Therefore, we aimed to determine how α- and β-adrenoceptor (AR)-mediated haemodynamic responses are affected by isoflurane anaesthesia in experimental type 2 diabetes and obesity n = 7-9 per group) were instrumented with radio telemeters to record blood pressure and heart rate and with vascular access ports for non-invasive intravenous drug delivery in vivo. Haemodynamic effects of α-AR  or β-AR  stimulation were assessed under conscious and anaesthetised  conditions.Sixteen-week old male Zucker type 2 Diabetic Fatty (ZDF) rats, Zucker Obese rats and their lean counterparts  and obese  conscious rats. Interestingly, anaesthesia exacerbated and prolonged the increased α-AR function in both diabetic and obese animals . Meanwhile, β-AR chronotropic sensitivity was reduced in conscious diabetic and obese rats . Anaesthesia normalised chronotropic β-AR responses, via either a limited reduction in obese  or increased responses in diabetic animals .Vascular α-AR sensitivity was increased in both diabetic (non-diabetic 80 ± 3 vs. diabetic 95 ± 4 ΔmmHg at 100 μg.kgLong term metabolic stress, such as during type 2 diabetes and obesity, alters α- and β-AR function, its dynamics and the interaction with isoflurane anaesthesia. During anaesthesia, enhanced α-AR sensitivity and normalised β-AR function may impair cardiovascular function in experimental type 2 diabetes and obesity. The rapid expansion of the type 2 diabetes and obesity co-epidemics impacts heavily on cardiovascular health. One clinically important, but often overlooked, cardiovascular consequence is that diabetic and obese patients have increased requirements for surgical treatments. Following surgery they have longer hospital stays and poorer survival compared to non-diabetic and lean patients -3. Imporex vivo studies demonstrated decreased β-AR expression in [ex vivo studies or studies in anaesthetised rats variably reporting unchanged [Long-term changes in metabolism, such as during the metabolic syndrome , are chassion in -14 and rssion in  the hearssion in -20. Lessnchanged ,21, impanchanged ,23 or ennchanged ,25 α-AR et al. [in vivo, nor examine changes in type 2 diabetes. Furthermore, the lack of in vivo data under conscious conditions, limits the interpretation of anaesthetic effects on α- and β-AR function.While the long-term metabolic stress of diabetes and obesity leads to haemodynamic dysregulation ,26, cardet al.  showed iin vivo. To assess the direct effects of anaesthesia we measured haemodynamic responses in free-moving conscious and in isoflurane anaesthetised type 2 diabetic (Zucker Diabetic Fatty (ZDF)) rats following α- and β-AR stimulation. To this end, rats were implanted with a radio telemetric transmitter and a vascular access port to measure in vivo abdominal aortic blood pressure and inject intravenous drugs, respectively [Therefore, the present study aimed to assess how isoflurane anaesthesia affects the α- and β-AR-mediated haemodynamic responses in type 2 diabetes ectively . These mAll procedures were approved by the University of Otago Animal Ethics Committee and were conducted in accordance with the New Zealand Animal Welfare Act (1999). Zucker Diabetic Fatty (ZDF) rats are derived from a selected subset of the Zucker strain, which spontaneously develop diabetes from 12 weeks of age due to impaired pancreatic beta-cell function . Zucker N = 39; Charles River Laboratories, Wilmington, MA, USA) were housed at 20 ± 1°C under a 12 hour light–dark cycle and provided with food and water ad libitum. All ZDF animals were maintained on Purina 5008 diet  as recommended by the supplier, while Zucker rats were fed chow . Animals were gentled daily for one week prior to surgery  and antibiotic  were administered subcutaneously.Dual implantation of a radio telemeter and vascular access port was performed on 16-week old animals under 2–2.5% isoflurane anaesthesia  as previously described  with str−1; Hospira Australia, Mulgrave, Australia). The VAP reservoir was secured on the back of the animal between the scapulae, with the VAP cannula tunnelled subcutaneously to the femoral vein. A radio telemeter with pressure sensitive tip  was implanted into the abdominal aorta. Animals were allowed one-week post-surgical recovery before experimentation commenced  at minimum twice-weekly to maintain patency.Vascular Access Ports  were primed with heparin sodium  was administered at the beginning of each experimental session, as used previously to confirm VAP patency over the course of the study [−1) and β-adrenergic agonist dobutamine (2-120 μg.kg−1) were administered at five or ten minute intervals, respectively  to prevent coagulation. All chemicals were from Sigma-Aldrich  and diluted in saline  unless otherwise stated.Haemodynamic measures were equilibrated for 15 minutes following restraint and needle insertion. The nitric oxide donor sodium nitroprusside .Blood pressure data was derived from the telemeter according to the manufacturer’s instructions, and acquired using LabChart® 7 software . Heart rate (HR) and mean arterial pressure (MAP) were derived from blood pressure recordings using the LabChart® blood pressure module, and averaged over every ten consecutive cycles. Basal haemodynamic data for an individual animal were averaged over up to four conscious replicates and up to two replicate anaesthetised measures. Haemodynamic responses were assessed as the calculated change between the peak response to and the baseline immediately preceding each individual bolus injection. Time course dynamics were assessed over 5 second averages. Statistical analysis was performed for baseline characteristics via t-test, or Mann–Whitney rank sums test where the assumptions were not met; or via two-way repeated measures ANOVA for all haemodynamic data. Differences between groups were identified using Student-Newman-Keuls post-hoc analysis  and significance assumed at the level of Type 2 diabetic rats exhibited body weights 25% higher than their non-diabetic littermates Table . This waBaseline haemodynamics were assessed under conscious resting conditions or following stabilisation of 2% isoflurane anaesthesia Table . Type 2 −1.min−1 [in vivo.Administration of phenylephrine (PE), an α-AR agonist, primarily elicited a rapid, transient increase in MAP in a dose-dependent manner Figure . Conscio−1.min−1 . Under a−1 vs. non-diabetic −3.0 ± 0.3 bpm.mmHg−1 at 100 μg.kg−1; p < 0.05). Anaesthesia markedly reduced the baroreflex-mediated bradycardia in all animals, eliminating the between group differences.Secondary to the changes in MAP, PE elicited a dose-dependent reduction in HR Figure c and d. −1). This dose is within the therapeutic range of approximately 2-20 ug.kg−1.min−1 [−1 dobutamine in healthy human volunteers [in vivo.Administration of dobutamine, a non-specific β-AR agonist, primarily elicited a dose-dependent increase in HR in both non-diabetic and type 2 diabetic animals under all conditions Figure . Conscio−1.min−1 , making lunteers ; indicat2-ARs in the vasculature . Conscious obese rats also showed a trend toward reduced maximal bradycardia , similar to that seen in type 2 diabetic animals. Baroreflex-mediated bradycardia was generally reduced during anaesthesia  similar to type 2 diabetic rats. Isoflurane anaesthesia significantly reduced the maximal β-AR-mediated chronotropic response in both groups . However, during anaesthesia the time to peak response was significantly prolonged in control animals compared to their diseased littermates , despite similar peak values . Isoflurane non-selectively slowed this HR recovery time to plateau. Therefore, alterations in the dynamics of β-AR function in type 2 diabetes and obesity, particularly during anaesthesia, may be reflected more by a briefer, rather than smaller, response.The time taken to reach peak β-AR HR response was similar in all conscious animals  and dobutamine (15 μg.kg−1). Conscious type 2 diabetic and obese rats exhibited significantly increased α-adrenergic and reduced β-adrenergic sensitivity. Isoflurane anaesthesia decreased α-adrenergic responsiveness in non-diabetic but not in type 2 diabetic animals, while it increased β-adrenergic responses in type 2 diabetic rats with no effect on control responses  and obese models . Alternatively, some studies reported unchanged ,21 or rein vivo preparations [in vivo under conscious conditions.The reduced cardiac β-AR sensitivity observed aligns with and extends literature reports. During the metabolically compromised state of diabetes, it is suggested that the sympathetic drive to the heart is increased ,7, eventarations  of streparations . Similararations ,20 and aarations  obese ro1-AR expression has been described in various models of the metabolic syndrome [1-AR variability is proposed to be attributable to disease duration [1-ARs was shown in myocardium of type 1 diabetic rodent models [1-AR expression in right atrial tissue from type 2 diabetic patients [et al. [While the mechanisms underlying the altered AR function are poorly understood, and determination was not the aim of this study, changes in AR expression have been implicated. Elevated cardiovascular αsyndrome -48, althsyndrome . This α1duration ,49, withduration . Decreast models ,13,50. Hpatients . Similar [et al.  found un [et al. . Thus, fin vivo techniques, confirms the relevance of these α- and β-AR-dysfunctions in type 2 diabetes and obesity under physiological conditions and provides valuable new insights. Additionally, the paucity of suitable data in conscious animals has made it difficult to elucidate the effects of anaesthetics per se, and few investigations have addressed this issue. Amour et al. [in vivo investigations, including neural, hormonal and vascular feedbacks, which are most likely geared to compensate for excessive fluctuations in the cardiovascular system.Much of the previous experimental evidence for α- and β-AR-dysfunction has been derived from models of type 1 diabetes, and conducted in anaesthetised or isolated heart or vessel preparations. Therefore, this study, using improved conscious r et al.  showed iIt is unclear how defects exclusively at the α- and β-ARs themselves would directly interact with anaesthesia. Likewise, simple interruption of central autonomic signalling by anaesthetics would be unlikely to selectively interact with α-AR function. The phenylephrine-generated baroreflex-induced changes in HR were overall markedly depressed under isoflurane. Thus, it could be speculated that isoflurane prevents appropriate central control of sympathetic withdrawal during MAP elevation in the vasculature causing an anaesthetic-mediated exacerbation of α-AR sensitisation in type 2 diabetic and obese rats.By utilising models of type 2 diabetes and obesity with a common underlying defect in leptin signalling, we were able to directly address the influence of hyperglycaemia. The observed alterations in α- and β-AR function were broadly similar between type 2 diabetic and obese rats. Thus, these impairments are likely to be a function of the general metabolic syndrome components of overweight and insulin resistance, rather than the hyperglycaemic phenotype of diabetes; in agreement with previous findings that α- and β-AR dysfunction is not tied to the development of type 2 diabetes . FurtherRegardless of the cause of exacerbated metabolic α- and β-AR dysfunction, differences in α- and β-AR responsiveness (in magnitude and duration) remain an important consideration in this large patient group. During chronic metabolic stress, such as obesity and type 2 diabetes, sympathetic drive to the heart is suggested to be increased ,7; whichin vivo. Under conscious physiological conditions, type 2 diabetic and obese rats exhibited increased α-AR and decreased β-AR responses. Meanwhile, during anaesthesia, enhanced α-AR sensitivity and normalised β-AR function may further impair cardiovascular function in type 2 diabetes and obesity.In summary, this study is the first to determine the haemodynamic consequences of altered α- and β-AR function in conscious type 2 diabetic and obese animals, and the interaction between adrenergic dysfunction and isoflurane anaesthesia


Recent years have provided deeper mechanistic insights into compartmentalized cAMP signaling and its link to cardiac disease. In this mini review, we summarize newest developments in this field achieved by cutting-edge biochemical and biophysical techniques. We further compile the data from different studies into a bigger picture of so far uncovered alterations in cardiomyocyte cAMP microdomains which occur in compensated cardiac hypertrophy and chronic heart failure. Finally, future research directions and translational perspectives are briefly discussed. Stimulation of cardiac contractility by catecholamines and their receptors, in particular β-adrenoceptors (β-ARs) which are central to the well-established physiological fight-or-flight response, leads to generation of cAMP that acts in distinct subcellular microdomains . Such miIn healthy cells, cAMP microdomains are supposed to provide specificity of A-kinase (PKA) substrate phosphorylation at different functionally relevant locations. In terms of contractility, several cAMP microdomains exist around calcium handling proteins such as L-type calcium channels (LTCCs), ryanodine receptors (RyRs), and phospholamban (PLN) which regulates the activity of the cardiac sarcoplasmic/endoplasmic reticulum (SR) calcium ATPase 2a SERCA2a; . Each of1- and β2-AR-cAMP signals, the former having more diffuse far-reaching and the latter highly confined nature (Advent of fluorescence resonance energy transfer (FRET) based biosensors enabled a real-time monitoring of cAMP in intact cells . Very ead nature .1-AR is localized across the whole membrane, while, in contrast, β2-AR is located exclusively in the T-tubules of healthy cells  combined with FRET. SICM is a non-optical imaging technique which utilizes an electrolyte-filled glass nanopipette as a scanning probe fixed on a three-axis piezo-actuator stage . The curhy cells . Moreoveodomains  to produodomains .2-ARs. Together with a local PDE, caveolin is thereby involved in compartmentation of β2-AR-cAMP signals in this microdomain. In contrast, AC6 associated the β1-AR is localized outside the T-tubules and is responsible for β1-AR-mediated augmentation of LTCC current. Interestingly, yet another functional population of β1-ARs is targeted to T-tubules and the AC5-PDE signalosome , with the most predominantly expressed cardiac AC5 and AC6, can center cAMP signalosomes in myocytes and other cells . A recennalosome .2-AR  where it should localize in close proximity to LTCC and β2-AR . This ne3, and 2 . Second,3, and 2 . Here, h3, and 2 , a pheno3, and 2 . However1-AR or guanylyl cyclase A  desensitization can be detected. Instead, there was a subcellular relocation of PDE2 between β1- and β2-AR, and local decrease of the major PDE3-mediated control at the β2-AR , not much is known about changes in local cAMP signaling in early compensated cardiac hypertrophy. To address this question, pmEpac1-camps and Epac1-camps-PLN mice were subjected to transverse aortic constriction which induces only a mild compensated phenotype in the FVB/N1 mouse background. Interestingly, in this case, no changes in total whole-cell PDE activities and no βR Figure . This letraction . This mi1-AR to SERCA2a (Figure The study using cAMP biosensor targeted to SERCA2a demonstrated that cardiac hypertrophy leads to local decrease of PDE3 and PDE4 effects which confine this microdomain from the bulk cytosol. Furthermore, it causes changes in PDE composition at various subcellular locations in a way that leads to impairment of the above described PDE3/4-dependent “channeling” of cAMP from βa Figure . In the a Figure . Future 1-AR, GC-A, ACs, SERCA2a, and impairment of PKA-dependent phosphorylation of major contractile substrates (2-AR to detubulated areas where it gets uncoupled from its microdomain and generates far-reaching cAMP signals (In human and rodent failing myocytes, a series of well-established signaling alterations occurs, including desensitization/downregulation of βbstrates . Structubstrates . The whobstrates  or upregbstrates . Loss of signals . Altered signals .Better understanding of cAMP dynamics in various functionally relevant microdomains and especially of their changes in disease should ultimately provide more precise ways of therapeutic correction. To improve cAMP or cGMP flow in the microdomains, one can imagine approaches aimed at depletion of specific PDEs or PKA from desired signalosomes. More specific PDE inhibition and treatments aimed at improvement of membrane structure, receptor localization and protein composition of the microdomains can also be considered. These developments should enable more targeted and specific cardiac therapeutics.AF and VN discussed the concept, wrote and edited the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


We investigate the steerability of two-qubit Bell-diagonal states under projective measurements by the steering party. In the simplest nontrivial scenario of two projective measurements, we solve this problem completely by virtue of the connection between the steering problem and the joint-measurement problem. A necessary and sufficient criterion is derived together with a simple geometrical interpretation. Our study shows that a Bell-diagonal state is steerable by two projective measurements iff it violates the Clauser-Horne-Shimony-Holt (CHSH) inequality, in sharp contrast with the strict hierarchy expected between steering and Bell nonlocality. We also introduce a steering measure and clarify its connections with concurrence and the volume of the steering ellipsoid. In particular, we determine the maximal concurrence and ellipsoid volume of Bell-diagonal states that are not steerable by two projective measurements. Finally, we explore the steerability of Bell-diagonal states under three projective measurements. A simple sufficient criterion is derived, which can detect the steerability of many states that are not steerable by two projective measurements. Our study offers valuable insight on steering of Bell-diagonal states as well as the connections between entanglement, steering, and Bell nonlocality. One approach for detecting steering is to prove the impossibility of constructing any non-steering model3910111213111213820Despite these fruitful achievements, steering detection and quantification have remained challenging tasks, and many basic questions are poorly understood. For example, no conclusive criterion is known for determining the steerability of generic two-qubit states except for Werner states32223In this work, we investigate the steerability of two-qubit Bell-diagonal states under projective measurements by the steering party. These states are appealing to both theoretical and experimental studies since they have a relatively simple structure and are particularly suitable for illustrating ideas and cultivating intuition. In addition, generic two-qubit states can be turned into Bell-diagonal states by invertible stochastic local operation and classical communication (SLOCC)We first consider the steerability of Bell-diagonal states under the simplest nontrivial measurement setting on the steering party, that is, two projective measurements. We solve this problem completely by virtue of the connection between the steering problem and the joint-measurement problem142627293432Finally, we explore the steerability of Bell-diagonal states under three projective measurements. Although such problems are generally very difficult to address, we derive a nontrivial sufficient criterion, which also has a simple geometrical interpretation. This criterion can detect the steerability of many states that are not steerable by two projective measurements. The relation between entanglement and steering in this scenario is also clarified.ρ with reduced states ρA and ρB for the two parties, respectively. Alice can perform a collection of local measurements as characterized by a collection of positive-operator-valued measures (POVMs) x labels the POVM and a labels the outcome in each POVM. Recall that a POVM measurement assemblage. If Alice performs the measurement x and obtains the outcome a, then Bob’s subnormalized reduced state is given by x is an ensemble for ρB, and the whole collection of ensembles state assemblageConsider two remote parties, Alice and Bob, who share a bipartite quantum state unsteerable if there exists a local hidden state (LHS) model34142627The state assemblage λ are a collection of subnormalized states that sum up to ρB and thus form an ensemble for ρB. This model means that Bob can interpret his conditional states λ, where only the probabilities are changed due to the knowledge of Alice’s measurements and outcomes.where compatible or jointly measurable26272834The steering problem is closely related to the joint-measurement problem. A measurement assemblage Physically, this means that all the measurements in the assemblage can be measured jointly by performing the measurement ρB is of full rank, the state assemblage When x forms a POVM, which is referred to as Bob’s steering-equivalent observable (or POVM)Note that the set of operators Any two-qubit state can be written in the following formσj for j = 1, 2, 3 are three Pauli matrices, σ is the vector composed of these Pauli matrices, a and b are the Bloch vectors associated with the reduced states of Alice and Bob, respectively, and a = b = 0 where with two completely mixed marginals, that is, T in (5) can be turned into diagonal form, so thatWith a suitable local unitary transformation, the correlation matrix As an implication of this observation, a Bell-diagonal state is steerable by one party iff it is steerable by the other party, so there is no one-way steeringIn the case of a qubit, any projective measurement T induces a map from projective measurements of Alice to noisy projective measurements of Bob. Alice can steer Bob’s system using the measurement assemblage Note that this observable is uniquely characterized by the subnormalized vector T, note that the end point of To see the geometric meaning of the map induced by In this section we derive a necessary and sufficient criterion on the steerability of a Bell-diagonal state under two projective measurements. We also introduce a steering measure and illustrate its geometrical meaning. Our study shows that a Bell-diagonal state is steerable by two projective measurements iff it violates the CHSH inequality. Furthermore, we clarify the relations between entanglement, steering, and Bell nonlocality by deriving tight inequalities between the following three measures: the concurrence, the steering measure, and the volume of the steering ellipsoid.Theorem 1. A Bell-diagonal state with correlation matrix T is steerable by two projective measurements iffwhereare the two largest eigenvalues ofProof. Suppose Alice performs two projective measurements Note that c and c and where c and c and The choices of S is attained when S introduced here. This observation has an important implication for the relation between steering and Bell nonlocality.The proof of Theorem 1 also suggests a steering measure of a Bell-diagonal state under two projective measurements, namely, Corollary 1.  A Bell-diagonal state is steerable by two projective measurements iff it violates the CHSH inequality.S, it is convenient to choose a concrete Bell basis. Here we shall adopt the following choiceTo clarify the geometric meaning of Theorem 1 and the steering measure Note that S/2 of this Bell-diagonal state is equal to the maximum over S is convex in Geometrically, the set of Bell-diagonal states forms a regular tetrahedron, whose vertices correspond to the four Bell states3636S, and the volume of the steering ellipsoid. Since S is equal to the maximal violation of the CHSH inequality, our discussion is also of interest to studying Bell nonlocality.In the rest of this section we clarify the relations between the following three measures: the concurrence, the steering measure T, the normalized volume V of the steering ellipsoid is defined as T is diagonal, say Recall that a two-qubit state is entangled iff it has nonzero concurrence and that the concurrence of a Bell-diagonal state is given by Calculation shows that Here the lower bound in (12) is applicable to entangled Bell-diagonal states, while the other five bounds in (12), (13), and (14) are applicable to all Bell-diagonal states. The inequality Two types of Bell-diagonal states deserve special attention as they saturate certain inequalities in (12), (13), and (14). A Werner state has the formf is equal to the singlet fraction when where The Werner state is steerable by two projective measurements iff edge states . If an edge state has two nonzero eigenvalues p and Those states lying on an edge of the tetrahedron in The edge state is steerable by two projective measurements whenever C, S, V. When the concurrence C is large, the three measures are closely correlated to each other, while they tend to be more independent in the opposite scenario. Quite surprisingly, the normalized volume V of the steering ellipsoid seems to have a closer relation with concurrence C rather than the steering measure S. In addition, for given concurrence C > 0, the volume V attains the maximum when the steering measure S attains the minimum, and vice versa.In this section we explore the steerability of Bell-diagonal states under three projective measurements by the steering party. To this end, we need a criterion for determining the compatibility of three unbiased noisy projective measurements. Fortunately, this problem has been solved in refs Here T, suppose Alice performs three projective measurements Given a Bell-diagonal state with correlation matrix as a steering measure of the Bell-diagonal state under three projective measurements, where When which imply thatTheorem 2.Any Bell-diagonal state withis steerable by three projective measurements, whereis the Frobenius norm of the correlation matrixProof. Let If the Bell-diagonal state is not steerable by three projective measurements, then The Frobenius norm C, V can be derived with similar methods used in deriving (12) and (14), with the resultsThe relations between Here the lower bound in (23) is applicable to entangled Bell-diagonal states, while the other three bounds are applicable to all Bell-diagonal states. As in (12) and (14), the two lower bounds are saturated by Werner states, while the two upper bounds are saturated by edge states; see In summary, we studied systematically the steerability of Bell-diagonal states by projective measurements on the steering party. In the simplest nontrivial scenario of two projective measurements, we solved the problem completely by deriving a necessary and sufficient criterion, which has a simple geometrical interpretation. We also introduced a steering measure and proved that it is equal to the maximal violation of the CHSH inequality. This conclusion implies that a Bell-diagonal state is steerable by two projective measurements iff it violates the CHSH inequality. In the special case of edge states, our study shows that entanglement is sufficient to guarantee steering and Bell nonlocality. In addition, we clarified the relations between entanglement and steering by deriving tight inequalities satisfied by the concurrence, our steering measure, and the volume of the steering ellipsoid. Finally, we explored the steerability of Bell-diagonal states under three projective measurements. A simple sufficient criterion was derived, which can detect the steerability of many states that are not steerable by two projective measurements.Our study provided a number of instructive analytical results on steering, which are quite rare in the literature. These results not only furnish a simple geometric picture about steering of Bell-diagonal states, but also offer valuable insight on the relations between entanglement, steering, and Bell nonlocality. They may serve as a starting point for exploring more complicated steering scenarios. In addition, our work prompts several interesting questions, which deserve further studies. For example, is the steering criterion in Theorem 2 both necessary and sufficient? Is there any upper bound on the number of measurements that are sufficient to induce steering for all steerable Bell-diagonal states? We hope that these questions will stimulate further progress on the study of steering.C, the steering measure S (under two projective measurements), and the volume V of the steering ellipsoid. We also determine those Bell-diagonal states that saturate these inequalities. Similar approach can be applied to derive (23) and (24), which are pertinent to steering of Bell-diagonal states by three projective measurements.Here we derive the inequalities in (12), (13), and (14) in the main text, which characterize the relations between the concurrence ρ has the form in (6) with ρ is given byWithout loss of generality, we may assume that where the eigenvalues are arranged in nondecreasing order. The minimal and the maximal eigenvalues are respectively given by If the Bell-diagonal state is separable, that is ρ is an edge state with two nonzero eigenvalues equal to 1/2. The inequality ρ is a Werner state which either has singlet fraction 1/2 or is proportional to a projector of rank 3. Here states that are equivalent to S and V and is applicable to both separable and entangled states. It is saturated iff ρ is a Werner state.So the inequalities ρ and the requirement If the Bell-diagonal state is entangled, then These inequalities determine a triangular region in the parameter space of The maximum In summary, the lower bound in (12) is applicable to entangled Bell-diagonal states, while the other five bounds in (12), (13), (14) are applicable to all Bell-diagonal states. The two inequalities How to cite this article: Quan, Q. et al. Steering Bell-diagonal states. Sci. Rep.6, 22025; doi: 10.1038/srep22025 (2016).


AR−/−) were noted to have reduced fertility with abnormal ovarian function that might involve the promotion of preantral follicle growth and prevention of follicular atresia. However, the detailed mechanism of how AR in granulosa cells exerts its effects on oocyte quality is poorly understood. Comparing in vitro maturation rate of oocytes, we found oocytes collected from AR−/− mice have a significantly poor maturating rate with 60% reached metaphase II and 30% remained in germinal vesicle breakdown stage, whereas 95% of wild-type AR (AR+/+) oocytes had reached metaphase II. Interestingly, we found these AR−/− female mice also had an increased frequency of morphological alterations in the mitochondria of granulosa cells with reduced ATP generation  and aberrant mitochondrial biogenesis. Mechanism dissection found loss of AR led to a significant decrease in the expression of peroxisome proliferator-activated receptor γ (PPARγ) co-activator 1-β (PGC1-β) and its sequential downstream genes, nuclear respiratory factor 1 (NRF1) and mitochondrial transcription factor A (TFAM), in controlling mitochondrial biogenesis. These results indicate that AR may contribute to maintain oocyte quality and fertility via controlling the signals of PGC1-β-mediated mitochondrial biogenesis in granulosa cells.In the ovary, the paracrine interactions between the oocyte and surrounded granulosa cells are critical for optimal oocyte quality and embryonic development. Mice lacking the androgen receptor ( Androgens classically mediate their genomic effects via the androgen receptor (AR), a protein encoded by an X chromosome gene, which exerts its biological function through activation of target gene expression via a sequence of processes ,2. The eAR−/− [AR−/− female mice [AR−/− female mice [By using Cre/LoxP system, we and others generated the global AR−/− ,13,14 anale mice ,16. Thosale mice . All togale mice  and prevale mice . Moreoveale mice ,16 have in vitro maturation rate of oocytes was evaluated as the preliminary indication for oocyte quality. In addition, oocyte maturation often required the energy sources from the surrounding nursing cells, such as granulose cells, as we reported here. Thus, the objective of this study was to determine whether lack of AR in granulosa cells has impacts on the oocyte quality by changing mitochondrial status and differentiation status in granulosa cells. We found alterations in mitochondrial morphology, biogenesis and metabolism in the granulosa cells of AR−/− mice, suggesting that ablation of AR leads to mitochondrial dysfunction. In addition, the results in this study demonstrated that pregnant mare’s serum gonadotropin (PMSG)-induced granulosa cell differentiation was impaired in AR−/− ovaries as indicated by decreasing the expression of genes involved in the granulosa cell differentiation. These consequences may be interrelated to significantly reduce invitro maturation rate of AR−/− oocytes.Earlier studies suggested that mitochondria dysfunction in granulosa cells leads to poor oocyte quality and contribute to female subfertility ,20,21. IAR gene see AR, AR−/− and +/+AR mice. We were able to identify AR−/− mice by using “select” and “2–9” primers to PCR amplify the 238-bp DNA  was observed in the AR−/− oocytes  stage . To detect the mitochondria membrane potential, we used flow cytometry analysis of JC-1 staining. JC-1 exists as a monomer in the cytosol (green fluorescent) and also accumulates as aggregates in the mitochondria (red fluorescent). In apoptotic and necrotic cells, JC-1 exists in monomeric form and stains the cytosol green. Results are expressed as the ratio of the aggregate to monomeric form of JC-1. As shown in AR−/− mice as compared to +/+AR mice, which suggesting a decline of mitochondrial function.Based on the above findings, we determine whether mitochondrial metabolism and mitochondria membrane potential were disturbed in granulosa cells of function . Thus, t+/+AR and AR−/− mice by quantitative real-time PCR. Data are expressed as the ratio of mtDNA to nuclear DNA, as shown inAR−/− mice than in +/+AR mice . AR−/− mice exhibited decreased expression of PGC-1β, TFAM and NRF1 mRNA compared with +/+AR mice  expression were significantly decreased in granulosa cells of AR−/− mice  was observed in the AR−/− oocytes. This is consistence with earlier studies that such a declined ATP content in oocytes has been suggested to significantly affect oocyte quality, embryonic development and even the implantation process [AR−/− mice might contribute to the decreased oocyte competence to undergo final maturation, as observed in this study.Within the follicle, cumulus cells surround the oocyte and directly contact with the oocyte via gap junctions . The par process ,42. We sAR−/− granulosa cells exhibit reduced FSHR, Cyp11a1 and Cyp19a1 mRNA expressions , optimal mitochondrial function, the necessary enzymatic activity, and the essential receptor signaling pathways. All of those factors converge to provide the follicle with the normal capacity to respond to the LH surge and expel a healthy oocyte that is fully competent for fertilization.Combining our previous findings  with theAll the culture media and chemicals were purchased from Sigma-Aldrich Chemical Company, unless otherwise stated.AR−/− female mice and heterozygous female mice (AR+/−) were generated by crossing AR-flox mice (exon 2 flanked by loxP sites) with transgenic β-actin-Cre (ACTB-Cre) mice, as previously described [AR/ar ACTB-Cre (AR+/−) to produce female AR−/− mice carrying the genotype ar/ar ACTB-Cre. Genotype of offspring was confirmed by PCR. Based on the sequence of the AR genomic DNA, three primers have been designed to distinguish the +/+AR, AR−/−, and floxed AR X chromosome on mice. The primer “select” is the 5' primer which is located in the intron 1 and its sequence is 5'-GTTGATACCTTAACCTCTGC-3'. The primer “2–9” is the 3' end primer which is located in intron 2 and its sequence is 5'-CTTACATGTACTGTGAGAGG-3'. The “2–3” primer is the 3' end primer which is located in the exon 2 and its sequence is 5'-CTTCAGCGGCTCTTTTGAAG-3'. If the mouse contains +/+AR, the primer pairs (select and “2–9”) will generate a product with 580 bp and the other pair of primers (select and “2–3”) will generate a product with ~460 bp. If the mice carry AR−/−, the primer pairs (select and “2–9”) will generate a product with ~270 bp and the other pair of primers (select and “2–3”) will not have a product. The expression of Cre and internal control interleukin 2 (IL-2) were confirmed by PCR during genotyping. The primer design and PCR conditions of Cre and IL-2 follow The Jackson Laboratory’s suggestions as previously described [All mouse studies were approved by the Animal Studies Committee at Taipei Medical University and conformed to the Guide for the Care and Use of Laboratory Animals published by the National Institutes of Health. escribed ,53. Brieescribed ,53.To determine the expression levels of AR, the protein extracts of ovaries were subjected to sodium dodecyl sulfatepolyacrylamide denaturing gel electrophoresis. Proteins were transferred to hybond-P PVDF membranes  and processed by routine procedures. Immunoreactive bands were visualized by blotting with primary antibodies against AR , followed by incubation with horseradish peroxidase-conjugated secondary antibodies and detection with enhanced chemiluminescence .AR−/− and +/+AR) were treated with 7.5 IU PMSG by intraperitoneal injection. After 48 h, the ovaries were removed and placed in a dish containing M2 medium. For the oocyte collection, cumulus-oocyte complexes (COCs) and granulosa cells were harvested by manually puncturing of large antral follicles with a sterile needle. Oocytes were denuded with gentle pipetting with pulled-glass Pasteur pipettes as previously described [AR−/− mice were compared with those of their +/+AR littermates. Each gene expression pattern was confirmed using at least three pairs of AR−/− and +/+AR mice. Primer sequences used for studying gene expression were designed by Beacon Designer II software  and are listed below: PPARγ co-activator 1-α (PGC-1α)-forward (f): GACATAGAGTGTGCTGCTCTGGT; PGC-1α-reverse (r): GTTCGCAGGCTCATTGTTGT; PGC-1β-f: CGCTCCAGGAGACTGAATCCAG; PGC-1β-r: CTTGACTACTGTCTGTGAGGC; NRF1-f: TTACTCTGCTGTGGCTGATGG; NRF1-r: CCTCTGATGCTTGCGTCGTCT; TFAM-f: AGTTCATACCTTCGATTTTC; TFAM-r: TGACTTGGAGTTAGCTGC; FSHR-f: GAACGCCATTGAACTGAGATT; FSHR-r: CGGAGACTGGGAAGATTCTG; LHCGR-f: AGTCCATCACGCTGAAACTGT; LHCGR-r: GGCCTGCAATTTGGTGGAAG; Cytochrome P450 side-chain-cleavage (Cyp11a1)-f: GGTGGACACGACCTCCATGA; Cyp11a1-r: TGCTGGCTTTGAGGAGTGGA; Cyp19a1-f: TTCGCTGAGAGACGTGGAGA; Cyp19a1-r: AGGATTGCTGCTTCGACCTC; Progesterone receptor (PR)-f: CTCATGAGTCGGCCAGAGAT; PR-r: CACTGTCCTCTTCCACCTCC; β2-microglobulin (β2m)-f: ACCCTCATCAATGGCCTGTGGA; β2m-r: CATGGGCTTTGACCCTTGGG. Mouse β2m was used as a housekeeping gene.To collect fully grown germinal vesicle (GV) oocytes and granulosa cells, a minimum of six mice per genotype  were obtained from PMSG treated animals. Ovaries were fixed in 4% paraformaldehyde at 4 °C and then paraffin embedded. Thereafter, 5-µm sections were taken at 30-µm intervals, mounted on slides, and subjected to hematoxylin and eosin staining for histological examination by light microscopy. All follicles with a visible oocyte nucleus were subsequently classified by stage of development. The follicle classification system was based on Pedersen’s system [Ovaries from 4.5-week-old s system : (1) Pris system ,56.AR−/− and +/+AR mice were collected followed by 48 h PMSG treatment then fixed in a mixture of glutaraldehyde (1.5%) and paraformaldehyde (1.5%) in phosphate buffer at pH 7.3. They were then post-fixed in 1.0% osmium tetroxide, 1.5% potassium hexanoferrate, before being rinsed in cacodylate and 0.2 M sodium maleate buffers (pH 6.0) followed by block-staining with 1% uranyl acetate. Following dehydration, the ovaries were embedded in Epon and sectioned for TEM. Thin sections were cut, mounted on 200-mesh grids, stained with uranyl acetate and lead citrate, and examined using a H7100 Hitachi electron microscope . Digital images were captured using a MegaView III digital camera . The morphology of mitochondria in granulosa cells was examined.For ultrastructural analysis of mitochondria, the ovaries from Delta Vision Elite Microscope .For mitochondrial localization, granulosa cells were collected and cultured overnight in μ-Slide 8 well plates  to allow cell attachment. Granulosa cells were stained with 200 nM MitoTracker Green  for 45 min at 37 °C and cells were then fixed with 4% paraformaldehyde for 20 min and treated with 0.5% Triton X-100 for 20 min, the liquid removed and blocked by 0.5% BSA in PBS 1 h. After empty the well, granulosa cells were counterstained with 4',6'-diamidino-2-phenylindole  for 10 min at 37 °C, samples were observed by Ct) of a mitochondria-encoded gene cytochrome c oxidase subunit 2 (COX2)  vs. a nuclear-encoded gene . Data were expressed as mtDNA/nuclear DNA. All measurements were performed in triplicate.Total DNA was extracted from granulosa cells using a DNeasy kit (Qiagen). mtDNA content was calculated using quantitative real-time PCR as described previously ,58 by meGranulosa cells were measured for ATP content by ATPlite™ Luminescence ATP Detection Assay System . Granulosa cells were homogenized in 50 µL mammalian cell lysis buffer and then 50 µL substrates solution were added. Adapt the plate to darkness for 10 min and then measure the luminescence. Reactions were normalized to total protein, and metabolite contents were expressed as µM/mg protein.+/+AR and AR−/−) injected with 7.5 IU PMSG 48 h later. To get positive control from cells treated with CCCP  to depolarized the mitochondrial membrane potential. Cells were incubated with 500 nM JC-1  in the PBS for 15 min at 37 °C in the dark and then analyzed by flow cytometry . The acquired data were further analyzed using FCS express V4 analysis software.Granulosa cells were collected from 4-week-old female mice . The volume of serum used for ELISA was 50 μL, the minimal detectable concentration was 4.38 pg/mL, and the intra- and interassay coefficients of variation were 8.7% and 9.8%, respectively.To determine the level of estradiol (E2) in the experimental animals, sera were collected from both t test. p ≤ 0.05 as considered to be significant.Data are presented as mean ± standard error mean (SEM), unless otherwise indicated. Statistical comparisons were made with Student’s


Angiogenesis in the developing central nervous system (CNS) is regulated by neuroepithelial cells, although the genes and pathways that couple these cells to blood vessels remain largely uncharacterized. Here, we have used biochemical, cell biological and molecular genetic approaches to demonstrate that β8 integrin (Itgb8) and neuropilin 1 (Nrp1) cooperatively promote CNS angiogenesis by mediating adhesion and signaling events between neuroepithelial cells and vascular endothelial cells. β8 integrin in the neuroepithelium promotes the activation of extracellular matrix (ECM)-bound latent transforming growth factor β (TGFβ) ligands and stimulates TGFβ receptor signaling in endothelial cells. Nrp1 in endothelial cells suppresses TGFβ activation and signaling by forming intercellular protein complexes with β8 integrin. Cell type-specific ablation of β8 integrin, Nrp1, or canonical TGFβ receptors results in pathological angiogenesis caused by defective neuroepithelial cell-endothelial cell adhesion and imbalances in canonical TGFβ signaling. Collectively, these data identify a paracrine signaling pathway that links the neuroepithelium to blood vessels and precisely balances TGFβ signaling during cerebral angiogenesis. Summary: Neuropilin 1 and β8 integrin cooperatively promote cerebral angiogenesis by mediating adhesion and signaling events between neuroepithelial cells and vascular endothelial cells in the mouse brain. Tgfb1−/− mice  in endothelial cells, but not neuroepithelial cells, results in brain vascular pathologies that are similar to phenotypes that develop in β8 integrin and TGFβ1/3 mutant mice , which is consistent with published reports  using Tie1-Cre leads to lethality by E10.5 resulting from heart and yolk sac vascular defects  or mutant  progeny. Genotyping of newborn mice [n=27 postnatal day (P) 0 mice from six different litters] revealed no viable fl/flAlk1-Cre/+;Nrp1 mutant pups. Therefore, we analyzed embryos at E11.5, E13.5 and E16.5. Expected Mendelian ratios of control and knockout embryos were found at E11.5  and E13.5 . All E13.5 mutant embryos were viable and appeared developmentally normal, although some knockouts displayed microhemorrhages in the head and body  were growth-impaired and displayed widespread edema and hemorrhage  mutants revealed similar pathologies within the ganglionic eminences and thalamus . Blood vessel patterning defects and hemorrhage were detected in mouse embryos lacking αv integrin in the neuroepithelium via Nestin-Cre , revealing that specific loss of the αvβ8 integrin heterodimer in the neuroepithelium contributes to these vascular defects.Vascular pathologies in Nrp1 conditional knockouts appeared strikingly similar to phenotypes that have been reported in mice lacking αv or β8 integrin in the neuroepithelium . Indeed,fl/flAlk1-Cre/+;Nrp1 conditional knockout embryonic brains we detected blood vessels that failed to properly sprout and form more elaborate networks near the subventricular zone. By contrast, sprouting blood vessels in −/−β8 embryos reached subventricular regions but formed abnormal glomeruloid-like tufts , which is consistent with a prior study showing hyperactive angiogenic sprouting in β8 integrin mutant brains . By contrast, Nrp1 protein was absent in cerebral blood vessels in fl/flAlk1-Cre/+;Nrp1 mutant mice owing to gene ablation . Similarly, Nrp1 protein was expressed in detergent-soluble brain lysates from control and −/−β8 mutant embryos .We next analyzed microscopic blood vessel morphologies in control and mutant mice by labeling brain slices with fluorescently conjugated Isolectin B4 to visualize vascular endothelial cells. Blood vessels in control embryos showed radial patterns of invasion throughout the brain parenchyma A. By cont brains . To detefl/flAlk1-Cre/+;Nrp1 and −/−β8 mutant mice . Similar results were found with an antibody targeting the pericyte-enriched protein desmin (data not shown). Analysis of murine gene expression databases revealed that Itgb8 mRNA is expressed primarily in the embryonic neuroepithelium . Nrp1 showed a broader pattern of expression, although within the brain parenchyma Nrp1 mRNA was present most notably in blood vessels . Immunofluorescence labeling of brain sections revealed αv integrin protein expression in the neuroepithelium and Nrp1 expression in blood vessels, with co-localization at points of neuroepithelial-blood vessel contacts . Consistent with these in vivo expression patterns, we have shown previously that β8 integrin, which dimerizes exclusively with the αv subunit, is expressed in cultured neuroepithelial cells .Pericytes are essential for cerebral angiogenesis and endothelial barrier formation , which pal cells . In addial cells  and primfl/flAlk1-Cre/+;Nrp1 and −/−β8 brains did not closely juxtapose blood vessels , whereas αvβ8 integrin is expressed only in neuroepithelial cells . These results are also consistent with a prior report showing that Nrp1 can signal via both cis and trans mechanisms . However, deletion of the entire Nrp1 cytoplasmic tail or various extracellular domains  did not block binding to β8 integrin , suggesting the involvement of more than one Nrp1 domain in mediating integrin interactions. Using transfection strategies in HEK-293T cells, we also detected protein complexes containing Nrp1 and TGFβR2, which is consistent with a recent report showing that Nrp1 suppresses TGFβ receptor signaling in sprouting endothelial cells .To identify Nrp1 domains that mediate binding to β8 integrin we generated various Nrp1 deletion constructs lacking the cytoplasmic tail or different extracellular domains involved in dimerization or ligand binding .If Nrp1 and β8 integrin interact physically we expected that they would also display a genetic interaction. A decrease in expression of both genes should reveal a phenotype, whereas decreasing expression of either gene individually will not. However, revealing this interaction might require decreasing the level of each below that found in heterozygotes for either gene. Indeed, Nrp1/β8 integrin double heterozygotes, which express 50% of each gene product, do not display obvious brain vascular defects (data not shown). To further investigate genetic interactions we used the zebrafish  mammals . Zebrafi mammals A or spli mammals B MOs tarp to 16% C. The rap to 16% D. The efAlk1-Cre mice with mice harboring a conditional Tgfbr2 gene (fl/flTgfbr2) (Alk1-Cre) and mutant  embryos. fl/flAlk1-Cre;Tgfbr2 mutant mice developed massive intracerebral hemorrhage  protein , and differences in β8 integrin protein expression were not detected in fl/flAlk1-Cre;Nrp1 brain lysates   to genermorrhage A-D, and morrhage . The braericytes E,F, but ericytes G,H. Alk1 protein I-L. Tgfb lysates F.Fig. 5in vivo, we labeled brain sections from control and mutant embryos with antibodies recognizing phosphorylated Smad3 and CD31 , respectively. We focused on blood vessels within the developing ganglionic eminences and thalamus, where angiogenesis defects were evident but severe hemorrhage was absent. Phosphorylated Smad3 protein was detected in endothelial cells of control cerebral blood vessels. A significant decrease in Smad3 phosphorylation in endothelial cells was detected in −/−β8 brains . In support of the in vivo data, silencing Nrp1 gene expression in cultured endothelial cells using lentiviral-expressed shRNAs caused significantly enhanced baseline levels of phosphorylated Smad3 and Smad1/5/8. Addition of TGFβ1 to cells expressing Nrp1 shRNAs led to higher levels of Smad phosphorylation in comparison to controls , cells expressing Nrp1 shRNAs exhibited faster spreading when compared with control cells. Nrp1 shRNA cells showed poorly developed lamellipodia, presenting irregular edges that lacked active actin polymerization in the periphery (Movie 2). Furthermore, the presence of actin aggregates rather than incipient actin fibers was observed in the lamella of endothelial cells lacking Nrp1. These actin aggregates appeared to collapse into ring-like structures in the perinuclear region. At later time points the actin filaments initially observed in the lamella bundled into transverse arcs in control cells (Movie 3). Perpendicular actin fibers resembling stress fibers anchoring the cytoskeleton to sites of cell-substrate adhesion were also clearly distinguishable. By contrast, Nrp1-silenced cells showed a collapsed cytoskeleton with the presence of F-actin aggregates throughout the cell body and shorter, poorly organized actin bundles (Movie 4). Endothelial cells expressing Nrp1 shRNAs did not show apparent defects in proliferation (data not shown) or formation of focal adhesions . These data, showing Nrp1 functions in cultured endothelial cells, combined with our molecular genetic and biochemical results, reveal that the αvβ8 integrin-Nrp1 adhesion pathway balances TGFβ signaling to control proper sprouting angiogenesis. Targeting any component in this paracrine axis leads to cell adhesion and sprouting defects resulting in similar brain vascular pathologies , and (v) Nrp1-dependent defects in Smad signaling and actin cytoskeletal dynamics are detected in cultured endothelial cells  genetic ablation of Nrp1 in vascular endothelial cells via morrhage ; (ii) bral cells ; (iii) Nal cells ,4; (iv) al cells ; Fig. S9al cells . Collectal cells .Alterations in Smad phosphorylation in β8 integrin, TGFβR2, and Nrp1 mutant mice suggest that these proteins functions at distinct, yet interconnected nodes in the TGFβ activation and signaling pathway. αvβ8 integrin is crucial for promoting TGFβ signaling via Smads by adhesion to latent TGFβs in the ECM and activating canonical receptor signaling in endothelial cells. Cell type-specific deletion of integrin expression in the neuroepithelium or TGFβR2 in endothelial cells leads to a major decrease in Smad phosphorylation. Unexpectedly, deletion of Nrp1 in endothelial cells results in increased levels of phosphorylated Smad3 and Smad1/5/8, revealing that Nrp1 acts to suppress TGFβ signaling in endothelial cells. Collectively, these results reveal that a precise balance of TGFβ signaling is essential for normal control of angiogenesis, with abnormally high or low levels of Smad3 activation in endothelial cells leading to similar defects in blood vessel sprouting and brain hemorrhage. Our results differ from other reports showing that Nrp1 promotes canonical TGFβ signaling in non-endothelial cells , indicat−/−Nrp1 endothelial tip cells display defects in actin-rich filopodia in vivo.Although TGFβR2 dimerizes with different type 1 receptors, the brain vascular pathologies in Nrp1 mutant mice are most likely a result of defective signaling via the TGFβR2/Alk5 complex. We have reported that selective ablation of Alk5, but not Alk1, phenocopies brain vascular pathologies in TGFβR2 mutants . Althougin vivo  (itgb8 ATG MO (ATGCAGGAAGTCATAGCAGCTTGA), 0.67 ng nrp1a ATG MO (GAATCCTGGAGTTCGGAGTGCGGAA) (itgβ8 SB e2i2 MO (GCGCTCTGGCATACATTACCTCCTG) (nrp1a SB e2i3 (AATGTTTTTTCCTTACCCGTTTTGA)   as well TGCGGAA) , 1.33 ngCCTCCTG)  and 1.33GTTTTGA) . All MOsEmbryonic and neonatal brain regions were lysed in 50 mM Tris, pH 7.4, 150 mM NaCl, 1% NP40, 1 mM EDTA containing a cocktail of protease and phosphatase inhibitors (Roche). Detergent-soluble lysates were resolved by SDS-PAGE and then immunoblotted with anti-integrin rabbit polyclonal antibodies at 1:3000 as described previously . The HRP+ endothelial cells in vivo, ratios of the total fluorescence intensity  was determined in representative regions of the ganglionic eminence and thalamus (n=3 images per region) in control and knockout brain sections  prepared with a vibratome. Brain sections were analyzed using a Zeiss confocal microscope.Embryos were fixed in cold 4% PFA/PBS for 12-16 h and then embedded in paraffin or agarose and sectioned. The following primary antibodies used for immunofluorescence were purchased from commercial sources: rabbit anti-laminin , rat anti-CD31 , rabbit anti-NG2 , goat anti-rat Nrp1 , rabbit anti-Erk1/2 , anti-pSmad3 , pSmad1/5/8 , rabbit anti-total Smad2/3  and chicken anti-Nestin . The anti-β8 integrin polyclonal antibody has been described elsewhere . Alexa FHUVECs and growth media were purchased from ScienCell. HEK-293 and bEND.3 cells were purchased from ATCC. Serum-starved HUVECs were incubated with TGFβ1 (5 ng/ml) for varying times at 37°C. The pGIPZ lentiviral vectors expressing shRNAs targeting mouse or human Nrp1 were purchased from Dharmacon. To quantify cell adhesion, HUVECs were plated on dishes coated with collagen I (Corning) and stained with crystal violet. Alternatively, adherent HUVECs were fixed, permeabilized, and labeled with Texas Red-conjugated Phalloidin . All HUVECs were analyzed prior to passage 8.Co-immunoprecipitation experiments to test for cis versus trans interactions between Nrp1 and β8 integrin were performed in HEK-293T cells. V5-tagged human β8 integrin in pcDNA3.1A, full-length rat Nrp1 in pcDNA3.1A, or full-length human NRP1 in pcDNA3.1 were forcibly expressed in HEK-293T cells using Effectene (Qiagen) according to manufacturers' instructions. Twenty-four hours after transfection cells were trypsinized, mixed in various combinations, and co-cultured for an additional 48 h. Detergent-soluble lysates were prepared and immunoprecipitated with anti-V5 antibodies. Antibodies used to distinguish human versus rat Nrp1 were goat anti-rat Nrp1  and goat anti-human NRP1 . Alternatively, Nrp1 mutant constructs with various deletions in the extracellular or cytoplasmic domains in pMT21 or pcDNA3.1A mammalian expression plasmids were generated by site-directed mutagenesis. HEK-293 cells were transfected with mammalian expression plasmids using Effectene and lysed in RIPA buffer containing phosphatase and protease inhibitor cocktails (Roche). Plasmids encoding V5-tagged β8 integrin and wild-type rat Nrp1 have been described elsewhere .Nrp1 shRNAs.For cell spreading assays acid-washed coverslips were coated with 10 µg/ml of fibronectin (Millipore) or 5 µg/ml collagen IV (Sigma) in PBS for 1 h at 37°C. Cells were added to coverslips, incubated at 37°C, and then permeabilized with 0.1% Triton X-100 at room temperature for an additional 10 min. Staining was performed with Texas Red-Phalloidin (Life Technologies) and NucBlue Live Cell Stain ReadyProbes (Life Technologies) to visualize the actin cytoskeleton and nuclei, respectively. Statistical analyses were performed using Minitab. Within the same set of images, population analysis of cells with actin accumulation was performed using ImageJ . For quantitative analysis, background corrected images were thresholded to measure intensity of each individual image. Actin accumulation was determined using the masking tool and image statistics tools available in ImageJ. Areas of each individual cell with actin accumulation were normalized to total cell area. Mann–Whitney non-parametric analysis was performed when comparing cells expressing control or


At eye opening, neurons in primary visual cortex (V1) are selective for stimulus features, but circuits continue to refine in an experience-dependent manner for some weeks thereafter. How these changes contribute to the coding of visual features embedded in complex natural scenes remains unknown. Here we show that normal visual experience after eye opening is required for V1 neurons to develop a sensitivity for the statistical structure of natural stimuli extending beyond the boundaries of their receptive fields (RFs), which leads to improvements in coding efficiency for full-field natural scenes (increased selectivity and information rate). These improvements are mediated by an experience-dependent increase in the effectiveness of natural surround stimuli to hyperpolarize the membrane potential specifically during RF-stimulus epochs triggering action potentials. We suggest that neural circuits underlying surround modulation are shaped by the statistical structure of visual input, which leads to more selective coding of features in natural scenes. •V1 firing is more selective to natural than phase-scrambled surround stimuli•Improved selectivity is caused by Vm hyperpolarisation prior to RF-spiking events•Natural surround sensitivity is experience dependent, absent in immature/deprived V1•Vision shapes circuits to improve V1 coding of natural scenes across RF and surround Pecka et al. show that surround modulation in primary visual cortex is tuned during development so that neurons become more selective for features embedded in full-field natural scenes. The visual system is specialized to extract features from complex natural scenes that have a unique statistical structure , includiHow do neural circuits become specialized to integrate and efficiently represent information from complex natural scenes, which contain image features that extend beyond the RF of any individual neuron? Neurons in V1 are feature selective already at eye opening . HoweverIn this study, we show that circuits mediating surround modulation require sensory experience to become preferentially sensitive to natural stimulus statistics across the RF and its surround. In mature mouse V1, neuronal firing to natural movies presented to the RF became more selective when costimulating the surround with natural movies than with phase-scrambled movies lacking the higher-order statistical regularities of natural scenes. In contrast, this preferential sensitivity of center-surround interactions for natural scenes was absent in immature, visually naive V1 after eye opening and in mature animals that were reared without visual input. Mechanistically, the surround-induced increase of response selectivity was mediated by transient membrane potential hyperpolarization that coincided with moments of greatest depolarization during RF stimulation. These transient hyperpolarizing events were most effective in limiting spiking during full-field natural movie stimulation in adult V1, consistent with the increased effectiveness of the natural surround stimuli in improving response selectivity. Therefore, normal visual experience is required for the refinement of neuronal circuits that contribute to the selective coding of natural scenes by spatially integrating information from the entire field of view.To study the effectiveness of surround modulation during postnatal development, we carried out in vivo whole-cell recordings from individual neurons in cortical layer 2/3 of monocular V1 in immature mice with limited visual experience  and in visually mature mice with at least 18 days of normal visual experience . To determine the exact RF size of each recorded neuron, we alternated the presentation of a naturalistic movie within apertures of increasing size (isoluminant gray surround) and the corresponding surround (annulus) regions . In bothTo determine how the developmental strengthening of surround suppression influences the selectivity of neuronal responses, we computed a measure that captures the distribution of spiking across stimulus repetitions , increased response selectivity , because responses to natural images in the RF are suppressed less when randomizing the phase of natural images in the surround . We therWe next determined whether the increased sensitivity of V1 neurons for natural surround stimuli is already apparent within a few days after eye opening. In immature mice, the costimulation of the RF with either natural or phase-randomized surround stimuli generated significant spike rate suppression . Strikingly, in both age groups, ΔVm exhibited a negative linear dependency on membrane depolarization during RF stimulation: neurons were relatively most hyperpolarized during RF + surround stimulation (negative ΔVm) specifically at times when VmRF was closest to spiking threshold  elicited by the RF stimulus at each time point during movie presentation (Vmhreshold E and 3J.−)-mediated conductances on the inverse relationship between ΔVm and VmRF. We performed whole-cell recordings using an elevated Cl− concentration in the intracellular solution  and somatostatin (SOM) inhibitory interneurons with whole-cell recordings . Since PV and SOM cells maintained relatively high firing rates during RF + surround stimulation, both interneuron classes can be expected to contribute to the increased inhibition of Pyr cells during surround stimulation.Given that the increased Clcordings . We founcordings E.The relRF relationship after elevating [Cl−]i was not associated with a change in the slope of the relationship  in mature mice  and relative to RF spike time . These findings are consistent with the greatest spike rate suppression during natural surround stimulation in mature V1 , but not in immature V1  14–19  or P32–P40 . For dark rearing, mice were kept in complete darkness from P13 until placed under anesthesia. Mice were initially anaesthetized with a mixture of fentanyl (0.05 mg/ml), midazolam (5.0 mg/kg), and medetomidin (0.5 mg/kg). Anesthesia was maintained with a low concentration of isoflurane  delivered by a small nose cone. Details of the surgery are given in The position and size of a neuron’s RF were determined in similar way as described before . First, Next, the naturalistic movie was presented in one of the following ways: In the RF condition, the naturalistic movie was presented within a RF-sized aperture, masking all portions of the movie outside the calculated RF with an isoluminant gray screen. To ensure a smooth transition to the surround, linear alpha-blending (0.3/°) was applied at the border of the RF and gray surround. In the natural surround condition, the naturalistic movie was shown full-field. In the phase-randomized surround condition, the natural movie was shown in the central aperture, while the phase-randomized movie covered all the surrounding portions of the screen. To determine the influence of the surround alone, the movies were additionally shown only in the annulus surrounding the central aperture. The duration of each stimulus condition was 7,000 ms. After each stimulus presentation, a constant gray screen was shown for 1,000 ms. Each condition was typically presented 11 times, and the first repetition was discarded from the analysis to eliminate onset-related effects.Cells were included for further analysis if during at least one movie frame if any of the two RF + surround conditions elicited a significant response modulation . There were no significant differences in the cortical recording depth between the age groups .− reversal potential, 5 mM of potassium gluconate was replaced by 5 mM KCl in the internal solution. Recordings were obtained with a Multiclamp 700B amplifier . The membrane potential was filtered at 50 Hz (Humbug) and digitized at 10 kHz .Details are given in PV and SOM cells were targeted for whole-cell recordings in different transgenic mouse lines . Selectivity index (SI) and mutual information (MI) were calculated as described before  and are Moment-to-moment differences in Vm (ΔVm) between RF and RF + surround conditions for each neuron were calculated in frame-wide bins 33 ms, D and 3I Analysis of depolarizing events was carried out by quantifying the number and size of transient positive membrane deflections. Events were detected with a moving window (bin width 5 ms) with an amplitude threshold of 3 mV. An individual event was regarded to have triggered a spike if the peak amplitude of the event was followed by an action potential.Statistical significance for repeated measurements of the same cell with different stimuli was assessed using the paired Student’s t test and ANOVA for reaped measurements (parametric data) or Wilcoxon sign-rank test and Friedman’s test (nonparametric data).M.P. and T.D.M.-F. conceived of the experiments and wrote the paper. E.S., Y.H., and M.P. collected while M.P. and Y.H. analyzed the data.


The androgen receptor (AR) has been identified for decades and mediates essential steroid functions. Like most of biological molecules, AR functional activities are modulated by post-translational modifications. This review is focused on the reported activities and significance of AR phosphorylation, with particular emphasis on proline-directed serine/threonine phosphorylation that occurs predominantly on the receptor. The marked enrichment of AR phosphorylation in the most diverse N-terminal domain suggests that targeting AR phosphorylation can be synergistic to antagonizing the C-terminal domain by clinical antiandrogens. The identification of steroid receptors (including AR) in the mid-1980s led to the definition of a family of ligand-mediated transcription factors that occupy specific chromatic locus for gene regulation. The next chapter in advancements is the identification of cofactors participating chromatin remodeling, including histone “writers”, “erasers”, and “readers” that have continuously been researched up to now. Besides the well-established AR activity in mediating transcriptional activation, recent studies further revealed novel functions of AR in transcriptional repression, genomic translocation, and mTOR activation . AbnormaThe AR molecule is structurally organized into distinct domains: the N-terminal domain (NTD) that has a potent activation function 1 (AF-1), DNA-binding domain (DBD), hinge domain (H), and ligand-binding domain (LBD) that binds to androgens and has a modest activation function 2 (AF-2) . The AR The identification of AR was immediately followed by the recognition that the receptor is a phosphoprotein and that phosphorylated AR is localized to the nucleus upon ligand stimulation –10. MoreAs shown in The enrichment of phosphorylation at NTD implies its function in AR-mediated transactivation. Indeed, AR phosphorylation status is strongly correlated with the transcriptional function and the agonistic activity of ligands . ConsistDespites the scattered reports on AR phosphorylation at various residues, it is well documented that the receptor phosphorylation occurs predominantly on the Pro-directed serines, as evidenced by the studies based on phosphoamino acid and mass-spec analyses (data not shown) . As indiNext, we will concentrate on three Pro-directed Ser residues  that are most robustly phosphorylated based on multiple phosphoamino acid and mass-specanalyses  12,14].,14.12,14Ser81 is the most stoichiometrically serine residue phosphorylated in response to androgens and its phosphorylation occurs with distinct dynamics compared to other AR phosphorylation residues ,17. The In the prostate cancer (PCa), Ser81 phosphorylation contributes to cell growth, AR-mediated transcription, and AR sensitivity to ligand –39. AlthMechanistically, the initial work from our Lab identified Cdk1 as a Ser81 kinase that can phosphorylate Ser81 to stimulate AR nuclear functions . FurtherThe Ser94 locates to the C-terminal of the NTD poly-Q track  and its The Ser650 in the only Pro-directed serine residue that locates outside of the NTD. It resides in the hinge region and centers on the diverse PEST sequence that potentially mediates AR protein degradation . The hinThe findings that phosphorylated AR is transcriptionally active are essentially consistent with the observations that AR dephosphorylation impairs receptor functional nuclear activities like ligand binding ,51. ConsAR phosphorylation has been extensively implicated in pathogeneses, as exemplified by that the development of castration-resistant prostate cancer (CRPC) can be attributed to AR phosphorylation at Tyr267 (by the Ack1 pathway) and Ser515/Ser578 , respectively ,57. The In summary, altered and amplified phosphorylation can contribute to abnormal AR activities, including its ligand-independent activation in diseases including PCa. The AR NTD is bestowed with highly selectivity and enriched phosphorylation, providing ample opportunities for specific interventions. Targeting NTD phosphorylation (by kinase and phosphatase modulators) can be applied in synergy with the LBD antagonists (such as antiandrogens) in therapy. Targeting AR phosphorylation is also an option to overcome the AR splicing variants that lose the functional ligand binding capacity and are overexpressed in advanced PCa . Finally


Stroke complications can occur not only in the acute ward but also during the subsequent rehabilitation period. However, existing studies have not adequately addressed the incidence of various complications among stroke in patients undergoing rehabilitation using a longitudinal method. We aimed to investigate the longitudinal impact of age on complication rates in patients undergoing inpatient stroke rehabilitation at different disease stages.Five hundred and sixty-eight first-time stroke patients transferred to the rehabilitation ward between July 2002 and June 2012 were included in the study. Patients were stratified into age groups for comparison: <65 years (young), 65 years to <75 years (younger old), and ≥75 years (older old). In total, 30 different complication types were recorded for analysis.Constipation, shoulder pain, symptomatic urinary tract infection (UTI), and fever were common complications during initial stay in the rehabilitation ward, and incidence was >10% in all three age groups. The frequency of incidence of upper gastrointestinal bleeding (UGIB) was higher in the younger old (17.9%) and older old (20.6%) groups than in the young group (4.1%) during initial stay in the rehabilitation ward (p < 0.001). The incidence of UGIB was higher in the younger old (8.04%) and older old (8.33%) groups than in the young group (0.19%) during subsequent stay in the rehabilitation ward (p = 0.011). The incidence of symptomatic UTI was higher in the younger old (21.0%) and older old (20.0%) groups than in the young group (11.5%) during initial stay in the rehabilitation ward (p = 0.019). The incidence of symptomatic UTI was higher in the older old group (29.17%) than in the younger old (9.21%) and young (3.14%) groups during subsequent stay in the rehabilitation ward (p < 0.001).Age does not affect every complication type. UGIB and symptomatic UTI occurred more frequently in stroke patients aged ≥65 years during their stay in the rehabilitation ward. Stroke is a leading cause of long-term disabilities with respect to balance, movement, speech, swallowing, urination, and defecation, which has become a global public health concern. Complications occur not only in the acute ward,2 but alIt has been reported that 44%–75%,7 of strAlthough older age is associated with increased stroke incidence,15, its Although some stroke patients may be hospitalized in the rehabilitation ward more than once for post-stroke rehabilitation, existing studies using a longitudinal method have not adequately addressed the incidence of various complications among stroke inpatients undergoing rehabilitation. We hypothesized that older age may influence the incidence of particular complications, such as UGIB or infections, in these patients. Thus, the objective of this study was to retrospectively investigate the effect of age on the occurrence of various complications among first-time patients with stroke from the acute stage to subsequent hospitalization in the rehabilitation ward.The medical records of patients consecutively admitted to the rehabilitation department between July 2002 and June 2012 were retrospectively reviewed. Study patients met the following inclusion criteria: (a) confirmed, acute, first-time stroke on the basis of the World Health Organization criteria at our hospital; (b) limb motor deficits; and (c) transfer to rehabilitation ward from an acute ward during first-time stroke hospitalization. The Institutional Review Board for Human Studies at Chang Gung Memorial Hospital approved the study protocol.Demographic data, including age, gender, mean length of stay in the rehabilitation ward, and duration of stay in the acute ward during first-time stroke hospitalization, were recorded. In addition, data on stroke type (ischemic or hemorrhagic), location , and improvement in Brunnstrom’s stage of motor recovery (BMR) in the affected limbs following transfer to the rehabilitation ward were also collected. Brain computed tomography and/or magnetic resonance imaging performed at stroke onset were reviewed for stroke type and location. BMR staging classifies the sequential motor recovery of stroke patients into six stages, with the recovery being better as the stage increases. Improvement in BMR is defined as any change from the lower to higher stage of the affected limbs  between transfer to the rehabilitation ward and discharge.Post-stroke neurological deficits such as neurogenic bladder, speech problems (aphasia or dysarthria), dysphagia, and numbness were recorded according to medical records. A complication was defined as one medical event or neurological problem requiring a doctor’s evaluation or management. Data regarding complications, including UGIB, constipation, fever, infection, fall, seizure, depression, anxiety, stroke progression, pressure ulcer, musculoskeletal pain, uncontrolled hypertension, uncontrolled diabetes mellitus (DM), dermatitis, scabies, deep vein thrombosis, pulmonary embolism, electrolyte imbalance , hypoalbuminemia, allergic reaction, and acute coronary syndrome, were obtained from patient medical records. Infections recorded included pneumonia, symptomatic urinary tract infection (UTI), upper respiratory tract infection, cellulitis, bloodstream infection (not concurrent with any other infections), herpes zoster, surgical wound infection (after craniotomy or craniectomy), and central nervous system infection. Depression and anxiety were diagnosed by a psychiatrist when the symptoms met the Diagnostic and Statistical Manual of Mental Disorders criteria, fourth edition. Musculoskeletal pain included that of the shoulder, knee, hip, wrist, ankle, back, and neck. Uncontrolled hypertension was defined as elevated blood pressure requiring a cardiologist consultation for adjustment of antihypertensive therapy. Uncontrolled DM was defined as elevated blood glucose requiring an endocrinologist consultation for the adjustment of oral hypoglycemic/insulin therapy. Hyponatremia and hypernatremia were defined as serum sodium <134 and >148 mEq/L, respectively; hypokalemia and hyperkalemia as serum potassium <3.6 and >5.0 mEq/L, respectively; and hypoalbuminemia as serum albumin <3.5 g/dL.In general, individuals are defined as elderly when they are aged >65 years (retirement age in Taiwan) and younger old when they are aged 65–75 years. In thisSubsequent hospitalization was defined as readmission to the rehabilitation ward. The incidence of each complication in the rehabilitation ward for each patient during subsequent hospitalizations was defined as the percentage of the complication occurring relative to the number of readmissions . The incidence of each complication during subsequent hospitalizations in each age group was defined as the average of the incidence of each complication of all patients in each age group. In the case of a patient having recurrent stroke, complications and readmissions to the rehabilitation ward were not included in the calculations.t-tests, and differences in incidence of various complications in these wards was analyzed using McNemar’s test.SPSS 12.0 for Windows was used for analysis. Length of stay (days) in the acute and rehabilitation wards was compared using paired One-way analysis of variance was used to compare continuous variables among the three groups, and Bonferroni correlation for post-hoc comparison between any two groups. Chi-square and Fisher’s exact tests were employed to compare categorical variables. A p-value of <0.05 was considered statistically significant.Between July 2002 and June 2012, among 719 stroke patients hospitalized in the rehabilitation ward, we enrolled 568 who met the study criteria  were less likely to have symptomatic UTI during their first stay in rehabilitation, and in older patients (>75 years) this was more likely to occur during subsequent stays. Stott et al. showed tSum of the complication types >3 included <20% of the patients in both the acute and first hospitalization in rehabilitation ward groups. It appears that the trend of the association between case numbers and number of complication types was similar in both the acute and rehabilitation ward  groups. For stroke patients in the rehabilitation ward, Hung’s retrospective study showed tKnoflach et al. found agNeurogenic bladder and dysphagia were significantly improved from the acute to the rehabilitation wards, with the incidence of both conditions being lower in patients aged <65 than in those aged >65 years. Although the incidence of speech problems also decreased from the acute to the rehabilitation wards, lower age had no effect. Numbness followed a different pattern, with slow recovery and no effect of age on incidence with respect to transfer from acute to rehabilitation ward.The incidence of shoulder pain 23.2%) ranked as the second highest complication in stroke patients first transferred to the rehabilitation ward, this being similar to the results of Kuptniratsaikul (19%).2% ranke; in addin = 5), this was significantly higher in patients >75 years of age during subsequent readmission to the rehabilitation ward (n = 5). According to Wang’s report[In the elderly, increased skin fragility with age may be a risk for skin injury, including pressure ulcers. Although the incidence of pressure ulcers showed no difference among the three age groups during initial stay in the rehabilitation ward in our study (total, s report, the incHyponatremia is a common electrolyte imbalance in hospitalized patients and is used as an indicator for outcome in acute coronary syndrome and stroOur study mainly focused on the effect of age on various complications, but other factors may also contribute to their incidence. The major limitation of this study is the limited case numbers, with the low incidence of some complications limiting the analytical proof with respect to age distribution. Another limitation is the retrospective study design which may not reflect the true incidence of complications due to errors in documentation of classification. In addition, BMR staging used as the only outcome measurement may have been insufficient for the outcome analysis. Despite these limitations, this is the first study to elucidate the overall complication rates according to age for inpatient stroke rehabilitation. Future studies should enroll higher patient numbers for further analysis and utilize more outcome measurements in a prospective manner.To summarize, age can affect the incidence of UGIB and symptomatic UTI in stroke patients in the rehabilitation ward. Patients under 65 years were less likely to have UGIB, whereas those over 75 years were more likely to have symptomatic UTI than those under 65 years. No difference with respect to improvement in limb movement was found among age groups with respect to initial transfer to the rehabilitation ward. These findings will help clinicians to understand the effects of age on various complications during different stages of inpatient rehabilitation in stroke patients.UGIB: Upper gastrointestinal bleeding; UTI: Urinary tract infection; BMR: Brunnstrom’s stage of motor recovery; DM: Diabetes mellitus.The authors’ declare that they have no competing interests.Chien-Min Chen, Hung-Chih Hsu, and Chia-Hao Chang conceived project. Chu-Hsu Lin, Kai-Hua Chen, Wei-Chi Hsieh, and Wen-Ming Chang were responsible for data collection and management. Chia-Hao Chang was responsible for data analyses. Chien-Min Chen wrote the first draft of the article and all authors contributed to the development of the manuscript. All authors read and approved the final manuscript.The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1471-2318/14/41/prepub


Escherichia coli partition asymmetrically and deterministically more damage to the old daughter, the one receiving the mother’s old pole. By modeling in silico damage partitioning in a population, we show that deterministic asymmetry is advantageous because it increases fitness variance and hence the efficiency of natural selection. However, we find that symmetrical but stochastic partitioning can be similarly beneficial. To examine why bacteria evolved deterministic asymmetry, we modeled the effect of damage anchored to the mother’s old pole. While anchored damage strengthens selection for asymmetry by creating additional fitness variance, it has the opposite effect on symmetry. The difference results because anchored damage reinforces the polarization of partitioning in asymmetric bacteria. In symmetric bacteria, it dilutes the polarization. Thus, stochasticity alone may have protected early bacteria from damage, but deterministic asymmetry has evolved to be equally important in extant bacteria. We estimate that 47% of damage partitioning is deterministic in E. coli. We suggest that the evolution of deterministic asymmetry from stochasticity offers an example of Waddington’s genetic assimilation. Our model is able to quantify the evolution of the assimilation because it characterizes the fitness consequences of variation.Non-genetic phenotypic variation is common in biological organisms. The variation is potentially beneficial if the environment is changing. If the benefit is large, selection can favor the evolution of genetic assimilation, the process by which the expression of a trait is transferred from environmental to genetic control. Genetic assimilation is an important evolutionary transition, but it is poorly understood because the fitness costs and benefits of variation are often unknown. Here we show that the partitioning of damage by a mother bacterium to its two daughters can evolve through genetic assimilation. Bacterial phenotypes are also highly variable. Because gene-regulating elements can have low copy numbers, the variation is attributed to stochastic sampling. Extant  The benefit of non-genetic variation in phenotypic traits is debated. We show that the partitioning of damage by a mother bacterium to its two daughters is a variable trait that provides an advantage by generating fitness variation. Present day bacteria partition asymmetrically more damage to the old daughter, the one receiving the mother’s old pole. By modeling damage partitioning in a population, we find that the asymmetry is advantageous because it increases fitness variation and hence the efficiency of natural selection. However, our model also shows that symmetrical but randomly variable partitioning can be similarly beneficial. To examine why bacteria evolved asymmetry, we modeled the effect of damage anchored to the mother’s old pole. While anchored damage strengthens selection for asymmetry by creating additional fitness variation, it has the opposite effect on symmetry. Thus, symmetrical but randomly variable partitioning may have been sufficient to protect early bacteria from damage. However, natural selection then supplanted it with a genetically controlled mechanism in the form of asymmetrical partitioning. The change from random to genetic control is an important evolutionary transition that is poorly characterized. We are able to quantify this transition because our model estimates the costs and benefits of fitness variation. The costs and benefits of non-genetic phenotypic variation are a long-standing topic of interest in evolutionary biology –3. WhileDrosophila melanogaster, Waddington was motivated by his observations on the evolution of the crossveinless (CVL) phenotype, which appeared as a gap in the venation of the fly wing. The phenotype was initially determined by environmental factors because wild type flies, which were not CVL under normal conditions, expressed the gap after their pupae were exposed to a brief heat shock. Waddington then selected for the CVL phenotype after heat shock by using flies expressing the gap as the parents for the next generation. After several generations, not only did the frequency of CVL flies increase in the population, but the flies also had evolved to express the gap without a heat shock. Thus, the CVL phenotype had become genetically assimilated.The transition from stochasticity to genetic determinism was independently suggested by Waddington and Schmalhausen –6, who aThe evolution of Waddington’s genetic assimilation can be explained by invoking an activation process . In ordeTo date, most studies examining the evolution of canalization and genetic assimilation have focused on metazoan examples . This paThe possibility of using microbes to model and test the evolution of canalization and genetic assimilation is appealing. Their ease of culture, short generation times, and amenability to genetic manipulation would allow for using experimental evolution to study the process in real time by natural selection. Although Waddington observed evolutionary changes, he used artificial selection and the fitness benefit of crossveined is unknown. Additionally, because many mathematical and computational models have been developed to describe specifically the generation of phenotypic variation in bacteria –24, the -1 and a second split accounts that starts with $50 at 6% and $50 at 10%. Over time, the split accounts will accrue more money. Asymmetrical partitioning splits the lineages, the lineages with less damage correspond to the 10% account, and exponential growth by binary fission provides the compounded interest. The relationship between fitness variation and the efficiency of natural selection was first recognized by Fisher, who named it the Fundamental Theorem of Natural Selection [Here we present a computational study aimed at identifying the potential costs and benefits of non-genetic stochastic variation in the growth rate phenotype of bacterial cells. We employ a model that we first developed to describe the process by which a mother bacterium deterministically partitions in an asymmetric manner her load of non-genetic damage, for example oxidized macromolecules, to her two daughters . We choselection . HoweverOur results show that stochastic partitioning, in the absence of asymmetrical partitioning, also provides a fitness advantage, but asymmetrical partitioning is more advantageous when some damage is anchored to the older poles of the daughter cells. We propose that asymmetrical partitioning, the extant phenotype in bacteria that have been examined , 10, evoWe present first our basic model of damage partitioning, which will be later modified to incorporate stochastic partitioning. We provide here only an abbreviated summary, which should be sufficient for understanding the application of the model. A more detailed derivation and analysis is provided in E. coli cell division is deterministically asymmetric because a mother cell allocates more non-genetic damage to her old daughter [E. coli when the septum cleaves the long axis of the cell  between the predicted and observed T1 and T2. Those estimates were only for parameter means, which were a = .4843, λ = 0.0077 min-1, and Π = 18.95 min, because the 128 differences were pooled and minimized as one number. To estimate σS2, we reanalyzed the data set by fitting our model to each individual trio, minimizing the difference, and obtaining 128 separate estimates of a, λ, and Π. From the mean and variances of the 128 estimates  = .52 reflect the deterministic process, and σS2 = .00046 represents the magnitude of the stochastic component.Thus, although asymmetrical partitioning creates in a deterministic manner a difference between new and old daughters, it is still subject to stochasticity or noise. The mean values a = ½ and σS2 = 0), a stochastic population (a = ½ and σS2 = .00046), and an asymmetrical population (a = .48 and σS2 = .00046). The values of Π = 18.30 min and λ = 0.0095 min-1 were used for the analysis. The value of λ was set higher because previous analyses have shown that the fitness advantage of asymmetrical partitioning is negligible when λ is small [λ favors asymmetrical partitioning because a bacteria that partitions symmetrically cannot survive if λ >1/6Π [Π = 18.30, λ = 0.0095 min-1 > 1/6Π.Natural selection for stochastic and asymmetrical partitioning was modeled by creating a computational model for a population of bacteria. Following descriptions presented in is small . Elevati λ >1/6Π . Thus, iλ; it went extinct. The stochastic population achieved an intermediate mean fitness that equilibrated around 0.571, while the asymmetrical population fared even better and had a mean fitness of 0.620. However, it is remarkable that the stochastic population was able to survive the damage, when the symmetrical population was not. Its ability to handle damage results from the fact that stochastic partitioning also introduces asymmetry. If a stochastic population partitions damage between old and new daughters with a = ½ and σS2 = .00046, the distribution of damage is randomly distributed in regards to the polarity of daughters. A new daughter is just as likely to get more damage as an old daughter (S2٠2 / 3.141593…) = .483, half of the daughters in a stochastic population are receiving on the average a small percentage of the damage from the mother  and (½ + D/2) in the new and old daughter populations, where D is the difference in the mean proportion of damage asymmetrical partitioning allocates to the old and new daughters. As we estimated the mean proportion to the new daughter to be .48 (see above), D = (1–.48)–.48 = 0.04.Let a(i), x(i), and y(i) are the ith amount of damage received by individuals in the stochastic, new, and old populations, and g(i) and f(i) are their frequencies. If g(i) = f(i), the partitioning of damage is subject to the same level of stochasticity or noise within the three population.Thus,½, and thus its total variance isVNew = VOld, the result simplifies to  of non-anchored damage is still asymmetrically partitioned as before, and anchored damage accumulates at a rate C λ and non-anchored damage at a rate (1 –C) λ. The amount of anchored and non-anchored damage in a mother cell at time t is v(t) and w(t) respectively, andv0 and w0 are the amounts of anchored and non-anchored damage the cell receives at birth from her own mother and k0 is redefined to represent the total amount of damage. Becausea of the non-anchored damage and none of the anchored damagea from a Gaussian distribution.To test our prediction that some anchored damage may have triggered the evolution of asymmetrical partitioning, we modified our basic model to allow for the buildup of anchored damage in the old pole of the mother. A new parameter fraction -C of nona = .5 and σS2 = .00086) and asymmetric (a = .48 and σS2 = .00046) bacterial populations with C = .05. While mean fitness varied previously around similar values of .617 and .620 in the control stochastic and asymmetric populations (C = .05). Thus, anchored damage has a strong effect on polarizing evolution to favor the asymmetrical partitioning of damage to the old daughter.The effect of anchored damage was first investigated by comparing the fitness of stochastic  the fitness ratio of the two populations was 1.0 when the variance (σS2) ratio equaled .00046 / .00086 = .53, all ratios reported as asymmetric over stochastic. However, as C was initially increased from zero, the variance ratio needed to be decreased for the fitness ratio to remain equal to 1.0. In other words, increasing C harmed the stochastic population, which then needed to increase its variance to compensate. Anchored damage is harmful because it reduces variance in the stochastic population by opposing the effects of stochastic partitioning  have been considered to be the major sources of variation. The production of asymmetrical daughters by seemingly symmetrical E. coli  adds a nE. coli . The onlE. coli , 9. OverAlthough our results demonstrate how asymmetric partitioning is evolutionarily advantageous, they also show how stochastic variance created by random noise can be similarly beneficial. Because a population that is stochastic and symmetrical is effectively asymmetric, it also creates daughters that have different levels of damage Figs , 4 and 5S2 = .00046 is the stochastic variance of damage partitioning in separate populations of new and old daughters, then the total variance in the entire population is σS2 + D2/4 = .00046 + .0004 = .00086. Because the difference D between the means of the new and old daughter populations is deterministically caused by the biology and genetics of E. coli, D2/4 = .0004 is deterministic variance. Thus, nearly ½ of the total variance of damage partitioning is deterministic, or (D2/4) / (σS2 + D2/4) = 47%. The remaining σS2 / (σS2 + D2/4) = 53% is due to stochasticity.Our results can be used to estimate the stochastic and deterministic contributions to the variance of damage partitioning. If σE. coli, one could postulate that the ancestral state was 100% stochastic. Stochasticity may have been critically needed to elevate fitness early in evolution, perhaps when the first proto-cells began to evolve. The irony is that the greater the advantage of stochasticity, the stronger natural selection would have favored supplanting it with a deterministic adaptation such as asymmetric partitioning. Repairing damage is another solution [Because asymmetrical partitioning is the extant phenotype of solution , 30, 31,solution , 25, 26,solution , 25. ThuIf our reconstruction of the evolution of asymmetric partitioning is correct, the supplanting of stochastic process by a deterministic one could constitute a microbial example of Waddington’s genetic assimilation. The main difference is that it was a phenotypic trait, and not its variance, that was assimilated in Waddington’s crossveinless example. However, variance is as good of a trait as any other quantifiable phenotype, and variance was under selection in our model. Moreover, if an increase in the variance of the activation factor, as we proposed in t isk0 is the amount of damage the cell receives at birth from her own mother and λ is the rate at which new damage accumulates. The mother cell divides when it has built up an intracellular product P to a threshold quantity Π. Assuming that damage hinders function linearly, P accumulates at a rateP(t) = Π, the mother cell divides. Denoting that time point t = T0 as her doubling time, P(T0) = Π andP(0) is set to zero because a new pool of the product P is assumed to be built de novo for every cell division. At the time of division, the mother cell partitions her damage k(T0) to her two daughters andk(T0) is partitioned asymmetrically to the cell’s daughters in the proportions a and (1 –a). Thus, the daughters receivea ≤ ½ and the subscripts 1 and 2 denote the new and old daughters. When each daughter in turn becomes a mother, i = 1 or 2.The model assumes that the amount of damage in a mother cell at any time T0 for a mother cell, Ti of her two daughters can be determined. k0 in Thus, given a, σS2, λ, and Π were chosen to represent stochastic and asymmetrical partitioning, the starting bacterial population of 1000 individuals was established with no initial damage (k0 = 0). With T0 was determined and used in conjunction with Eqs T1 and T2 values for the population of cells the next generation. After reproduction the population was randomly culled to reduce it to 1000 individuals. The process was then iterated forward in time by letting the surviving cells reproduce, which was accomplished by letting their k1, T1, k2 and T2 values serve as k0 and T0 for the next iteration, and so forth until the mean doubling time of the population remained stable for a sufficiently long time  to the inside of the summations, rearranging, and combining similar terms∑ g(i) x(i) = (½ –D/2) and ∑ g(i) y(i) = (½+D/2) are the means of the new and old daughter populations, ∑ g(i) = 1, ∑ g(i)k = k if k is a constant, and VNew= VOld,Equation and notation as described in text.