Despite rendering serum free thyroxine (FT4) and thyrotropin (TSH) within the normal population ranges broadly defined as euthyroidism, many patients being treated for hyperthyroidism and hypothyroidism persistently experience subnormal well-being discordant from their pre-disease healthy euthyroid state. This suggests that intra-individual physiological optimal ranges are narrower than laboratory-quoted normal ranges and implies the existence of a homeostatic set point encoded in the hypothalamic-pituitary-thyroid (HPT) axis that is unique to every individual.We have previously shown that the dose–response characteristic of the hypothalamic-pituitary (HP) unit to circulating thyroid hormone levels follows a negative exponential curve. This led to the discovery that the normal reference intervals of TSH and FT4 fall within the ‘knee’ region of this curve where the maximum curvature of the exponential HP characteristic occurs. Based on this observation, we develop the theoretical framework localizing the position of euthyroid homeostasis over the point of maximum curvature of the HP characteristic.The euthyroid set points of patients with primary hypothyroidism and hyperthyroidism can be readily derived from their calculated HP curve parameters using the parsimonious mathematical model above. It can be shown that every individual has a euthyroid set point that is unique and often different from other individuals.In this treatise, we provide evidence supporting a set point-based approach in tailoring euthyroid targets. Rendering FT4 and TSH within the laboratory normal ranges can be clinically suboptimal if these hormone levels are distant from the individualized euthyroid homeostatic set point. This mathematical technique permits the euthyroid set point to be realistically computed using an algorithm readily implementable for computer-aided calculations to facilitate precise targeted dosing of patients in this modern era of personalized medicine. Thyroid stimulating hormone [TSH] and free thyroxine FT4] constitute most standard thyroid function tests (TFT) and play a central role in the process of diagnosis and treatment of thyroid diseases such as hypothyroidism and thyrotoxicosis. Evidence indicates that the laboratory-quoted [TSH] reference range is not always appropriate for everyone in clinical practice -5. Clini constituTo solve this problem, it is crucial to appreciate that the normal operation of a negative feedback loop implies the existence of a point of reference, or a set point intrinsic to the system -12. The In physiology, both optimal control and steady states are critical for survival and good health. Homeostatic mechanisms operate with great efficiency to restore equilibrium from acute perturbations. However, various biological constraints due to disease or environment changes may lead to failure of achievement of the steady state and physiological optimum. In the terminology of systems theory, a system in steady state has numerous characteristics that are constant over time such that the partial derivative of these characteristics with respect to time is zero and the recently observed behavior of the system will continue into the future. The steady state is usually not attained till sometime after an initial ‘transient warm up’ period. Notably, the steady state is more general than dynamic equilibrium in that the former may not be a state of dynamic equilibrium as some processes are irreversible while the latter is always a steady state in which the forward and reverse processes are occurring at the same rate. Optimal feedback control refers to the process of determining the control and state trajectories for a dynamic system over time to maximize or minimize a performance index while satisfying specified constraints where the control variables are determined as functions of the current state of the system, a principle widely exploited as part of Nature’s strategies to confer the best probabilities for survival.For the HPT axis, optimal feedback control and systems theory explain how thyrotropic hormones are governed and maintained within a preferential normal range that allows people to live and enjoy good health. In individuals whose HPT feedback loops have been disrupted by diseases, we hypothesize that their state of health may be restored back to the original, provided that their [FT4] and [TSH] are driven towards their pre-disease set points. Molecular, tissue, biochemical and clinical euthyroidism appropriate to the individual, will ultimately be achieved when the [FT4] and [TSH] are both therapeutically constrained to dwell within the set point and its immediate vicinity over a sufficiently long timeframe.Mathematical modeling of the HP function had previously yielded an inverse exponential law governing the [TSH] and [FT4] relationship which is sigmoidal in profile with an inflexion point that can be approximated by a negative exponential curve in most practical instances . This fiA key observation we discovered, is the consistent localization of the normal population ranges of [TSH] and [FT4] values within the “knee” region coinciding to the most pronounced bend on the negative exponential plot of the HP function on the TSH-FT4 Cartesian plane . The obvAlthough triiodothyronine [T3] is the main active thyroid hormone, the response characteristics analysis as confined purely to the relationship between [FT4] and [TSH] is sufficient for all intents and purposes. This is valid because the local DIO2 (type II 5’-deiodinase) in the hypothalamus and pituitary converts [FT4] into [T3] locally, which together with ambient circulating [T3] contributed by peripheral DIO1 (type I 5’-deiodinase)-mediated deiodination of [FT4] and by direct thyroidal secretion of [T3], then exerts negative feedback signal responsible for the inhibition of [TSH]. Moreover, a model involving key observable variables of interest (primarily [FT4] and [TSH]) is pragmatic and will thus find the widest clinical application. In contrast, any modeling attempt incorporating [T3] or [FT3] to encompass a more complete picture actually suffers from the serious drawback of severely limited practical utility as both [T3] and [FT3] are generally measured only in specific clinical situations rather than routinely in the assessment and monitoring of thyroid status .As mentioned above, the properties and form of the HP characteristic have been derived from fundamental physiological considerations . This thS and φ) model where parameters S and φ are real positive numbers which are derived from measured individualized thyroid function tests.This model has been published  and alsoP1 and P2 in the [FT4]-[TSH] plane according toOne and only one exponential function is completely defined by the coordinates of two different points S and φ is dependent on the fitting quality of the exponential function as discussed in detail elsewhere  = x, we haveWriting [TSH] = Working out (2.0.8) according to (2.0.6), we findFor the value of x where K is a maximum, the following condition will be investigated:thenorresulting infrom which we findorSubstitution in equation (2.0.1) gives:Notably, the euthyroid set point has been derived from the model parameters of the HP function with coordinates on the FT4-TSH plane given by the ‘Leow-Goede equations’ as follows:In Figure FT4] = xIf we write for the variable [The curvature function:The theory for the maintenance of homeostasis around the set point is as follows.We investigate the second derivative of K:2.0.8d2Kdx2=0We can better appreciate and understand this robust control and calibration of [FT4] and [TSH] by an intact HPT axis towards euthyroidism in a healthy biological system by applying the notion of a control system represented by the HP unit and the thyroid coupled in a feedback loop. The control system is governed by the HP controller characteristic, unique for every individual like a fingerprint. In this control loop, the HP is the main ‘master’ controller and the thyroid behaves as a ‘slave’ accommodating to the secretory demands, both in rate and magnitude, resulting in two independent thyroid secretory parameters, A and α, such that the loop gain is optimized for the set point position. The loop gain is defined as the modulus of the product of the HP gain factor and the thyroid gain factor. The value of the loop gain is dimensionless and has to be greater than unity in order to maintain optimal and stable control . The looParameterization of the negative exponential HP characteristic:The HP transfer function as mentioned in section The HP gain factor is defined as the first derivative of the HP transfer characteristic noted asA and α. Parameter A defines the upper asymptotic secretory [FT4] level and α represents the steepness with which the saturation level is reached as a function of the variable [TSH]. The output signal of the thyroid is represented by [FT4]. The function is written as:The thyroid transfer characteristic is derived from a Michaelis-Menten model . This moHere, A and α are the independent model parameters of the thyroid transfer function.GT can be determined as:The thyroid gain factor GL is defined as the modulus of the product |GHPGT| resulting in:The loop gain GL is solely a function of the variable [TSH]. We can examine the properties of GL related to an optimum value. For this purpose, we determine the first derivative of GL to [TSH] and examine the solution when this equals zero.We note that GL is a function of that variable. It follows that at optimum GL,The use of [TSH] as the common variable for differentiation should be maintained because the loop gain Therefore,Using the original expression for the thyroid,and substituting the result for α, we have:with e = 2.7182, we then find A:Based on these relationships, the thyroid will operate such that the loop gain will be optimal at the set point. This means the thyroid accommodates to both the demands of secretory amplitude (A) and steepness (α). In a calculation example, we demonstrate the properties of the optimum in the loop gain belonging to the set point, [FT4] = 15 pmol/L and [TSH] = 1.6 mU/L.This results in φ = 0.442.As earlier shown in Figure The exponential thyroid model is thus:The thyroid function to be depicted in an inverted axis superimposed into the same plot as the HP function, because the common variable is [TSH], results in:The loop gain function was derived before as:GL declines to zero exactly over the [TSH] value of 1.6 mU/L at which the maximum of the loop gain occurs. As can be checked by the application of:As depicted in Figure this maximum loop gain equals 3.85.This shows that the absolute value of the loop gain decreases when [TSH] deviates from the set point value. This negative feedback loop itself will maintain this stable condition for homeostasis.The euthyroid set point in this example is shown by the negative exponential curve defined by parameters S = 1211 and φ = 0.442 (ie. TSH = 1211 exp (−0.442[FT4])). From these parameters, the set point at the maximum curvature of this HP curve is: [FT4] = 15 pmol/L and [TSH] = 1.6 mU/L. When we substitute [FT4] = 15 pmol/L into equation (2.0.21), we find [TSH] = 1.6 mU/L, which also satisfies the condition of the set point occurring at the intersection of the HP characteristic curve and the inverted thyroid characteristic derived from (2.0.21):This intersection Figure  is the mBased on the formulation describing the [FT4]-[TSH] characteristic, when two (or more) measured points  and ) from an individual are distinctly separated on the [FT4]-[TSH] plane such as typically observed during the dose titration process of treatment, it is possible to calculate the HP characteristic based on parameters S and φ as follows:We will distinguish the various dependencies of φ and S in relation to [FT4] and [TSH] as follows. The dependency of φ for variations in [FT4] holding [TSH] constant, can be written as:The dependency of φ for variations in [TSH] holding [FT4] constant, can be written asFrom these graphs, we can determine the partial derivatives which represent the gain factor for small deviations around a certain point on either the blue or the red curve. Thus,shown in Figure shown in Figure It can be readily appreciable that the degree of error in the estimation of φ escalates rapidly when FT4 < 2 pmol/L, whereas variations in [TSH] < 0.5 mU/L will contribute to relatively large errors in φ. For S, we find the following:as a straight dashed blue line in Figure as depicted in Figure Errors in S estimation are independent of [TSH] but escalate with increasing [FT4]. Fortunately, modern FT4 assays are robust to errors while third generation TSH assays are sensitive and precise.Clinical examples in this paper illustrate that S and φ estimates are reassuringly accurate in practice for the purpose of elucidating the set point to guide individualized therapeutic targets.For the purpose of clinical validation of this theoretical framework, a group of normal euthyroid individuals N = 14) were randomly sampled and their TFTs were traced to assess if [FT4] and [TSH] of each individual essentially remained stable over time  is thus expected to be tightly regulated with a physiological window far narrower than the usual normal population reference ranges of [FT4] and [TSH] and is likely to be unique in any given person.It is remarkable that each person, when healthy, continues to show TFTs that are closely clustered together even after a decade later as shown in Table such that the values returned by this computation lie between 0 and 1, whereby 0 means no similarity and 1 implies complete similarity . VirtualFT4] ± 1 [Given that the [FT4] data in Table FT4] ± 1 ,22. For As shown above, there is strong evidence that the euthyroid set point is relatively constant and stable in most healthy people at least over a span of one to two decades. From a teleological perspective, it benefits long-term health for physiological functions driven by metabolically potent thyroid hormones to be optimally regulated within feedback threshold hormonal levels encompassing the euthyroid set point and its surrounding narrow neighborhood for maximal disease-free survival. Our theoretical modeling has clearly demonstrated the natural tendency of such a set point to be robustly defended at the point of maximum curvature of the HP function. Clearly, it is still crucial to validate the model with supporting clinical data. In an intact HPT axis, the closed feedback loop controls the [FT4] and [TSH] to the set point and thus obscures the unique negative exponential HP function necessary to test the theory. It requires a pathological thyroid state to break open the closed loop and unravel the HP characteristic for testing. A number of independent methods as listed below may be employed by researchers keen to study the validity of this set point theory, with the caveat that some could be considered challenging to perform, logistically unfeasible or possibly ethically untenable depending on the circumstances.In ascending order of difficulty and feasibility, the following are various methods of clinical validation strategies that may be employed to test the set point theory:(1) Tracking the TFTs during the treatment of those with total thyroidectomy  who require life-long L-T4; their original euthyroid pre-operative FT4-TSH levels would be considered their original set points that can be compared to the set points calculated using their plotted HP curves.(2) Patients with Graves’ disease who successfully achieved a sustained long term clinical remission after successfully weaning off antithyroid drugs; their TFTs during remission may be considered their euthyroid set points which can be compared with the set point values computed from their HP curves while they were previously still on treatment.(3) Patients presently on anti-thyroid drugs for hyperthyroidism or L-T4 for hypothyroidism with a prior historical record of previously normal euthyroid FT4-TSH data long before the onset of thyroid disease that subsequently requires definitive thyroid-specific treatment and dose adjustments, whereupon their computed set points on their HP curves can be matched against their original normal FT4-TSH data.(4) Searching existing epidemiologic literature with published laboratory data documenting the natural history of those screened positive for thyroid autoimmune markers associated with an euthyroid state initially and who then subsequently develop thyroid disease requiring treatment.(5) Patients who received radiation therapy of the neck for cancers  who then developed hypothyroidism allowing HP curves to be plotted and set points computed; any euthyroid TFTs pre-radiotherapy would serve as a benchmark for comparison with the computed set points.(6) Euthyroid healthy human volunteers transiently rendered hypothyroid using thionamides and/or administered either L-thyroxine (L-T4) or liothyronine (L-T3) to induce experimental thyrotoxicosis according to ethically approved safe research protocols  in order to generate unique HP curves for set points determination which can then be compared against their own natural set points.(7) Unusual patients with “euthyroid Graves’ disease”, whose TFTs are consistently within the normal ranges could arguably be considered euthyroid set points due to an equimolar mixture of TSH receptor stimulating and blocking autoantibodies with a ‘tug-of-war’ stoichiometric ratio resulting in euthyroidism; subsequent development of thyrotoxicosis or hypothyroidism due to antibodies imbalance allows HP curves to be plotted for set point computations.(8) Prospective follow-up of euthyroid people positive for thyroid autoantibodies (with previous euthyroid TFTs prior to developing thyroid autoimmunity) over years until their thyroid dysfunction manifests, after which the calculated set points on their respective HP curves can be compared with their initial euthyroid TFTs.The following clinical data formally illustrate and constitute an elegant proof-of-concept of our set point theory. We demonstrate five case examples  to allow an in-depth analysis of the set point confirmation with real clinical data. However, the remaining cases are summarized graphically as shown in Figure 14A-D and Figure 15.This patient has bipolar affective disorder treated with lithium by her psychiatrist two years ago. This precipitated overt symptomatic hyperthyroidism. Serial paired FT4 (in pmol/L) and TSH (in mU/L) and drug dosing (Rx) with carbimazole (CMZ in mg) and levothyroxine (L-T4 in μg) are:Her thyroid was ablated with 18 mCi of radioiodine-131, following which CMZ could be stopped while LT4 started. She has some cold intolerance when FT4 was 10 pmol/L but felt better as her FT4 started rising above 10 pmol/L.Her pre-lithium euthyroid TFT six years ago was: FT4 = 14.6 pmol/L and TSH = 1.72 mU/L which matched the calculated set point closely (FT4 = 14.28 pmol/L and TSH = 2.00 mU/L)  therapy with CMZ, her serum TSH receptor autoantibody (TRAb) fell below immunoassay detection limit of < 0.4 U/L when CMZ was tapered off and she remained in full remission till today.The computed euthyroid set point is FT4 = 14.7 pmol/L and TSH = 1.37 mU/L . Given that TPO Ab predicts a risk of thyroid failure, annual TFTs were serially monitored. Her TFT a decade ago during a health screening was normal: FT4 = 12 pmol/L and TSH = 1.53 mU/L.The computed set point is FT4 = 10.1 pmol/L and TSH = 2.02 mU/L Figure . This esThis patient has a history of laryngeal squamous cell carcinoma for which he underwent total laryngectomy with radical neck dissection followed by adjuvant chemo- and radiotherapy. His pre-surgery, pre-radiotherapy TFT was FT4 = 17.8 pmol/L and TSH = 0.88 mU/L which can be considered his original euthyroid set point. His subsequent TFTs post-cancer treatment were:From the computed set point (FT4 = 15.35 pmol/L and TSH = 1.45 mU/L) Figure  and his This woman was healthy and well until 2004 when she discovered a painless right thyroid swelling.She was clinically and biochemically euthyroid (pre-operative FT4 = 13.0 pmol/L and TSH = 1.35 mU/L). Thyroid ultrasonography revealed a solid-cystic nodule and fine needle biopsy showed a suspicious follicular lesion. She underwent right thyroid lobectomy which showed nodular goitre with cystic degeneration but no malignancy. Subsequent regular monitoring with serial TFT showed development of subclinical hypothyroidism which progressed over a span of two years to overt hypothyroidism requiring LT4 replacement as she fatigued readily and put on weight easily.Her computed set point was FT4 = 14.0 pmol/L and TSH = 1.35 mU/L which matched her original TFT very closely Figure .In the common clinical setting when patients with either hyperthyroidism or hypothyroidism present to the medical doctor, there is no prior TFT done by the patient previously before the disease onset. As such, the set point theory can be put to the acid test to evaluate if the patients’ health outcomes are optimized or improved when their thyroid medications are dose titrated till the their TFTs approach the computed set points.This man was diagnosed with Graves’ disease in February 2002 when he presented with thyrotoxic periodic paralysis associated with severe hypokalemia (plasma potassium = 1.8 mmol/L) due to transcellular potassium shift precipitated by hyperthyroxinemia.His initial TSH receptor antibody (TRAb) level was 9.7 U/L. After 46 months of daily propylthiouracil (PTU) therapy, he was weaned off PTU completely when TRAb became undetectable and has remained euthyroid ever since December 2005. Regular follow-up revealed stable TFTs with FT4 ~ 11–13 pmol/L and TSH ~ 1.3-1.9 mIU/L approximately. These values may be reflective of his original HPT axis euthyroid set point. Using our minimal model, his set point was computed as: FT4 = 11.58 pmol/L and TSH = 1.86 mIU/L , we have: Since this loop gain exceeds unity, the negative feedback loop is operational and the set point is stable in this patient’s HP control system.This elderly woman presented with classical primary hypothyroidism due to Hashimoto’s thyroiditis, including weight gain, lethargy, cold intolerance, dry skin and constipation. Her serum thyroperoxidase autoantibodies (TPO Ab) exceeded 500 IU/L and anti-thyroglobulin (anti-Tg Ab) titre was greater than 102,400. She was initiated on L-T4 replacement at 25 mcg daily and titrated gradually to 100 mcg daily. Unfortunately, she had memory lapses which led to suboptimal compliance to L-T4 dosing as we subsequently discovered. Hence, her L-T4 dose was eventually fixed at 100 mcg daily till she finally attained clinical and biochemical euthyroidism.She persistently experienced cold intolerance despite TFTs within the normal ranges. Remarkably, she felt normal for the very first time when FT4 = 17 pmol/L and TSH = 0.99 mIU/L was attained through full medication compliance, thus implying this to be her euthyroid set point. This agrees closely with the computed set point: FT4 = 16.26 pmol/L and TSH = 1.63 mU/L Figure . The looThis woman has underlying Graves’ disease on CMZ for 18 months before she underwent total thyroidectomy. Post-operatively, she developed overt hypothyroidism while on L-T4 50 μg daily. L-T4 was thus escalated to 75 μg daily which stabilized her at FT4 = 15 pmol/L and TSH = 1.15 mU/L and rendered her fully asymptomatic. Thus, this probably represented her euthyroid set point though she had no pre-disease TFT to countercheck. Her computed her set point was FT4 = 14.83 pmol/L and TSH = 1.05 mU/L Figure , which wThe calculated loop gain here equals 5.78, indicative of a very stable position of homeostasis.It has been established for decades that the log-linear relationship seems to operate very well in correlating the [TSH]-[FT4] hormone pair in the HPT axis -21. Howe2) well exceeding 80% which strongly supports the parameterizable log-linear relationship  of 88%  who is a clinician scientist have conducted experiments with SICS (A*STAR) scientists using healthy wild-type adult male C57BL/6 inbred mice in our investigations of perturbing the HPT axis in a murine model. Animal care and experimentation were in accordance with the Guidelines for the Care and Use of Laboratory Animals and were ethically approved by the Institutional Animal Care and Use Committee, Biological Resource Centre (IACUC #120723), Singapore. These mice were housed in husbandry under conventional conditions  and maintained with free access to food and water under a 12-h light/dark cycle in compliance to the guidelines of the National Advisory Committee for Laboratory Animal Research (NACLAR) of Singapore. The protocol for induction of hypothyroidism was 0.15% 6-n-propyl-2-thiouracil (PTU) in low iodine chow (TD.95125 from Harlan Laboratories) for 28 days. For induction of thyrotoxicosis, adult mice were treated with intraperitoneal 5 μg of L-T3  for 14 days. As an illustration, we computed the set point and showed that the dataset from a mouse model  is valid with a goodness-of-fit , thus guaranteeing that predicted euthyroid set points occurring within the reference ranges are likely to be accurate. Thus, for all intent and purposes, our model should yield predicted HPT set points that are sufficiently robust and reliable for routine clinical applications.To the best of our knowledge, our mathematical theory of the HPT set point is novel and radical, being the very first of its kind ever to have been proposed in the thyroidology literature as there are no parallel conjectures forwarded or published by anyone else to date comparable with ours. The case examples provided cogent proof by directly confirming the observed human data against the matched euthyroid set points as predicted by our theoretical calculations. Indeed, the difference between the patients’ presumed set point [FT4] and the estimated set point [FT4] varied from as low as 0% to about 16% while that for [TSH] varied between 0% to about 38%. In contrast, given the wide population normal ranges in TFT, our present clinical practice can grossly under-estimate or over-estimate the true set point by as much as about 80% and 400% for [FT4] and [TSH] respectively depending on the circumstances. This probably accounts for the commonly observed phenomenon of numerous people who still complain of persistent dysthyroid symptomatology even though they have TFT values falling within the normal ranges.In conclusion, we have developed a rigorous theoretical framework for computation of the HPT axis set point of any individual which can be used to assist clinicians in the treatment of thyroid patients. This is a revolutionary step forward by allowing clinicians to more precisely target their doses of thyroid medications so as to attain TFTs that fall within the set point region predicted by the theory. Obstacles that have hindered widespread adoption of mathematical calculations among healthcare professionals still abound. But such barriers are gradually eased with the increasing acceptance of computer technology among medical doctors in the modern era. While these calculations may seem cumbersome, we have patented a computerized algorithm currently developed into software (Thyroid-SPOT: Set Point Optimization and Targeting) to greatly facilitate the euthyroid set point determination . We enviWe recognize the lack of a randomized clinical trial to prove the superiority of such a set point-targeted approach over the standard ‘normal range guided’ treatment. A prospective clinical trial using the set point theory as developed above can be employed in future to confirm if patients randomized to a set point-centric approach will have better clinical outcomes compared to those treated using the standard conventional approach. As well, because the construction of an accurate HP curve requires multiple TFT data points, it means that it could take at least 3–6 months before the set point can be estimated. Using only 2–3 paired [FT4]-[TSH] data points obtained at the initial phase of treatment to deduce the set point is thus unlikely to generate an accurate prediction due to possible confounding hysteresis factors likely to operate in the early stages of treatment of either severe hyperthyroidism or hypothyroidism.Exploit Technologies Pte Ltd (ETPL), A*STAR’s tech-transfer arm, has filed a patent on the HPT axis set point algorithm that has been developed into a computer program (Thyroid-SPOT software) and MKSL and SLG are both listed as two of three co-inventors. The patent is successfully granted in Singapore.SLG and MKSL jointly developed the mathematical model, tested the performance of the model on the clinical data and participated in the analysis of results, optimization and manuscript preparation. Both authors read and approved the final manuscript.Melvin Khee-Shing Leow is a Senior Consultant Endocrinologist in Tan Tock Seng Hospital, Clinical Associate Professor in National University of Singapore, Adjunct Associate Professor in Duke-NUS Graduate Medical School, and Clinician Scientist in Brenner Centre for Molecular Medicine, Singapore.Simon L. Goede is an Electronic Engineer in Oterlekerweg 4, 1841 GP Stompetoren, The Netherlands.


Using feature extraction from the Ca2+ traces on this reference data set, we identified 2 distinct populations of cells with β-like responses to glucose. To the best of our knowledge, this report represents the first unbiased cluster-based analysis of human β-cell functional heterogeneity of simultaneous recordings. We hope that the approaches and tools described here will be helpful for those studying heterogeneity in primary islet cells, as well as excitable cells derived from embryonic stem cells or induced pluripotent cells.Worldwide efforts are underway to replace or repair lost or dysfunctional pancreatic β-cells to cure diabetes. However, it is unclear what the final product of these efforts should be, as β-cells are thought to be heterogeneous. To enable the analysis of β-cell heterogeneity in an unbiased and quantitative way, we developed model-free and model-based statistical clustering approaches, and created new software called TraceCluster. Using an example data set, we illustrate the utility of these approaches by clustering dynamic intracellular Ca In other words, it is not clear exactly what the features are of the target cell type, or cell types, that need to be generated. This question is not trivial, and attempts to answer it reveal critical gaps in the understanding of human islet cell physiology. Indeed, heterogeneity in cell state and cell fate remains a poorly understood aspect of β-cell physiology, despite several studies.https://jimjohnsonsci.shinyapps.io/TraceCluster), a software app designed to enable the unbiased, high-throughput analysis of functional heterogeneity between islets cells using model-free and model-based clustering. We demonstrate the utility of these approaches and the new software on a rare set of ∼300 high quality simultaneous recordings of human islet cells from a young donor and find two functional groupings of β-cell like responses and one functional grouping of non-β-cell responses.Here, we present TraceCluster  from a healthy 11.8-year old male who died suddenly of head trauma (isolation code HR196). The warm ischemic time was 0 min and the cold ischemic time was 135 min. The pancreas weight was 61 g. The digestion time was 10 min. The final isolation yielded 378,006 IE  with >90% purity. Some islets were embedded in agar, fixed, sectioned and examined with antibodies to insulin, glucagon or Pdx1  as descr2+ imaging was performed in Ringer's solution containing (in mM): 5.5 KCl, 2 CaCl2, 1 MgCl2, 20 HEPES, 141 NaCl and 3 glucose according to standard protocols.Reagents were from Sigma , unless otherwise indicated. CaThe minor signal drift  was corrected per cell by estimating median increase in fluorescence signal per time step under baseline conditions (first 20 minutes). Correction for signal drift did not significantly alter the cell feature estimates described in this work. Fifteen cells (∼5%) were filtered from further analysis due to poor overall signal response, defined as a median KCl response less than 5% over baseline . All data normalization, QC and analyses were performed within the R environment, details of which are provided in the Supplementary Information.The islets used to demonstrate the utility of our cluster analyses were isolated without complication and dispersed into single cells within 24 h (see Online Methods for details). Prior to dispersion, islets were collected for characterization of cellular composition using immunofluorescence staining for insulin, glucagon and PDX1, a critical regulator of islet-cell health and function2+ signals were simultaneously recorded from 291 cells, in 3 imaging fields, while sequentially exposed to either low glucose (3 mM) or high glucose (20 mM) before depolarization with 30 mM KCl  was initially used to explore low dimension projections of the intracellular Ca2+ traces acquired using Fura-2 imaging. The distance matrix for the projections was calculated as (1-ρij)/2, with ρij being the Spearman correlation between cell i and j. As shown in 10P = 4.98 for the null hypothesis that the proportions across the fields are the same). However, no consistent spatial effect could be detected within the imaging fields .Our goal was to analyze functional responses to defined stimuli of human islet cells without using 2+ response features were extracted from the Ca2+ imaging traces for further study. ‘High glucose response’ was defined as the median high glucose (20 mM) signal above baseline , normalized as a ratio of median KCl signal above baseline. ‘High glucose oscillation’ was defined as the magnitude of oscillations during high glucose exposure, expressed as a ratio of the median absolute deviation (MAD) to median KCl response above baseline. ‘Low glucose oscillation’ was defined as the magnitude of oscillations during the first 2 low glucose exposures (3 mM before and after high glucose respectively), estimated in a similar manner to the high glucose oscillations. ‘Response speed’ was defined as the inverse of time to first oscillation peak with high glucose exposure, a measure of time responsiveness to perturbation. Number of ‘counted peaks’ during high glucose exposure were estimated as local maxima from each trace, with the constraint that a local maximum be considered a true peak if at least one third of the signal difference between median KCl and baseline glucose signal. Peak periodicity was used also to estimate the mean ‘oscillation frequency’. ‘Return to baseline’ was defined as the local minimum during the second low glucose exposure, normalized as a ratio of median KCl signal above baseline. ‘KCl response’ was defined as the maximum KCl response above baseline, normalized as a ratio of median KCl signal above baseline.Next we sought to perform less naïve analyses of glucose responses in our human islet data set. To do this, nine Ca10P = 15.05). The second observed feature cluster (10P = 11.44) and magnitude of low glucose oscillations after high glucose exposure (Spearman ρ −log10P = 7.61). This suggests a sub-type of predominantly rapid responders, usually with low/no oscillation during high glucose but some oscillation during subsequent low glucose instead of complete return to baseline. The final observed feature cluster  and responding (β-like cells) population, with a further sub-division of the responders into oscillators and non-oscillators. We anticipate that similar high quality samples from the community will enable the meaningful study of further functional sub-divisions. Moreover, we expect that post-hoc immunostaining and/or single-cell transcriptomics will enable characterization of functional islet cell sub-types. After filtering out cells that did not respond to KCl, the proportion of cells responding to high glucose (71%) was reasonably similar to the expected β-cell frequency within the endocrine cell population of this preparation . Interes2+ response heterogeneity from simultaneously imaged cells controls for any technical variation in this unique high-quality reference resource of Ca2+ responses from a young healthy donor. We expect that these data may serve as a target for efforts to generate functionally young pancreatic β-cells and for studies of the systems biology of these sub-types using emerging single-cell ‘omic’ technologies. It is important to note that the goal of our study was not to characterize β-cell heterogeneity, but instead to merely provide the tools to do so. Robust characterization of β-cell heterogeneity will require highly powered studies with perhaps hundreds of donors.The goals of the present study were to develop new statistical approaches for the analysis of functional heterogeneity from live-cell imaging data and to develop a software app, called TraceCluster, (Supplementary Software) to allow direct comparative analysis of similar data sets with the presented data. Details for the installation and running of the software app are provided in the Supplementary Information. The thorough characterization of Cabona fide human β-cells. Several key questions remain. Should we attempt to generate functionally homogeneous β-cell replacements, and if so, what functional characteristics are ideal? On the other hand, perhaps the goal should be to generate a range of functional islet cell types that more accurately mimics primary human islets. There is also the question of age. The peak age of type 1 diabetes diagnosis is between 10–14 years of age, so perhaps the ideal β-cell replacement cells would respond to glucose in a manner similar to the ‘teen-aged’ cells studied here. Little is known about age-dependent changes in human β-cell function, after the initial post-natal maturation.2+ responses in the current case exhibited the transient decrease in Ca2+ that initiates the response to glucose, known as ‘phase 0’,2+ responses to glucose that resemble those observed commonly in mouse β-cells.Complete characterization of human islet cell functionality is essential for efforts aimed at β-cell replacement in type 1 diabetes or even type 2 diabetes,Indeed, an obvious limitation of the experimental work described here is that it was conducted on a single donor, preventing any broad conclusions about the heterogeneity between donors. However, our main goal was to develop a statistical framework for analyzing heterogeneity of individual responses in populations of cells. These approaches and the software tools are modular and can be adapted to a variety of biological problems.2+ responses from ∼300 human islet cells imaged side-by-side was capable of identifying 2 functional β-cell states within this test sample. The approaches applied to this high-quality data set can be used to examine other β-cell states and in vitro generated replacement β-cells, or any other cell type.In summary, our statistical clustering to Ca


Backbone torsional state transitions on time scales ranging from nanoseconds to beyond microseconds were found to be associated with various types of molecular interactions. Even at nanoseconds temporal resolution, the number of conformational substates that are of statistical significance is quite limited. These observations suggest that detailed analysis of conformational substates at multiple temporal resolutions is both important and feasible. Transition state ensembles among various conformational substates at microsecond temporal resolution were observed to be considerably disordered. Life times of these transition state ensembles are found to be nearly independent of the time scales of the participating torsional DOFs.Hierarchical organization of free energy landscape (FEL) for native globular proteins has been widely accepted by the biophysics community. However, FEL of native proteins is usually projected onto one or a few dimensions. Here we generated collectively 0.2 milli-second molecular dynamics simulation trajectories in explicit solvent for hen egg white lysozyme (HEWL), and carried out detailed conformational analysis based on backbone torsional degrees of freedom (DOF). Our results demonstrated that at micro-second and coarser temporal resolutions, FEL of HEWL exhibits hub-like topology with crystal structures occupying the dominant structural ensemble that serves as the hub of conformational transitions. However, at 100 These motions are qualitatively termed as flexibility, which is widely acknowledged to be important or sometimes critical in various molecular interactions [During last two decades, great progress has been made in the study of major conformational transitions for some functionally important proteins –10. Suchractions . Howeverractions , 15. HowNative  protein FEL has been analyzed in detail by utilizing atomistic molecular dynamics (MD) simulation trajectories that are a few hundred nanoseconds to microseconds-long . Major mms MD trajectories for HEWL in explicit solvents (water and NaCl). Based on distributions of backbone dihedrals, 50,000,000 snapshots were clustered at temporal resolutions ranging from ∼ ns to ∼ 20μs. It is found that at μs and coarser temporal resolutions, native FEL exhibit a hub-like topology with the dominating ensemble, which harbors nearly all crystal structures, serving as the hub connecting smaller structural ensembles among which mutual transitions happen occasionally. At 100ns and finer temporal resolutions, however, HEWL clusters form network-like organization, and crystal structures are associated with significant ensembles that form kinetic traps. The number of backbone CS that is of statistical significance is found to be rather limited even at ns temporal resolution, revealing strong conformational correlations among backbone dihedrals. Comparison with available crystal structures indicates that backbone torsional state transitions involved in various molecular interactions span time scales ranging from ns to ∼ 10μs.Great breakthroughs have been achieved in understanding folding mechanisms of small proteins by millisecond MD simulations , 21–24. ns MD trajectories and saved 50,000,000 structures . To verify that our MD trajectories have achieved sufficient sampling for the native HEWL conformational space, we performed clustering on various subsets of trajectories. The high level agreement regarding the relative importance of significant clusters indicate that our sampling of the HEWL conformational space is reasonably sufficient , two snapshots belong to the same cluster if and only if for each of the torsional DOF that has the same or coarser time resolutions , they share the same torsional state , the statistical weight (W) of snapshots in each cluster (used interchangeably with CS hereafter) is plotted in n clusters (Wsum) were plotted as a function of n in T4). These observations suggest that quantitative analysis of significant CS at temporal resolutions as fine as ns is potentially feasible, at least for backbone conformational space. It is noted that the number of clusters depends highly on the temporal resolution used to perform clustering, and is much smaller for coarser temporal resolutions , CSs of HEWL exhibit network-like organization, and both the average number of neighboring clusters (that have direct transitions to and from a given cluster) and its variation increases , crystal structures are scattered in more and more clusters that are significant but not dominant anymore. This observation might indicate the deficiency of the utilized force fields in differentiating CS on such fine temporal resolutions. Dominance by a structural ensemble that does not correspond to crystal structure(s) has been attributed to inaccuracy of force fields [T3 and T4). At coarse temporal resolutions (T1 and T2), each major CSE seems to be “contaminated” by many non-CSE solution states on finer temporal resolutions . Briefly, for backbone torsional transitions associated with various molecular interactions that were captured by crystal structures, their corresponding time scales were found to vary from ∼ ns to multiple μs. Functionally relevant substrate-bound and inhibitor-bound structures, while sharing large hydrophobic solvent accessible surface area (hSASA)  , locate losteric . All HEWlosteric  seems toThere are many crystal structures available in PDB for a wide variety of HEWL mutants , the number of native contacts (nNC), radius of gyration (Rg), and hSASA were calculated for major CSs at multiple temporal resolutions. As shown in Fig nHB, nNC and smaller hSASA than other ones, while sharing similar average Rg.To examine structural differences within each and among different clusters. We calculated the pair-wise root mean squared deviation (pwRMSD) based on backbone atoms, and the results are shown in T2, transition state ensembles at various temporal resolutions exhibits larger hSASA, larger Rg, smaller nHB and nNC. Similar but less significant observations were made at other temporal resolutions . As shown by ps to hundreds of ns [Life time for TSEs of protein folding have been investigated extensively by experimental, theoretical and computational studies and found to vary from multiple ds of ns –34. No qχ1 for all rotatable side chains that have at least one heavy atom beyond Cβ. It is found that each χ1 significantly populate all three major rotameric states  or pwRMSD is widely utilized for clustering and a number of accelerated methods are developed for this purpose –42. Thisa priori, becomes a challenge. Additionally, the clustering itself become computationally intensive for large number of snapshots as in our case. It would be interesting to have a detailed comparison between our backbone dihedral based clustering and MSM analysis in the future.Markov state models (MSM) is a powerful technique with explicit temporal resolution consideration, and has been successfully applied to analyze major functionally important metastable states for many proteins . There hT2), dozens of transitions are observed between the dominating cluster that harboring nearly all crystal structures and other small clusters, suggesting that the force fields is effective in locating the major native structural states. Therefore we believe that our results, despite the fact that it does not strictly reflecting the global FEL of HEWL under physiological conditions, give a highly realistic model, and the conclusions regarding the topology and organization of CS are likely to be representative for many globular proteins.While admitting that each current force field parameter set has its own limitations, it is certainly true that they describe very realistic models of proteins. The significance of simple lattice model –51 and Gμs bottom region of the native HEWL FEL explored by 0.2ms MD simulations. Five out of the remaining six crystal structures are obtained under extreme conditions such as low hydration and high sodium nitrate concentration (see supporting information for details). Our simulation results, together with the large crystal structural ensemble, suggest that HEWL is likely to have only one narrow major native FEL well (within a few microseconds) that harbors structural states to bind substrates and interact with other proteins. Since force fields are always defective to some extent, very long trajectories might get lost in unrealistic conformational states, running multiple moderately long trajectories in the vicinity of high resolution experimental structures may alleviate this artifact to some degree. Therefore, to sample conformational space of proteins with similar type of native FEL in the vicinity of a crystal structure, utilizing multiple independent microseconds-long MD trajectories might be a better strategy than running a single milli-second or longer MD trajectory.Crystal structures of proteins, despite their being obtained from non-physiological conditions, have beautifully rationalized numerous critical molecular biological processes . This is consistent with our remarkable observation that 114 out of 120 crystal structures, which were obtained under widely different conditions, are located within a central 2 ns to μs. We observed hub-like topology at microsecond and coarser temporal resolutions, and increasingly diversified structural states and more connectivity among CS at increasingly finer temporal resolutions. Various molecular interactions captured in CSE were found to associate with CS transitions covering time scales from nanoseconds to microseconds. CSE for HEWL are found to be associated with kinetic-trap clusters at ∼ 10–100ns temporal resolution. The number of CS that have non-negligible statistical weight is quite limited, even at ns temporal resolution. These observations suggest that to study CS of native globular proteins at temporal resolutions ranging from ns to μs is both important and potentially feasible for prediction of molecular interactions. However, our study is limited to one specific protein. The apparent immediate questions needs to be answered are: i)How is distribution and organization of CS related to specific protein size, folds and sequences; ii)What are the roles of hierarchical CS in protein-protein and protein-ligand interactions. We are working on a few more proteins with different sizes and folds to further increase our understanding in these directions. we hope that this work will stimulate more investigations in this line.In this study we performed a hierarchical conformational analysis for HEWL, a typical globular protein with sufficient structural complexity, at multiple temporal resolutions ranging from www.pdb.org). Each structure is solvated with 6575 TIP3P water molecules and neutralized with 5 Na+ and 13 Cl− ions, resulting in a system with 21703 atoms. The 120 HEWL simulation systems were first equilibrated for 200ps in NVT ensemble and for 1ns in NPT ensemble, both harmonic restraint on protein heavy atoms. After that, restraints were released and 3ns of NPT run were performed to obtain a proper volume (a cubic box with 59.582 Å sides) that is used in the following NVT production runs. Starting configurations for production NVT runs were selected from the last 1ns of the previous NPT run with the criteria of having right box size (within 0.01Å). CHARMM22 (with CMAP) force fields were utilized with a 9Å non-bonded cutoff distance in production runs. The simulation time step is 2fs for equilibration with NAMD and 4fs with hydrogen repartition for production run with ACEMD. Electrostatics were treated by PME with gird size being approximately 1Å. 20 independent trajectories were started from each equilibrated PDB structure by using 20 different random number seeds for initial atomic velocity assignment, resulting in 2400 initial trajectories. Trajectories stopped due to machine failure  were discarded. 2000 100 − ns trajectories, with collectively 50,000,000 snapshots, were utilized for final analysis.MD simulations systems were setup and equilibrated with VMD  and NAMDϕ, ψ) is constructed by using histograms with bin size being 1°. To perform clustering, local minima are found for each backbone dihedral distribution. Whenever the angle distance between two local minima of a given dihedral is smaller than 60, the minimum with smaller probability is taken as an effective. After this initial filtering, a backbone dihedral is selected as a potential clustering dihedral if two or more effective local minima exist. Each region between two neighboring local minima is defined as a torsional state for that torsional DOF. As dihedral angles are cyclic variables, the number of state is equal to the number of local minima utilized for splitting corresponding dihedrals. We found that 127 backbone dihedrals  exhibit two-peak distributions and are defined as two-state torsional DOFs that were used in clustering.Backbone dihedral distributions and torsional states. Distribution of each backbone dihedral angle . Specifically, within our collective trajectory time of 200μs, if N transitions (Ntrans) happened between the two states of an given dihedral, then the average waiting time is Time scales. The time scale for each specific two-state backbone dihedral is defined by the average waiting time between two transition events regardless of its specific directions and routes (For circular two-state system with state T0 (20μs < tw < 200μs), T1 (2μs < tw < 20μs), T2 (200ns < tw < 2μs), T3 (20ns < tw < 200ns) and T4 (2ns < tw < 20ns). Two structures are assigned to the same cluster only if for each clustering participating torsional DOF, both structures are in the same torsional state. When performing clustering at a given temporal resolution, two-state backbone dihedrals with shorter time scales are treated as single-state DOF and are excluded. For example, when clustering at temporal resolution T2, we use backbone dihedrals that have time scales within the range of T0, T1 and T2, but ignore those with time scales within the range of T3 and T4. Due to limited statistics, we did not perform detailed analysis at temporal resolution T0. Backbone torsional DOFs utilized for each temporal resolution is listed in Table A in Clustering at five temporal resolutions. To establish backbone based hierarchical clustering, we first divided all 127 two-state backbone dihedrals into five groups corresponding to five different temporal resolutions ϕ and ψ) as follows. At temporal resolutions T3 and T4, a 5 degree region  is defined as the transition state. At temporal resolutions T0, T1 and T2, for a given local minimum of a specific torsional distribution, number of snapshots in 2.5 degree bins to each side of the minimum are assigned to N+1, N+2, N+3, ⋯ and N−1, N−2, N−3, ⋯. If Ni+2)±( − Ni+1)±( ≫ Ni+1)±, then bins 1, ⋯, i + 1 are defined as the transition state region of the corresponding local minimum. Due to finite sampling, limited connectivity on each level of hierarchical conformational space, and correlations between (among) different backbone torsional DOF, local minima in distributions of each two-state torsional DOF do not necessarily correspond to the transition ensembles between different clusters. Only when transition state of a specific DOF coincide with transition between two clusters at a given temporal resolution, it is taken as transition state of corresponding clusters and snapshots within that state are counted as transition state structures.Transition state ensembles. First we define transition state ensemble for effective local minimum of all two-state backbone torsional DOFs (ϕ and ψ) [qi−12 = cos ϕi, qi2 = sin ψi, with i running through the number of residues. Subsequently, covariance matrices σij = ⟨(qi − ⟨qi⟩)(qj − ⟨qj⟩)⟩ are constructed for selected  trajectories and diagonalized to obtain principal components. We also performed PCA analysis based on cartesian coordinates for protein backbone atoms.Principal component analysis. Dihedral principal component analysis (dPCA) is utilized in this study. To tackle the circular property of dihedral angles, we used the following trigonometric functions to represent backbone dihedrals (ϕ and ψ) . q2i−1 mi and ri being the mass and the distance to the molecular center of mass for atom i respectively, natom is the total number of atoms in HEWL.Radius of gyration. Radius of gyration for each snapshot is calculated as Cα distance being smaller than 6.5Å. Residue contacts that are shared by two thirds (80) or more of the 120 crystal structures utilized in this study are defined as native contacts.Native contacts. A residue contact is defined for two non-sequential residues with Å-diameter sphere is used to probe HEWL surface of hydrophobic residues (as defined by VMD) with VMD [Hydropobic solvent accessible surface area (hSASA). A 1.4with VMD .Å (cutoff distances ranging from 3.0Å to 3.5Å gives similar ordering among different clusters when the number of hydrogen bonds is compared), and by the corresponding “donor → H → acceptor” bend angle being larger than 130.Hydrogen bonds. Existence of a hydrogen bond is defined by a distance between a donor and an acceptor being smaller than 3.5S1 File(PDF)Click here for additional data file.


Control and manipulation of the spin of conduction electrons in industrial semiconductors such as silicon are suggested as an operating principle for a new generation of spintronic devices. Coherent injection of spin-polarized carriers into Si is a key to this novel technology. It is contingent on our ability to engineer flawless interfaces of Si with a spin injector to prevent spin-flip scattering. The unique properties of the ferromagnetic semiconductor EuO make it a prospective spin injector into silicon. Recent advances in the epitaxial integration of EuO with Si bring the manufacturing of a direct spin contact within reach. Here we employ transmission electron microscopy to study the interface EuO/Si with atomic-scale resolution. We report techniques for interface control on a submonolayer scale through surface reconstruction. Thus we prevent formation of alien phases and imperfections detrimental to spin injection. This development opens a new avenue for semiconductor spintronics. Impressive progress in data storage technology has arisen from the development of metallic spintronics based on giant magnetoresistanceThe cornerstones of semiconductor spintronics – creation, manipulation and detection of spin polarization – are extremely challenging in nonmagnetic Si. Optical orientation of spins is inefficient in silicon, motivating approaches based on electrical spin injection. Direct injection of spin-polarized electrons from a ferromagnetic metal into Si is ineffective due to the impedance mismatchAs metals are ineffective injectors, a number of alternatives have been proposed. The use of ferromagnetic tunnel contacts is thought to be a robust approach – the spin polarization of electrons thus injected into Si is detected using opticalSpin injection technologies based on insulating tunnel barriers are plagued by high contact resistance at the interface: the next generation of spin MOSFETs would require a drastic reduction of the resistance between source and drain. The impedance mismatch problem suggests half-metallicEuO is a semiconductor with inherent ferromagnetism which can be tuned by strain23252629303132333435Here, we report a novel technology for integration of functional oxides with silicon which solves the long-standing problem of direct epitaxial growth of the EuO/Si structure. We demonstrate that interface engineering through surface reconstruction controls the outcome of the growth. High-resolution transmission electron microscopy (TEM) shows a clean atomically sharp EuO/Si interface without any alien phases, which were an insurmountable obstacle in previous attempts. Well-developed thickness fringes – coherent oscillations of X-ray diffraction (XRD) intensity – provide another strong confirmation of the atomically abrupt EuO/Si interface. Furthermore, TEM reveals the mechanism for relaxation of strains arising from the lattice mismatch between the semiconductors.3O4 and Eu2O3. Both Eu and O2 react with the substrate forming europium silicide and silicon oxide, respectively, phases preventing direct contact between EuO and Si. High temperature may cause intermixing of EuO and Si at the interface. This is a most critical issue because alien phases at the interface are highly detrimental to spin injection. The same is true for integration of EuO with Si through a spacer preventing chemical reactionsIntegration of ionic functional oxides with covalent Si is always challenging but an epitaxial growth of EuO directly on Si faces additional difficulties. Although both Si and EuO are cubic, the lattice mismatch is large (+5.6%). The most important problem, however, is the high chemical reactivity of the substances involved. First, an excess of oxygen leads to higher oxides Euin situ reflection high-energy electron diffraction, RHEED). They stem from the two surface terminations of the Si lattice, separated by steps of an odd number of Si monolayers. Unpaired electrons make the surface highly susceptible to chemical reactions.The unreconstructed bare Si (001) surface constitutes a square array of atoms with two singly occupied dangling bonds. Then, pairs of Si atoms dimerize leaving one dangling bond per atom. Dimer rows along 2) is chemically resistant even if oxide growth transforms it into a surface silicate39The Si surface with free valences saturated by metal atoms However, the 1 × 2 superstructure does not enable direct EuO/Si contact with subsequent epitaxial growthet al.Following the metal-based superstructure paradigm we first tested the 1 × 2 reconstruction . To iden3O4 and Eu2O3 (monoclinic and cubic), and silicides EuSi2 , Eu3Si4, EuSi, Eu5Si3 and Eu2Si may form. The known ternary compounds are Eu (II) orthosilicate Eu2SiO4 (monoclinic and orthorhombic) and Eu (III) disilicate Eu2Si2O7. 1/amd, space group #141) EuSi22 matching the Fourier spectrum is given in 2 but oriented along the [201] axis.The ternary phase diagram of the Eu-O-Si system is rich. Among binary compounds, oxides EuO, Eu2+ and Sr2+ ensure the well-known isomorphism of Eu (II) and Sr compounds with close structural parameters. One can expect similar phase diagrams for superstructures of these metals on the Si surface. Indeed, not only stoichiometric MSi2 but also equivalent 2 × 3 surface reconstructions are known for Eu and Sr43The presence of precipitates calls for a better protection of the substrate surface. The formation of bulk Eu silicide suggests that the surface requires protection from Eu. On the other hand, surface reactions with oxygen which lead to disintegration of the substrate protection are equally important to suppress. As a consequence, we endeavoured to find a better way to prevent surface reactivity. The solution comes from our realization that metal superstructures other than 1 × 2 can be used for interfacing Si and oxide. The almost identical ionic radii of Eu2 structure. This fact suggests breaking of some surface Si dimers susceptible to oxidation and saturation of the broken bonds by metal atoms. It is likely that at the initial stage of the growth the 1 × 5 surface silicide is partially oxidized similar to that for the 1 × 2 reconstructionThe use of metal-rich silicide templates is in line with the original recipe for the growth of crystalline oxides on silicon0.7Sr0.3O on Si (001)352 alien phase at the interface as revealed by XRDB while the Curie temperature (69 K) matches that of bulk EuO (The replacement of the 1 × 2 by 1 × 5 reconstruction  is a funbulk EuO . RBS itsin direct contact with the Si (001) surface. The eye-catching effect of the technology change is revealed by electron microscopy. Thus, the long-standing problem of interfacing EuO with Si is solved. The atomically sharp interface unravels the reason for well-developed thickness fringes in XRD imagesIn summary, we have successfully demonstrated the epitaxial growth of the ferromagnetic semiconductor EuO directly on silicon. Electron microscopy reveals an atomically abrupt EuO/Si interface. This quantum leap in the quality of EuO films comes from interface engineering – the first monolayer is formed by the 1 × 5 metal superstructure instead of the standard 1 × 2 reconstruction. It strongly suppresses unwanted chemical reactions. However, the change of the reconstruction is not sufficient for engineering the direct EuO/Si contact. Diligent tuning of the growth conditions is indispensable.Future research should address a number of questions: the usefulness of other reconstructions, benefits for the growth of other functional oxides on Si, the structure of the surface reconstructions, possible oxidation of the silicide during oxide growth, the effect of the silicide on the resulting electronic properties of the interface. We hope that this breakthrough in the material engineering will be followed by a successful spin injection through the manufactured spin contact.−10 Torr. 4N Eu and SiO (for capping) are supplied from Knudsen cell effusion sources. Molecular oxygen (6N) flux is tuned with the gas flow system based on the mass flow controller and Baratron manometer. The cell and substrate temperatures are controlled with thermocouples while the absolute temperature of the substrate is determined with PhotriX ML-AAPX/090 infrared pyrometer (LumaSense Technologies) operating at the 0.9 μm wavelength. The intensity of molecular beams is measured with a Bayard-Alpert ionization gauge fitted at the substrate site.EuO films are grown in Riber Compact 12 system for molecular beam epitaxy furnished with a UHV system comprising Gamma Vacuum Titan Ion Pump, cryopump Cryo-Torr 8 (Brooks CTI Cryogenics), a titanium sublimation pump and cryopanels cooled down by liquid nitrogen. The pressure of residual gases is less than 10−9 Torr. The corresponding Eu flux comes from the effusion cell heated to 500 ± 10 °C. The growth rate at these conditions is determined to be ∼2 monolayers per minute. The surface of EuO is protected either by a capping layer of SiO or by controlled oxidation of its topmost layer with formation of Eu2O3. The quality of the films does not depend on the capping layer and does not deteriorate with time for at least one year.The substrates are high-ohmic compensated Si (001) wafers with miscut angles not exceeding 0.5°. The natural surface oxide is removed by heating at 950 °C. The (2 × 1) reconstructed Si surface is exposed to a flux of Eu atoms at 660 °C until a stable (1 × 5) Eu/Si superstructure is formed. EuO films are grown at a temperature of 340 ± 10 °C. The oxygen pressure is about 6·10+ ions) results in 2 μm thick cross-sections of approximately 8 × 5 μm2 area; then attached to the Omniprobe semiring. Electron transparency is achieved by further thinning and final cleaning with 5 keV and 2 keV Ga+ ion beams, respectively. The cross-sections are covered by thin C layers to prevent oxidation of EuO in the Helios chamber before breaking the vacuum. The specimens are studied with a 300 kV TEM/STEM Titan 80–300 (FEI), with a 0.8 Å STEM probe size and an EELS energy resolution of 0.75 eV. The microscope is equipped with a spherical aberration (Cs) corrector, a HAADF detector, an atmospheric thin-window energy dispersive X-ray spectrometer  and a post-column Gatan energy filter (GIF). Images are analysed with Digital Micrograph (Gatan) and Tecnai Imaging and Analysis (FEI) software.The samples for analytical TEM/STEM are prepared in a Helios (FEI) scanning electron microscope (SEM)/Focus Ion Beam (FIB) dual beam system equipped with gas injectors for C and Pt deposition and a micromanipulator (Omniprobe). First, a 2 μm Pt layer is deposited on the surface of the sample. FIB milling . This system allows for a 3D representation of the RHEED pattern (α X-ray source). Rutherford backscattering spectra are recorded for He ions with the energy 1.7 MeV. Magnetic properties are measured with SQUID magnetometer Quantum Design MPMS XL-7. Transport measurements are carried out using Lake Shore 9709A Hall effect measurement system.The surface of the films is controlled  pattern  which diHow to cite this article: Averyanov, D. V. et al. Atomic-Scale Engineering of Abrupt Interface for Direct Spin Contact of Ferromagnetic Semiconductor with Silicon. Sci. Rep.6, 22841; doi: 10.1038/srep22841 (2016).


Pectobacterium spp. This unusual bacteriocin lacks the intrinsically unstructured translocation domain that usually mediates translocation of these bacteriocins across the outer membrane, containing only a single globular ferredoxin domain connected to its cytotoxic domain by a flexible α-helix, which allows it to adopt two distinct conformations in solution. The ferredoxin domain of pectocin M2 is homologous to plant ferredoxins and allows pectocin M2 to parasitize a system utilized by Pectobacterium to obtain iron during infection of plants. Furthermore, we identify a novel ferredoxin-containing bacteriocin pectocin P, which possesses a cytotoxic domain homologous to lysozyme, illustrating that the ferredoxin domain acts as a generic delivery module for cytotoxic domains in Pectobacterium.The colicin-like bacteriocins are potent protein antibiotics that have evolved to efficiently cross the outer membrane of Gram-negative bacteria by parasitizing nutrient uptake systems. We have structurally characterized the colicin M-like bacteriocin, pectocin M2, which is active against strains of  These include the S-type pyocins from Pseudomonas aeruginosa, klebicins from Klebsiella pneumonia and syringacin M from P. syringae  receptor, colicins utilize an intrinsically unstructured translocation domain (IUTD) to recruit the inner membrane-bound Tol or Ton complex  and Pectobacterium carotovorum (Pbc) , separated from the colicin M-like cytotoxic domain  by a linker region  that forms an α-helix  is co-ordinated by a key catalytic aspartic acid side-chain in conjunction with two backbone carbonyls. Mg2+, Ca2+ or Mn2+ ions are required for catalytic activity of M-class bacteriocins, and analysis of these proteins has shown co-ordination at this position to be essential for activity  is orientated towards the other key catalytic residues Fig. . The eleet al., et al., et al., In contrast to the compact structures of the homologous bacteriocins, colicin M, pyocin M and syringacin M, where the receptor binding and catalytic domains are not separated by linker regions and do not form obviously structurally distinct elements  is suggestive of such flexibility and indicates that the crystal structure may not be wholly representative of pectocin M2 in solution.et al., Rg = 27 Å) obtained from Guinier analysis of the experimental scattering data is somewhat larger than that calculated from the pectocin M2 crystal structure (Rg = 24 Å) using SOMO . SAXS data were obtained for a range of pectocin M2 concentrations. Comparison of these data with a theoretical scattering curve generated, using CRYSOL (Svergun I(q)q4 as a function of q4. This analysis reports directly on particle flexibility and typically for compact globular particles an asymptotic plateau is reached for the low q part of the data. However, for pectocin M2 no discernible plateau was observed q2 versus q] for pectocin M2 normalized to the scattering intensity I(0) and Rg, has two maxima with increasing scattering at higher angles. The Kratky plot reports directly on inter-domain flexibility and for pectocin M2 is consistent with a two-domain protein connected by a flexible linker  that approximates closely to the conformation found in the pectocin M2 P21 crystal structure for which Rg and Dmax were calculated as 24 and 77 Å respectively. The second peak represents an ensemble of pectocin M2 conformers in an extended conformation with Dmax values ranging up to 98 Å, which correlates closely with the experimentally determined value of Dmax (96 Å). These analyses suggest that pectocin M2 can adopt both bent and elongated linear conformations in solution.To determine if the SAXS data for pectocin M2 could be better described by an ensemble of conformations we first used discrete molecular dynamics (DMD) simulations  form and the original P21 form, based on their cytotoxic or ferredoxin domains, show a major difference in the relative orientations of these domains . The resulting vector was designated pJPP1. Vectors for expression of pectocins M1 and M2 were as previously described  were spotted directly onto the surface of the overlay, once solidified. Plates were incubated at 28°C for 16 h, and monitored for zones of growth inhibition.The cytotoxicity of purified pectocins was tested using the soft agar overlay method (Fyfe −1 were used. Average buffer scattering was subtracted from the sample scattering. The first 200 points (low angle data) of the scattering curve obtained for 1 mg ml−1 protein were merged with the rest of the high angle data from the 4 mg ml−1 sample to avoid the influence on the data of any inter-particle interference. All data processing was performed using PRIMUS q4 versus q4] and normalized Kratky [I(q)q2 versus q] plots were used to assess particle flexibility as described in the Results section  versus q2] was used to determine the radius of gyration, Rg, of pectocin M2 and pyocin M. US-SOMO . Pectocin M2 and pyocin M concentrations between 0.4 and 4.0 mg mlet al., et al., T) was set to 0.5 kcal mol−1 K−1 to allow for sufficient sampling of conformational dynamics around the native state without melting the structure of the linker. The run time and pdb output step were adjusted in order to generate 5000 models. Next, the pool of 5000 ‘random’ pectocin M2 conformers generated was refined by a genetic algorithm implemented in the program GAJOE as part of the ensemble optimization method  were undertaken with US-SOMO , 0.1 M bis-tris pH 6.5], cryoprotected by increasing PEG 3350 to 30% and data were collected at 100 K to 2.3 Å in the space group P21, at the SLS (Zurich). Re-crystallization screening of pectocin M2 was performed, using a custom screen with variations in the concentration/ratio of precipitants from the original condition (ammonium sulphate and PEG 3350), pH and additives. Clusters of large rod-shaped crystals formed at high ammonium sulphate concentrations. This was optimized giving a final condition of 1.8 M ammonium sulphate, 3% MPD, 0.1 M MES, pH 6.5. These crystals were manually separated and cryoprotected with 15–20% glycerol. Data were collected at 100 K on beamlines I02 and I03 at the Diamond Light Source . Automatic data-processing was performed with Xia2 within the EDNA package  with pectocin M2 at a final concentration of 15 mg mlP21 and P3121 datasets were obtained from the anomalously scattering substructure from the pectocin–ferredoxin domain iron–sulphur cluster, determined for the iron-edge dataset using the Hybrid Substructure Search from the Phenix package (Adams et al., et al., et al., et al., et al., et al., et al., et al., et al., et al., Phases for the et al., et al., et al., f of 0.7 as reported previously (Barreteau et al., Lipid II hydrolysis assays were performed and visualized as previously described by (Grinter


A difficulty in this issue comes from the small magnitude of the nodal gap, which has been preventing experimentalists from solving it. Here we use a laser ARPES capable of ultrahigh-energy resolution, and detect the point nodes surviving far beyond Tc in Bi2212. By tracking the temperature evolution of spectra, we reveal that the superconductivity occurs when the pair-breaking rate is suppressed smaller than the single-particle scattering rate on cooling, which governs the value of Tc in cuprates.In contrast to a complex feature of antinodal state, suffering from competing orders, the pairing gap of cuprates is obtained in the nodal region, which therefore holds the key to the superconducting mechanism. One of the biggest question is whether the point nodal state as a hallmark of  The pairing gap of the high-Tc cuprates has been expected to close at the transition temperature, similarly to the case of conventional superconductors. Here the authors perform ARPES measurements on Bi2212, and reveal a point nodal gap formation beyond Tc, characterized in terms of three parameters. Tc, in some cases above room temperature. Many experimental evidences1234567857101161391516171819201120In cuprates, the energy gap (pseudogap) starts opening at a temperature much higher than Tc6151617202122236Tc25It has been proposed that the pairing-gap evolution with temperature simply follows the conventional Bardeen-Cooper-Schrieffer (BCS) functionTc18Tc is still missing, and strongly desired to unveil the nature of Fermi arc, which is tied to the pairing mechanism of cuprates.Recently, a contrasting view was proposed918Tc20The determination of the momentum-resolved gap structure has been also attempted by STM studies through the spectral line-shape analysis212727hν=7 eV) enabled us to obtain high-quality spectra with an extremely sharp line shape. We demonstrate, within the quasiparticle picture, the absence of the gapless Fermi arc at Tc, and an isotropic temperature evolution of point nodal pairing state persistent far above Tc. We find that not only the single-particle scattering rate (Γsingle), but also the pair-breaking rate (Γpair) is required to reproduce the ARPES spectra. Furthermore, the magnitude of Tc is determined by the mutual relation between Γsingle and Γpair in the form of Γsingle(Tc)=Γpair(Tc). Importantly, the momentum-integrated spectra of ARPES and STM previously investigated are not capable of separating these two quantities (Γsingle and Γpair) (see Here we examine the momentum-resolved single-particle spectra of Bi2212 obtained by a laser ARPESair) see ; thus, tTc6151620kF) over a wide range of temperature in ɛpeak) in ɛpeak of energy distribution curves (EDCs) symmetrized about the Fermi energy (EF) to remove the effect of Fermi cutoffTc (=92 K) (see green spectra in ɛpeak(T) disagrees with the BCS gap evolution  still does not fit to the data.In ɛpeak(T) for the optimally and overdoped samples (OP92K and OD72K) in Tc regardless of kF points. The symmetrized EDCs around the node for OP92K are plotted in T=10 K) and T=Tc). We find that the d-wave gap with a point node persists at Tc  is not linearly extrapolated to zero at T=0 against the nodal liquid behaviour  to the maximum value at the lowest temperature in the bottom panels of ɛpeak(T) behaviour with a steep drop to zero becomes more gradual with getting away from the node, and it eventually follows a BCS-type gap function (green curves) with an onset much higher than Tc .For a further examination, we normalize each curve of Tc, here we investigate another spectral measure, so-called leading edge of EDC, which is also commonly used for a gap estimation. ɛLE), at which the spectral intensity becomes half , is plotted in T-linear behaviour, which is expected for the spectra dominated by the Fermi cutoff effect. While the nodal ɛLE(T) could have a complex behaviourɛLE(T) from the T-linear behaviour. Such a deviation is indeed observed for all the k points off the node (ɛLE(T) from the T-linear behaviour is extracted. An astonishing result we found is that the onset temperatures are almost the same (∼135 K) regardless of the directions (φ), which validates that the point nodal state persists up to ∼135 K.To clarify the anomalous feature above the node . It is mɛpeak<Δ)931Tc (ɛpeak(T) in T) having the same onset temperature at ∼135 K and ∼89 K, respectively, for all directions (φ).Importantly, the gap opening temperature is coincident with the onset of the BCS-type gap function obtained with the symmetrized EDCs far off the node (a green curve in <Δ)931Tc ; the speπA=Σ′′/[(ω−Σ′)2+Σ′′2], with such a BCS-type Δ indeed reproduces the ARPES spectra, whereas the traditionally used assumption of Δ≡ɛpeak is invalid. The self-energy (Σ=Σ′+iΣ′′) we use has a minimal representation with two different scattering rates, Γ0 and Γ1 . For clarity, we label the former Γsingle and the latter Γpair in the rest of this paper. We emphasize that the intensity at EF in a gapped spectrum becomes non-zero only when Γpair≠0 as simulated in T≪Tc) have a negligible intensity at EF, which ensures that our data are almost free from impurity-causing pair-breaking effect. At elevated temperatures, we observe a remarkable gap filling , we can rule out the possibility, assumed before with setting Γpair≡0  and Γpair (or Γ0) to be independent free parameters in T)≡ɛpeak(T), which is a traditional way of gap estimation (single(T)  has an energy gap (Δ≠0); thus, the spectral width overestimates the scattering rate.Following this consideration, we set Γtimation . The obtφ. In the φ=13.5° for OP92K is shown in single(T) (single(T) at the node, which can be determined simply from the spectral width. Similarly, the Γpair(T) curves are also almost identical for all the φ. The consistency in our results pointing to the isotropic scattering mechanism validates our model spectral function characterized by the BCS-type Δ. The famous ‘hot spots', at which the scattering rate is abruptly enhanced, should be situated at much higher φ (2536Tpair) of OP92K and OD72K, respectively. This is further supported by the signature of pairing seen in the behaviour of Γsingle(T) 39Tc is compatible in these observations. The doping variation of Tpair/Tc  obtained in our studies is consistent with the phase-fluctuating superconductivity, which merges to the superconducting dome with heavily overdopingTc even in the overdoped sample.We find that this circumstance is corrected by applying a BCS-type gap function with an onset at 135 and 89 K for OP92K and OD72K (green curves in the bottom panels of ingle(T)  in the ghigher φ . The appingle(T) ; the decpair and Γsingle should provide rich information relevant for the pairing mechanism. Intriguingly, the superconductivity occurs when the magnitude of Γpair is reduced smaller than that of Γsingle; the Tc is coincident with the temperature at which Γsingle(T) and Γpair(T) crosses (magenta circles in single(Tc)=Γpair(Tc). The magnitude of Tpair is reported to be comparable (120∼150 K) among different cuprate families with significantly different Tcssingle(T) also seems to be less sensitive to the different compounds43pair<Γsingle, is predicted to be a critical factor determining the Tc value of cuprates. Notably, a remarkable difference in filling behaviours of the spectral gap is indeed observed between Bi2212 and Bi2Sr2CuOδ6+ with about three times different Tcs9The relationship between ΓTc, against the previous expectation1516172021Tpair . The ARPRS spectra are reproduced by the spectral function with a minimal model, which has a single energy gap all the way up to the gap closing temperature. It is consistent with the expected ‘pure' pairing state with no contamination by the pseudogap around the node at least in the optimally and overdosed regions. While the gap evolution with an onset at Tpair might be reminiscent of a phase-transition phenomenon, it is against a gradual temperature variation of the specific heatc. To fully understand the present results, insight of the spacially inhomogeneous stateEF with temperature1Tc from Tpair. To evaluate this speculation, however, the more detailed theoretical inputs are required.We summarize our conclusion in 2Sr2CaCu2Oδ8+ (OP92 K) and overdoped 2Sr2CaCu2Oδ8+ (OD72 K) single crystals with Tc=92 and 72 K, respectively, were grown by the conventional floating-zone technique. A sharp superconducting transition width of ∼1 K (OP92K) and ∼3 K (OD72K) were confirmed .Supplementary Figures 1-17, Supplementary Notes 1-9 and Supplementary References


The mechanical function of soft collagenous tissues is largely determined by their hierarchical organization of collagen molecules. While collagen fibrils are believed to be discontinuous and transfer load through shearing of the interfibrillar matrix, interfibrillar shear stresses have never been quantified. Scaling traditional shear testing procedures down to the fibrillar length scale is impractical and would introduce substantial artifacts. Here, through the use of a novel microscopic variation of notch tension testing, we explicitly demonstrate the existence of interfibrillar shear stresses within tendon fascicles and provide the first measurement of their magnitude. Axial stress gradients along the sample length generated by notch tension testing were measured and used to calculate a value of 32 kPa for the interfibrillar shear stress. This estimate is comparable to the interfibrillar shear stress predicted by previous multiscale modeling of tendon fascicles, which supports the hypothesis that fibrils are discontinuous and transmit load through interfibrillar shear. This information regarding the structure-function relationships of tendon and other soft collagenous tissues is necessary to identify potential causes for tissue impairment with degeneration and provide the foundation for developing regenerative repair strategies or engineering biomaterials for tissue replacement. Soft collagenous tissues  are primarily composed of collagen fibrils, which consist of a semi-crystalline organization of type I collagen molecules connected through naturally occurring inter-molecular crosslinks125679Notch tension testing, an approach typically used to evaluate crack propagation and fracture toughnessyy) under the microscope at multiple locations along the sample length. At a grip-to-grip strain of 8%, the measured axial strain field matches that predicted by a separate finite element analysis  gelatin gel containing a semi-circular notch  on a cusanalysis , which danalysis . Furtherσxy) and axial stress gradient along the sample length (dσyy /dy) is described by the axial force equilibrium equation . In the absence of shear stress (dσxy /dx = 0), the axial stress (and strain) distribution will not change with distance from the notch  (dεyy /dy ≠ 0), demonstrating that non-zero shear stresses exist within the material. Therefore, by measuring the change in the axial stress with distance from the notch (dσyy /dy), we can determine whether shear stresses are generated within a tissue or biomaterial. Furthermore, as we will show for tendon fascicles, the magnitude of the axial stress gradient along the sample length produced by notch tension testing can be used to estimate the value of the interfibrillar shear stress acting within an aligned soft collagenous tissue.These changes in the axial strain (and hence stress) distributions in the linear elastic isotropic gel are a classic feature of notch tension testing and are produced by shear stresses that transmit load from the uncut to the cut side of the sample. This relationship between the shear stress (/dy = 0) . Howeveryy) on the uncut side  demonstrates the existence of strain gradients across the fascicle width  or shear strain (εxy) of the interfibrillar matrix can be neglected, which is common for tendon and other soft collagenous tissues16In order to estimate the magnitude of the shear stresses, we converting the averaged axial strains to stresses using empirical non-linear stress-strain data collected from previous testing of intact tendon fascicles 15 and quThere is evidence to suggest that the shear stress value calculated above is representative of the interfibrillar shear stress produced by relative sliding of fibrils and shearing of the interfibrillar matrix. Prior to the discontinuity initiation and propagation, the photobleached lines were continuous down to the limiting resolution of the microscope . This su−8). These data are consistent with previous X-ray diffraction dataTo verify this assumption and confirm that the axial stress gradient was indeed due to interfibrillar shear stress, we tracked the course of 1,213 individual fibrils by serially imaging cross-sections of a tendon fascicle over a length of 8.7 μm using serial block-face scanning electron microscopyfascicular matrix protects against tendon rupture due to failure of individual fasciclesIn this study, we used microscale notch tension testing to make the first explicit demonstration and measurement of interfibrillar shear stresses within a soft collagenous tissue. We found that interfibrillar shear stresses in rat tail tendon fascicles reach approximately 32 kPa prior to failure at the cut/uncut tissue interface. This value is comparable to that predicted by shear lag modeling of the same tissue921A limitation to the techniques described in this study is that the calculation of the interfibrillar shear stress is limited to soft collagenous tissues with highly aligned fibrils. While notch tension testing will still produce shear stresses in less organized tissues, these shear stresses will result from rotation and realignment of the collagen fibrils as well as from interfibrillar shear. Additionally, it was necessary to assume that only the fibril strains contribute to the axial stress within the fascicle in order to convert the measured axial strains into stress values. While this is acceptable for tendon16We chose not to use a constitutive model and instead used a simplified analysis involving a finite difference approximation based on the equations of equilibrium see  for a co5See A 20% (w/v) gelatin gel was crosslinked with 0.05% glutaraldehyde in phosphate buffered saline (PBS) in order to prevent swelling and stabilize the mechanical propertiesPrior to testing, a 1 mN preload was applied to define the reference length (33.0 mm). Sets of four lines were photobleached onto the gel surface at 0, 0.4, 0.8, 1.2, 2.0, and 4.0 mm from the notch midline. Grip-to-grip strains were applied to the gel in 4% strain increments at 0.05%/s and held for 5 min before imaging the photobleached lines at each location. This was repeated to a total grip-to-grip strain of 20%. The applied load was continuously recorded with a 10 N load cell .Data analysis. A custom Matlab algorithm was used to find the pixel locations of the photobleached lines in each image at all locations. Axial strains (εyy) were calculated as the change in the distance between line pairs compared to their positions at 0% applied strain. The Young’s modulus of the gel (E = 585 kPa) was determined by performing a least-squares fit of the line σ = Eε, where σ is the applied stress and ε is the average axial strain at the 4 mm location measured for each grip-to-grip strain increment (R2 = 0.993). Note that 4 mm was suitably far-field from the notch so that the axial strains at this location were uniform ( uniform .The finite element model was constructed within SolidWorks (Dassault Systemes) with the same geometry as the imaging area of the physical gel sample and composed of triangular two-dimensional shell elements. A fixed constraint was applied at a distance 5 mm from the notch and a 0.4 mm displacement was applied to the notch midline, simulating an applied tensile strain of 8%. The material was defined as isotropic, linear elastic, and incompressible with a Young’s modulus of 585 kPa. The resulting axial strain field was compared graphically to the experimental measurements taken at a grip-to-grip strain of 8%.Eight fascicles were harvested from five tails of 7-month-old Sprague-Dawley rats sacrificed in accordance with IACUC approval and relevant guidelines. Each fascicle was cut to a length of 45 mm and fluorescently stained with 10 μg/ml of 5-aminofluorescein. Previous testing of intact samples demonstrated that staining at this concentration has a minimal effect on tendon fascicle mechanicsyy) were calculated as described for the gel construct.A 1 mN preload (~5 kPa) was applied to the tissue to define the reference length (31.9 ± 0.1 mm). The sample was preconditioned and then partially transected with a scalpel blade 8.7 ± 0.3 mm from either the left or right grip producing a sharp notch extending 48 ± 13% across the sample width. The notch was placed near each grip for an equal number of samples to ensure that the measured strain gradients were due to the presence of the notch and not gripping artifacts. Sets of four lines were photobleached onto the tissue surface at 0, 4, 8, and 12 mm from the notch. Grip-to-grip strains were then applied in 1% strain increments at 0.05%/s and held for 5 min before capturing image stacks (0.82 × 0.82 × 3.7 μm/pixel) of the photobleached lines at each location. This was repeated to a total grip-to-grip strain of 8%. Image stacks (80–100 images spanning 300–350 μm) were obtained since the curved surface of the fascicles meant that no single focal plane contained an image spanning the full tissue width. After testing, the microscale image stacks were flattened to a single image of the full tissue width using a custom Matlab algorithm see . Using t∂σyy /∂y + ∂σxy /∂x = 0, an estimate for the interfibrillar shear stress (σxy) was calculated from the axial stress gradient (∂σyy /∂y) on the uncut side of the fascicle. The boundary of the uncut side was determined as the x-position of the initial discontinuity within the photobleached lines at each imaging location  were computed using the axial force balance σxy Ax = Δσyy Ay, where Δσyy is the decrease in axial stress between the 4 mm and 8 mm locations or the 8 mm and 12 mm locations at each grip-to-grip strain, Ax is the interfacial area between the cut and uncut sides, and Ay is the average uncut cross-sectional area . The raw images were processed using FijiOne fascicle was harvested from the tail of a 7-month-old Sprague-Dawley rat and cut into segments approximately 10 mm long. According to a protocol specifically developed for tracking collagen fibrils in tendon using serial block-face scanning electron microscopy (SBF-SEM)How to cite this article: Szczesny, S. E. et al. Quantification of Interfibrillar Shear Stress in Aligned Soft Collagenous Tissues via Notch Tension Testing. Sci. Rep. 5, 14649; doi: 10.1038/srep14649 (2015).