident with those for NSH2CSH2 but instead are located on the vectors connecting those for NSH2CSH2 and NSH2CSH2-pY783 b; a, sugge” states b, whereOverall, the picture is that the extended C-terminus and the nSH2 domain represent countervailing influences on the chemical shifts of cSH2 crosspeaks, consistent with two-way dynamic allosteric communication between the pY783-binding site and the nSH2-cSH2 junction. In energetic terms, the effects must be weak because the “open”-“closed” population balances for different residues vary only within a small range, but this is sufficient to lead to distinct influences on the chemical shifts that are directionally coherent .ΔCT and NSH2CSH2ΔCT-CTpY must indicate a C-terminal-linker-“independent” impact of Tyr783 phosphorylation. As outlined in b) suggests that the former pathway is mostly dominant, other than in the pY783 peptide binding site.The foregoing experimental observations support the concept that binding of the Tyr783 region to the cSH2 domain influences the nSH2-cSH2 junction in a C-terminal-linker-dependent manner, in line with expectations from the MD simulations described above. Therefore, crosspeak positions that differ for particular residues in NSH2CSH2αB-helix and the nSH2-cSH2 junction that were predicted in the MD simulations are supported by the NMR data, as discussed in αB-helix, adjacent to the nSH2-cSH2 junction (c). Glu742 shows a fast-exchange type peak pattern that indicates that it is part of the dynamic C-terminal-linker-dependent allosteric pathway. In addition, we found evidence that pY783 peptide binding to NSHCSH2ΔCT also modulates the dynamic equilibrium at this residue. Specifically, C-terminal-linker-dependent and -independent Tyr783 binding have opposing effects on the Glu742 chemical shift (a). A more detailed chemical shift and MD analysis results suggest that the nearby nSH2-cSH2 junction structure is modulated in a different manner in each case  leads to significant loss of autoinhibition of phospholipase activity . The Arg687Trp change likely impacts the nSH2-cSH2 junction itself, as suggested by the large CSPs for Thr660 (b). Significant CSPs were observed for several residues in the putative contact regions between the extended C-terminus and the cSH2 domain, for example Ala690, Gly710, Gly758, Ala770, Leu761, Gly772, Ala773, and Thr766, as well as for the αB-helix residue Glu742 . Data for R687W-NSH2CSH2 indicate a similar trend (b). The data reveal that the pre-C-terminus and C-terminal linker populate the “closed” state to a lesser degree in Arg687Trp constructs than in the WT, suggesting that the Arg687Trp substitution modulates the C-terminal-linker-dependent allosteric pathway.We prepared Arg687Trp tandem SH2 constructs to experimentally probe the impact on structure, dynamics, and the dynamic allostery. The pre-C-terminus Gly765 crosspeak for the Arg687Trp mutant construct is located well away from the fast-exchange “open”-“closed” vector, indicating CSPs dominated by the local effect of the side-chain substitution over other influences. The overall pattern suggests that Arg687 could be in direct contact with residues in the C-terminus. However, CSPs between NSH2CSH2-pYe Arg687 a. The Ar Thr660  b. Signilu742 b; c. Data ar trend b. The dd). The Arg687Trp mutation selectively perturbs the dynamic C-terminal-linker-dependent pathway and exerts its functional influence either by weakening the association of the C-terminus with the cSH2 domain or by impact upon the nSH2-cSH2 junction.It is noteworthy that there are no major CSPs for residues belonging exclusively or even mostly to the C-terminal-linker-independent pathway upon nSH2 domain removal or upon Arg687Trp mutation; namely, Leu692, Lys695, Ala703, Ile704, Glu720, Val724, Gly727, Asn728, and Ser733 have the same or very similar chemical shifts in the mutant d. The Aa, b, and b and a), consistent with the notion that the junction plays a role in relaying the presence of the nSH2 domain to the tandem construct C-terminus.Returning to the WT proteins, in addition to the fast-exchange phenomena described above, peak doubling or broadening was also observed in the spectra. Residues for which peak doubling, and even tripling or more, was evident are located in the extended C-terminus or in regions of the cSH2 domain predicted to be in close proximity, for example Gly689, Ala690, Gly710, Gly727, Gly765, Thr766, and Gly777  exchange discussed above for NSH2CSH2. However, these additional slowly exchanging states of the C-terminus and pre-C-terminus differentially influence the apparent  affinity of a given residue for the cSH2 domain. For the “simpler” case of CSH2 peak-doubling, we can envisage the following: in one slow-exchanging state (state “1”), the effective “open” → “closed” on-rate is kon,1, and the “closed” → “open” off-rate is koff,1; in the second slow-exchanging state “2,” at least one of the effective on-rates and/or off-rates kon,2, koff,2 is different. Whereas the rate for the “1” ⇌ “2” interconversion is slow, in each of states “1” and “2” (with populations p1 and p2), the exchange between “open” and “closed” is fast on the NMR timescale. For residue i, we will thus observe two effective binding constants, namely Ki1 = pi1,closed/pi1,open = ki1,on/ki1,off and Ki2 = pi2,closed/pi2,open = ki2,on/ki2,off. In the absence of multiple slow-exchanging states, a single crosspeak would sit at a position along the vector joining the chemical shift coordinates for the “open” and “closed” forms. When the “1” ⇌ “2” exchange is slow, two crosspeaks would be expected, with intensities defined by the state populations pi1 and pi2. However, when both of the states X=“1,” “2” are each also in “open”X ⇌ “closed”X fast exchange, the crosspeaks are again positioned along the “open”-“closed” vector. The whole scenario can be encapsulated in the schema:∗ and † indicate fast and slow exchange, respectively.The peak doubling pattern was observed consistently over several independently prepared samples and therefore cannot be attributed to chemical heterogeneity and must arise because of slow exchange between different states. As a result, the relative intensity of the crosspeaks is defined by the respective state populations. In the cases in which (only) two CSH2 crosspeaks are observed, one peak is frequently located at the position of, or very close to, the corresponding peak for NSH2CSH2c, animated Thus, there are two populations of molecules, each demonstrating “open” ⇌ “closed” equilibria but spectroscopically separated by a “remote” slow-exchange phenomenon. “Remote” here is meant in the sense that the difference in molecular properties that gives rise to slow exchange does not influence the chemical shifts underlying the concomitant fast-exchange process but can influence the populations for the fast exchange in each of the two (slowly exchanging) states “1” and “2.” The general scenario can be conveniently depicted in cartoon form (β (PDGFRβ)-derived phosphopeptide with CSH2 (a). As outlined in b; Our model for the dynamic origin of the detected crosspeak patterns is bolstered by our observations of crosspeak doubling in a titration of a platelet-derived growth factor receptor ith CSH2 a. As oucis ⇌ trans isomerism of X-Pro peptide bonds  in γSA compared to the respective tandem nSH2-cSH2 proteins. However, the relative  CSPs within each construct group (γSA and tandem SH2) are essentially identical, indicating that the underlying source of the shift difference is present in both the tandem and γSA contexts. Further, CSP analysis for residues Ser672, Gly765, Gly772, and Gly777 . MD simulations suggested structural connectivity between occupation of the canonical cSH2 phosphopeptide binding site and the nSH2-cSH2 interdomain junction. As part of the experimental validation of the key MD predictions, we uncovered a surprisingly complex set of NMR characteristics for the tandem SH2 domain protein. The MD simulations also provided an invaluable context within which to effectively design and assess tandem SH2 domain variants to decipher the emergent NMR characteristics of allostery in the cSH2 domain. We have shown that the C-terminus is partially bound in the nonphosphorylated state and that presence of the nSH2 domain changes the dynamic properties of the cSH2 domain. The comparison of multiple protein variants revealed evidence for allosteric connectivity that importantly involves the polypeptide tether between the globular part of the cSH2 domain and the Tyr783 phosphorylation site. The allosteric connection is dynamic in nature and involves the presence of multiple combined fast- and slow-exchange processes. We have demonstrated that the disease-relevant mutation Arg687Trp weakens the dynamic allosteric connection (γ1. Importantly, the modulated binding of the extended C-terminus in Arg687Trp mutants was also detected in the context of the larger γSA fragment of PLCγ1, indicating that the impact of the dynamic modulation extends beyond tandem SH2 constructs and should be taken into account in any examination of the upstream regulation of PLCγ proteins by RTKs and small G-proteins.This work has highlighted a hitherto unappreciated and complex pattern of allosteric influences within the receptor adaptor domains of PLCnnection , provokiH.K., M.K., and P.C.D. designed the research. H.K. performed and analyzed the MD simulations. H.K. and T.D.B. performed the mutagenesis experiments. H.K. and T.D.B. expressed and purified proteins. H.K. and D.E. performed the NMR experiments. H.K. analyzed the NMR data. M.M. conducted the enzyme activity measurements. H.K. and P.C.D. wrote the article.