The emergence of robotic Cone Beam Computed Tomography (CBCT) imaging systems in trauma departments has enabled 3D anatomical assessment of musculoskeletal injuries, supplementing conventional 2D fluoroscopic imaging for examination, diagnosis, and treatment planning. To date, the primary focus has been on trauma sites in the extremities.To determine if CBCT images can be used during the treatment planning process in spinal instrumentation and laminectomy procedures, allowing accurate 3D‐printed pedicle screw and laminectomy drill guides to be generated for the cervical and thoracic spine.www.slicer.org) where vertebral models and specific guides were developed and subsequently 3D‐printed. In the ovine cadaver, 11 pedicle screw guides from the T1–T5 and T7–T12 vertebra and six laminectomy guides from the C2–C7 vertebra were planned and printed. In the porcine cadaver, nine pedicle screw guides from the C3–T4 vertebra were planned and printed. For the pedicle screw guides, accuracy was assessed by three observers according to pedicle breach via the Gertzbein–Robbins grading system as well as measured mean axial and sagittal screw error via postoperative CBCT and CT scans. For the laminectomies, the guides were designed to leave 1 mm of lamina. The average thickness of the lamina at the mid‐point was used to assess the accuracy of the guides, measured via postoperative CBCT and CT scans from three observers. For all measurements, the intraclass correlation coefficient (ICC) was calculated to determine observer reliability.The accuracy of drill guides generated from CBCT images was assessed using animal cadavers (ovine and porcine). Preoperative scans were acquired using a robotic CBCT C‐arm system, the Siemens ARTIS pheno . The CBCT images were imported into 3D‐Slicer version 4.10.2 (n = 32), the mean axial and sagittal screw error measured on the postoperative CBCT scans from three observers were 3.9 ± 1.9° and 1.8 ± 0.8°, respectively. The ICC among the observes was 0.855 and 0.849 for the axial and sagittal measurements, respectively, indicating good reliability. In the ovine cadaver, directly comparing the measured axial and sagittal screw angle of the visible screws (n = 14) in the postoperative CBCT and conventional CT scans from three observers revealed an average difference 1.9 ± 1.0° in axial angle and 1.8 ± 1.0° in the sagittal angle. The average thickness of the lamina at the middle of each vertebra, as measured on‐screen in the postoperative CBCT scans by three observes was 1.6 ± 0.2 mm. The ICC among observers was 0.693, indicating moderate reliability. No lamina breaches were observed in the postoperative images.Compared with the planned screw angles for both the ovine and porcine procedures (Here, CBCT images have been used to generate accurate 3D‐printed pedicle screw and laminectomy drill guides for use in the cervical and thoracic spine. The results demonstrate sufficient precision compared with those previously reported, generated from standard preoperative CT and MRI scans, potentially expanding the treatment planning capabilities of robotic CBCT imaging systems in trauma departments and operating rooms. Intraoperatively, using 2D and 3D imaging (when available) has been shown to considerably lower perforation rates compared with using free‐hand techniques  reported.CT is currently the modality of choice for developing 3D‐printed pedicle screw guides. Recently, there has been an emergence of robotic Cone Beam Computed Tomography (CBCT) imaging systems in trauma, providing additional 3D imaging capabilities to supplement conventional 2D fluoroscopic imaging for examination, diagnosis, and treatment planning of musculoskeletal injuries. To date, trauma in the extremities  have been the primary focus of examination, diagnosis, and treatment planning from robotic CBCT imaging systems.2The accuracy of patient‐matched 3D‐printed pedicle screw and laminectomy guides generated from CBCT images was assessed using ovine and porcine cadavers, as depicted Figure 2.1syngo DynaCT Body protocol on the Siemens ARTIS pheno  robotic CBCT C‐arm system. The 3D field of view of the syngo DynaCT Body protocol is limited to 17 cm. Therefore, for the ovine cadaver, five planning scans were acquired to capture from C1 to T12. For the porcine cadaver, two planning scans were acquired to capture from C4 to T7. The syngo DynaCT Body protocol acquires 397 individual X‐ray projections evenly spaced over a 200° arc around the subject in 5 s. The 3D images were reconstructed using the in‐built software on the ARTIS pheno system, and exported to an external hard drive for processing, segmentation, and creation of the patient‐specific guides.The animal cadavers were imaged using the clinically available 2.2www.slicer.org).Patient‐matched drill guides for each vertebra were constructed by a spine surgeon (A. K.), using 3D‐Slicer version 4.10.2 . After removal of supports, the models were inspected to exclude printing failures or errors. No additional postprocessing was required. An example of the 3D‐printed patient‐matched guide for the T7 (pedicle screw) vertebra for the ovine cadaver is provided in Figure The patient‐matched pedicle screw guides and laminectomy guides, as well as the vertebral biomodel files, were imported into Formlabs Preform software version 3.0.2  to be printed using Formlabs Form 2 (Formlabs Inc.) desktop 3D printer using Surgical Guide resin (Formlabs Inc.). The patient‐matched guides were oriented on the build platform to avoid placing supports on parts of the templates that would be in contact with the bone. The 2.4The patient‐matched 3D‐printed screw guides were used to place a total of 36 screws in the cervical and thoracic spine of an ovine (T1–T12) and a porcine (C4–T7) cadaver.For both procedures, the cadavers were placed in a prone position. A midline posterior incision and approach was utilized. A subperiosteal dissection was performed for all the involved vertebrae. The areas where the planned guides were to be positioned were cleaned of soft tissues, with care taken not to disturb facet joint capsule and bone. Stability of the drill guides was confirmed with gentle downward digital pressure. A 4.2 mm drill was used to create a pilot hole for the pedicle screws. A ball‐tipped pedicle probe was used to confirm no palpable breach. The templated Evolution Surgical  pedicle screw was then inserted.Following the procedure, the placement of the pedicle screws was examined by CBCT (ovine and porcine cadaver) and CT (ovine cadaver only). The accuracy of the screw insertion was evaluated using the Gertzbein‐Robbins grading system and via calculating the mean axial and sagittal screw error, measured using an onscreen protractor2.5The patient‐matched 3D‐printed laminectomy guides were used to perform 10 laminectomy cuts in the cervical spine of an ovine cadaver.The ovine cadaver was placed in the prone position. A midline posterior incision and approach was utilized. A subperiosteal dissection was performed of all the involved vertebrae. The areas where the planned guides were to be positioned were cleaned of soft tissues. Stability of the drill guides was confirmed with gentle downward digital pressure. A 3.5 mm round‐tipped burr was used to thin the bone through the laminectomy guide. The burr length was set to 14 mm; however, the template was designed to allow 1 mm of bone in the base of the laminectomy trough, to allow accurate postoperative imaging assessment of the depth‐stop design of these guides. The average thickness of the lamina at the mid‐point of the lamina, in the cranial‐caudal direction, was used to assess the accuracy of the guides, measured via postoperative CBCT and CT scans from three observers . For all measurements, the ICC was calculated to determine observer reliability.33.1In total, 42 screws were inserted with the aid of patient‐matched 3D‐printed screw guides in two procedures involving ovine and porcine cadavers. In the ovine cadaver, 24 pedicle screws were placed in 12 thoracic vertebrae (T1–T12). In the porcine cadaver, 18 pedicle screws were placed in nine vertebrae (C4–T5). Images of the pedicle screw placement during both procedures are provided in Figure Starting with the ovine cadaver, five vertebra levels (corresponding to 10 pedicle screws) were excluded from postoperative analysis due to either guide instability (T1) or misplaced guides (T6–T9 inclusive). The lamina footprint of the T1 guide was too small and was unstable when placed on the spinous process. Screw insertion for this level was abandoned during the procedure for this reason. A pedicle screw template for the T6 vertebrae was not created as the T6 was not visible in the planning images, falling in the overlap of two consecutive images. However, during the procedure, the guide for T7 was accidently placed on the T6 vertebra and pedicle screws inserted. This mistake was not corrected until T10, resulting in the wrong guides being used for the T6, T7, T8, and T9 levels.For the remaining levels in the ovine cadaver, the accuracy of the guides was assessed according to pedicle breach as well as the mean axial and sagittal screw error via postoperative CBCT and CT scans. The postoperative CBCT images revealed four cortical breaches, which were evaluated using the Gertzbein–Robbins grading system. The breaches occurred at T1 Left (Grade E), due to guide instability, and T6 left (Grade C), T7 Left (Grade B), and T9 Right (Grade C), due to misplaced guides. An example of the 3D reconstructed images following the pedicle screw procedure in the ovine cadaver from in‐room CBCT, and conventional CT, displaying the breach at the T9 vertebra are provided in Figure The planned and measured (three observers) axial and sagittal angles from postoperative CBCT and CT images of the pedicle screws correctly placed and visible T2–T5, T10–T11) in the ovine cadaver are provided in Tables 0–T11 in From the postoperative CT images, the average difference between the planned and measured screw angles from the three observers was 2.7 ± 1.4° in axial angle and 1.7 ± 0.7° in the sagittal angle. For the axial angle measurements, the ICC among observers was 0.899, indicating good reliability.Directly comparing the measured axial and sagittal screw angles of the 14 pedicle screws from the postoperative CBCT and CT images revealed an average difference of 1.9 ± 1.0° in axial angle and 1.8 ± 1.0° in the sagittal angle respectively from the three observers.In the porcine cadaver, all levels were included in the analysis with no guide instabilities or misplaced guides reported during the procedure. There were no cortical breaches observed for the procedure in the porcine cadaver. The planned and measured (three observers) axial and sagittal angles from postoperative CBCT images of the pedicle screws placed in the porcine cadaver are provided in Tables Comparing the planned axial and sagittal screw angles from the preoperative CBCT with the measured axial and sagittal screw angles from the postoperative CBCT images for the 18 pedicle screws from the C4 to T5 revealed an average difference of 4.9 ± 2.4° in axial angle and 2.2 ± 0.8° in the sagittal angle. For the axial angle measurements, the ICC among all observers was 0.488, indicating poor reliability,Across all pedicle screw insertions , the average difference between the planned and measured angles from all observers was 3.9 ± 1.9° in axial angle and 1.8 ± 0.8° in the sagittal angle respectively. Across all axial angle measurements, the ICC among all observers was 0.855, and across all sagittal angle measurements, the ICC among all observers was 0.849, indicating good reliability in both cases.3.2In total, 10 laminectomy cuts with the aid of patient‐matched 3D‐printed laminectomy guides in an ovine cadaver from C3 to C7 were made. Images of one of the 3D‐printed laminectomy guides during the procedure and cuts post procedure are provided in Figure Example of the postoperative CBCT images with on‐screen measurements of the remaining lamina thickness at the middle of each of the five vertebrae from Observer 1 are provided in Figure 4In this study, the effectiveness of using conventional CBCT scans to develop patient‐matched 3D‐printed pedicle screw drill and laminectomy guides was examined in ovine and porcine cadavers. The 3D‐printed guides enabled the procedures to be performed accurately, with cortical breaches only occurring during the pedicle screw procedure in the ovine cadaver due to unstable or misplaced guides. The results  demonstrated sufficient precision compared with those previously reported generated from standard preoperative CT and MRI scans,Three observers (two experts and one nonexpert) completed the measurements . For all the screw angle measurements, the three observers demonstrated good to excellent reliability as defined from the ICC. When considering only the two expert observers  could be utilized to plan subsequent procedures to address the musculoskeletal trauma. This has the potential to eliminate the need for additional CT imaging  and limit unnecessary transfer/handling of the patient for additional scans. However, it should be noted that intraoperative imaging is not universally available and therefore such a workflow can currently only be considered for facilities with the required clinical infrastructure. Alternatively, emerging systems such as the Siemens Multitom RAX robotic imagerDespite the success of the procedures performed, there were a number of limitations associated with the studies reported here. First, these studies used animal cadavers, meaning that there was no motion  to contend with during the preoperative imaging. Motion artifacts in the planning scans can propagate errors throughout the planning process from segmentation, guide development to 3D‐printing. Future studies involving live animals will be used to quantify the extent of these errors and determine whether adaptive CBCT imaging approachesThe third limitation was the small numbers of vertebrae examined. The number of vertebrae examined in the studies was limited by the combination of how long the cadavers could be stored between acquiring the planning scans and performing the procedure, availability of surgical personnel and the time required to design and print the guides. Future studies will look to scale‐up the 3D‐printing capabilities, allowing a larger number of guides to be printed simultaneously, reducing the time required between planning and procedure. An additional limitation was not having access to a surgical grade burr for the laminectomy procedure, potentially reducing the accuracy of the cuts. Future studies will look to use a surgical grade burr to ensure maximal precision in the depth of the laminectomy cuts can be achieved.More generally, another potential drawback of using CBCT scans to develop 3D printed surgical guides is the limited field of view. In the ovine cadaver, for example, the planned procedures spanned 62.5 cm and required five conventional CBCT scans to capture the C1 through to T12 vertebrae. Unfortunately, the T6 vertebrae fell in the overlap between scan number 3 and 4, preventing clear visualization of the vertebrae. Therefore, it was not possible to create a pedicle screw guide for T6. In practice, this could have been rectified by acquiring an additional scan. However, due to the timing of the study and limited access to the cadaver, it was not possible to rescan the cadaver and print a new guide prior to the procedure taking place. If conventional CBCT scans are going to be used to develop 3D printed surgical guides in the future, care must be taken to ensure every vertebra within the required procedural field of view can be visualized. Alternative  imaging trajectories5Here, CBCT images have been used to generate accurate 3D‐printed pedicle screw and laminectomy drill guides for use in the cervical and thoracic spine. Further research, including studies in live animals, will be required to determine if generating 3D‐printed pedicle screw drill guides from CBCT images can be clinically viable.The authors have no conflicts to disclose.


They activated cell-surface αIIbβ3 on CHO cells, which lack machinery for inside-out signaling or chemokine receptors, quickly (<1 min) and at low concentrations (1–10 ng/mL) compared to activation of soluble αIIbβ3, probably because chemokines bind to cell surface proteoglycans. Furthermore, activation of αIIbβ3 by the chemokines was several times more potent than 1 mM Mn2+. We propose that CCL5 and CXCL12 (stored in platelet granules) may allosterically activate αIIbβ3 upon platelet activation and trigger platelet aggregation. Transmembrane CX3CL1 on activated endothelial cells may mediate platelet–endothelial interaction by binding to and activating αIIbβ3. Additionally, these chemokines in circulation over-produced during inflammation may trigger αIIbβ3 activation, which is a possible missing link between inflammation and thrombosis.Activation of platelet integrin αIIbβ3, a key event for hemostasis and thrombus formation, is known to be mediated exclusively by inside-out signaling. We showed that inflammatory chemokines CX3CL1 and CXCL12 in previous studies, and CCL5 in this study, bound to the allosteric binding site (site 2) of vascular integrin αvβ3, in addition to the classical ligand binding site (site 1), and allosterically activated integrins independent of inside-out signaling. Since αIIbβ3 is exposed to inflammatory chemokines at increased concentrations during inflammation  and platelet activation, we hypothesized that these chemokines bind to and activate αIIbβ3 in an allosteric activation mechanism. We found that these chemokines bound to αIIbβ3. Notably, they activated soluble αIIbβ3 in 1 mM Ca Integrins are a superfamily of cell-surface heterodimers that recognize extracellular matrix (ECM) proteins, cell-surface ligands , and soluble ligands  ,3. Integ2+ in cell-free conditions by binding to the second ligand-binding site (site 2), which is distinct from the classical ligand-binding site (site 1) in the integrin headpiece NRLTIGEGQQHHLGGAKQAGDV] was conjugated with the C-terminus of GST (designated γC390-411) in pGEXT2 vector (BamHI/EcoRI site). The protein was synthesized in E. coli BL21 and purified using glutathione affinity chromatography. CHO cells that express recombinant human αIIbβ3 were described . The fibhttp://cptweb.cpt.wayne.edu/DbD2/) [Cyclic β3 site 2 peptide fused to GST-The 29-mer cyclic β3 site 2 peptide C260-RLAGIV[QPNDGSHVGSDNHYSASTTM]C288 was synthesized by inserting oligonucleotides encoding this sequence into the BamHI-EcoRI site of pGEX-2T vector. The positions of Cys residues for disulfide linkage were selected by using Disulfide by Design-2 (DbD2) software (u/DbD2/) . It predWells of 96-well Immulon 2 microtiter plates  were coated with 100 µL PBS containing CCL5 for 2 h at 37 °C. Remaining protein binding sites were blocked by incubating with PBS/0.1% BSA for 30 min at room temperature. After washing with PBS, GST-tagged cyclic site 2 peptide was added to the wells and incubated in PBS for 2 h at room temperature. After unbound GST-tagged site 2 peptides were removed by rinsing the wells with PBS, bound GST-tagged site 2 peptides were measured using HRP-conjugated anti-GST antibody and peroxidase substrates. 3, 0.4 mM NaH2PO4, 2.5 mM KCl, 0.1% glucose, 0.1% BSA) with 1 mM MnCl2 for 1 h at room temperature. After unbound αIIbβ3 was removed by rinsing the wells with binding buffer, bound αIIbβ3 was measured using anti-integrin β3 mAb (AV-10) followed by HRP-conjugated goat anti mouse IgG and peroxidase substrates.ELISA-type binding assays were performed as described previously . Briefly2 for 1 h at room temperature. After unbound αIIbβ3 was removed by rinsing the wells with binding buffer, bound αIIbβ3 was measured using anti-integrin β3 mAb (AV-10) followed by HRP-conjugated goat anti mouse IgG and peroxidase substrates. ELISA-type binding assays were performed as described previously . BrieflyαIIbβ3-CHO cells were cultured in DMEM/10% FCS. The cells were resuspended with HEPES-Tyrodes buffer/0.02% BSA (heat-treated at 80 °C for 20 min to remove contaminating cell adhesion molecules). The αIIbβ3-CHO cells were then incubated with chemokines for 30 min on ice and then incubated with FITC-labeled γC390-411 (50 µg/mL) for 30 min at room temperature. The cells were washed with PBS/0.02% BSA and analyzed in BD Accuri flow cytometer  or Attune flow cytometer . For time-course studies, FITC-labeled γC390-411 was added to cell suspension first and the mixture was kept on ice, and then incubated with chemokines for the time indicated before being analyzed in flow cytometry. The data were analyzed using FlowJo 7.6.5, BD Bioscience, Franklin Lakes, NJ, USA.Docking simulation of interaction between CCL5 1EQT.pdb) and integrin αvβ3  was performed using AutoDock3 as described previously [EQT.pdb aTreatment differences were tested using ANOVA and a Tukey multiple comparison test to control the global type I error using Prism 7 .The primary goal of this study is to determine if three chemokines bind to and activate integrin αIIbβ3. Active and inactive conformations, 1L5G.pdb (open headpiece αvβ3) and 1JV2 (closed-headpiece αvβ3), are defined in αvβ3 but not in αIIbβ3. We have shown that CX3CL1 binds to the classical ligand (RGD)-binding site (site 1) in open headpiece αvβ3 and to the allosteric site (site 2) in a closed headpiece αvβ3 in docking simulation . Additio2+. We found that soluble αvβ3 bound to immobilized CCL5 in a dose-dependent manner (Kd = 6.7 µg/mL)  did not support the binding (2+ (2+-dependent manner.We studied whether αvβ3 binds to CCL5 in ELISA-type binding assays. CCL5 was immobilized to wells of 96-well microtiter plates and incubated with soluble αvβ3 in 1 mM Mn7 µg/mL) a. The αv binding b. Inhibiding  b, we stut manner e, but ret manner f.Since docking simulation predicted that CCL5 binds to site 1 and site 2 of integrin αvβ3, and bound to and activated integrin αvβ3, we studied whether CCL5 binds to and activates integrin αIIbβ3. We found that CCL5 bound to soluble αIIbβ3 in a dose-dependent manner a. HoweveDocking simulation predicts that CCL5 binds to the allosteric site (site 2) of αvβ3 at high affinity. We previously showed that peptides from site 2 bind to CX3CL1, CXCL12, and several integrin activators , and blocked allosteric activation integrins αvβ3, α4β1 or α5β1 ,14,40, i2+ (to keep integrins inactive) in cell-free conditions [2+) bound to γC390-411 in ELISA-type assays in a dose dependent manner  than 1 mM Mn2+  was required to fully activate αIIbβ3  enhanced the binding of monovalent ligand to integrins, we propose that site 2-mediated allosteric integrin activation enhanced ligand affinity of αIIbβ3. It is possible that inside-out signaling induces integrin binding to multivalent ligands  and site 2-mediated allosteric binding enhances ligand affinity. Since transport of platelet granules and their contents to the surface is known to require inside-out signaling, allosteric activation by chemokines also requires inside-out signaling. It is imperative to determine the role of each pathway in the future studies.2+ produced the most striking increase in integrin ligand affinity compared with other divalent cations (Mg2+ or Ca2+) in a wide variety of integrins. Subsequently, Mn2+ has been widely used as a positive control for integrin activation. Mn2+-induced integrin activation was thought to mimic physiologic integrin activation because Mn2+ activates integrins in the absence of a bound ligand and induces similar epitope exposure [2+. It is likely that αIIbβ3 is less sensitive to Mn2+ than other integrins. It is possible to use chemokines as the standard of αIIbβ3 activation in future studies.Binding of integrins to their ligands requires the presence of divalent cations, and different cations can markedly alter integrin affinities to fibronectin , and Mn2exposure . It is s2+ (It is unclear if αIIbβ3 activation mediated by the binding of chemokines site 2 requires global conformational changes in αIIbβ3. Previous studies have shown that sPLA2-IIA allosterically activated integrins αvβ3, α4β1, and α5β1 . sPLA2-I2+ . It is t


Neuronal networks encode information through patterns of activity that define the networks’ function. The neurons’ activity relies on specific connectivity structures, yet the link between structure and function is not fully understood. Here, we tackle this structure-function problem with a new conceptual approach. Instead of manipulating the connectivity directly, we focus on upper triangular matrices, which represent the network dynamics in a given orthonormal basis obtained by the Schur decomposition. This abstraction allows us to independently manipulate the eigenspectrum and feedforward structures of a connectivity matrix. Using this method, we describe a diverse repertoire of non-normal transient amplification, and to complement the analysis of the dynamical regimes, we quantify the geometry of output trajectories through the effective rank of both the eigenvector and the dynamics matrices. Counter-intuitively, we find that shrinking the eigenspectrum’s imaginary distribution leads to highly amplifying regimes in linear and long-lasting dynamics in nonlinear networks. We also find a trade-off between amplification and dimensionality of neuronal dynamics, i.e., trajectories in neuronal state-space. Networks that can amplify a large number of orthogonal initial conditions produce neuronal trajectories that lie in the same subspace of the neuronal state-space. Finally, we examine networks of excitatory and inhibitory neurons. We find that the strength of global inhibition is directly linked with the amplitude of amplification, such that weakening inhibitory weights also decreases amplification, and that the eigenspectrum’s imaginary distribution grows with an increase in the ratio between excitatory-to-inhibitory and excitatory-to-excitatory connectivity strengths. Consequently, the strength of global inhibition reveals itself as a strong signature for amplification and a potential control mechanism to switch dynamical regimes. Our results shed a light on how biological networks, i.e., networks constrained by Dale’s law, may be optimised for specific dynamical regimes. The architecture of neuronal networks lies at the heart of its dynamic behaviour, or in other words, the function of the system. However, the relationship between changes in the architecture and their effect on the dynamics, a structure-function problem, is still poorly understood. Here, we approach this problem by studying a rotated connectivity matrix that is easier to manipulate and interpret. We focus our analysis on a dynamical regime that arises from the biological property that neurons are usually not connected symmetrically, which may result in a non-normal connectivity matrix. Our techniques unveil distinct expressions of the dynamical regime of non-normal amplification. Moreover, we devise a way to analyse the geometry of the dynamics: we assign a single number to a network that quantifies how dissimilar its repertoire of behaviours can be. Finally, using our approach, we can close the loop back to the original neuronal architecture and find that biologically plausible networks use the strength of inhibition and excitatory-to-inhibitory connectivity strength to navigate the different dynamical regimes of non-normal amplification. The non-normality of a matrix can be assessed through the Schur decomposition, an orthogonal similarity transformation that results in an upper triangular matrix on which the eigenvalues appear along the diagonal. The Schur decomposition of a matrix W can be formally written as W = U(Λ + T)U†, where U is an unitary matrix , Λ is a diagonal matrix containing the eigenvalues of W , and T is a strictly upper triangular matrix. The strictly upper triangular part contains information related to the interactions between the corresponding Schur modes [Recurrent network models are known to produce different types of dynamics, ranging from regular to irregular, and from transient to persistent activity –6. Mouldur modes —it’s useur modes ) of the Therefore here, we consider upper triangular matrices and manipulate their spectrum and non-normality, such that their characteristics can be directly translated into dynamical properties . These mTo better understand how the manipulations in eigenspectrum and non-normality of a connectivity matrix are translated to biologically plausible networks, in this work we manipulate them directly in upper triangular matrices and then translate our main findings to biologically plausible networks. We start by defining the relationship between the network’s activity and the eigenmodes given by the Schur decomposition, showing how simple manipulations of the eigenspectrum’s imaginary diameter and real distribution can drastically affect the neuronal dynamics. We then systematically explore how the eigenspectrum’s imaginary diameter and the feedforward norm control the different regimes of transient amplification, showing that either shrinking the eigenspectrum’s imaginary diameter or increasing the feedforward norm increase amplification levels. Analysing the neuronal dynamics of these networks via the effective rank of the eigenvectors of the connectivity matrix, we find a trade-off between amplification and the underlying dimensionality of the possible dynamics of the network: networks with high (respectively low) levels of amplification produce dynamics in low (respectively high) dimensional subspaces. After a dissection of the underlying mechanisms of transient amplification using general upper triangular matrices, we consider biological constraints on the spectral distributions, and consequently, on the dynamics. Finally, we show how we can implement our findings in a biological plausible connectivity matrix with excitatory and inhibitory neurons, i.e., a matrix satisfying Dale’s law. We explore three different manipulations: lack of autapses, global inhibition, and ratio between excitatory-to-inhibitory and excitatory-to-excitatory connections. We show that increased global inhibition can lead to more amplifying dynamics due to its connections with the eigenspectrum, and that changing excitatory-to-inhibitory connections affect the eigenspectrum’s imaginary diameter.W for a generic connectivity matrix, WB for a matrix following biological constraints (x(t) is the internal state of the network at time t, and xi(t) can be understood as the membrane potential of the thi neuron of the network . This internal state of the neurons evolves with a characteristic time constant τ (fixed at τ = 200 ms throughout the paper) and is affected by the activity of other neurons of the network through the recurrent connections determined by W. Finally, the activation function, f(x(t)) = r(t), represents the input-output relation between the internal state, x(t), and the firing rate deviation, r(t), from the baseline activity, r0. We assume linear dynamics, r = f(x) = x, for the mathematical analysis and compare to networks with richer dynamics using a known non-linear function given byrmin = 1 Hz and rmax = 4 Hz are the bounds of the sigmoid function f(x). Note that in this case, and generally used in previous works [ri(t) means less than baseline activity ‖, by decomposing it along the directions of the eigenvectors of W,rk(t) and 〈vk, vj〉 is the inner product of the complex vectors vk and vj  < 1, ∀k, the system exhibits a single fixed point that represents the baseline activity. An increase of the response norm, ‖r(t)‖, with respect to the norm of the initial condition, ‖r(t0)‖ , defines the phenomenon of transient amplification. A necessary condition for this to happen is the non-normality of W, i.e., the eigenvectors do not form an orthogonal basis [vk, vj〉 ≠ 0, for some j, k.Throughout the paper we use the following notation for the connectivity matrix: straints . The dynus works , negativd vj see . Here, ral basis : 〈vk, vjΛ, containing the eigenvalues [T, representing the feedforward structure between patterns of activation  < 0.5) to ensure stability. For our analysis, we define the spectrum norm as the Frobenius norm of the matrix Λ, spectral norm [T in two different ways: from the Schur decomposition of a Stability-Optimised Circuit (SOC) [k) > 1 for some k), whose inhibitory connections are modified (optimised) so that no eigenvalue has real part greater than unity . We creit (SOC)  or samplnity see . After oΛ|| and ||T||, respectively, for different regimes of transient amplification, analysing the dimensionality of the dynamics in such regimes. Finally, we link some of the findings from abstract to biological networks through manipulations in a biologically realistic weight matrix that satisfies Dale’s law.The subsequent sections are organised as follows. First, we explore the effects of changing the distribution of the eigenspectrum’s imaginary and real parts. We then examine the influence of the spectrum and feedforward norms, ||dim and dre, respectively (evoked energy [x(t = 0) = a, ||a|| = 1, then a1 that maximises ai, that maximise a1, …, ai−1}. To make sure that the evoked energy is due to an amplified response rather than merely a slower exponential decay, we compute the maximum value of the norm of the firing rate vector, for all vectors in We start our investigation of how the eigenspectrum affects the dynamics by drawing both real and imaginary parts from uniform distributions with diameters d energy , E(a): iWith broad distributions, the system can slightly amplify a few conditions . When thMore surprisingly, shrinking, instead, the imaginary distribution also leads to more amplification , and shrW, which can be partly quantified by the angles between the eigenvectors .The feedforward norm is more directly linked to the non-normality , and as 1 = γ, and two complex eigenvalues, v2, v3〉 = 0. The inner product of the non-orthogonal eigenvectors is given by  the less the eigenvectors are aligned, which we confirm with a large upper triangular matrix, λRe(λ) = 0.5  = 0.5 . The eigW or the eigenvector matrix V are not full rank—on the contrary, they almost always are. What it means is that, in order to quantify the global eigenvector geometry, we have to use the effective rank of V. The effective rank of V measures the average number of significant dimensions in its range, and is formally defined as the exponential of the spectral entropy of its normalised singular values [σ1, σ2, ⋯, σN are the singular values of V, and H is the Shannon entropy, i.e., If most eigenvectors are pointing in similar directions, the dynamics will be biased towards these directions too . This dor values . SpecifiV is indeed small in the highly amplifying regimes ‖ ≥ 1 for the nonlinear network  based on our results from upper triangular matrices. First, we consider the effect of the absence of self loops in the connectivity matrix. We then focus on the indirect manipulation of the spectrum norm and the distribution of eigenvalues via modifications of global inhibition and the indirect manipulation of the eigenspectrum’s imaginary diameter via modifications of the ratio between excitatory-to-inhibitory and excitatory-to-excitatory connections, respectively.Up to here we explored different regimes of transient amplification in networks defined by an upper triangular connectivity matrix. This allowed us to have precise control over both eigenspectrum and feedforward structure of the connectivity matrix. However, these abstract networks do not represent biologically realistic neural networks, especially because of Dale’s law, i.e., neurons are either excitatory or inhibitory. In an upper triangular connectivity matrix, (i) stable asymptotic dynamics (limt→∞ ‖r(t)‖ = 0, i.e., maxλRe(λ) < 1); (ii) transient amplification (‖r(t)‖ > ‖r(0)‖ for t0 < t < t0 + Δt, with t0 ⩾ 0 and Δt > 0); and (iii) neurons are excitatory or inhibitory. To do so we build biological weight matrices, WB, with the algorithm from Stability-Optimised Circuits (SOC) [αmax, αmax < 1 (maxλRe(λ) < αmax). Moreover, it allows for additional constraints to be implemented, such as the level of global inhibition, and whether neurons have autapses, which we use to translate the results from upper triangular matrices, WB.In the simulations of networks satisfying Dale’s law, half of the neurons are chosen to be excitatory (only positive output weights) and the other half to be inhibitory (only negative output weights) , 8, 12. WB without self loops has λRe(λ) = αmax < 1, bounds the real distribution from below and above, restricting it to a limited diameter that is less than αmaxN. The maximum range for the real distribution is bounded by −αmax(N − 1) and αmax, when all real parts but one—defined here as the outlier—are equal to αmax and the outlier is equal to −αmax(N − 1). This observation explains why the spectrum of a stability-optimised circuit [Experimental evidence supports the existence of autapses , 26, yet circuit , which d circuit . The zerγ, reflects the level of global inhibition [E and I are the sum of excitatory and inhibitory weights per postsynaptic neuron, respectively , the bigger the amplification  and the hibition , 12, 29,ectively .Router = 10 and various ratios of inhibition and excitation, p is the probability of a connection being non-zero, taken from a uniform distribution. As a result, the eigenspectrum is mostly distributed inside a circle in the complex plane of radius Router [Router, with a denser region near the origin. The denser region is limited by an inner circle [Taking into account that a large outlier reflects a connectivity matrix with inhibition dominating over excitation , i.e., ts Router , given be origin ; properte origin . The oute origin . Considee origin , the latI/E = 40, the strength of every nonzero excitatory-to-excitatory connection is 0.08, and yet the network is capable of stronger amplification compared to when I/E = 3 in which the nonzero excitatory-to-excitatory weights are set to 1.05  that enables the network to amplify certain inputs in the short transient regime  as the mean connectivity strength of inhibitory-to-excitatory (I-to-E), excitatory-to-inhibitory (E-to-I), excitatory-to-excitatory (E-to-E), and inhibitory-to-inhibitory (I-to-I) groups, respectively. The eigenvalues are complex when the condition 4WEIWIE > (WEE + WII)2 is satisfied  with the SOC algorithm, and linearly scaled all weights to maintain the same Frobenius norm of the connectivity matrix, ‖WB‖, for all realisations. We found that, in line with WIE/WEE  algorithm  with var WIE/WEE . As a co WIE/WEE . This in WIE/WEE . These rIn this article we used upper triangular matrices as abstract representations of the dynamical properties of a connectivity matrix to control the quantities that are relevant for the neural dynamics in the transient amplification regime. By by-passing, temporarily, the connectivity matrix and focusing on a hypothetical Schur transformation, we found new dynamical regimes of large amplification that translated into long transients in non-linear networks. We showed that the amount of transient amplification that a network can produce may be controlled by the ratio between the norms of the spectrum and hidden feedforward structure. Increasing the feedforward norm or decreasing the eigenspectrum’s imaginary diameter resulted in larger amplifying dynamics.Different combinations of the eigenspectrum’s and feedforward norms resulted in regimes of transient amplification that lay in subspaces with different dimensionalities and evolved with distinct timescales for non-linear networks. Very short transient periods in non-linear networks spanned the entire output space but only a few orthogonal conditions elicited large amplification. Short transient periods in non-linear networks lay in a lower subspace, but more orthogonal conditions elicited large amplification. Finally, long transient periods in non-linear networks lay in the same low-dimensional subspace, but many orthogonal initial conditions evoked large amplification. The real distribution could considerably change the levels of amplification, but did not affect the relationship between amplification and spectrum or feedforward norms. When the majority of real parts were close to the upper bound of stability, a zero trace condition had an interesting effect: the larger the negative outlier, the closer the real parts were to the stability limit, thus creating larger amplification levels. Moreover, we found a trade-off between the number of orthogonal initial conditions that elicit large amplifications  and the dimensionality of the underlying neuronal dynamics. The source of amplification, i.e., the overlaps of the eigenvectors, inevitably restricted the subspace in which the dynamical outputs evolve, indicating that any noise added to the system is also amplified in the same subspace, giving rise to low robustness to noise .In biologically plausible networks that satisfy Dale’s law , we found that stronger global inhibitory dominance controlled the spectrum norm due to its relationship with the eigenspectrum outlier and a non-uniform distribution of the remaining eigenvalues. Additionally to global inhibition affecting the spectrum norm, we also showed that excitatory-to-inhibitory connections, more specifically its relationship to excitatory-to-excitatory connections, can alter the eigenspectrum’s imaginary diameter. We could therefore link the results from upper triangular matrices and biologically plausible networks via two properties related to specific connectivity patterns: global inhibition and excitatory-to-inhibitory connectivity.Our work complements previous studies relating manipulations of eigenspectrum and their consequence to neuronal dynamics e.g., , 21, 30), 3021, 3i, results in large amplification of oscillatory inputs [Any structure imposed to a connectivity matrix affects its eigenspectrum in a particular way. Excitatory-inhibitory balance constrains the eigenspectrum to a well defined circle for finite-sized networks, with a non-uniform distribution of eigenvalues inside the circle when the distribution of excitatory and inhibitory weights differ . Cyclic y inputs . Complemparadoxical decrease in inhibitory activity as a result of an increase of external (excitatory) input onto inhibitory neurons [Our results in matrices following Dale’s law allowed us to find a potential role for changes in global inhibition in neuronal networks. Quick changes in the efficacy of inhibitory synapses, both inhibitory-to-inhibitory and inhibitory-to-excitatory, could act as a switch in the dynamical state of the network, changing from amplifying to non amplifying by reducing all inhibitory efficacies. This switch may be controlled by neuromodulators such as the neuropeptide proctolin , acetylc neurons . We did The dynamics of real biological neuronal networks, assessed from large-scale recordings of neural activity, has been shown to typically lie in a low-dimensional space , i.e., tWe limited our exploration in upper triangular matrices to the effects of simple changes in the spectrum and feedforward structures, by controlling their range and norm. In networks that satisfy Dale’s law, excitatory weights were sparsely connected with the same connection strength for all non-zero entries, changing only the ratio between excitatory-to-inhibitory (E-to-I) and excitatory-to-excitatory (E-to-E) connections. In reality, synapses are constantly changing, following stereotypical synaptic plasticity rules that allow learning of memories , 41–43 oOur work opens the door for the exploration of new questions related to neuronal dynamics, such as how the structure—besides the norm—of the feedforward part as well as how non-uniform imaginary distributions affect the dynamics of biologically plausible networks.α ± βi in the spectrum, we add the block1,2 = α1 ± iβ1, λ3,4 = α2 ± iβ2, and λ5 = γ, while the feedforward structure is defined by {ϕi}, i = 1, …, 8. Note that all elements of To construct the upper triangular matrices we take inspiration from the real Schur transformation of real matrices. In this form, the matrix is upper triangular with some 2 × 2 blocks on the diagonal. These blocks have real entries and their eigenvalues are the complex eigenvalues of the initial matrix (a pair of conjugates). We fix the triangular part that is not involved in the eigenvalue blocks (more details on this below) and assign to it the norm that we wish by scaling its entries. For the manipulation of the spectrum we construct our distributions as follows. To have the pair of complex eigenvalues The real distributions we use in this work are the following:A single valued distribution: all real parts are the same and equal to a fixed value. We use Re(λk) = 0, ∀k in k) = −0.5, ∀k in k) = 0.5, ∀k in A distribution with a negative outlier: in this construction we add a purely real negative outlier, λout, at a specific point in the complex plane. In M = λout/αmax = 2λout of eigenvalues are equal to αmax = 0.5 and the rest is equal to zero so that the zero trace condition is satisfied. The value of the outlier is indicated in the figure legends. In A uniform distribution on the interval : all real parts, except for the last one, are distributed uniformly between the values −0.5 and 0.5. As before, because of the zero trace condition, we have to add a small outlier  to complement for the non-zero sum of the rest of the values. We use this type of distribution in Figs erval −0., 0.5: alre, 0.5)A uniform distribution on the interval , with respect to the randomness of the imaginary distribution, and final quantities are averaged across all realisations for plotting.I/E = 3 (explained below). The SOC is a matrix known to create strong non-normal amplification and its corresponding feedforward structure is not random, but finely tuned to create amplification. In the simulations shown in Figs In the simulations shown in To understand whether the surprising effect that arises from shrinking the imaginary spectrum is due to the clustering of the eigenvalues, we checked what happens when the imaginary parts of the eigenvalues are not uniformly distributed around zero, but clustered around symmetrically displaced points on the imaginary axis  inset. Iθ, between two complex vectors is given byπ − θ) = −cos(θ), when computing the percentage of small eigenvector overlaps , we consider as angle the minimum angle between θ and π − θ. We would like to note here that non-normality depends on the complex inner product between eigenvectors, and not only its real part. However, we have chosen to compute this more intuitive version of an angle between two complex vectors (which is commonly used in the literature) as a characterisation of the amplification dynamics. We compare these results with an alternative computation of the eigenvector overlap in Recall that the eigenvectors are, in general, complex, in conjugate pairs and that in order to compute the overlap between the eigenvectors we need to consider their inner product. The inner product of two complex vectors is defined asV. This is understood as the number of significant dimensions in the range of a matrix. For example, if the effective rank is equal to κ, then a trajectory evoked by a random initial condition in the range of V is sufficiently approximated by κ dimensions (see section 3 of ref. [Here we briefly explain the intuition behind the effective rank of the eigenvector matrix  of ref. ). The faN × M matrix M is the same as the number of conditions that lead to an amplified response and provides a maximum bound for the effective rank of matrix We construct the matrix The effective rank of κi is the number of principal components needed to explain at least 85% of the variance of the neuronal response, when initialised at the thi (amplified) condition of N. The fact that even though the number of columns is much larger than N in the long transient, but the effective rank still fails to reach its bound, verifies the intuition obtained by the main results in In WB are strictly positive and the second half strictly negative. The connections are initially generated at random from a uniform distribution with probability of connection p = 0.1 and individual weights given by: N is the size of the network. The initial weight, w0, is defined asRouter = 10 is the radius of the eigenspectrum distribution. After the initialisation of a matrix, we implement the SOC optimisation algorithm, which modifies only inhibitory weights to enforce that the spectral abscissa is less than 0.5 (maxλRe(λ) = αmax = 0.5). In this process, both zero and non-zero inhibitory connections are modified. Thus, to maintain a certain level of sparsity in inhibitory connections, we keep the density of inhibitory connections lower than 0.4. Additionally, we keep the absence of self loops and the same I/E ratio by linearly scaling all non-zero inhibitory weights. We impose different conditions to connections depending on which aspect of the connectivity we explore, as define below.The recurrent networks satisfying Dale’s law are constructed following the Stability-Optimised Circuit (SOC) algorithm . In our I/E and then optimise the inhibitory connections. In Figs I/E = 40. We linearly scale all inhibitory weights and calculate the resulting outlier in I/E = 30, 20, 10, 5, 3. We linearly scale all inhibitory weights by the fraction 1/40 to get a resulting weight matrix with I/E = 1 in In WIE/WEE = 1) as described above, optimised using I/E = 3. For each ratio E-to-I to E-to-E, WIE/WEE = {0.4, 0.6, 0.8, 1.2, 1.4, 1.6, 1.8}, we start with a new matrix with weights defined as above and then linearly scale all E-to-I non-zero weights by WIE/WEE. After scaling E-to-I weights, we run the SOC algorithm, as described above, keeping I/E = 3. Finally, after optimisation we linearly scale all weights so that the Frobenius norm of the resulting WB is the same as the standard weight matrix, which has WIE/WEE = 1.In k, given byα, β, and γ can be interpreted as the average of the real part of the eigenspectrum distribution, the eigenspectrum’s imaginary diameter, and the outlier. The other two non-zero entries, ϕ1 and ϕ2, represent the feedforward structure with norm To get an intuition for the role of the eigenspectrum, feedforward norm, and outlier, we analyse a simplified 3-by-3 upper triangular matrix,k areThe eigenvectors associated with λη| (from β in ϕnorm in α and γ are described in the caption). We also plot |η| , inhibitory-to-excitatory (I-to-E), excitatory-to-inhibitory (E-to-I), and inhibitory-to-inhibitory (I-to-I) connections, respectively. The eigenvalues of this connectivity matrix areTo get an intuition for the role of the real and imaginary distributions of a Dalean weight matrix, we analyse a 2-by-2 matrixThe eigenvalues are complex whenI/E, we consider a special case in which the sum of all rows of a biological weight matrix, WB, are equal to γ,N is the number of neurons. Additionally, we consider that the sum of excitatory and inhibitory weights in each row is the same,To find the relationship between the negative outlier and the inhibition-to-excitation ratio, p from a uniform distribution, and thus the total excitatory (E) and inhibitory (I) input weights per neuron arew0, is based on the eigenspectrum’s radius, Router . When inhibition is stronger than excitation, the distribution with smaller variance is the excitatory one, and thus The distribution of eigenvalues is not uniform when the variance of excitatory and inhibitory weight distributions are different . In thisS1 TextSections “Why upper triangular?”, “Alternative feedforward structures”, and “Biologically plausible network dynamics with strictly positive rates”.(PDF)Click here for additional data file.S1 FigA, Linear dynamical response; the network shows an amplified response, effectively due to superposition of almost identical frequencies. Inset: eigenspectrum distribution. B, Nonlinear responses are not amplifying; the very high frequency together with the saturation point prevents the network’s modes from driving each other in order to create an amplifying response. C, Clustering at other finite points, {±10, ±30, ±50, ±70, ±90}, shows the same discrepancy between the linear and nonlinear behaviour, as measured by the percentage of amplified responses.Dynamical responses of a spectrum that is clustered around the points 100 and −100 with respect to the imaginary axis. The imaginary radius around these points is 0.5. The real distribution is uniform on the interval . (EPS)Click here for additional data file.S2 FigA, Exploring the single valued real distribution. We compare results for three real values: −0.5, 0 and 0.5. Top: maximum response norm for preferred initial condition. Naturally a larger real part leads to more amplification as the decay envelope becomes slower. Middle: % of amplified conditions that are amplified by at least 50%; this is also affected by the value of the real part, indicating that the amplification landscape changes its shape in a uniform way. Bottom: the percentage of pairwise eigenvector angles is independent of the real value, i.e., the increased amount of amplification is mainly a result of the slower decay times. Results in all cases are qualitatively similar in their dependence on the imaginary radius. B, Comparing results for two different feed-forward structures. One is the feedforward structure taken from the corresponding feedforward part of a matrix constructed using the Stability-Optimised algorithm [C, Same as panel A but the real part of the eigenspectrum is uniformly distributed between . Values of dre are indicated in the figure (colour coded).lgorithm  (pink). (EPS)Click here for additional data file.S3 FigA, Comparison of the number of columns and effective rank of the dynamical matrix N = 200. B, Number of columns and effective rank of N = 200. The matrix ai in κi principal components stored as columns in the matrix κi is the number of principal components that are needed to capture at least 85% of the total variance of the dynamical response given condition ai. The large discrepancy between the number of columns and the effective rank in the long transient regimes verifies the results shown in the manuscript.(EPS)Click here for additional data file.S4 FigA, Effective rank of the eigenvector matrix, V, for an upper triangular matrix (dashed cyan line) and a recurrent matrix (pink solid line) as a function of the imaginary diameter (left) and feedforward norm (right). The recurrent weight matrix, Wrec, is the upper triangular matrix, U: B, Same as panel A, but the effective rank is calculated for the weight matrix. C, Amplified directions and effective rank of the matrix N = 200. The feedforward Frobenius norm is fixed at 75 for the plot varying the imaginary diameter. The imaginary diameter is fixed at 20 for the plot with varying feedforward norm.(EPS)Click here for additional data file.S5 Figt, for which ‖r(t)‖ ≥ 1 for the nonlinear network. The feedforward structure is random from a uniform distribution, and the real distribution is uniform on . The network size is N = 200, and the feedforward Frobenius norm is fixed at 75 for the plot varying the eigenspectrum’s imaginary diameter (left). The imaginary diameter is fixed at 20 for the plot with varying feedforward norm (right).Timescale is defined as the period, Δ(EPS)Click here for additional data file.S6 FigA-F, Timescale of response (time for which ||r(t)‖ ≥ 1) for distinct eigenspectra and feedforward structures (specified below) from simulations with N = 200 neurons. A, Random uniform eigenspectrum distribution and random uniform feedforward distribution. Same plot as in B, Eigenspectrum’s real part fixed at zero, random uniform distribution of the eigenspectrum’s imaginary part, and random uniform feedforward distribution. C, Inhibitory dominance in the eigenspectrum and random uniform feedforward distribution. D, Random uniform eigenspectrum distribution and feedforward distribution from stability-optimised circuit (SOC). E, Eigenspectrum’s real part fixed at zero, random uniform distribution of the eigenspectrum’s imaginary part, and feedforward distribution from SOC. F, Purely real eigenspectrum with inhibitory dominance and feedforward distribution from SOC. G-I, Normalised inner product of two eigenvectors from a 3-by-3 upper triangular matrix (α − γ = 0 (G), α − γ = 128 (H), and α − γ = 1024 (I).r matrix  as a fun(EPS)Click here for additional data file.S7 FigN = 200 and the Frobenius norm of all matrices is normalised to 100. Different colours correspond to four different outlier values (colour coded). The rest of the eigenspectrum’s real distribution is the same: uniformly distributed between −0.5 and 0.5.Maximum response norm for the preferred initial condition (left), percentage of directions whose norm is amplified more than 50% (middle), and percentage of angles, between pairs of eigenvectors, that are less than 45° (right) as a function of the imaginary diameter. In all cases the network size is (EPS)Click here for additional data file.S8 FigI/E ratio, set to be constant by the SOC algorithm. In all cases the network size is N = 200 (100 excitatory and 100 inhibitory neurons), and the Frobenius norm of all matrices is normalised to 100.All matrices were generated with the SOC algorithm . The y-a(EPS)Click here for additional data file.S9 Figθ) = Re, for the complex eigenvectors α, β (green). Alternatively, we can compute the percentage of pairs for which the magnitude of the complex–valued inner product |〈α, β〉| is larger than 0.7 (pink). Both yield similar results qualitatively.We compare the eigenvector overlap statistics as a function of the imaginary diameter. On one hand we compute the percentage of pairs that form angles < 45°. This is defined using the real part of the inner product, i.e., cos((EPS)Click here for additional data file.S10 FigMaximum response norm for the preferred initial condition (left), percentage of directions whose norm is amplified more than 50% (middle), and effective rank of the eigenvector matrix (right), as a function of the imaginary diameter. Three feedforward structures are compared. Green: uniform distribution as in (EPS)Click here for additional data file.


The hoof is one of the most delicate parts of a horse’s body and its quality depends on a combination of endogenous and exogenous factors. The type of nutrition that a horse receives is a very important factor in determining hoof quality, and a horse’s diet can be supplemented to ensure that it is an adequate source of the energy, proteins, vitamins, and minerals required for healthy growth of all structures comprising the hoof. The aim of this study is to compare two types of horse diets, silage and commercial concentrate, and their impacts on hoof tensile strength.p < 0.05) in the silage than in the commercial concentrate, and hoof Mg, Zn, K, and tensile strength were also influenced by the hormonal stage (p < 0.05). The type of diet directly affected the hoof Mg, Zn, K, Na, and tensile strength (p < 0.05), which Mg, K and Na were higher in horses fed with concentrate. It was found that for each unit of Zn (μg/g and Na (μg/g)), in the hoof, the tensile strength is affected by −0.10 N/mm2 and −0.003 N/mm2, respectively for each mineral.The type of diet that a horse consumes is one of the most important factors determining the mineral profile and tensile strength of its hooves, so the quality and nutritional value of the supplied feed are fundamental to achieving satisfactory hoof quality. The objective of this study was to compare the differences in the mineral concentrations of sodium (Na), potassium (K), magnesium (Mg), zinc (Zn), and Iron (Fe) between two diets, namely silage and a commercial concentrate, using atomic absorption spectrometry and to determine which led to higher increases in the hoof tensile strength of horses consuming these diets. Thirty-two Spanish horses were randomly divided into two groups, where the diet of the horses in group 1 was silage oat hay, and that of the horses in group 2 was a commercial concentrate and oat hay. Both diets were provided for 12 months. The hoof tensile strength was then measured using an Instron universal testing machine. Mg and Fe levels were higher ( The hoof is one of the most delicate parts of a horse’s body. The stratum medium and outermost stratum externum are responsible for protecting the hoof from external factors such as abrasive, harmful substances, or infectious agents . The quaThe type of nutrition that a horse receives is a very important factor in determining hoof quality, and the diet can be supplemented to ensure that it is an adequate source of the energy, proteins, vitamins, and minerals that ensure healthy growth in all structures comprising the hoof. The quality of hoof structures depends on the availability of necessary minerals such as calcium, zinc, and copper ,4. SourcDue to environmental conditions and the unavailability/instability of pastures, many horse owners choose to feed their horses preserved forages , which therefore represent all or part of their forage intake . Silage It has been shown that supplementing with vitamins, minerals, and amino acids results in improved hoof quality, but there is a need for indicators that allow the implementation of strategies toward optimizing this quality . The objHoof samples were obtained from 32 Spanish horses that were housed at a facility in Mexico City, with a mean body mass of 429.53 ± 51.23 kg and a mean age of 7.53 ± 2.06 years. The horses were randomly divided into two groups: group 1  was fed a diet of silage (3 kg per day) and oat hay (8 kg per day), and group 2  was fed a diet of commercial concentrate (3 kg per day)  and oat hay (8 kg per day). Both diets were provided for 12 months. In addition, the hormonal status of the horses (whole or castrated) was considered.To quantify the mineral elements of the two diets administered to the horses (silage made from corn (50%), alfalfa (25%), and oats (25%) and a commercial feed), samples were taken every 3 months. Samples were processed according to the specifications of the atomic absorption spectrometry equipment . For the protein and fiber crude detection methods, the Official Methods of Analysis,  were used respectively.Equine hoof samples (65 ± 21 g) were obtained from hoof trimmings resulting from shoeing and/or trimming routinely performed on the horses. Separate samples were obtained from the right forelimb, wall area. Prior to trimming, each hoof was cleaned with a wire brush and scrubbed with deionized water. Clippings from each hoof were placed in labeled plastic bags and stored for subsequent analysis .®; Mount Prospect, IL, USA), the samples were chiseled in their central area until they were 2 mm thick. The remainder of each hoof clipping was repackaged into a labeled plastic bag and stored at room temperature until processing for mineral analysis [To determine the tensile strength, the samples were cut to a uniform thickness of 0.5 ± 0.1 mm, and subsequently cut to 5 cm × 0.05 cm. Then, using a Dremel tool , which was held by the ends and subjected to tension until breaking [The tensile strength of the hoof was measured using an Instron universal testing machine  with a load capacity of 5 kilonewtons (kN) and an acceleration of 2 mm/min; the results are expressed in Newtons (N) as the threshold amount of kg over mm2 necessary to break the sample. This measurement was conducted on a millimeter portion of the hoof cutout (between 10 and 40 mmbreaking ). All anThe remaining hoof cuttings were used to determine the association between mineral elements . Firstly, the organic matter was removed followed by pulverizing and digestion with nitric acid at 70 °C for 12 h [Means and standard errors were obtained for the mineral elements  of both diets (silage and concentrate) and equine hooves in addition to the hoof tensile strength. A comparison was also made between the results obtained by atomic absorption spectrometry and the values mentioned by the NRC through t-testing of means, since the assumptions of normality were met.A linear model with an identity link function was used for a two-factor factorial design, described below:The assumptions of the model, homogeneity of variance, and normality in the errors, were tested; all models fulfilled the assumptions in the case of the different response variables.To find out which minerals were best associated with tensile strength, a saturated model was used (hoof strength = Ca + Mg + Zn + K + Na) that can be represented as follows:To choose the optimal model using the AIC, a mixed step-by-step algorithm was used. The final model with AIC = 138.89 was as follows:The assumptions of linearity, homogeneity of variance, collinearity, and normality in the residuals were tested, and all assumptions were met.To determine the correlation of the hoof mineral elements and tensile strength with the mineral elements of the feed (concentrate or silage), Pearson correlation testing was performed.Statistical analyses were performed using the functions lm, glm, step, lmtest, shapiro.test, and Durbin–Watson test of the statistical package R 4.0.2 .p < 0.05); the mineral levels in commercial concentrate were below those stipulated by the NRC (p < 0.05).p-values obtained for each variable due to the effect of fixed factors, in the last column the adjusted R2 for each variable. It is important to highlight that most of the response variables had an adjusted R2 above 80%, which reflects the goodness of fit of the model for the variable to be explained.p < 0.05). The diet factor had an effect on the minerals Mg, Zn, K, and Na and tensile strength (p < 0.05)2. The same scenario was presented for Na, with a coefficient equal to −0.003 N/mm2. The behavior of the two independent variables (Zn and Na) can be seen in p-value < 0.05 was obtained for both, allowing us to conclude that they were statistically associated in a linear manner.p < 0.05) and, likewise, Mg is positively correlated with K and Na . Regarding the correlation of particular minerals between hoof and concentrate, the following was observed: hoof Zn was negatively correlated with concentrate Mg  and hoof K had the same behavior as concentrate Ca . p < 0.05) and, likewise, K was positively correlated with Na . Finally, regarding the correlation between silage minerals, Ca was positively correlated with K .Through atomic absorption spectrometry analysis, it was found that Mg was lower and Fe was higher in silage, compared to what is presented in the NRC, but it must be considered that forage quality is greatly influenced by the plant environment such as the type of soil, availability of soil nutrients, water, temperature and solar radiation, therefore the end product changes in chemical composition. An improved understanding of the factors that can modify plant development will make it possible to predict the optimal harvest time for forages in order to obtain optimum quality ,13. On tIn contrast to the study carried out by Meyer, where it was found that the absorption of Mg was increased by increasing the amount of fiber , it was We had expected to find associations between the minerals present in the hoof and those of the administered diets, but the mineral elements of the hoof were only correlated with those of the concentrate , and in studies such as the one by Domínguez 2017), a correlation was found between the mineral elements of the food and the mineral elements of the animal, but only when the latter were measured in the blood serum . What wa17, a corGeldings presented lower hoof tensile strength than intact males, which may be due to the tendency of intact males to be heavier due to the effects of the hormone testosterone, which is responsible for the structuring of long bones and the disposition of muscle mass . StudiesIn an exploratory study with 165 horses, a negative correlation was found between Zn and tensile strength , and theExcessive or low amounts of mineral elements were found in both diets, where the characteristics of the forage are the cause of imbalances in minerals in the resulting silage. Even so, it was observed that there were other factors that caused changes in the mineral elements in hoof samples, such as a horse’s hormonal status (whole or castrated). This factor also influenced the tensile strength of hooves as well as the presence of mineral elements such as Zn and Na. There are still some gaps in current knowledge, regarding the influence of diet’s mineral composition on hoof tensile strength. The present study is to investigate the effects of dietary types on hoof mineral contents and tensile strength, and further research areas are proposed according to some valuable results.


The molecular docking indicated that VVVPQN can combine with ACE to form eight hydrogen bonds. The results of the stability study showed that VVVPQN maintained high ACE-inhibitory activity in weakly acidic and neutral environments and that heat treatment (20–80 °C) and Na+, Mg2+, as well as Fe3+ metal ions had little effect on the activity of VVVPQN. Moreover, it remained relatively stable after in vitro simulated gastrointestinal digestion. These results revealed that VVVPQN identified in camellia seed cake has the potential to be applied in functional food or antihypertensive drugs.The camellia seed cake proteins (CP) used in this study were individually hydrolyzed with neutral protease, alkaline protease, papain, and trypsin. The results showed that the hydrolysate had the highest ACE inhibitory activity at 67.36 ± 0.80% after four hours of neutral protease hydrolysis. Val-Val-Val-Pro-Gln-Asn (VVVPQN) was then obtained through ultrafiltration, Sephadex G-25 gel chromatography separation, LC-MS/MS analysis, and in silico screening. VVVPQN had ACE inhibitory activity with an IC Hypertension is a common chronic disease that can cause cardiovascular and cerebrovascular diseases, arteriosclerosis, and kidney diseases, among other conditions . The preCamellia oleifera Abel) is one of the four major woody oil crops  in the world [Camellia  from rabbit lungs (0.1 U) , ACE subw/v), stirred at room temperature for 2 h and the supernatant was discarded (repeat twice); the defatted powder was obtained after drying. Subsequently, the powder was mixed with 80% ethanol at a ratio of 1:10 (w/v) and stirred at 40 °C for 2 h; the supernatant was discarded (repeated twice). The defatted desaponin powder was obtained after drying. The powder was then dispersed in deionized water at a ratio of 1:20  and extracted by stirring at 50 °C for 2 h. The supernatant was collected by centrifugation and the pH was adjusted to 4.5. Following a 1-h standing period, the precipitate was centrifuged and washed with 80% ethanol (repeated three times). Finally, the precipitate was redissolved at pH 7 and lyophilized to obtain CP. The protein content of the CP was determined by the Kjeldahl method.The preparation of CP was carried out by the method of Li  with somw/v) was dispersed in deionized water and placed in a 95 °C water bath for 15 min. The pH of CP solution was adjusted with 1 mol/L NaOH or HCl to the optimal pH for each protease after cooling to room temperature. The solution was then treated with protease (5000 U/g) and hydrolyzed for 6 h. The optimum conditions for each protease are as follows: neutral protease , alkaline protease , papain , trypsin . Every hour, a portion of the solution was taken out, placed in 95 °C water for 15 min to inactivate the enzymes, cooled to room temperature, and then centrifuged at 8500 rpm for 30 min. The degrees of hydrolysis (DH) and ACE inhibitory activity were measured, respectively. The protease, the hydrolysate of which had the highest DH and ACE inhibitory activity, was selected as the optimal protease, and its hydrolysate was collected as CPH.To denature the protein, the CP ; P is the CP’s protein content in percentage (78.58%); 0.1 is the sample volume in liters (L); and α, β, htot is entirely dependent on the type of raw material .The DH was determined by the o-phthaldehyde (OPA) method, which is based on the reaction of free amino groups with OPA to form a yellow complex . The abs0 and A1 equal the HA peak areas of the blank control and sample, respectively.The ACE inhibition rate was determined using High-Performance Liquid Chromatography (HPLC) . In summThe CPH solution was fractionated using an ultrafiltration system  with molecular weight (MW) cutoffs of 3 kDa and 10 kDa. Three fractions were obtained: CPH1: > 10 kDa, CPH2: 3–10 kDa, and CPH3: < 3 kDa. The ACE inhibitory activity of all fractions was determined as described in The active fraction was further purified using a Sephadex G-25 gel column (Φ16 × 700 mm). The sample solution at a concentration of 10 mg/mL was filtered through a 0.45 μm membrane filter. The filtrate was collected and separated on a Sephadex G-25 gel column eluted by deionized water with an elution rate of 0.8 mL/min and monitored at 280 nm.The peptide sequence was determined by liquid chromatography coupled with tandem mass spectrometry (LC-MS/MS) at the Beijing Biotech-Pack Scientific Co., Ltd. The mass spectrometer used was a Q Exactive™ Hybrid Quadrupole-Orbitrap™ . The peptide sample was reduced by 10 mM DTT at 56 °C for 1 h, alkylated by 50 mM IAA at room temperature in the dark for 40 min, and lyophilized to dryness. Prior to LC-MS/MS analysis, the peptide was resuspended in 20 μL of 0.1% formic acid. Data analysis was performed using PEAKS Studio (8.5) De novo software.8 were selected to be further processed for molecular docking analysis. Peptides with potential ACE inhibitory activity were screened according to binding energy. The pI and GRAVY were determined using a Thermo Fisher Peptide analyzing tool server . In order to verify the ACE inhibitory activity, the selected peptides were synthesized by GenScript . The MW and purity of the synthetic peptides were determined by MS and HPLC, respectively.Only peptides with a De novo score higher than 95 and an area higher than 10Molecular docking was performed with AutoDock Vina software. The 3D structure of ACE (PDB: 1O8A) was derived from the Protein Data Bank. The 3D structure of peptides was generated by ChemBioDraw Ultra 14.0 and the energy minimized by ChemBio3D Ultra 14.0 software . All hetero molecules in 1O8A, including water, were removed prior to docking, while the cofactors zinc and chloride ions were retained. The optimal binding pose for a peptide with ACE was predicted based on binding affinity. The 3D-structure diagrams showing the interaction between the peptide and ACE were drawn with PyMol 1.7 software.The ACE inhibition pattern of the VVVPQN was determined in accordance with the method reported by Urbizo-Reyes , with soThe 0.4 mg/mL VVVPQN solution was placed in a water bath at varying temperatures  for 2 h. After cooling to room temperature, the ACE inhibition rate of VVVPQN was determined using the method described in The 0.4 mg/mL VVVPQN solution was adjusted to varying pH values  with HCl (1 mol/L) or NaOH (1 mol/L). After incubation at 37 °C for 2 h, the pH was adjusted to 7.0 before the ACE inhibition rate was measured.+, Na2+, Ca2+, Mg2+, and Fe3+ solutions at concentrations of 0, 2, 4, 6, and 8 mmol/L, respectively. The mixture was incubated at 37 °C for 2 h, and 20 μL of the mixture was sucked out and used to measure the ACE inhibition rate.VVVPQN was dissolved in distilled water (10 mg/mL), and diluted to 0.4 mg/mL with Kw/w) pepsin at pH 2.0 for 2 h. The pH was then adjusted to 7.0 before trypsin was added at a 1:50 enzyme to substrate ratio. After digestion for 2 h at 37 °C, the enzyme was inactivated by heating for 10 min at 95 °C. The stability of VVVPQN was evaluated by comparing the ACE inhibition rate before and after the digestion.The stability of VVVPQN after in vitro treatment with digestive enzymes was carried out by the method of Chai  with somp < 0.05.All the experiments were performed in triplicates, and the results were expressed as mean ± SD (n = 3). The SPSS 23.0 software  was used to perform a one-way analysis of variance (ANOVA) on the data in this study. Significant differences were considered when The effects of protease species on the DH and ACE inhibitory activities of hydrolysates of CP are shown in Ultrafiltration was commonly used to separate peptides of different molecular weights. In general, peptides with a lower molecular weight showed more significant ACE inhibitory activity . CPH wasWhen CPH3 was purified by a Sephadex G-25 column, there were two major absorbance peaks a at 280 8, and a binding energy below −7.5 kcal/mol were selected, including seven peptides . Some physicochemical properties, such as pI and GRAVY, of the seven peptides were shown in 50 value of the ACE inhibitory activity of VVVPQN was 0.13 mg/mL (198.66 μmol/L), which was lower than GYGYNY’s from camellia glutelin-2 hydrolysates (IC50: 384 μmol/L) [Channa striatus) myofibrillar protein hydrolysate, have indicated that peptides with Val at the N-terminal have high ACE inhibitory activity [ACE inhibitory peptides are usually short-chain peptides containing 2–12 amino acids . A total μmol/L) . The rat μmol/L) . The con μmol/L) , peptide μmol/L) , and pepactivity . This ma−1 HHL) and three concentrations of VVVPQN . It can be seen in Ganoderma Lucidum [The inhibition pattern of VVVPQN was analyzed by a Lineweaver–Burk plot with four concentrations of substrate  and a noncompetitive inhibition mode. Molecular docking showed that VVVPQN could form eight hydrogen bonds with ACE. In addition, VVVPQN had good thermal stability (20–80 °C) and it remained stable under neutral and weak acid conditions. The addition of Na+, Mg2+, and Fe3+ had no significant effect on ACE inhibitory activity and showed satisfactory residual activity after simulating gastrointestinal digestion conditions in vitro. Therefore, it can be assumed that VVVPQN has a potential application prospect as a functional additive in food or health products.The purified and identified novel ACE inhibitory peptide (VVVPQN) from CP exhibited an IC


Facial amphiphilicity is shown to be a crucial structural feature, with para-substituents enhancing (hydrophobic) or decreasing (hydrophilic) IRI activity. Both amino and acid groups were found to be essential. Solution-phase self-assembly of Phenylalanine was not observed, but the role of self-assembly at the ice/water interface could not be ruled out as a contributing factor.Ice recrystallisation inhibition (IRI) is typically associated with ice binding proteins, but polymers and other mimetics are emerging. Here we identify phenylalanine as a minimalistic, yet potent, small-molecule IRI capable of inhibiting ice growth at just 1 mg mL Phenylalanine is demonstrated to inhibit ice recrystallisation at low mM concentrations. Sequential modifications demonstrate the importance of amphiphilicity on activity. Ben 18 hydrophobic modifications to galactose increase IRI activity,13 and patchy hydrophobicity has been reported.19–21 Safranin-O is a small molecule ice growth inhibitor,22 where the activity is linked to self-assembly into larger structures. Warren et al. recently reported that the amino acid l-α-alanine could slow ice growth, but that the isomeric β-alanine could not.23 Molecular simulations suggested that this was not due to ice-binding affinity, but rather differences in the compatibility with the ice lattice and ability to become overgrown by the ice. This presents the exciting possibility for the use of amino acids, and their (easily available) derivatives, as scaffolds for minimal ice growth inhibitors. Small peptides have been used as minimal24 protein mimics for gels and enzymes and hence are ideal targets as minimal IBP mimetics.A common (but not exclusive) feature of many IRIs is facial amphiphilicity where hydrophilic and hydrophobic domains are segregated. For example, rigid poly(norbornene)s only inhibit ice growth when a hydrophobic face is present,l-phenylalanine (Phe) derivatives are potent IRIs capable of inhibiting ice growth at concentrations as low as 1 mg mL−1. Sequential modifications reveal that the amine/acid groups are crucial and that the para-position of the phenyl ring can be used to modulate activity. Self-assembly could be seen in the solid state, but not in solution suggesting that is not crucial for activity.Here we demonstrate that 25,26 and hence this screening was conducted in 10 mM NaCl.27 . Smaller mean grain size (MGS) indicates smaller ice crystals and hence greater inhibition activity. To assess hydrophobicity, we employed octanol-water partition coefficients (log P) and surface area (SA) normalised log P values.28 In P and log P/SA values indicate increasing the hydrophobicity of the side chain from a methyl group on l-alanine to an isobutyl group on l-leucine and l-isoleucine decreased MGS values (i.e. more IRI activity). Furthermore, Phe was discovered to be very potent stopping all growth at just 20 mM. Log P (partition coefficient) and surface area (SA) normalised log P values28 for each amino acid are also shown in P (more hydrophobic) and activity. l-Threonine controls resulted in larger MGS, supporting the need for hydrophobic side chains . Example ice wafers to highlight this dramatic effect are shown in −1. These observations support a hypothesis that the hydrophobic face is essential for activity, with mean grain sizes correlating well with log P  of amino acid derivatives to explore structure-function relationships, not (easily) possible with other inhibitors. log P ESI. To furtlog P ESI. Switchi22 The magnitude of its IRI activity was linked to its ability to self-assemble into extended 1-dimensional fibres, leading to a larger ice binding face.22 In contrast, Ben et al. have reported alkyl glycosides with IRI, which was not linked to their micellization, showing self-assembly alone is not a predictor of function.14 Aromatic amino acids have been reported to form amyloid-like fibrils,30 including the phenylalanine shown here to have IRI. To probe the role (or not) of self assembly, 2 which does not form extended fibrillar structures, but rather ill-defined aggregates. Similarly, Phe-CN did not produce these fibres and does not significantly inhibit ice growth (more images are included in the ESI2 (inactive) was undertaken at 1.5 mg mL−1, The small molecule IRI-active agent safranin-O is also facially amphiphilic, but that is not the only reason for its IRI activity.30 and cytotoxicity to mammalian cell lines. High concentrations of Phe also inhibit the growth of E.coli.31These data show that the amino acid scaffolds are valuable for discovering new IRIs and understanding structure/function relationships. It is important to note, however, that for any future biomedical translation alternative inhibitors must be discovered, as Phe assembly has been linked to phenylketonuriapara position on the phenylalanine was sequentially modified with more polar amino and cyano groups removing activity, and halogens (Cl/F) retaining all activity. It was also found that both the amino/carboxylic acid are essential for ice growth inhibition, with the modification of either group significantly reducing activity. Phe self-assembly in the dye-state was associated with activity, but it cannot be proven that the self-assembly itself was essential for activity as no assembly was seen in solution. This demonstrates that small molecule modulators of ice recrystallisation can be discovered using the simple but versatile amino acid platform. This offers opportunities to probe fundamental mechanisms through precision alteration of the chemical structure and assembly, which would be more challenging to achieve with proteins or polymeric inhibitors.In conclusion, we have introduced phenylalanine scaffolds as a versatile small molecule tool to probe ice recrystallisation inhibition. A panel of amino acids were screened, revealing that hydrophobic side chains lead to increased IRI activity compared to hydrophilic groups. The M. T. W. thanks the MRC for a studentship through the MRC Doctoral Training Partnership in Interdisciplinary Biomedical Research (MR/S502534/1). The EPSRC are thanked for a studentship to IG (EP/1938894). This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme grant agreement no. 866056. MIG thanks the Royal Society for an Industry Fellowship (191037) joint with Cytivia. We thank Max Hill for collecting the confocal images and Daniel McDowall for help collecting the SAXS data. For the purpose of open access, the author has applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising from this submission.There are no conflicts to declare.CC-058-D2CC02531K-s001