The predominant population of γδ T cells in human blood express a T cell receptor (TCR) composed of a Vγ9  and Vδ2 domains. These cells came into the limelight when it was discovered they can respond to certain microbial infections and tumorigenic cells through the detection of small, pyrophosphate containing organic molecules collectively called “phosphoantigens” or “pAgs.” These molecules are intermediates in both eukaryotic and prokaryotic metabolic pathways. Chemical variants of these intermediates have been used in the clinic to treat a range of different cancers, however, directed optimization of these molecules requires a full understanding of their mechanism of action on target cells. We and others have identified a subclass of butyrophilin-related molecules (BTN3A1-3) that are directly involved in pAg sensing in the target cell, leading to engagement and activation of the T cell through the TCR. Our data and that of others support the pAg binding site to be the intracellular B30.2 domain of BTN3A1, which is the only isoform capable of mediating pAg-dependent stimulation of Vγ9Vδ2 T cells. Here, we review the data demonstrating pAg binding to the B30.2 domain and our studies of the structural conformations of the BTN3A extracellular domains. Finally, we synthesize a model linking binding of pAg to the intracellular domain with T cell detection via the extracellular domains in an “inside-out” signaling mechanism of the type characterized first for integrin molecule signaling. We also explore the role of Vγ9Vδ2 TCR variability in the CDR3 γ and δ loops and how this may modulate Vγ9Vδ2 cells as a population in surveillance of human health and disease. Gamma delta T cells represent a conundrum when trying to understand the mechanisms of T cell ligand recognition that results in T cell activation. T cells expressing αβ T cell receptors (TCRs) that develop normally in the thymus recognize all antigens with the requirement of an antigen-presenting molecule belonging to the MHC superfamily. This MHC requirement encompasses conventional αβ T cell recognition of classical class I and class II MHC molecules as well as innate-like or semi-invariant T cell recognition of non-classical or MHC-like molecules. Examples include Type I invariant Natural Killer T (iNKT) and Type 2 NKT cell recognition of CD1d, Mucosal Associated Invariant T (MAIT) cell recognition of MR1, and non-conventional αβ T cell recognition of the human Group 1 CD1s  protein family as a key mediator in this process . BTN3 prThree isoforms of BTN3A are present in humans, BTN3A1, BTN3A2, and BTN3A3, each encoded by a separate gene . The ext2 whereas Dimer 2 buried ∼1080 Å2. Both dimer interfaces were also highly conserved between the three BTN3A isoforms; only 2 out of the 18 interface residues in Dimer 2 differed between the BTN3A isoforms. However, the Dimer 2 interface was observed in the crystal structures of all three BTN3A isoforms indicating these differences were tolerated. Residues involved in the Dimer 1 interface differed at three positions across the three BTN3A isoforms although examination of the contacts in this interface revealed that these interactions involved only main chain atoms, thus tolerating variation in the composition of the side chain residues. This suggests that these extracellular domains can form heterodimers adopting both dimeric conformations when co-expressed on the cell-surface. Using soluble extracellular domains, we were able to establish that BTN3A molecules exist as stable homodimers in solution and, using a FRET approach, that the dimer conformation in solution was Dimer 1  in complex with BTN3A1 . These cThese results lead us to propose a model whereby these two dimeric states are related to the stimulatory potential of the cell upon which they are expressed. In normal, non-stimulatory conditions, BTN3A molecules would exist in the Dimer 2 state (head-to-tail) and thus not be in a state to provide a stimulatory signal to surveying Vγ9Vδ2 T cells. Upon addition of the 20.1 antibody, BTN3A molecules in the Dimer 2 conformation would be converted to Dimer 1; these would be cross-linked on the cell-surface via binding of one 20.1 antibody to two BTN3A dimers, and thus be converted into a “stimulatory” conformation permissible to stimulate Vγ9Vδ2 cells Figure . The potBut what is the role of pAg in this process? Failed efforts to show a direct interaction between the Vγ9Vδ2 TCR and pAg early on suggested additional players were involved in this process; the requirement of cell–cell contact for Vγ9Vδ2 T cell stimulation also supported this hypothesis . Based oThe three BTN3A molecules differ substantially in their intracellular domains; A1 and A3 each contain a B30.2 domain  whereas A2 lacks this domain Figure . The intDirect interactions between both endogenous and exogenous pAgs with the B30.2 domain of BTN3A1 were measured with a highly sensitive technique called Isothermal Titration Calorimetry (ITC), which measures the heat absorbed or lost during binding events , 35. TheThe crystal structure of the B30.2 domain of BTN3A1 Figure  was highCharge swapping mutagenesis studies, where the basic residues were mutated to acidic (negatively charged), completely abrogated pAg binding and reactivity in cell stimulation assays, providing compelling evidence that this indeed was the pAg binding pocket . HoweverAdditional insight into the mechanics of pAg binding to the B30.2 domain, pursued through crystallization and NMR experiments, have revealed evidence for a conformational change induced in the B30.2 domain upon pAg binding. The first insight into this was during our pursuit of a complex structure between the B30.2 domain and pAg where we attempted to “soak” pAg into already existing crystals . This i. More diMycobacterium tuberculosis and Listeria monocytogenes, which can enter and survive within the host cells (Escherichia coli can also be phagocytosed by immune cells like neutrophils (intracellularly, is critical for Vγ9Vδ2 T cell activation and function. Admittedly, exogenous pAgs can also be secreted by some extracellular pathogens or immune cells like neutrophils, and administration of soluble pAgs in the presence of BTN3A-expressing antigen-presenting cells trigger Vγ9Vδ2 T cell activation, as was demonstrated in early studies of these T cells (This model of intracellular sensing of pAgs is consistent with the fact that many of the physiologically relevant pAgs are first generated and accumulate inside target cells. Endogenous pAgs, such as IPP or DMAPP, are intermediates of the MVA pathway, which is conserved in eukaryotes and archaea for isoprenoid biosynthesis . It has st cells , 42. Immst cells –46. Extrtrophils . The subtrophils . These s T cells . It is uThe variable chemical structures of pAgs relate directly to their bioactivity. The pyrophosphate moiety is central since its strong negative charge can make electrostatic contacts with the positively charged binding pocket of the B30.2 domain. Indeed, monophosphate substituents have significantly reduced specific activity compared with their pyrophosphate counterparts . On the Since the pyrophosphate moiety is essentially the same for every pAg, the potency of pAgs is largely dependent on their organic moieties. Changes in the length of the alkyl chain and positions of the double bond, even though very subtle, can lead to dramatic change in potency . NotablyOf course, the detection of pAgs intracellularly needs to translate to a signal that can be detected by surveying Vγ9Vδ2 T cells. We and others have proposed an inside-out signaling model , 33 wherA feature of Vγ9Vδ2 TCRs that may be important in answering the question regarding a direct interaction between the TCR and BTN3A is that despite the fact that this population uniformly use a Vγ9 and a Vδ2 chains in their TCR, there exists considerable diversity within the Vγ-Jγ and Vδ-Dδ-Jδ rearrangement, which translates into significant amino acid diversity within the CDR3γ and CDR3δ loops of these TCRs –60. Thesin vitro (Clearly, we have just begun to pull the curtain back on the inner-workings of Vγ9Vδ2 T cell ligand recognition and activation; identification of the B30.2 domain as the pAg sensor has already resulted in compounds developed with higher potency in vitro . IdentifThe 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.


Distributed optical fibre sensors possess the unique capability of measuring the spatial and temporal map of environmental quantities that can be of great interest for several field applications. Although existing methods for performance enhancement have enabled important progresses in the field, they do not take full advantage of all information present in the measured data, still giving room for substantial improvement over the state-of-the-art. Here we propose and experimentally demonstrate an approach for performance enhancement that exploits the high level of similitude and redundancy contained on the multidimensional information measured by distributed fibre sensors. Exploiting conventional image and video processing, an unprecedented boost in signal-to-noise ratio and measurement contrast is experimentally demonstrated. The method can be applied to any white-noise-limited distributed fibre sensor and can remarkably provide a 100-fold improvement in the sensor performance with no hardware modification. Optical fibres offer a way of sensing across a wide area, providing a spatial and temporal map of the measured parameter. Here, the authors use image and video processing to remove noise and increase the contrast in such a distributed optical fibre sensor, improving the signal-to-noise ratio by a factor of 100. Distributed fibre sensors11137891012131516171819202122231624122526192829303124The clear understanding reached in recent years on the factors ultimately limiting the sensor capabilities has motivated researchers to propose and demonstrate specially designed methods for performance enhancement3334353637383940414243444546474849505152533435363839404142444546474849505253Among several existing methods, signal processing techniques, such as optical pulse coding38394041424445464738121339404142In the following, we propose and experimentally demonstrate an approach that exploits correlated patterns of information and their high degree of redundancy for enhancing the measurement quality and performance of distributed optical fibre sensors. In particular, this approach makes use of image and video enhancement processing for removing noise and increasing the contrast of noisy measurements obtained by any kind of distributed sensor. To the best of our knowledge, this is the first time that such a multidimensional approach is used to restore information and enhance the capabilities of distributed fibre sensors. Here we demonstrate an unprecedented boost in SNR, which can reach two orders of magnitude , being equivalent or even superior to the use of extensively complex hardware sophistications but at a minor fraction of the cost. Any dB gained in SNR can be used to improve the sensor performance, that is, to extend the range, to sharpen the spatial resolution, to reduce the measurement time (reducing the number of averages), or simply to improve the measurand accuracy7891012131516171819202122235M in the position z and frequency Δf domains, from which the environmental information is retrieved by detecting spectral shifts of the peak gain frequency. f. In this case we use a sampling rate of 5 ns per digital point in the analogue-to-digital converter, corresponding to a sampling interval of 0.5 m per point , whereas a spectral range of 200 MHz is scanned with steps of 1 MHz. The measurement process therefore results in a 2D matrix M of 100,000 × 200 data points containing the local BGS at each sampled fibre location. Image processing58z,Δf) to a pixel  of a noisy digital image  with values belonging to a 1D space, such as in a greyscale image58z and frequency offset Δf. For a better visual perception of the data, a blue scale is chosen in 58M; this actually becomes evident if we consider that the same BGS  is repeatedly measured along the fibre, being only spectrally shifted at positions where the local environmental conditions change16M can still be decomposed into small 2D patches containing several closely located longitudinal points having essentially the same average amplitude.We first tested the proposed method on measurements obtained by a standard Brillouin optical time-domain analyser15To exploit the high level of similitude and redundancy present in the 2D domain of the data, we here use two of the best-known image denoising methods as proof-of-concept, to evaluate the effectiveness of the proposed approach: the so-called non-local means (NLM)596061626465666465242551521645The SNR enhancement demonstrated above has actually a massive impact on the quality of the obtained BGS. To corroborate that the proposed technique does not actually lead to a penalizing loss of information  and eliminates mostly the uncorrelated noise present in the measurements, it is essential to demonstrate that the applied 2D processing does not excessively blur the ‘denoised images'. For this purpose, a 2-m section of fibre at 50 km distance is heated up to 40 °C, while the rest of the fibre is kept at room temperature (27 °C). M every ∼42 s. Although this measurement time can be still reduced due to the small averaging number (four averaged traces per scanned frequency), the response time of the equipment used in this lab demonstration eventually limited our minimum acquisition time.The principle of distributed fibre sensing assumes that the temporal evolution of the measurand changes slowly compared with the acquisition time. In the case of Brillouin and Rayleigh sensors, this leads to consecutive 2D measurements containing highly correlated information. Based on this feature, the concept proposed in this study can be extended to the 3D case6061Considering that the temporal evolution of the measurand might reduce the correlation existing between consecutive measurements, the effectiveness of video processing60616061Measurements are processed using a 3D NLM algorithm606160616061In sensors measuring only 1D data, such as Raman-distributed temperature sensors, a 2D image can be formed considering time as a second dimension when stacking successive sequential measurements. To validate the proposed method in this case, we use a generic Raman-distributed sensor scheme1213MaS and MS of 18,000 × 21 points (including the raw measurements of the ‘current' and previous 20 anti-Stokes and Stokes traces) are processed by the 2D NLM method. This procedure is continuously repeated for each new measured trace and independently for the Stokes and anti-Stokes signals. After applying image denoising to the raw measurements, the ratio anti-Stokes to Stokes is calculated at each fibre location, and by following a standard calibration procedure the actual distributed temperature profile is finally obtained12As suggested, we form two 2D images  stacking together consecutive time-domain traces. In this study, we have proposed and demonstrated the use of image/video denoising techniques5859606162636465664445464748495033343536373839404142434445464748495051525333343536373839404142Although the Brillouin system used in this study as a proof-of-concept is thermal-noise dominated, it is worth mentioning that the efficiency of the proposed technique would be similar if shot noise, spontaneous-signal beat noise (when using an erbium-doped fibre amplifier in the receiver) or relative intensity noise (RIN) had an impact on the measurements25Although the concept proposed in this study has only been demonstrated for BOTDA and Raman sensors, it is envisaged that image/video processing can also be applied to improve SNR of other sensors, such as Brillouin optical-time domain reflectometers19789109105An interesting aspect that should be highlighted is that the 3D approach here proposed has proved to be very efficient when dealing with the dynamical character of the measurements. This is because video sequences are also inherently non-stationary60616061686960616869686960It is also worth mentioning that the experimental results shown in this study have been obtained by simple image/video denoising implementations, where parameters have been selected by following standard recommendations and fine empirical adjustments to maximize the noise removal avoiding any loss of relevant information. However, more dedicated strategies for adjusting parameters could be still developed and further investigated. For instance, the possibility for auto-tuning parameters and adaptive window sizes to avoid oversmoothing fast spatial and temporal changes of the measurand could also be investigated.The processing time of the method could also be further investigated and improved. No special hardware has been here used to optimize the processing time. Considering the large number of acquired points in the demonstration sensors, the implementation of a standard NLM algorithm turns out to be computationally very demanding. Using a conventional computer with a 3.5-GHz processor and 8 GB RAM, the 2D NLM processing time of each matrix of 18,000 × 21 points in the implemented Raman sensor turns out to be about 1 s. On the other hand, denoising the 2D data matrix of 100,000 × 200 points in the BOTDA sensor takes about 30 s: this is about one order of magnitude larger than the time required by the WD, which requires <1 s for processing the same data. Furthermore, the 3D NLM denoising of the same matrix size, but considering ten consecutive frames, is about 4 min. This time can however be highly reduced following specific strategies62Although in this study we demonstrate only the effectiveness of image denoising methods, other techniques for image enhancementj= that surround a certain pixel at i and j is performed by comparing, not only the values f(j)=f assigned to the pixels but the entire 2D patches or neighbourhoods surrounding the pixels of interest59ηi surrounding the pixel i is defined and then compared with all other similarity neighbourhoods ηj of the same size existing in the entire 2D matrix containing the data provided by the sensor.This technique59606162f(ηi)-f(ηj)|| between all values f(ηi) and f(ηj) within neighbourhoods ηi and ηj. It turns out that the Euclidean distance is small when a high level of similitude exist between both compared windows ηi and ηj, and therefore the highly similar values f(i) and f(j) associated to both pixels i and j can be averaged to reduce noise59i in the 2D data matrix, the value f(i) associated to such a pixel is processed by the NLM method calculating the following weighted average59The degree of similitude and redundancy in the data is evaluated in a patch-by-patch basis by calculating the Euclidean distance59I is the entire domain of the image, f(j) corresponds to the value of the image associated to the pixel j and w are the weighting factors calculated as5960where h is a smoothing control parameter and Z(i) is a normalization factor defined so that the sum of all values of w, for a given pixel i, results to be equal to one. It should be noted that the weighting factors w are independent of the geometry and only depend on the similarity of the data around pixels i and j. This feature characterizes the method as non-local, as pixels j whose surroundings are similar to the pixel i are associated to a higher weight w, regardless of the relative  distance between the two pixels.where × 3. This size, corresponding to three longitudinal data points , is smaller than the spatial resolution of the system, ensuring that the processing does not have any detrimental impact on the real spatial resolution of the sensor.A strict condition for the processing is that the similarity window size must be comparable to the smallest details in the image59h controls the level of blurring of the method and its optimum value depends on the noise level of the data. Following the recommendation given in ref. h has been set to ten times the noise standard deviation σ. In the Brillouin gain data shown in σ=7.2 × 10−4; thus h has been set to 7.2 × 10−3. In the case of the Raman sensor implemented in this work, the noise standard deviation of data in σ=6.9 × 10−4 and therefore h has been set to 6.9 × 10−3.On the other hand, the parameter × 3 and h=7.2 × 10−3, it is empirically observed that a satisfactory noise removal is obtained at a reasonable computational cost when defining a search window of 13 × 13. Increasing this search area has only led to a marginal SNR improvement, at the cost of a substantial increase in the processing time.Furthermore, we should consider the large amount of data obtained by the implemented sensors. For instance, in the case of the implemented BOTDA sensor 20 M points  are acquired to cover 50 km of sensing fibre, sampled every 0.5 m and scanning 200 frequencies, so that the calculation of x,y) that have high level of similarity; however, in this case the search for repeated patterns is also extended to several consecutive frames6061As in the 2D case, the 3D spatio-temporal NLM method6061× 23 is used for 2D NLM denoising.Finally, in the case of processing 1D data provided by the implemented Raman distributed sensor, two 2D images (one for the Stokes and another for the anti-Stokes component) are formed by stacking together consecutive time-domain traces. A sliding search window of size 23 σ=7.2 × 10−4 for the BOTDA measurements, the threshold value is set to 2.6 × 10−3 (≈3.6σ). The output 2D data matrix (considered as the ‘output image') is reconstructed from the result of this thresholding stage, using an inverse 2D DWT procedure, which converts the data back to the spatial domain of the image.The method is based on the 2D discrete wavelet transform (DWT) and a wavelet shrinkage strategy6465How to cite this article: Soto, M. A. et al. Intensifying the response of distributed optical fibre sensors using 2D and 3D image restoration. Nat. Commun. 7:10870 doi: 10.1038/ncomms10870 (2016).Supplementary Figures 1-2.Hot-spot detection in a 50 km-long BOTDA sensor. Brillouin frequency shift retrieved from the raw (blue curve) and denoised (red curve) data, when 2 m of fibre at the end of a 50 km sensing range is heated from 10°C up to 40°C during the measurement process. Measurements are obtained with a spatial resolution of 2 m and 4 averages, with a measurement time  of 42 s. The 3D nonlocal means method is used considering 10 consecutive (‘current' and 9 preceding) frames for denoising.


This occurs when positive feedback (component Allee) effects are dominant at low densities and negative feedback effects are dominant at high densities. This scenario allows population survival when r  is less than 1, provided population densities are sufficiently high. For r>1  the extinction equilibrium is unstable and a strong Allee effect cannot occur. We give criteria sufficient for a strong Allee effect to occur in a general nonlinear matrix model. A juvenile–adult example model illustrates the criteria as well as some other possible phenomena concerning strong Allee effects (such as positive cycles instead of equilibria).In nonlinear matrix models, strong Allee effects typically arise when the fundamental bifurcation of positive equilibria from the extinction equilibrium at  The discrete time dynamics are described by the equationwhere n×n matrix and the prime ‘′’ denotes the distribution vector at the next time step  guarantees the existence of Theorem 1 A1, the matrix Equation (4) has an unbounded continuum r, x)= and for which Under assumption r, x)=. Letspectrum ofr values corresponding to positive equilibria from the continuum range ofr and Ξ in This theorem says, under assumption A1, that the matrix equation (4) has an unbounded continuum of positive solution pairs that bifurcates from = in Theorem 1 is said to be forward  if r>1 for those equilibrium pairs r<1 for equilibrium pairs backward .The bifurcation occurring at . Since r of pij, the sign of The next theorem shows that the stability of the equilibria lying on the bifurcating continuum Theorem 2 ,14 A1. Near the point =, we have the following two alternatives.x∈Ξ from the continuum (a) κ<0 implies the bifurcation of x∈Ξ from the continuum (b)  κ>0 implies the bifurcation of Assume Note 1. If all partial derivatives of entries in the projection matrix satisfy For κ<0 to hold, at least one derivative Note 2. Given the generality of Theorems 1 and 2 , they can together be referred to as a fundamental bifurcation theorem for nonlinear population dynamics.3. r, x)=. Therefore, we assumeIn this section, we consider the matrix equation (3) when it has a backward bifurcation at (A2: κ<0 where κ is given by Equation (7).r=1 and consequently has unstable positive equilibria for x=0 is stable when r<1. In addition, we make the following assumption.Under this assumption the matrix equation (3) has, by Theorem 2, a backward bifurcation at A3: (a) there exists an r=1 and (b) this positive equilibrium is  stable by linearization.Another way of stating A3 is that (a) there exists a positive equilibrium Theorem 3 A1, A2 and A3 matrix equation (3) has a strong Allee effect at least for Under assumptions For a proof of this theorem, see Appendix 2.Note 3. For the case n=1 of one-dimensional maps, Theorem 3 provides criteria that are sufficient for the occurrence of a strong Allee effect involving a stable positive and extinction equilibria. These criteria, which are sufficient (but not necessary) for a strong Allee effect by our definition, are the same criteria used in [ used in  to definr is unbounded in R+. From these facts it follows that One way to guarantee A3(a) holds is to show two things: that the bifurcation is backward , defined for r≥1 and bounded on bounded subintervals, such that for every equilibrium pair ∈ holds.A4: There exists a real-valued function r is unbounded  the spectrum ΣCorollary 1 A1 and A4 hold. The spectrum Σr is unbounded and hence Suppose rmin<1. It follows that r=1.If the spectrum is unbounded and a backward bifurcation occurs, then Corollary 2 A1, A2 and A4 hold, then If Note 4. It is, of course, possible that A3(a) holds but A3(b) fails to hold. We will see an example of this possibility in Section 4.Note 5. We have assumed that the projection matrix P(x) in the matrix equation (1) has the form:r is the spectral radius of the projection matrix at x=0 and is therefore the inherent population growth rate. This normalization is convenient for theoretical purposes, but in applications it is unlikely possible to write the normalization explicitly since formulas for r are not in general available. Instead, it is often more convenient to use the inherent net reproductive number R0 as the bifurcation parameter, which as it turns out can be substituted for r in the theorems above. The quantity R0 is defined as follows.F(x) is a non-negative matrix consisting of class-specific fecundities  x). The transition matrix T(x) describes how surviving individuals move between classes. Specifically, the ijth entry in T(x) is the fraction of j-class individuals that survive (a unit of time) and move to class j. The transition matrix T(x) is therefore non-negative, has entries that are less than or equal to 1 and column sums less than or equal to 1. The inherent net reproductive number is defined to beI is the n×n identity matrix). If r and R0 satisfy one of the following [In models of populations closed to immigration/emigration, the projection matrix can be additively decomposedollowing ,17,22:x=P(x)x can be replaced byR0 as the bifurcation parameter. For these reasons,The equilibrium equation r can be replaced by R0 in assumption A4, Theorems 1–3, and Corollaries 1 and 2. The spectrum R0 values from the continuum C of positive equilibrium pairs  replaces that of the spectrum of r values.R0 as the bifurcation parameter is that it is often the case that explicit formulas in terms of the entries in the projection matrix P are available for R0, but not for r [The advantage of using ot for r ,14. We w4. in the matrix model (1) describes a population classified into juveniles x1 and adults x2. It assumes that the density effects occur in juvenile survival bβ(x2) and depend only on adult density x2. Adult survivorship s2 is assumed density independent.The 2×2 projection matrixx2, at all levels, has a negative effect on juvenile survival so that σ(x2) is a decreasing function of x2. On the other hand, we assume that increased adult density x2, at least at low densities, has a positive effect on adult fecundity so that β(x2) is an increasing function of bβ(x2) entails a component Allee effect.We assume that increased adult density We apply Theorem 3 using the inherent net reproductive number in place of r (see Note 5)Specifically, we assume the entries in the projection matrix (9) satisfy the following conditions:v and w associated with eigenvalue 1 of P(0) when R0=1, i.e. of the matrixwv=1 and hence This inequality is interpreted as meaning that the positive feedback effect of adult density on adult fecundity, as measured by Right and left eigenvectors For any positive solution of these equations we have, by Equations (10) and (12b), the bound k1>0. From Equation (12a) we obtain, for some constant k2>0 such that To investigate A3(a) we re-write the equilibrium equationsR0 replacing r, as in Note 5) is satisfied. Corollaries 1 and 2 imply that A3(a) holds, i.e. that there exists a positive equilibrium R0=1.The requirement A4 , namely the requirement that the positive equilibriums2 and that the eigenvalues of J(x+) are λ1=1 and λ2=0 when s2=1. Define J(x+) as functions of Since the product From Theorem 3, we get the following result.Theorem 4 Consider the juvenile–adult matrix model (1) with projection matrix (9) under the smoothness assumptions (10) on β and σ. Assume the backward bifurcation condition (11) and the inequality (13) hold. Then for These functions satisfy the conditions required in Equation (10) with Ω taken to be the interval We illustrate Theorem 4 with a specific example. This example will also illustrate other features of an Allee effect that can occur when created by a backward bifurcation. Takex2=0 andWhat remains to be verified for the application of Theorem 4 is that the inequality (13) holds at a positive root of the equation x2 from the equilibrium equation (12b) and arrive at the equationsfor positive equilibria. In the specific case (14), we can easily solve the second equationfor positive solutionsx± for x+ for R0=1, we have the (unique) positive equilibriumFor this example, we can in fact carry out further analysis. For positive equilibria, we can cancel R0, x±) isJ±. The characteristic quadratic for J± isq(λ) defines a concave upward parabola with a vertical intercept at det J±<0. It follows that q(λ) two real rootsthe equilibrium x−is unstable  stable for all there is a strong Allee effect for all R0satisfyings2<⅓. Since q(−1)=0 if and only ifx+ with component Suppose Case 2: Supposethere is a strong Allee effect for all R0satisfyinga/c>2.Note thatCase 3 SupposeR0 satisfying there is a strong Allee effect.R0 increases through − decreasing through −1. This suggests a period doubling bifurcation of (stable) periodic 2-cycles. We will not formally prove that here, but the numerical simulation evidence  with values less than 1. In general, strong Allee effects occur when there is a backward  bifurcation at r=R0=1 and a saddle-node (blue-sky or tangent) bifurcation at a value of r (or R0) less than 1. This approach using bifurcation theory is different from that taken in [We have seen that the interplay of positive feedback effects at low population densities (component Allee effects) and negative feedback effects at high population densities can together produce, in population matrix models, a strong Allee effect for an interval of inherent net reproductive numbers taken in  where dir (or R0) is less than 1, provided its density remains sufficiently high, i.e. does not lie in the basin of attraction of the extinction equilibrium (the Allee basin). The boundary of the Allee basin constitutes a threshold in phase space between extinction and survival. For r>1  the extinction equilibrium is unstable and a strong Allee effect cannot occur.A strong Allee effect allows for the survival of a population when r<1  and, as a result, for the possibility of a strong Allee effect (should one of the positive equilibria be stable).For a strong Allee effect to occur in this way, the component Allee (positive feedback) effects at low population density must be sufficiently large in magnitude, relative to any negative feedback terms (in the sense that κ defined by Equation (7) is positive), in order to produce a backward bifurcation of the bifurcating continuum We focussed in this paper on strong Allee effects in which a stable extinction equilibrium coexists with a stable positive  equilibrium. However, in the example in Section 4 we saw that a strong Allee effect can occur in matrix models in which a stable extinction equilibrium coexists with a positive attractor other than an equilibrium .Because the fundamental bifurcation Theorems 1 and 2 are the result of general bifurcation theorems and techniques from nonlinear functional analysis, analogs of these theorems have been proved for population dynamic models based on many other types of mathematical equations, including autonomous and periodically forced ordinary and partial differential equations, integro-differential equations and integro-difference equations. For some examples see ,16,19,25


Natural and artificial light-harvesting processes have recently gained new interest. Signatures of long-lasting coherence in spectroscopic signals of biological systems have been repeatedly observed, albeit their origin is a matter of ongoing debate, as it is unclear how the loss of coherence due to interaction with the noisy environments in such systems is averted. Here we report experimental and theoretical verification of coherent exciton–vibrational (vibronic) coupling as the origin of long-lasting coherence in an artificial light harvester, a molecular J-aggregate. In this macroscopically aligned tubular system, polarization-controlled 2D spectroscopy delivers an uncongested and specific optical response as an ideal foundation for an in-depth theoretical description. We derive analytical expressions that show under which general conditions vibronic coupling leads to prolonged excited-state coherence. Two-dimensional spectroscopy revealed oscillatory signals in photosynthesis' exciton dynamics, but crowded spectra impede the identification of what sustains the oscillations. Here the authors probe an J-aggregate, whose uncongested response shows that vibronic coupling is responsible for the sustained coherence. The remarkably high efficiency in photosynthesis, where nine out of ten absorbed photons reach the reaction centre, is a fascinating field of modern research. In such photosynthetic complexes, structure, dynamics and function are inextricably linked. A conserved building block comprises strongly absorbing pigments arranged in close proximity to one another supported by the surrounding protein scaffold13Exciton dynamics can be efficiently probed by two-dimensional (2D) electronic spectroscopy68911121314151617181920111213141617In this work, we show that the relatively simple excitonic structure of a molecular J-aggregate provides an ideal test case to identify the microscopic mechanism behind long-lived oscillations in electronic 2D signals. The investigated J-aggregate is tubular and aligns along the sample's flow direction when in solution. In addition, the J-aggregate exhibits excitonic bands with roughly orthogonal transition dipole moments. It is this combination of perpendicular excitonic transitions and macroscopic alignment that makes electronic 2D spectroscopy with polarization-controlled excitation pulses an ideal tool to study coherence effects between the excitonic bands. This approach significantly reduces the complexity of retrieved 2D signals, leading to only two peaks with oscillatory components in specific regions of the 2D maps, that is, one on the diagonal and one as a cross-peak for non-rephasing and rephasing signal components, respectively. Employing a vibronic model, we derive analytical expressions that show how system parameters such as electronic decoherence rates and exciton–vibrational resonance determine the amplitude and lifetime of oscillatory signals. Fitting the analytical expressions to measured data, the vibronic model achieves quantitative agreement with experimental observations. Concerning potential functional relevance of the observed oscillations, we show that the long-lived oscillatory signals in our system are dominated by excited-state coherence rather than ground-state coherence.J-aggregates of cyanine dyes are promising candidates for artificial antenna systems2223242528The structural properties of the aggregate are remarkable: the 11-nm outer diameter is contrasted by a length of several micrometres. Circulating solvated C8O3 with a wire-guided jet  leads to31≈690 cm−1 and ΔΩ32≈460 cm−1 for bands 2 and 3. Both exciton energy splittings are close to vibrational frequencies ν1≈668 cm−1 and ν2≈470 cm−1 observed in non-resonant Raman spectraν1 and ν2 and exciton energy splittings ΔΩ31 and ΔΩ32 provides us with an interesting scenario of possible coherent interaction between bands (excitons) and vibrations111314213738Fitting the well-defined absorption peaks of C8O3 with Lorentzian functions see  reveals The absorption spectrum of a light-harvesting system may be heavily congested because of overlapping excitonic bands and the resulting 2D signal would exhibit significant overlap between diagonal and cross-peaks, thereby impeding further analysis. It has been suggested to employ laser pulses of different relative polarization to selectively address relevant excitation pathways to obtain a clearer 2D signalt2 for all points on the 2D  map. The resulting ω2 plots allow the lineshape of beating signal with frequency ω2 to be visualized as a function of position in  space. The slice at the exciton energy splitting between bands 1 and 3  reveals a non-rephasing diagonal peak N11 and a rephasing cross-peak R31 as shown in ω1, ω3)= with exciton energy Ω1≈16,405 cm−1 of band 1 and a symmetric linewidth 2Γg1≈130 cm−1 along both ω1 and ω3 axes = with exciton energy Ω3≈17,125 cm−1 of band 3 and asymmetric linewidths 2Γg3≈300 cm−1 and 2Γg1≈130 cm−1 along ω1 and ω3 axes, respectively (ω2 slice corresponding to the energy splitting between bands 2 and 3 (ω2=462±20 cm−1), ω1, ω3)= with the exciton energy Ω2≈16,672 cm−1 of band 2 and a symmetric linewidth 2Γg2≈225 cm−1 along ω1 and ω3 axes. The amplitude of N22 is only 5% of N11.The ideal pulse sequence to isolate beating signals between states with orthogonal transition dipole moments, that is, bands 1 and 3 in the present case, is depicted in  ω3 axes . The cenectively . In peakν1. Consider a system with electronic ground state |gk〉 and excited states for bands 1 and 3, denoted by |1k〉 and |3k〉, respectively, where k=0 and 1 denote the vibrational ground and excited states, respectively −ν1 denotes the detuning between |30〉 and |11〉, that is, between the exciton energy splitting and vibrational frequency, and S1 denotes the Huang–Rhys factor of the vibrational mode, which in turn quantifies the strength of the vibronic coupling −1. The difference in electronic and vibrational decoherence rates can be rationalized from the fact that excitons and vibrations are related to the motion of electrons and nuclei, respectively. The lower mass of electrons as compared with nuclei makes excitons more mobile and therefore more sensitive to environmental fluctuations, such as local electric fields, than vibrations. We note that the vibronic mixing leading to long-lived beating signals in 2D electronic spectra is described by a vibronic coupling that induces coherent energy exchange between excitons and quasi-resonant vibrations  is equivalent to N11 (ΔΩ31≈ν1≈668 cm−1). The crucial difference is that band 2 has a higher decoherence rate than band 1, as band 2 is localized on the outer layer exposed to solventg2≈(47 fs)−1, the presented theory predicts the strength of N22 to be 5% of N11  and detection (ω3) frequencies within the laser pulse spectrum. The absorption frequency ω1 is obtained by precise scanning of the time delay between the first two pulses and subsequent Fourier transformation (t1→ω1). In detection, the signal is spectrally dispersed, leading directly to the detection frequency ω3. Varying time delay t2 between pulses 2 and 3 provides information about evolution of the system on a femtosecond timescale5051λ/4 wave plates and wire grid polarizers for each of the laser beams to select the desired polarization with high accuracy. Polarization-resolved 2D experiments change the relative contributions of distinct pathways depending on the polarization of the laser pulses, orientation of the transition dipole moments and isotropy of the sample12ω2 maps in t2→ω2) with zero-padding up to 27 data points. All measurements were carried out at room temperature.In 2D electronic spectroscopy, three ultrashort laser pulses generate an optical response of a molecular ensemble, which is spectrally resolved along both absorption .Supplementary Figures 1-7, Supplementary Notes 1-3 and Supplementary References


Compared to bulk crystalline Bi2Te2Se, film TIs exhibit distinct behaviors in the phase and amplitude of emitted THz radiation. In particular, Bi2Se3 grown on Al2O3 shows an anisotropic response with a strong modulation of the THz signal in its phase. From x-ray diffraction, we find that the crystal plane of the Bi2Se3 films is inclined with respect to the plane of the Al2O3 substrate by about 0.27°. This structural anisotropy affects the dynamics of photocarriers and hence leads to the observed anisotropic response in the THz emission. Such relevance demonstrates that THz emission spectroscopy can be a sensitive tool to investigate the fine details of the surface crystallography and electrostatics of thin film TIs.We investigate the surface states of topological insulator (TI) Bi Topological insulators (TIs) behave as a charge-gapped insulator in their interior but hosting a spin-momentum-locked Dirac state at the surface. When the Fermi level crosses over a conduction/valence band, a bulk charge transport can overwhelm the surface contribution, so that thin film TIs have been highlighted as a method to reduce bulk carrier effects due to a large surface to bulk volume ratio –6. DurinTerahertz (THz) spectroscopy also can provide useful information about the surface state of the TIs. From conventional THz time-domain spectroscopy, Aguilar et al. could retrieve optical response functions, such as optical conductivity, of the TI surface state, and determine electrodynamic parameters of Dirac fermions , 19. Sim2Se3 thin films grown on Si nanocrystals (NCs) and Al2O3 and also from the bulk Bi2Te2Se. Whereas the bulk crystalline Bi2Te2Se shows an isotropic behavior of the THz emission, film TIs exhibit contrasting behaviors in the phase and amplitude of emitted THz radiation. In particular, the Bi2Se3 film grown on the Al2O3 substrate exhibits a strong modulation of the THz electric field profiles upon the variation of the sample azimuth. We will discuss the details of such emitted THz waves from the surface of Bi2Se3 films by considering the anisotropic dynamics of the photocarriers under the structural anisotropy in the thin film TI.In this paper, we demonstrate that time-domain THz emission measurement can be a sensitive method to investigate the details of the surface crystallography and electrostatics of thin film TIs. We examine an azimuth-dependent THz radiation emitted from Bi2Se3 films with 30–33-nm thickness were grown on Si NCs [2O3 by a molecular beam epitaxy (MBE) system. Si NCs were fabricated by annealing SiOx/SiO2 multilayers grown on Si wafers by ion beam sputtering, whose detailed processes were described in previous reports [2Te2Se sample using the self-flux method with a stoichiometry of chunks (Bi:Te:Se = 2:1.95:1.05) [High-quality Bin Si NCs , 21–24 a reports , 24. As 95:1.05) , 26.2, which is below the damage threshold [For THz emission spectroscopy, we use 70-fs laser pulses with a center wavelength of 800 nm generated from a Ti:sapphire oscillator at a repetition rate of 80 MHz. The beam is focused onto the sample with a 300-μm spot size at an incidence angle of 45°  of Bi2Se3 with the 2θ motion fixed to θB as indicated in Fig. θ between the film and substrate at the same azimuth angle Φ corresponds to the inclination angle (Δφ) of the film Bragg plane with respect to the crystal plane of the substrate.Although thin films were grown along the ion Fig.  to chara2Te2Se of which results are displayed in Fig. Φ, and they commonly show a single-cycle oscillation with a well-defined crest and trough. The THz signals at these points marked by an open square and closed circle are plotted as a function of Φ in Fig. Φ, in agreement with the previous report for bulk crystalline Bi2Se3 [2Te2Se studied here, since the remaining energy after absorption will raise the carrier temperature enhancing this effect [2Te2Se, it is not clear yet which has a more dominant contribution to the observed THz emission signals between the photo-Dember effect and surface field acceleration.We examine first the THz emission from the bulk crystalline Bie Bi2Se3 . Such ans effect . Also, is effect . Therefo2Se3 grown on Si NCs. Compared to the case of the bulk sample, the amplitude of the THz wave is comparable and the azimuth dependence is similarly isotropic  symmetry. Rather than such an intrinsic inversion symmetry breaking at the surface of Bi2Se3, we pay attention to an additional symmetry breaking possibly induced during the growth process of Bi2Se3 thin films on the substrate.Interestingly, the Bih Φ Fig.  We pick 2Se3 films and the substrate. Figure θ = 18.6° corresponding to a (006) peak of Bi2Se3 grown on Si NCs and near 2θ = 69.2° for the (004) peak of a Si substrate beneath the Si NC layer. The sample azimuth Φ is set to 225°. It should be noted that the maximum intensity of each peak cannot be obtained simultaneously in a single diffraction geometry. When φ is optimized to Si (004), the diffraction peak for Bi2Se3 (006) (line) has a smaller intensity (by about 20 %) than that of the peak obtained after the optimization to itself (open circle). φ is obtained by varying Φ for both the film and the substrate, and their difference Δφ is plotted in Fig. Φ variation where the largest deviation from zero value (gray line) appears near Φ = 45° and 225° with about Δφ = −0.1° and +0.1°, respectively. This angle corresponds to the degree of inclination of the Bragg plane in the Bi2Se3 thin film with respect to the substrate Bragg plane.Using the x-ray diffractometer, we examine the relative crystalline directions of the Bi2Se3 films grown on an Al2O3 substrate where the angle φ for the Al2O3 substrate is optimized to its (006) diffraction peak around 2θ = 41.7°. At the sample azimuth Φ = 90°, the Al2O3 (006) peak can be optimized to have a maximum intensity such as a line curve in Fig. φ is optimized to the Bi2Se3 (006) peak. Note that the estimated inclination angle from the azimuth-dependent Δφ shown in Fig. 2O2 substrates can have a larger vicinal angle than that of a Si wafer. When Bi2Se3 films are grown on such vicinal substrates, the crystallographic orientation of the films may not follow that of the substrate, and the tilting between the film and the substrate in their c-axis orientations can be proportional to the substrate vicinality.We employ the same procedures to BiETHz with a variation of Φ from the curves given in Figs. ETHz is negligible for the bulk Bi2Te2Se and thin film Bi2Se3 on Si NCs whereas it is relatively large for the film on Al2O3. This THz-response ΔETHz is plotted versus Δφ in Fig. φ of the bulk Bi2Te2Se is set to zero. From this plot, we can reasonably expect a possible relationship between these two quantities. To support this hypothesis, it is worthy to note a similar phase relationship between the THz amplitude and Δφ in their Φ dependences shown in Figs. It is intriguing to note that such an inclination of the crystal plane of the film is intimately connected to the aforementioned modulation in the THz electric field. We estimate the modulation amplitude of the THz electric field Δ2Se3 can have an anisotropic behavior along the c-axis with respect to an ab-plane, such as a dc-conductivity ratio σab/σc of about 3–4 [ab-plane is inclined from the sample surface, the surface-normal direction will be defined with contributions from both the crystallographic c-axis and the a- (or b-) axis even though the latter will have a minor contribution. Then the photocarriers generated at the surface, which otherwise are accelerated simply along the surface-normal direction, will experience an anisotropic electrostatic potential or anisotropic transport behavior as they travel inside of the film. Consequently, THz light emitted through a surge current can have the finite anisotropic response on the sample azimuth. Since x-ray diffraction results revealed the relative tilting angle between diffraction planes of the TI film and the substrate, crystallographic planes can be drawn differently as in Fig. Φ. Although the anisotropic THz responses in the variation of Φ were discussed in terms of the surge current THz emission process, it should be noted that the results would be explained also by the optical rectification process by considering the lowered surface symmetry.Actually, when the crystal plane is inclined with respect to the sample surface Fig. , the phobout 3–4 . When th2Se3 thin film grown on Si nanocrystals, the emitted THz electric field has an opposite phase to that from the bulk Bi2Te2Se crystal, and this can be attributed to different electrostatics related to the surface band bending of two samples. For the Bi2Se3 thin film grown on Al2O3, the THz emission occurs with a strong modulation particularly in its phase upon the variation of the sample azimuth. Through x-ray diffraction experiment, we found that the crystal plane of the film is inclined with respect to the substrate crystal plane, and the resultant planar anisotropy is responsible for the onefold symmetry in the anisotropic THz response. As topological insulators in the form of the thin film have been attracting much attention these days to exploit the Dirac fermionic surface state with less contribution of conventional bulk carriers, we expect that phase-sensitive THz emission spectroscopy can have a clear contribution in such researches by elucidating the lateral and longitudinal electrostatics related to the band bending as well as the structural symmetry at the surface and/or interface of the film.We demonstrate that the terahertz (THz) emission spectroscopy can be a sensitive tool to investigate the fine details of the electrostatics and surface crystallography of topological insulator thin films. For the Bi


The observed differences can be explained by drastic modification of the ligand field states due to the fluoride binding. This changes the magnetic anisotropy of the YbIII ground state from easy-axis to easy-plane type, and this change is easily detected in the observed magnetic anisotropy despite thermal population of more than just the ground state. The spectroscopic consequences of such drastic changes to the ligand field represent important new opportunities in developing fluoride-responsive complexes and contrast agents.Yb⋅DTMA forms a ternary complex with fluoride in aqueous solution by displacement of a bound solvent molecule from the lanthanide ion. [Yb⋅DTMA⋅F] Lanthanide complexes have been of interest for many years, partly as a consequence of their applications in time-resolved bioassay, luminescence microscopy and magnetic resonance (MR) imaging. More recHowever, while considerable effort has been expended upon lanthanide complexes of DOTA and related tetra-amide ligands, not to mention a host of related structures, there is still much that needs to be understood. Early work focused on the application of the theories developed by Bleaney to understand the NMR spectra of paramagnetic lanthanide complexes with axially symmetric ligand environments. In such systems, the observed chemical shift can be defined as the sum of diamagnetic and paramagnetic contributions, where the paramagnetic contributions, termed the lanthanide induced shift (LIS), can themselves be divided into contact (through bond) and pseudo-contact (through space) terms.pcδ the pseudo-contact term, is the dominant factor in determining the observed shift for a given nucleus. For an axially symmetric system, this term can be approximated byIn most lanthanide-containing complexes, θ and r are the polar coordinates relative to the principal axis, JC=Jg2J(J+1)(2 J−1)(2 J+3)〈J|α|J′〉 is the Bleaney constant and is dependent on the electronic configuration of the lanthanide ion given by the total angular momentum J, and Jg is the Landé factor. Parker and co-workers have studied the role of axially coordinated solvent molecules in determining the magnitude of the crystal field parameter,3+ in D2O in the presence and absence of sodium fluoride  geometry at the lanthanide center; its spectrum shows no evidence of the alternative diastereoisomers with capped twisted square antiprismatic (TSAP) geometry. The spectrum was assigned on the basis of the published crystal structure of [Dy⋅DTMA⋅OH2]3+,3+, lead to an improved agreement with experiment. No increased g-value resolution could in this case be obtained with the magnetically dilute solid, presumably reflecting a greater inherent microheterogeneity of the ligand coordination sphere in the presence of fluoride. The differences in the g-values and g-anisotropies between [Yb⋅DTMA⋅OH2]3+ and [Yb⋅DTMA⋅F]2+ reflect a significant change in the electronic structure of the complex, as already suggested by the NMR results.Addition of NaF to [Yb⋅DTMA⋅OH2]3+ and [Yb⋅DTMA⋅F]2+ were estimated by gas-phase geometry optimization and symmetrization of their lutetium analogues (see Supporting Information). The DTMA ligand geometry was not found to be significantly different in the two cases. The fluoride ion is calculated to bind with a Ln–F bond length of ca. 1.97 Å. Ab initio calculations for the Yb3+ analogues of these pseudo-solution structures (see Supporting Information) give the magnetic susceptibility (χ) tensors with the parallel and perpendicular components in Table χav) at 300 K are close to the free-ion Yb3+ value of 2.57 cm3 mol−1 K, but lowered 3–6 % due to the ligand field. The most important change on fluoride binding is a change from easy-axis (χ∥>χ⊥) to easy-plane (χ∥<χ⊥) magnetic anisotropy. This can be understood on the basis that the weak equatorial ligand field of DTMA will stabilize the prolate Jm=±7/2 states of the 2F7/2 ion; this is consistent with low temperature single crystal magnetic susceptibility studies on Na[Yb⋅DOTA⋅OH2]⋅4 H2O.⋅4 H2O. CoordinaThe paramagnetic pseudo-contact (dipolar) shifts for each proton were calculated employing Equation NA is Avogadro’s number, the susceptibility values are in units of cm3 mol−1, and r is in meters. The calculated 1H chemical shifts for [Yb⋅DTMA⋅OH2]3+ and [Yb⋅DTMA⋅F]2+ obtained using the calculated susceptibility values and optimized coordinates are given in Table 3+ complexes.[where omplexes.2]3+ are clearly in extremely good agreement with the experimental ones, verifying the easy-axis type electronic structure also shown by EPR. The calculated shifts for [Yb⋅DTMA⋅F]2+ all have the correct sense, due to the switch in magnetic anisotropy, but they are much larger than the experimental values. As the pseudo-contact shifts are only sensitive to the anisotropy of the susceptibility tensor and not its average, the shifts were then fitted by modifying the χ anisotropy while maintaining a constant χav 2+  imaging of fluoride are clearly very good, and we are currently exploring the potential of both 1H and 19F NMR methods.In conclusion, it is particularly worthy of note that the electronic structure of the ytterbium center in [Yb⋅DTMA]


Endophthalmitis may have devastating consequences for a patient's vision and therefore should be treated as an emergency. The time from diagnosis to treatment is critical for favourable outcomes. In order to achieve a rapid response, it is important to have an accessible protocol and an endophthalmitis kit at hand for all eye surgeons who see postoperative patients. We have produced a simple protocol of recommended practice collated from a range of sources (see opposite page).All intraocular procedures carry a risk of endophthalmitis, but – globally – they are most commonly reported following cataract surgery and intravitreal injections; this is due to the sheer numbers of both of these procedures carried out throughout the world. The prophylactic steps in the protocol have particular reference to cataract surgery, but similar practice should be adopted for any intraocular procedure. The clinical diagnosis and treatment is similar for all cases of endophthalmitis.not be cut as cutting the lashes does not reduce periocular bacterial flora and does not reduce the risk of endophthalmitis.Careful preparation of the patient prior to performing an intraocular procedure is vitally important to reduce the risk of endophthalmitis.The development of a red eye, pain and blurred vision in the days or weeks following an intraocular procedure should be considered as a case of endophthalmitis until proven otherwise. If intraocular inflammation is discovered, particularly if there is a hypopyon, treatment for endophthalmitis should be initiated without delay.NOTE: Do not try to treat with a course of corticosteroids first – this will delay treatment and may result in losing the eye.An endophthalmitis kit should be accessible in every practice where postoperative patients are seen and is invaluable to allow prompt diagnosis and treatment (see panel below). A vitreous biopsy/tap through the pars plana should be performed immediately for gram stain and culture. If the patient has perception of light only, a vitrectomy has been shown to be more beneficial than a vitreous tap.Intravitreal antibiotics (vancomycin and ceftazidime or amikacin and ceftazidime) should be given immediately, using separate syringes and needles for each drug (see panel for instructions to make up the required concentrations of each antibiotic). The use of intravitreal dexamethasone (a steroid) is controversial.Consider adjunctive systemic therapy –with the same antibiotics as those used intravitreally – for 48 hours to maintain higher levels within the posterior segment of the eye. If systemic antibiotics are not available, topical antibiotics are better than nothing. Careful monitoring of the patient is important. The response to treatment and the results of gram stain and culture should determine whether further intravitreal antibiotic therapy is required.Tetracaine (anaesthetic) dropsPovidone iodineDrapeSpeculumEquipment for sub-Tenon's anaesthetic injection– 10 ml 2% lidocaine– 10 ml syringe– Sub-Tenon's cannula– Westcott scissors23 G or 25 G needle5 ml syringeCalipers1 vial of 500 mg vancomycin or 1 vial of 500 mg (250 mg/ml) amikacin1 vial of 500 mg ceftazidime3 × 10 ml sodium chloride 0.9% injection 4 × 10 ml syringe2 × 5 ml ^syringe2 × 1 ml syringe1 × sterile galley pot (for amikacin)6 × 21 G needles for preparation of antibiotics2 × 30 G needles for intravitreal injectionVancomycin 1 mg/0.1 ml– Reconstitute 500 mg vial with 10 ml saline– Withdraw all 10 ml into 10 ml syringe– Inject 2 ml of this solution back into vial– Add 8 ml saline into vial to make up to 10 ml (10 mg/ml)– Use 1 ml syringe to draw 0.1 ml of this solution (1 mg/0.1 ml)Amikacin 400 μg/0.1 ml– Use 10 ml syringe to withdraw 1.6 ml of amikacin (250 mg/ml)– Make up to 10 ml in the syringe with saline– Discard 9 ml from syringe and make the remaining 1 ml up to 10 ml (in the syringe) with more saline– Transfer the solution into a sterile galley pot and use 1 ml syringe to draw 0.1 ml of this solution (400 μg/0.1 ml)Ceftazidime 2 mg/0.1 ml– Reconstitute 500 mg vial with 10 ml saline– Withdraw all 10 ml into 10 ml syringe– Inject 2 ml of this solution back into vial– Add 3 ml saline into vial to make up to 5 ml (20 mg/ml)– Use 1 ml syringe to draw 0.1 ml of this solution (2 mg/0.1 ml)


Targeting allosteric sites is gaining increasing recognition as a strategy for modulating the activity of enzymes, especially in drug design. Here we investigate the mechanisms of allosteric regulation of cathepsin K as a representative of cysteine cathepsins and a promising drug target for the treatment of osteoporosis. Eight novel modifiers are identified by computational targeting of predicted allosteric sites on the surface of the enzyme. All act via hyperbolic kinetic mechanisms in presence of low molecular mass substrates, as expected for allosteric effectors. Two compounds have sizable effects on enzyme activity using interstitial collagen as a natural substrate of cathepsin K and four compounds show a significantly stabilizing effect on cathepsin K. The concept of activity modification space is introduced to obtain a global perspective of the effects elicited by the modifiers. Analysis of the activity modification space reveals that the activity of cathepsin K is regulated via multiple, different allosteric mechanisms. The classical two-state conformational model proposed by Monod and co-workers to explain allosteric interactions in hemoglobin Cysteine cathepsins belong to the papain-like peptidases and constitute one of the major groups of lysosomal enzymes. They are involved in diverse physiological and pathological processes and have long been thought to be regulated primarily by macromolecular active-site directed inhibitors  and kcat (β) α represents the allosteric coupling constant that characterizes energy linkage between the modifier and the substrate β represents the effect exerted by the modifier on catalysis. The specific velocity plot α and β, as well as of the dissociation constant of the modifier. Refinement was then performed by fitting the rate All modifiers were tested for their effect on the hydrolysis of the low molecular mass synthetic substrate Z-FR↓AMC. Since all progress curves were linear from the beginning of the reaction, initial velocities were calculated from the slopes by linear regression. No significant deviations from linearity were observed for the first 120 s of the reaction and no substrate inhibition was apparent at the substrate concentrations used in this study. The basic mechanism considered for the analysis of the interactions was the general modifier mechanism shown in KA were in the 10−5 to 10−3 molar range, which was expected considering the size of the compounds and the fact that they were selected without optimization of the binding geometry. All eight modifiers acted by a hyperbolic mechanism, i.e. they caused a reduction of the reaction rate without driving it to zero at saturation. They can be subdivided into four groups according to their mechanisms of modification as determined from combinations of the coefficients α and β in α>1 and β<1, which can thus be classified as hyperbolic mixed, predominantly competitive inhibitors. Compounds 1 and 2 had large values of α, indicating a strong competitive component, whereas that of compound 3 was only slightly above 1, a property that accounts for the different behavior of compound 3 with respect to compounds 1 and 2 in assays described in the following subsections. The second group comprised the pair of compounds 4 and 5, which belong to a class of hyperbolic mixed modifiers with a dual behavior as inhibitors or activators depending on substrate concentration and characterized by values of α and β both larger than 1 and α>β. This rare mechanism, observed previously in the case of compound NSC13345 Km ratio σ, can be defined as σ0 = (β–α)/(1–β). Actually, this calculation is based on the [S]/Ks ratio that, in virtue of the quasi-equilibrium assumption made with the use of the specific velocity plot, is approximated to [S]/Km. At substrate concentrations that give [S]/Km smaller than σ0 these compounds behave as inhibitors, while at substrate concentrations giving [S]/Km larger than σ0 they behave as activators. If the substrate concentration is such that [S]/Km = σ0, no effect is observed. Compound 6, which is the only representative of the third group, behaved as a hyperbolic competitive inhibitor in which the ESA complex is turned over with the same catalytic constant as the ES complex (β = 1). The fourth group contains a pair of hyperbolic mixed inhibitors with uncompetitive character, compounds 7 and 8, which differ from the other groups for their values of α and β being less than 1. Kinetic experiments with these two compounds were the most erratic in the series investigated. With α>β the mechanism is classified as hyperbolic mixed, predominantly uncompetitive inhibition, while with α = β the mechanism is called hyperbolic uncompetitive inhibition. In the former case, the sheaf of straight lines in the specific velocity plot should intersect the ordinate at 1 and the abscissa at a negative value. In the second case, the lines should intersect at ordinate 1 and abscissa 0. The best-fit results from the relative velocity versus modifier concentration plots shown in α = β. It remains established that, for this type of modifiers, inhibitory efficiency increases with increasing substrate concentration.Specific velocity plots for all modifiers are shown in IC50 values were estimated at around 1 mM and 0.5 mM for compounds 1 and 2, respectively. Similarly, all compounds showed little or no inhibitory activity in azocasein degradation assays . They are discriminated among each other by their respective values of the coefficient α. For linear competitive inhibitors the value of α approaches ∞. Despite their absence from the representation in α>1. Finally, the mostly theoretical non-competitive mechanism would be characterized by the value of α = 1 and β = 0.Here the activity modification space concept is used in two independent ways to investigate the effects of all known modifiers of cathepsin K other than active-site directed inhibitors. Data for previously known modifiers was taken either from published sources or from experiments performed specifically for this purpose, as described in the previous subsections. First, a simple two-dimensional representation was constructed only from the values of the kinetic coefficients Z-FR↓AMC , the mos, NSC13345 and glycosaminoglycans, each form distinctive groups in the activity modification space distant from the position of unmodified enzyme. Not surprisingly, a significant degree of dispersion is observed in the glycosaminoglycan group , resulting from their diverse effects on cathepsin K described herein and previously The approach in The primary goal of this study was to investigate the range of effects that can be produced by allosteric modifiers of cathepsin K. The theory of enzyme kinetics does not set precise limitations in terms of the effects on substrate binding affinity or catalytic rate of any enzyme. However, the activity of enzymes is restricted by their structural limitations meaning that each enzyme can exhibit only a limited range of kinetic profiles, which can result either from its intrinsic flexibility or from the binding of an allosteric modifier. The concept of activity modification space was introduced to globally analyze the effect of the identified modifiers on cathepsin K. This method is similar to the concepts of ligand-activity space (or substrate-activity space) which uses a multidimensional representation to analyze the directed evolution of enzymes using multiple different substrates or ligands  using default values of all parameters. The best hits (about top 10%) were selected based on the binding energies calculated by the internal scoring function and re-docked to the receptor using AutoDock 4.2 Potential allosteric modifiers were predicted as described previously ex 383 nm and λem 455 nm. All tested modifiers were analyzed spectroscopically to determine their absorption properties under the conditions used in the assays. When necessary, appropriate corrections were made to the calculated reaction rates to take into account the inner filter effect All kinetic measurements were performed in 100 mM sodium acetate buffer pH 5.50 containing 1 mM EDTA and 2.5 mM dithiothreitol (DTT) in single-use acrylic cuvettes (1×1 cm) thermostatted at 25±1°C with magnetic stirring. The hydrolysis of Z-FR↓AMC was followed fluorometrically at λv0 is the reaction rate in the absence of modifier, KA is the equilibrium dissociation constant of the EA complex, α and β are dimensionless coefficients and σ = [S]/Km, approximated to [S]/Ks. To determine the mechanism of interaction, plot the kinetic data and calculate preliminary values of the interaction parameters, the specific velocity plot was used The effects of the modifiers on enzymatic activity were analyzed with the general modifier mechanism v0/vA versus σ/(1+σ) produces straight lines with intersection points at v0/vA = 1, regardless of the interaction mechanism. The parameters α, β and KA are determined by replotting the extrapolated values of the straight lines at σ/(1+σ) = 0 (a) and σ/(1+σ) = 1 (b) versus 1/[A] in the form:The plot of Soluble calf skin collagen  was diluted in 100 mM sodium acetate buffer pH 5.50 containing 1 mM EDTA and 5 mM DTT to a final concentration of 0.5 mg/ml. Experiments were started by addition of cathepsin K  to the reaction mixture containing collagen and increasing concentrations of modifier. All assays were performed at 28°C with shaking on an Eppendorf Thermomixer Comfort. Samples were incubated for 2 hours and the reactions then blocked by addition of E-64 to a final concentration of 1 µM. 10 µg of digested collagen were analyzed by SDS-PAGE on 8% polyacrylamide gels and protein bands visualized by Coomassie Brilliant Blue R-250 staining.IC50 values were determined as described previously Azocasein  was dissolved in 100 mM sodium acetate buffer pH 5.50 containing 1 mM EDTA and 5 mM DTT at a concentration of 3 mg/ml. Samples were incubated with 0.1 µM cathepsin K for 30 min at 37°C in the presence of each compound. All compounds were used at concentrations increasing up to 2 mM, except compound 2, which was used at a maximal concentration of 1 mM due to its limited solubility at higher concentrations. Reactions were stopped by addition of trichloroacetic acid , centrifuged, clear supernatants mixed with 0.5 M NaOH and the concentrations of solubilized peptides determined by measuring the absorbance at 440 nm. All experiments were performed in triplicates and appropriate blanks were run to take into account the absorption of azocasein and compounds alone. Cathepsin K was incubated at 37°C in 50 mM Hepes buffer pH 7.40 containing 1 mM EDTA and 5 mM DTT in the presence or absence of each modifier. The final enzyme concentration was 0.2 µM and final compounds concentrations were 2 mM, except compound 2, which was used at a concentration of 1 mM. All experiments were performed in Eppendorf Protein LoBind Tubes to minimize the adsorption of proteins on tube walls. Aliquots were withdrawn from the reaction mixtures at regular time intervals and their residual activity measured using the substrate Z-FR↓AMC . Inactivation curves had exponential profiles that were fitted with the mathematical model for one-phase exponential decay to determine the half-life of the enzyme in each reaction mixture.vA) at a low substrate concentration (0.1×Km) and a high substrate concentration (10×Km), both in the presence of a saturating modifier concentration (10×KA). For each modifier, vA using experimentally determined values of the parameters α and β. Stabilization of the enzyme was expressed as ln(sf), where the stabilization factor sf is the ratio of half-lives determined in the presence and absence of modifier. Azocasein degradation data was input as the fraction of residual enzyme activity . For collagenolytic assays, qualitative values of 1 and 0 were used to signify inhibition and lack thereof, respectively. For glycosaminoglycans, a value of −1 was used to signify their concentration- and environment-dependent activation/inhibition activity. Principal component calculations and graphical visualizations were performed in the Matlab environment.For analysis, the results of each experiment were presented as one data set termed the activity modification matrix . Data frTable S1The activity modification matrix used for principal component analysis.(PDF)Click here for additional data file.


B Acute Lymphoblastic leukemia (B-ALL) with Philadelphia chromosome (Ph′) is a neoplasm of lymphoblast committed to the B cell lineage. The clinical presentation of B-ALL Ph′+ is similar to B-ALL, but is more common in adults than in children. The e1a3 rare variant is produced by the fusion of BCR exon 1 to ABL exon 3. The presence of this translocation has been associated with good disease outcome for chronic myeloid leukemia in a very small series of only 5 cases; there is no such evidence for B-ALL. We report two new cases of B-ALL Ph+ with the rare e1a3 fusion transcript. The e1a3 and e1a2 (p190) transcripts have been reported to have a similar molecular weight and probably a similar clinical profile, thus in these cases the presence of e1a3 was associated with extramedullary infiltration and disease acceleration. FISH analysis confirmed the presence of BCR-ABL1 fusion gene  from an HLA-identical sibling donor, 7 months after diagnosis.9/L, Hemoglobin 11.60 g/dl, platelet count 118 · 109/L) and the presence of 80 % lymphoblasts in the Grunwald-Giemsa blood smear. The bone marrow aspirate found an infiltration of 25 % lymphoblast which was confirmed by immunophenotype . The karyotype was 46,XY,t [20]. FISH analysis confirmed the presence of BCR-ABL1 fusion gene . No SCT had been planned due to age and unfit status. It is noteworthy that the blood counts in a regular check-up 4 months before the diagnosis had a slight leukocytosis that was not studied.Overall only a few cases with the e1a3 BCRABL fusion proteins have been reported. This rare variant has mostly been described with an indolent clinical course in the setting of CML and its role in B-ALL is still unclear. We report two new cases of e1a3 Ph+ ALL patients in where we highlight the finding of the myeloid CD33+ marker expression by immunophenotype . This means that both cases could be defined as acute lymphoblastic leukemia with aberrant myeloid markers (ALL My+). We previously speculated that B-ALL e1a3 cases could represent CML in lymphoid blast crisis that underwent an under diagnosed chronic phase. In one of our cases we do not have any blood counts prior to the B-ALL diagnosis. However the other presented a non-evaluated leukocytosis in the blood count available before diagnosis.A review of the bibliography of reported cases of B-ALL with the e1a3 fusion protein, using the terms “B-Acute lymphoblastic leukemia” and “e1a3” found a total of 18 cases plus the 2 being reported in this manuscript. The rare e1a3 translocation was also previously reported in the literature in 6 patients with CML in chronic phase. Furthermore, we described for the first time a patient with CML diagnosis that after 5 months of Imatinib treatment evolved to lymphoid blast crisis [The review of our cases and the other previously reported shows an aggressive disease similar to other Ph+ ALL. More data is needed in order to clearly define the real prognosis of B-ALL cases with e1a3 translocation and state if these patients could benefit from TKI or other approaches such as Allo SCT at consolidation. The e1a3 and e1a2 (p190) transcripts have been reported to have a similar molecular weight and probably a similar clinical profile, meaning that e1a3 could be associated with the presence of extramedullary infiltration and disease acceleration, with both patients (one achieving CR and one with PD) having persistence of e1a3 at the molecular level after induction treatment. Moreover, it is important that our reference laboratory is able to detect the rare e1a3 BCR-ABL avoiding false e1a3 negatives, in both ALL and CML.We report 2 new cases of B-ALL with the rare e1a3 BCR-ABL fusion protein. At the moment the particular prognostic significance of e1a3 remains undetermined, but considering our cases and the other previously described, it seems that a clinical management with protocols of Ph+ ALL should be offered to eligible patients. The study of the clinical significance of these variants at diagnosis and follow up, is important to define if these patients have a higher risk of relapse or progressive disease in comparison to other BCR/ABL transcripts and could benefit from SCT.


At 240 K (=TMI), EuCu3Fe4O12 undergoes a very abrupt metal to insulator transition, a paramagnetic to antiferromagnetic transition and an isostructural transformation with an abrupt large volume expansion. Above TMI, optical conductivity reveals a bad metal behavior and below TMI, an insulating phase with an optical gap of 125 meV is observed. As temperature is decreased, a large and abrupt spectral weight transfer toward an energy scale larger than 1 eV is detected. Concurrently, electronic structure calculations for both high and low temperature phases were compared to the optical conductivity results giving a precise pattern of the transition. Density of states and computed optical conductivity analysis identified Cudxy3, Fed3 and Op2 orbitals as principal actors of the spectral weight transfer. The present work constitutes a first step to shed light on EuCu3Fe4O12 electronic properties with optical measurements and ab-initio calculations.Optical measurements were carried out by infrared spectroscopy on AA′ Unlike the A site of simple perovskite oxides ABO3, which is usually occupied by alkali, alkaline earth, or rare earth cations, the A′ site in AA′3B4O12 enables an accommodation of transition-metal ions, such as Cu2+ and Mn3+, which are Jahn–Teller active. Therefore, A′-A′ and A′-B interactions may give rise to novel physical properties in addition to the usual B-B interactions. Colossal magnetoresistance under weak field appears in ACu3Mn4O12 3Ru4O123Co4O1233Ti4O12 exhibits a giant dielectric constant over a wide temperature range53Fe4O12 shows an excellent catalytic activity for oxygen evolution reaction and its stability is enhanced by covalent bonding network between Cu–O–Fe bondsInvestigation of A-site ordered double perovskites AA′3Fe4O12 (noted LnCFO in the following) present a strong interest insofar as they undergo rare valence state transitions accompanied by intriguing functional properties. Metal-insulator transition (MIT) and negative thermal expansion (NTE)3B4O12 with a coordination number of 12, 6 and 4 for Ln, Fe and Cu respectively. As shown in 6 octahedra and CuO4 square planar complexes. According to the size of the Lanthanide3.75+ → 5Fe3+ + 3Fe5+ accompanied by a paramagnetic metal to a ferrimagnetic semiconductor transition around 255 K2+ + 4Fe3.75+ → 3Cu3+ + 4Fe3+ leading to a paramagnetic-metal to an AFM-insulator phase transition between 240 K and 350 K3+ at the square-coordinated A sites and the Fe3.75+ at the octahedron-coordinated B sites. The charge transfer occurs under high pressure conditions for many materialsMI = 310 K in SmCFO. LaxLnx1−Cu3Fe4O12 substituted systems could allow a modulation of the MIT temperature and LaCu3Fex)4(1−Mnx)4(O12 doped compounds is an example of a controlled NTE133Fe4O12 (ECFO) is very representative of large size LnCFO and its optical properties have never been measured yet. It exhibits the earlier cited intermetallic charge transfer between Cu and Fe at 240 K traduced by a MIT, a paramagnetic to antiferromagnetic transition and an isostructural volume change81316dxy3 and Fed3 via Op2 orbitals and the Fe-O bonds expand. Although many theoretical and computational studies have been recently devoted to describe the electronic structure and the mechanism of the MIT in LnCFO9161819Among A-site ordered quadruple perovskites, lanthanides composed LnCud3 and Cud3 bands are strongly modified at the transition, in relation with the charge transfer and the magnetic transition.In this paper, we report on low-energy electrodynamics of ECFO investigated by infrared spectroscopy. We found that ECFO undergoes an abrupt metal to insulator transition (MIT) at 240 K associated with a change of optical properties over an energy scale larger than 1 eV. The comparison with DFT calculations shows that, despite the large amount of energy involved in the MIT, ECFO is a moderately correlated system. Furthermore, both Feω), are shown for different temperatures from room temperature to around the MIT temperature in 21222324Reflectivity spectra of ECFO, R(σ(ω) deduced from reflectivity spectra by Variation Dielectric Function technique (VDF)2627−1cm−1 at 100 cm−1. It clearly deviates from usual Drude model since it exhibits a broad bump at 200 cm−1. This could be due to either localization by disorder2930322934−1. The optical gap energy is determined by a linear extrapolation at the inflection point of the onset of σ(ω)3Fe4O12 that predict Δ between 300 and 800 meV1618−1 (the lowest measured frequency), and the one obtained from transport measurementsThe optical conductivity −1cm−1) and the value of the 300 K optical conductivity at 100 cm−1 (1000 Ω−1cm−1). However, since the sample is a very small polycristal, such a discrepancy can easily be due to the determination of geometrical parameters , grain boundaries and low density of the sample. In order to estimate the typical energy scale involved in the MIT mechanism, the optical conductivity spectral weight (SW) was calculated from the optical conductivity:Note that we found a quite large discrepancy between the conductivity obtained by transport  clearly shows a step-like behavior.SW is related to the charge carrier density contributing to the optical properties up to a cutoff energy lculated  at ωc ≈ In order to get a better insight of the electronic structure and to identify low energy optical excitations, DFT + U calculations were performed. The calculation has been carried out for both the insulating and the metallic phases by using ECFO crystallographic data for 100 K and 300 K. Low temperature phase (LT) was taken anti-ferromagnetic G-type on Fe lattice, as shown in et al.In order to reproduce the order of magnitude of the experimental gap, we choose U = 1.5 eV. Such a value of U is not uncommon since it usually ranges between 2 eV and 7 eV in most transition metal compounds3940411618exp ≈ 125 meV. TDOS is constituted of a wide band of energy from −7 eV to −0.2 eV and three bands above the Fermi level, f, up to 3.75 eV. The PDOS  and site Projected DOS (PDOS) are displayed in The PDOS  allows tf is occupied by a wide valence band from −7 eV to 4.2 eV. The PDOS shows that Cud3, Fed3 and Op2 orbitals are hybridized around the Fermi level to constitute a wide spread band driving the metallic state. Also for this phase, Cudxy3 is the only orbital that differs from other Cud3 orbitals by crossing f. This supports the fact that Cudxy3 is involved in the low frequency (<600 cm−1) behavior of the HT optical conductivity , we used a ferrimagnetic structure FiM  show that the energy scale involved in the charge transfer is larger than 1.5 eV. This is roughly consistent with our spectral weight study  are presented in σRPA of the LT phase exhibits an electronic gap of 250 meV (2 000 cm−1). This is the same order, or even larger than our experimental gap of 125 meV and previous LnCFO DFT studies1618−1 on the low temperature σRPA (blue curve) is assigned to the LT optical conductivity excitation detected at 5 000 cm−1  σRPA presents a clear Drude-like peak below 2 000 cm−1 that differs from the low frequency behavior detected by spectroscopy for the HT phase (−1 (0 eV) to 26 000 cm−1 (3.2 eV). The behavior of σ beyond this range is necessarily in favor of the spectral weight recovering since the charge carrier density is conserved.For the purpose of the comparison with the experiment, we have calculated the optical conductivity by Random Phase Approximation (RPA) using our DFT electronic structure calculations. Although RPA does not take into account many body effects, it is expected to roughly capture the physics. LT and HT calculated optical conductivities . We identified the mechanism responsible for the MIT as being the redistribution of density of states from Fed3 orbitals to Cudxy3 with the hybridization to Op2 orbitals. The next step will consist in driving the MIT by physical pressure for others LnCFO in order to disentangle the role of magnetism in the transition.Based on reflectivity measurements and first principle calculations, we reported the first infrared spectroscopy study of the A-site ordered quadruple perovskite EuCuμm diameter was polished up to optical grade 0.25 μm. SXRD and Fe Mossbauer spectroscopy confirmed the composition of the samples and the valence state of both high and low temperature phases being EuCu+23Fe+3,754O12 and EuCu3+3Fe3+4O12 with a lattice constant of 7.33641(8) Å for 300 K and 7.37306(8) Å for 100 K.ECFO polycrystalline samples were synthesized under high pressure in a high pressure cell (15 GPa) and high temperature (1000 K)−1 and 30 000 cm−1, from 150 K to 300 K. Low temperature measurements on such a small sample were obtained by using a homemade high-vacuum microscope including a x15 Schwarzchild objective connected to a BRUKER IFS 66v/S Fourier-transform spectrometer. After the initial measurement, the sample was coated with a 150 nm aluminium film and remeasured in the previous temperature range. These additional data were used as reference to calculate the reflectivity in order to take into account light scattering on the surface of the sample and possible misalignement induced by heating. Note that, due to the small size of the sample, diffraction limit is reached around 100 cm−1. Above 10 000 cm−1, light scattering due to surface roughness prevents to obtain a good signal to noise ratio. Thus, although both the shape and level of the reflectivity were reasonable according to infrared measurements and high energy reflectivity obtained from x-ray atomic scattering functions as proposed by D. B. Tanner−1. As a consequence, temperature dependent infrared data have been merged with the room temperature UV data. Optical conductivity spectra were obtained consistently by Variation Dielectric Function analysis (VDF) and Kramers-Kronig (KK) analysis. In order to proceed the KK analysis, reflectivity spectra were extrapolated at low frequency with Hagens-Rubens formula in the metallic phase and a constant value in the insulating phase, and by using high frequency extrapolation based on x-ray atomic scattering functions techniqueeff = U−J term. Hereinabove, the term Ueff is denoted just as U for simplicity. The dielectric function was computed in the Random Phase Approximation (RPA).Near normal incidence reflectivity spectra were measured between 100 cmHow to cite this article: Brière, B. et al. On the energy scale involved in the metal to insulator transition of quadruple perovskite EuCu3Fe4O12: infrared spectroscopy and ab-initio calculations. Sci. Rep.6, 28624; doi: 10.1038/srep28624 (2016).