Finally, comprehensive experiments are conducted to validate their effectiveness in detecting noisy labels and mitigating the curse of dimensionality and suggest that our proposed model and algorithm can achieve promising outcomes. Moreover, we open-source our codes and distinctive datasets on GitHub (refer to https://github.com/DebtVC2022/Robust_Learning_with_MGC).Large datasets with noisy labels and high dimensions have become increasingly prevalent in industry. These datasets often contain errors or inconsistencies in the assigned labels and introduce a vast number of predictive variables. Such issues frequently arise in real-world scenarios due to uncertainties or human errors during data collection and annotation processes. The presence of noisy labels and high dimensions can significantly impair the generalization ability and accuracy of trained models. To address the above issues, we introduce a simple-structured penalized  Large datasets in industry, characterized by noisy labels and high dimensions, are increasingly common –9. The lData-driven methods , 5, 11 aγ-divergence, initially introduced as the “density power divergence of type-zero” ,where ∥gγ-logistic regression estimates β by minimizing X and , respectively.The X1, Y1), …, , and substituting }1-y,where π  and Kawa  and Kawr robust , which lr robust , 61. Hen. (2023)  as folloγ-logistic regression isn, and βj, j = 1, …, d, is an element in the vector β. Hence, the estimator Then the objective function of the penalized We still need consistent results here since we focus on a parametric model. We first show two regularity conditions in Lemmas 1 and 2 and then give the consistency and asymptotic normality of parameter estimation in Theorems 1 and 2.Lemma 1(Regularity Condition). Let Vi =  andwhereandβj, j = 1, …, d, is an element in the vectorβ.Let P(Yi = 1) be the probability that the sample label is 1 andthen the first derivatives of L(β) satisfying the equationsatβ = β0, whereLemma 2(Regularity Condition). The Fisher information matrix,is finite and positive definite atβ = β0.Theorem 1(Consistency and Convergence Rate). Let Vi =  be independent and identically distributed andbe a penalty function in classwith tuning parameter λn. LetandAssume thatandthere is a local maximizerofsuch thatunder some regularity conditions.I(β0) be the Fisher information matrix and let I1(β10) be the Fisher information knowing β20 = 0. We now show that the estimator It is clear from Theorem 1 that by choosing a proper property .Theorem 2Letbe a local maximizer ofin Theorem 1, Vi = {Xi, Yi} be independent and identically distributed andbe a penalty function in classwith tuning parameter λn. Letwhere assumingAssume thatand λn → 0, then for any constant C, under some regularity conditions, satisfy:(a)Sparsity:(b)Asymptotic Normality:whereandC(x) be the predicted label of {0, 1} value and given x, definef(x) and the noisy conditional probability Theorems 1 and 2 reveal that . (2020) , a modelDefinition 1. Given x, the optimal classifier under clean labels is Bayes classifier, denoted asC*(x), whereDefinition 2. Given x, the optimal classifier under noisy labels is Bayes classifier, denoted aswhereDefinitions 1 and 2 tell us that the Bayes classifier minimizes the classification risk under noisy labels. Furthermore, we then introduce the Tsybakov Condition by following Assumption 1, which is the basis of Lemma 3 and Theorem 3.Assumption 1. (Tsybakov Condition). There exist constants M, λ ≥ 0 andsuch that for all 0 ≤ t ≤ t0and x, the following inequality holds,η(x) is bounded. In other words, the margin region close to the decision boundary, t ≤ t0, This condition, also called margin assumption, stipulates that the uncertainty of Rour(x) and the Bayes classifier Rour(x) and the optimal Bayes model R*(x) under the case of noisy labels still have an upper bound of excess risk.Based on the above definitions and assumptions, Lemma 3 shows the bound of the model Lemma 3. (Upper bound of Excess Risk between Rour(x) andAssume η(x) statisfies the Tsybakov condition with constants M, λ > 0, andAssume again that τ01(x) + τ10(x) < 1. Given x, for all 0 ≤ t ≤ t0, then the excess risk is,as t ≤ t0 → 0, whereandTheorem 3. (Upper bound of Excess Risk between Rour(x) and R*(x)). Assume η(x) statisfies the Tsybakov condition with constants M, λ > 0, and Assume again that τ01(x) + τ10(x) < 1. Given x, for all 0 ≤ t ≤ t0, then the excess risk is,as t ≤ t0 → 0, whereandis a small value depend on λ.ϵ. If the estimation error ϵ is smaller, our model and the Bayes classifier are closer.Theorem 3 indicates that the risk bound between our model and the best Bayes classifier will be dominated by the model’s estimation error ϵ will tend to 0 as γ → ∞ and n → ∞, so our model will converges to the Bayes model in the case of large samples.Furthermore, the estimation error refers to the difference between the estimated parameters of the model and the real parameters. We can obtain from the consistency of parameters the estimation error Specifically, from Theorems 1 and 2, we can get γ-logistic regression to the generalized linear model (GLM) and obtain Corollary 1, as logistic regression is essentially a GLM. The proof of Corollary 1 is trivial and would not be repeated in our paper.Finally, we can easily generalize the conclusions of Theorems 1, 2, and 3 of Corollary 1. Under the regularity conditions 1 and 2 and Assumption 1, for each generalized linear model (such as the Probit model), we can obtain the same results as described in Theorems 1, 2, and 3: (i) consistency, (ii) asymptotic normality, and (iii) convergence of the model.Meta Gradient Correction (MGC), for noisy label data.Although we have proved in the above subsection that our proposed model possesses oracle properties even in the noisy-label case, recent study  has showγ-divergence weight function of , Yi is a noisy label. In other words, if ωi is larger, it means that  has a more significant effect on model training and is less likely to be a noisy label. If ωi is smaller, the sample Label Yi is more likely to be a noisy label. On the other hand, the estimation criterion of minimum γ-divergence is to maximize the objective function Q(β), which leads to using the stochastic gradient ascent algorithm.From Hung Hung et al. (2018) , the γ-dγ-divergence weight function ωi of the  is large, then gradient descent is performed to β. In contrast, the gradient ascent is performed to eliminate the effect of suspected noisy labels on model parameter convergence. To illustrate the validity of this algorithm, we further show Theorem 4.Hence, in this part, we propose an adaptive algorithm based on a meta approach that modifies the optimization algorithm. For example, if the corresponding value of the Theorem 4. . Let the number of samples for each batch be N, where the number of noisy labeled samples is Nnoisy, and the number of non-noisy labeled samples is Nnon − noisy, i.e., N = Nnoisy + Nnon−noisy. Without loss of generality, assume that Nnon−noisy > Nnoisy. Moreover, the function we want to minimize, is continuously differentiable, and we assume that Q(β) has Lipschitz continuous gradients with constant L, i.e., there exists a constant L > 0 such that, for allThis algorithm updates the gradient descent iteration as follows, βt+1 = βt−η∇Q(βt), where η > 0 is the learning rate. We then obtain that,for all t ≥ 0. The function values Q(βt) form a non-increasing sequence, which implies that Q(βt) converges.Q(β) converge when the proportion of noisy labels is small (refer to Nnon−noisy > Nnoisy). This is also consistent with the results shown in Section of Experiments and powerfully demonstrates the validity of our algorithm. Furthermore, following [βj, j = 1, …, d, is an element in the vector β. Another one is the MCP [j = 1, …, d, to solve the problem of variable selection and estimation in high-dimensional case. The last one is the Lasso [PLasso(βj) = |βj|, j = 1, …, d. For ease of description and understanding, we substitute Theorem 4 implicitly states that our proposed meta gradient correction algorithm makes our objective function ollowing , we give penalty  wherePS the MCP  where PMhe Lasso  where PLγ-divergence model for learning high-dimensional data and the robustness of adaptive classification algorithm in modeling noisy data.In this section, we evaluate the abilities of proposed model and algorithm, namely, the functionality of penalized We conducted numerous experiments on multiple simulation data and real data. These dataset has the following three characteristics.Simulation data: We generate noisy label dataset based on random seeds with three different sample dimensions and eight noisy label ratios. The training sample dimensions include: 200*500, 500*1000, and 1000*1500, and testing sample dimensions include: 100*500, 200*1000, and 200*1500. The noisy label ratios include 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, and 0.8.Real data: We obtain breast cancer data from the UCI Machine Learning Repository as real data (https://archive.ics.uci.edu/dataset/17/breast+cancer+wisconsin+diagnostic), which contains 571 samples and 31 feature variables. We randomly divide it into the training set and test set in a ratio of 0.8 and 0.2. The training set includes 456 samples, and the test set contains 115. We set the noisy label ratio in experiments to 0.1, 0.3, and 0.5. Following [ollowing , 47, 52,Each noisy label dataset is used to train and test the effectiveness and capability of the eight models in learning and detecting noisy labels. The final test results for each model are based on the average of tests after 50 different training sessions.https://github.com/DebtVC2022/Robust_Learning_with_MGC).This subsection provides brief information about the experimental settings, and more details can be found in our open-sourced codes , three penalty functions , and the proposed meta gradient correction algorithm. For all models, we select hyperparameters based on preliminary experiments and the prevalent findings [γ value of 0.5, λ value of 1, threshold value Tv of 0.5, learning rate η of 0.01.findings , 56, 61,Following the studies , 16, we Y:Accuracy based on contaminated label  Following the studies [ACC_noisy, which records the number of correctly predicted data points among all data points . studies , 16, we Y0:Accuracy based on true label  Following the studies [ACC_true, which records the number of correctly predicted data points among all data points . studies , 16, we Recall: We denote this evaluation metric by Recall, which records the percentage of samples that a model correctly identifies as belonging to noisy label samples out of the total samples for that class.Precision: We denote this evaluation metric by Precision, which records the ratio of correctly identified noisy label samples to the total number of noisy label samples.F1-score: We denote this evaluation metric by F1, which is calculated by These five metrics reflect the robustness of the model and its ability to detect noisy labels, and their larger values denote that the model has a stronger ability to model noisy labels. .In this subsection, we conduct comprehensive evaluations to demonstrate the effectiveness of our proposed model in learning with noisy labels. The evaluations are performed on simulated and real-world data by combining different backbone models , penalty functions , backbone models, and penalty functions. This indicates the robustness of our model against noisy labels. More importantly, our model substantially improves Recall, Precision, and F1, the critical metrics for noisy label identification [Y0 and what percentage of all noisy labels in the dataset are identified [ACC_true and Precision under the different noisy ratios .fication . The resentified . Hence, ACC_true) and Precision are further improved under various simulated scenarios. This demonstrates the effectiveness of the meta gradient correction algorithm in enhancing model robustness and resilience to noisy labels. According to our theoretical analyses (refer to Theorem 4), our model is effective when the noisy ratio is small, which is also validated by the experimental results.In addition, by incorporating the proposed meta gradient correction algorithm, the model accuracy on true labels . In ACC_true and Precision, are roughly the same for the same scenarios, with the performance of the training set being relatively smoother.e.g., ≥0.. In 4, tIn summary, the comprehensive experiments on simulated data validate the effectiveness of our proposed approach in modeling noisy labels and identifying noisy instances. The results are well aligned with our theoretical analyses.Overall analysis based on real data. We further benchmark our model on real-world datasets with synthetic noisy labels. As shown in Tables In conclusion, extensive experiments on both simulated and real-world datasets demonstrate the capability of our model in handling noisy labels. The meta gradient correction algorithm is verified to deliver consistent performance improvements. In future works, we will focus on alleviating the model fluctuation issue when the noise level is high and evaluating the approach on larger-scale and more complex real-world data. Advanced deep learning techniques can also be explored as backbone models to enhance model capacity and scalability.In this paper, we have proposed a novel penalized model and a meta gradient correction algorithm with grounded theoretical foundations to detect noisy labels. To illustrate the effectiveness of our proposed model and algorithm, we argue from both theoretical proofs and rich experiments.First, we derive theorems 1 and 2, which reveal that the (i) The proposed penalized model exhibits surprising robustness in modeling noisy labels. (ii) The proposed meta gradient correction algorithm demonstrates a promising ability to detect and find noisy labels. (iii) Our model can easily used in practical machine learning scenarios.Next, we conducted experiments on multiple simulated and real data. These experiments proved the following results: Finally, we plan to improve our algorithm to make it suitable for large-scale high-dimensional data. Possible improvements include introducing more complex models and smoother optimization algorithms. In addition, our algorithm can also be used in other fields, such as casual inference.S1 FileThe support information file contains all the proofs covered by the manuscript. Specifically, it contains the derivation of (PDF)Click here for additional data file.


Using in silico experiment in crop model, we identified different physiological regulations of yield and yield stability, as well as quantify the genotype and environment numbers required for analysing yield stability convincingly.Pi) was least affected among 11 SI. Pi was used as index to demonstrate that more than 150 environments were required to estimate yield stability of a genotype convincingly and more than 1000 genotypes were necessary to evaluate the contribution of a physiological parameter to yield stability. Network analyses suggested that a physiological parameter contributed preferentially to yield or Pi. For example, soil water absorption efficiency and potential grain filling rate explained better the variations in yield than in Pi; while light extinction coefficient and radiation use efficiency were more correlated with Pi than with yield. The high number of genotypes and environments required for studying Pi highlight the necessity and potential of in silico experiments to better understand the mechanisms behind yield stability.Identifying target traits for breeding stable and high-yielded cultivars simultaneously is difficult due to limited knowledge of physiological mechanisms behind yield stability. Besides, there is no consensus about the adequacy of a stability index (SI) and the minimal number of environments and genotypes required for evaluating yield stability. We studied this question using the crop model APSIM-Wheat to simulate 9100 virtual genotypes grown under 9000 environments. By analysing the simulated data, we showed that the shape of phenotype distributions affected the correlation between SI and mean yield and the genotypic superiority measure (The online version contains supplementary material available at 10.1007/s00122-023-04264-7. To ensure global food security, it is not only important to increase yield gain but also yield stability. Developing stable crop cultivars is therefore crucial maintaining the yield level and adapting to ever-changing weather schemes  under drought and heat stress. It suggests a potential to increase the yield of current wheat cultivars in Europe by 3.5–5.2 t ha−1  was used to simulate a dataset  grown under 9000 environments (Nenv = 9000). In short, virtual genotypes were created by varying the value of 90 independent physiological parameters in a range of ± 20% from the reference cultivar Hartog, which represents the default parameter values in the APSIM-Wheat. Environments in the dataset contain historical climate data of 125 years (1889–2013) in four locations in Australia , three nitrogen levels  and three sowing dates . Eight integrated model outputs , maturity date and flowering date) were used for trait stability analysis. Straw yield was calculated by subtracting grain yield from biomass.Crop model APSIM-Wheat R environment (R Core Team toolStability (Wang and Chen https://github.com/Illustratien/toolStability). The SI in toolStability include static and dynamic concepts of stability  and stability indices, indices which with squared units of trait were square-rooted to avoid artificial nonlinear relationship between trait and SI  depends on the number of environments. To ensure the comparability of Wi between calculations with different number of environments, a modified ecovalence (Wi‘) is proposed as dividing original ecovalence (Wi) with the number of environments. The dimension-less indices remained unmodified  grown under 100 environments  were first selected to test how the shape of phenotype distribution affects the relationship between mean yield and 11 SI.To calculate a SI of a genotype, data of multiple genotypes  grown under multiple environments  are required. If a SI is highly correlated with the mean yield from all environments in the studied genotypes, this SI indicates a high and stable yield at the same time. As a first step, we investigated whether the shape of phenotypic distribution (e.g. yield distribution in the SPG) affects the relationship between mean yield and SI . For this, three sampling methods were used: (1) “Pi,yield) was selected to demonstrate the minimal required Nenv for reliable estimation of a SI. We first calculated Pi,yield of 100 virtual genotypes (Ngen = 100) in 100 SPE, in combination with different Nenv ranging from 3–600 using “random” sampling method. Secondly, the coefficient of variation of Pi,yield  was calculated for each Nenv between 100 SPG. An arbitrary low threshold value  was applied.To represent both high and stable performance of yield, genotypic superiority measure of yield  between yield, Pi,yield and physiological parameters (referred to node) of genotypes  selected by three sampling methods  in a SPE. For each SPG, a table listing mean yield, Pi,yield and 90 physiological parameters of each genotype was created . The Pearson correlation coefficients between all columns in this table were calculated to produce a r-matrix , which was further transformed into a linear vector format  with 181 values  in each SPG was quantified by the ratio of absolute r value (|r|) for Pi,yield  to |r| for yield . If Tparameter > 1, this parameter is more related to Pi,yield than yield. On the other hand, a parameter explains yield more than Pi,yield when Tparameter < 1.A network analysis (node and edge graph) was performed to illustrate the Pearson correlation coefficient  100 SPG in combination with nine genotype numbers  and six environment numbers  were sampled to obtain 5400 r-vectors ; (2) a table listing r-vectors of 100 SPG was created for each combination of genotype and environment numbers ; (3) since the similarity between different r-networks can be represented by calculating r between two r-vectors in this table, an “edge-r-matrix” representing r between 100 r-vectors from 100 SPG in this table was calculated ; (4) the edge-r-matrix was squared (to represent power of explanation for correlation between nodes) and averaged to obtain an indicator S representing the similarity between networks of 100 SPG . If S is close to one, networks between SPG are similar and if S = 0, networks between SPG are completely different.To acquire the minimum toolStability”, which is an R package (Wang and Chen Ngen = 100) by three sampling methods  for 100 times  in 100 environments , resulting in different shape of phenotype distributions  which represent different strategies or steps in the breeding program.To facilitate and reproduce our yield stability analysis, we developed “r) between trait (e.g. mean yield) and SI was used to identify the SI that represent stable and high trait performance simultaneously. Three SI correlated positively to mean yield , coefficient of regression  and genotypic stability . Two SI negatively correlated with mean yield  and safety first index. Other five SI showed low correlations (R2 < 0.5) with mean yield and were not suitable for selecting high and stable yield at the same time  was expected due to the orthogonal relationship between genotypic mean yield and the effect of interaction of genotype by environment  to genotypic mean yield, as reported in the literature , followed by “random” (R2 = 0.76) and the lowest in “top 20” (R2 = 0.42). Among the 11 studied SI, the linear correlation between Pi,yield and mean yield was least affected by the sampling methods  created by APSIM-Wheat were first selected by “random” method, then their yields were simulated from 3 to 600 random environments (Nenv = 3–600). The selections of environments were repeated 100 times , and Pi,yield of genotypes in each SPE was calculated. Within one SPE  between different Nenv varied from 2.28 to 4.28 t ha−1, with coefficient of variation (CV) of 14.1%. In comparison with genotype 2396, a stable genotype (represented by genotype number 4743) under the same SPE had similar CV of Pi,yield (14.5%) but a smaller range of Pi,yield (from 0.36 to 0.6 t ha−1). Irregular variations in Pi,yield in both genotypes  varied largely in stable and unstable genotypes , indicating unreliable estimation of Pi,yield at low Nenv. Standard deviation of Pi,yield between 100 SPE decreased with the increase of Nenv, while the mean of Pi,yield from 100 SPE increased with Nenv slightly in an asymptotic manner.To test the minimum SPE Fig. a, the raPi,yield) between SPE was calculated for each Nenv . Stable genotype 4743 was found with larger CVPi,yield than unstable genotype 2396. The relationship between CVPi,yield and Nenv was fitted by an exponential function CVPi,yield = α*Nenvβ, where α adjusts the range of CVPi,yield and β controls the curvature. For a stable genotype 4743, CVPi,yield = 0.93 * Nenv−0.44 . For an unstable genotype 2396, CVPi,yield = 0.52 * Nenv−0.50 . According to these equations, at least 151 and 28 environments were required to reach the threshold of CVPi,yield = 10% for stable and unstable genotypes, respectively. If the threshold = 5%, minimal Nenv for stable and unstable genotypes is 718 and 111, respectively. This suggested that minimal Nenv for robust estimation of Pi,yield is genotype and threshold dependent. Under the threshold of 10% CVPi,yield, more than 150 environments are required. We expanded this analysis to three different sampling methods and 11 SI . In general, the choice of SI, rather than the sampling method, determined the minimal required Nenv for robust estimation of stability.Based on the results shown in Fig. env Fig. c. The miPi,yield (nodes), Pearson correlation coefficient, r (edges), between nodes were visualized by connecting the nodes with edges in a r-network . Since the robustness of Pi,yield is related to number of environments in an exponential manner  were used to ensure the robustness of Pi,yield estimation. From the 9100 virtual genotypes, we first selected 100 virtual genotypes for three times  using “random” sampling method to demonstrate the effects of genotype selection on the robustness of the edge in the r-network  of edges and type of nodes varied between r-networks with a threshold of |r| > 0.33 for displaying the edges , potential radiation use efficiency for biomass production  show medium correlation to yield and Pi,yield (Supplementary Table S1). Interestingly, while Pi,yield and yield were highly negatively correlated , a physiological parameter might tend to explain yield better than Pi,yield, and vice versa. For example, the mean tendency of ll_modifier (Tll_modifier) was 0.83 ± 0.11 (SPG = 3), indicating ll_modifier is more correlated to yield. In contrast, the mean Ty_rue was 1.13 ± 0.01, indicating y_rue is more correlated to Pi,yield.Between three randomly selected SPG with “Tparameter to three sampling methods , 100 virtual genotypes (Ngen = 100) were selected for 100 times (SPG = 100) and grown under 9000 environments . Six physiological parameters having the highest |r| with yield and with Pi,yield and with varying Tparameter were identified ; potential leaf specific area , which determines the final leaf size; efficiency of roots to extract soil water, linked to plant water status ; potential grain growth rate at grain filling ; number of growing leaves in the sheath , and temperature effect on biomass accumulation . Interestingly, the range of |r| between physiological parameters and yield  depends on the sampling method. For example, |r| between y_rue and Pi,yield was the highest (0.77 ± 0.03) from method “even”, followed by “random” (0.45 ± 0.08) and “top 20” (0.27 ± 0.1). In “top 20”, node_no_correction, showed the highest |r| with Pi,yield (0.29 ± 0.09), followed by “random” (0.18 ± 0.09) and “even” (0.15 ± 0.06). This indicates the effects of sampling method on the explanatory power of a physiological parameter for yield and Pi,yield.To investigate the response of ied Fig. : potentirandom” and “even” SPG, the most yield and Pi,yield relevant parameter was not y_rue in a “top 20” SPG, but the parameters controlling grain filling , leaf expansion (node_no_correction) and temperature effect on biomass accumulation (tfac_slope). Among these six parameters, ll_modifier, node_no_correction and potential_grain_filling explained yield better than Pi,yield. By contrast, tfac_slope, y_rue and y_sla explain Pi,yield better than yield , proper Ngen and Nenv required for a robust estimation of r-networks were tested using 100 SPG in combination with nine genotype numbers  and six environment numbers . The similarity between networks (S) increased with Ngen but not with Nenv  with k = 111.71 ± 5.43. Using the asymptotic function, S reached 0.90 with Ngen = 1006.Since rks Fig.  depend or-network  and Nenv = 9000 (SPE = 1). Among all traits, grain number correlated most positively with yield (r = 0.71), followed by straw (r = 0.64) and LAI (r = 0.60). By contrast, grain protein correlated most negatively with yield , followed by Pi,straw (r = 0.69) and Pi,LAI (r = 0.65) and Pi,grain_protein negatively correlated with Pi,yield (r = − 0.82). In general, correlations between Pi,Trait, were slightly higher than that between traits , while the variations in Pi,yield were best explained by radiation use efficiency . Thermal time between plant emergence and end of juvenile stage (tt_end_of_juvenile) most correlated to flowering time and explained this trait and its stability equally . Meanwhile, this physiological parameter also correlated with grain weight . LAI negatively correlated with thermal time before floral initiation  and efficiency of roots to extract soil water , while positively correlated with fraction of dry matter allocated to rachis for specific stage  and potential leaf specific area . The edge of r-networks in Fig. Grain yield was mostly explained by efficiency of roots to extract soil water . Despite concerns about Pi  present three common shapes of phenotype distributions in genetic pools used in breeding programs.To our knowledge, this is the first study that brings the shape of phenotype distributions (the distribution of genotypic means of a trait in a SPG) into the context of analysing yield stability Fig. , includiers Fig. , suggestrandom’) in combination with a large population size, a trait (e.g. yield) response will follow normal distribution  valuable for selecting favourable traits . However, the distributions of the most influential physiological parameters in random populations are relatively flat , implying the random combinations of evenly distributed physiological parameters might create a normal distribution of a complex trait . In contrast, trends and peaks can be observed in the distributions of parameters in “top 20” populations .Based on the central limit theorem Laplace , when thtop 20” method represents the elite population with a high mean yield . Our results further suggested that potential grain growth rate at grain filling  and closely (R2 close to one) than in an elite population  and radiation use efficiency (y_rue) have the highest correlations with yield and yield stability in the random population. Although it is not especially surprising the close relation between root water extractability (ll_modifier) and yield from an eco-physiological view , which was similar to the parameter “potential_grain_filling_rate” , which was similar to the parameter “y_sla” , flowering time, grain yield, grain size and grain number were predicted as a function of physiological assumptions of the model. The simulated dataset provides us a chance to glance at the contour of the complex physiological network and its relation to the shape of phenotype distributions Fig. . Our modte” Fig. j. In conla” Fig. h. Thila” Fig. . Our resla” Fig. .R2 of 0.6 has been reported  with Pi,yield and Pi,straw  and stable grain number , probably due to the effects of canopy condition at pre-anthesis stage on floral formation  have robust contributions to yield and yield stability and their contributions can be environment-dependent Below is the link to the electronic supplementary material.


These modes interact with a changing cellular environment to yield highly dynamic expression patterns2. In bacteria, the relationship between a gene’s regulatory architecture and its expression is well understood for individual model gene circuits4. However, a broader perspective of these dynamics at the genome-scale is lacking, in part because bacterial transcriptomics have hitherto captured only a static snapshot of expression averaged across millions of cells5. As a result, the full diversity of gene expression dynamics and their relation to regulatory architecture remains unknown. Here we present a novel genome-wide classification of regulatory modes based on each gene’s transcriptional response to its own replication, which we term the Transcription-Replication Interaction Profile (TRIP). We found that the response to the universal perturbation of chromosomal replication integrates biological regulatory factors with biophysical molecular events on the chromosome to reveal a gene’s local regulatory context. While the TRIPs of many genes conform to a gene dosage-dependent pattern, others diverge in distinct ways, including altered timing or amplitude of expression, and this is shaped by factors such as intra-operon position, repression state, or presence on mobile genetic elements. Our transcriptome analysis also simultaneously captures global properties, such as the rates of replication and transcription, as well as the nestedness of replication patterns. This work challenges previous notions of the drivers of expression heterogeneity within a population of cells, and unearths a previously unseen world of gene transcription dynamics.Organisms determine the transcription rates of thousands of genes through a few modes of regulation that recur across the genome Bacterial gene regulation occurs primarily at the level of transcription7, but while decades of research has produced a wealth of knowledge about RNA polymerase and its interactions with promoters, repressors, and activators of transcription, this work is primarily based on measurements averaged across a population of millions of cells. Therefore, much is still unclear about how transcription takes place in individual cells in the context of a constantly changing cellular environment2. In rapidly proliferating cells, transcription occurs on a chromosome that is under continuous replication9. However, although there has been some exploration of the effects of replication on individual genes11, the transcriptomes-wide consequences of this perturbation are unknown13. Measuring global gene expression during the replication cycle has traditionally been hampered by the requirement for analysis of synchronized populations at a bulk level, limiting this analysis to organisms such as Caulobacter crescentus16 where natural biological features facilitate synchronization, or to populations synchronized by batch synchronization methods such as starvation17 or temperature shift18 that may be both of questionable efficacy and liable to introduce artefacts19.Our ability to understand and manipulate bacteria, from design of synthetic regulatory circuits23 with a new cell cycle analysis framework to reveal extensive transcriptional variation during the cell cycle in two unrelated species – the model organism and Gram-negative rod Eschericha coli (E. coli), and the Gram-positive coccus Staphylococcus aureus (S. aureus), both major bacterial pathogens. We identified first a global replication-dependent pattern that depends on a gene’s chromosomal location, then developed a predictive computational analysis framework to reveal diverse types of divergence from this pattern. In E. coli, we found an effect of a gene’s position within its operon on expression dynamics that is largely absent in S. aureus. Other genes diverged from the expected pattern in both amplitude and timing of their expression in ways that are sensitive to gene-specific factors such as repression state. Therefore, while DNA replication introduces a universal perturbation, how individual genes respond to this perturbation depends on their local regulatory context, providing a new lens through which to understand the behavior of genes at their native loci.Here we combined state-of-the-art bacterial single cell RNA sequencing (scRNA-seq)20, to 73,053 individual S. aureus cells in exponential phase  method, an unsupervised deep learning approach24. Studying gene-gene correlations, we recovered the expected covariance of genes within operons  of E. coli grown at 37 °C in three medium conditions (td = 39.4 min), we predicted a correlation pattern similar to that observed for S. aureus , we also expect to find a relationship between origin distance and expression levels. Indeed, despite high variation in intrinsic promoter activity, we found that on average gene expression decreased with distance from the origin, and this effect was stronger at faster growth rates30  or 3 o’clock (oriZ) positions in addition to oriC27. In these strains, replication initiates simultaneously at both native and inserted origins, while ending at the same terminus, ter25. Our simulation predicted perturbed correlation patterns that were almost mirror images of each other, given that the ectopic origins of the mutants we chose were nearly equidistant from oriC on each side of the chromosome . Cells arranged into a “wheel” shape  was less than the full origin-terminus distance, meaning that genes at multiple positions on the origin-terminus axis had the same θg value. We can interpret this to mean that at high growth rates, overlapping rounds of replication lead to simultaneous replication of genes at multiple distances from the origin. Furthermore, we observed that in E. coli, the gradient of change of θg with respect to origin distance decreased with slowing growth rate  explains why, despite similar proliferation rates and DNA polymerase speeds  at a given point in the cell cycle (by θc), based on global replication-dependent trends 34. Overall, population-averaged expression measurements from the two methods were in close quantitative agreement  and one involved in the response to reactive electrophilic species (nemRA-gloA)37. Divergent genes within the same operon showed highly similar expression profiles  and cell surface synthesis (e.g. the mraZ-ftsZ operon). We found that genes with a more distal position within these operons exhibited a greater delay . Therefore, our data support the hypothesis that when a gene is replicated, the time for expression to increase to the higher-expressed state (due to higher gene dosage) correlates with the time for RNAP to reach that same gene after transcription from the replicated locus restarts.We first sought to determine what contributes to differential timing of expression profiles among divergent genes. In er delay . Moreoveion time . Across ion time . We hypoP 33 and . By perfP 33 and  and convnuo). We observed a delayed effect that increased with distance from the major TSS for this operon, similar to the delay recently observed for this operon in response to transcription initiation inhibition by rifampicin7  within the cell cycle for genes far from their TSS. Consistent with this, we observed a weak but significant correlation in E. coli between genes’ distance from their TSS and their amplitude of expression   contain internal promoters, and we suggest that these may contribute to expression by buffering the effects of replication-associated abortive transcription in long operons.To further understand the nature of this transcriptional distance effect, we focused on a single operon encoding the NADH dehydrogenase I complex (ampicin7 . Additioampicin7  & E. A sZ operon . A poten× 10−10) . We noteS. aureus. In contrast to E. coli, we did not observe an excess of “delayed” genes among the divergent genes   than its counterpart in E. coli measured by the same method (~48 nt/s)43. Therefore, the interplay between DNAP and RNAP processivity may lead to species-specific effects of operon position on cell cycle expression dynamics.Finally, we asked whether similar trends could be observed in nt genes . Moreovent genes , with no = 0.73) . From th = 0.73) . These d.73) 41, . One potE. coli, it can not explain divergent patterns for many other genes in both E. coli and S. aureus. Therefore, we investigated more closely the shape of cell cycle expression curves for those genes that had reproducible dynamics across replicates  12 comprised the nrdAB-yfaE operon and cluster Ec5 contained the dnaAN-recF operon and other delayed expression genes, including some nuo genes. Cluster Ec17 showed an early-peaking pulse in expression with greater amplitude than most genes   . Clusteror nemR) , also inor nemR) , such asr trends . Globallr trends , and thir trends  & E. PreS. aureus, we also observed a negative relationship between average expression and amplitude of cell cycle expression, suggesting similar principles  9, comprised of dnaAN. Analogous to clusters Ec17 and Ec9 in E. coli, we observed high-amplitude clusters with (Sa18) and without (Sa11) a “left” shift, indicating that expression peaked earlier than expected . Therefore, we focused on genes of the S. aureus GbaA regulon . Instead, gene expression fluctuations during the cell cycle appear to be responses to the local perturbation that each gene experiences upon passage of the replication fork. This appears to be the case even for major cell cycle regulators and explains why despite the known cell cycle-dependent fluctuations of ftsZ55, which encodes the major regulator of cell division in E. coli, division timing appears to be relatively insensitive to the expression patterns of this protein58. A direct link between ftsZ replication and transcriptional inhibition was previously postulated but the authors at the time could not provide a satisfactory mechanistic explanation55. Here, we explain these augmented fluctuations in ftsZ abundance as a consequence of transcription from a distant promoter40 , it is not clear which of these could lead to the dynamics we describe here. By redefining cell cycle expression of a gene relative to its replication time, as measured by θc-rep . Many operons under repression exhibit heterometry (Class 2 & 3), while a subset of these peak earlier than expected (heterochrony) (Class 2). Genes can also exhibit heterochrony as a “delayed” expression profile (Class 4). Finally, we note that in S. aureus, many genes located in MGEs, particularly those involved in mobilization, exhibit heterogeneity patterns that are entirely distinct from those of the host genome (Class 5). Future work will be required to fully describe the heterogeneous expression of these elements.Analysis of each species reveals a diversity of TRIPs that may reflect gene-specific variation in local regulatory motifs. This variation may arise from each gene’s distance from the promoter, local repression state, and possibly other factors such as chromatin structure, together generating a high degree of complexity that we are only beginning to untangle. Nevertheless, we can distinguish several archetypal behaviors of TRIPs . First, 62. Other modes of replication-induced transcription have also been suggested48. However, it is unclear what drives the precise timing of these transient increases. In E. coli, iclR, which encodes a transcriptional repressor that represses itself as well as the neighboring aceBAK operon, has a Class 2 TRIP, whereas its target, aceBAK, belongs to Class 3. This demonstrates that the presence of binding sites for a particular repressor may not alone be sufficient to determine the expression timing. For Class 4, the delayed pattern, the effect of gene position within operons in E. coli clearly points to the greater disruption experienced by genes far from their promoters, but in other cases, particularly in S. aureus, there must be other drivers. Overall, while certain themes emerge, many questions remain about how these myriad influences on gene expression interact to produce the observed patterns.Mechanistically, much remains to be explored. For genes with Class 2 or 3 TRIPs, many genes are under repression (or even autorepression). This suggests a possible mechanism in which the passage of the replication fork through the promoter transiently displaces the repressor, leading to a temporary increase in transcription shortly after replicationS. aureus tell us about their regulation, and how might this relate to the phenotypic heterogeneity in stress sensitivity and virulence observed in bacterial pathogens63? Our work demonstrates that this approach can be extended beyond standard model organisms to allow comparison across genes, genetic backgrounds, or even distantly-related species, helping to characterize control of virulence or resistance genes in an emergent pathogen, or regulation of a gene cassette with potential biotechnology applications64. Finally, our ability to infer global parameters directly from the data, including replication patterns and both RNA and DNA polymerase speeds, facilitates comparison across very different growth conditions and will allow us to connect gene-specific dynamics to the overall state of the cell.As our interpretation of these signatures continues to improve, we may be able to distinguish additional modes of regulation. For example, does low expression of a specific gene reflect weak intrinsic promoter strength (subject to positive regulation) or strong repression (subject to negative regulation)? A Class 2 or 3 TRIP would indicate the latter. Alternatively, what does the delay in expression of genes associated with stress responses or virulence in 67, we predict that these methods, in combination with microscopy and molecular genetics approaches that allow mechanistic dissection of these phenomena, will illuminate a diverse ecosystem of dynamic transcriptional processes.This work represents only an initial effort in this direction, but provides a foundational framework for genome-wide exploration of novel bacterial regulatory phenomena. As bacterial scRNA-seq methods evolve in scale, capture efficiency, and costE. coli strains (a gift from Dr. Christian Rudolph) were routinely grown in modified Luria Broth (LB) (1% tryptone (Sigma-Aldrich), 0.5% yeast extract (Sigma-Aldrich), 0.05% NaCl, pH adjusted to 7.426). For growth in minimal media, an M9 base , 2 mM MgSO4, 0.2 mM CaCl2) was supplemented with 0.4% glucose (M9G) or with both 0.4% glucose and 0.2% acid casein peptone (Acros Organics) (M9GA). All S. aureus strains were routinely grown in Bacto tryptic soy broth (TSB) (BD Biosciences). The gbaA transposon mutant was provided by the Network on Antimicrobial Resistance in Staphylococcus aureus (cat. # NR-46898).Strains used are listed in E. coli) or TSB (S. aureus) at 37°C, shaking at 225 rpm. For initial experiments with S. aureus (Datasets D3 & D4), strains were diluted to an A600 value of 0.05 in prewarmed TSB, after which A600 was measured at the times specified. A600 was measured on a BioMate 3S spectrophotometer (Thermo Scientific). For experiments with S. aureus in balanced growth (Datasets D5-D8), overnight cultures were diluted in TSB first to 0.005, then after 3 hr diluted again to 0.005 before measuring A600 at the time intervals specified. For E. coli growth curves, strains were diluted to an A600 value of 0.05 and incubated for 2 hr in the desired medium then diluted again in the same prewarmed medium to an A600 value of 0.005, after which A600 was measured at the time intervals specified. Where E. coli cells were diluted into a different medium, cells were washed once with PBS prior to dilution. To measure growth rate, a linear model log2(A600) ~ mT + c was calculated for the linear portion of this relationship (where T is the time in minutes) using the LINEST function in Microsoft Excel and the doubling time in minutes td was calculated as 1/m.Strains were grown overnight in LB  for S. aureus and 100 μg/ml lysozyme (Thermo Scientific) for E. coli. For Dataset D4, samples were split into processing with or without DNase treatment and subsequent wash steps, to test whether this would affect correlation patterns (suggesting contaminating genomic DNA could play a role). However, no difference was observed in the presence or absence of DNase treatment, although UMI/barcode was slightly higher after DNase treatment  as described in the latest version of the PETRI-seq protocol (available at https://tavazoielab.c2b2.columbia.edu/PETRI-seq/updates_April2021/PETRI_Seq_Protocol.pdf). Briefly, the transposase was loaded by incubating EZ-Tn5 with pre-annealed oligonucleotides (/5Phos/CTGTCTCTTATACACATCT and GTCTCGTGGGCTCGGAGATGTGTATAAGAGACAG) at 4 μM and 40% glycerol at room temperature for 30 min. Tagmentation was then performed incubating samples with loaded EZ-Tn5  and 2x Tagment DNA buffer; either using the Nextera 2x Tagment DNA (TD) buffer or 20 mM Tris(hydroxymethyl)aminomethane; 10 mM MgCl2; 20% (vol/vol) dimethylformamide, pH adjusted to 7.6 with acetic acid68. After incubating for 5 min at 55°C and decreasing the temperature to 10°C, either Nextera NT buffer (Illumina) or 0.2% sodium dodecyl sulfate was added, allowing neutralization to proceed for 5 min at room temperature. Final amplification was performed with Q5 polymerase (New England Biolabs) using the NEBNext Universal i5 primer (New England Biolabs) and the N7 indices from the Nextera XT Index Kit v2 Set A (Illumina) as also described in the updated PETRI-seq protocol. Sequencing was performed on an Illumina NextSeq 500 to obtain 58 × 26 base paired-end reads. For each barcoding experiment, multiple libraries of ~20,000 cells were prepared and sequenced, and no batch effects were noted across libraries.Cells were grown as described for the growth curves except that after specific time intervals (for constant ) cells wreatment . For bar20 except that feature quantification was performed at the gene level rather than operon level. Reference sequences and annotations were obtained from Genbank (https://www.ncbi.nlm.nih.gov/genbank/). E. coli reads were aligned to the K-12 MG1655 reference assembly (GCA_000005845.2) and S. aureus to the USA300_FPR3757 reference assembly (GCF_000013465.1). After initial processing, counts by cell barcode were pooled across different libraries and initial filtering was performed using Scanpy v1.7.169. Barcodes with UMI below a threshold  were removed, as well as any genes with fewer than 50 UMI across all included barcodes (100 for Dataset D3). To generate the denoised representation of the data, scVI v0.9.024 was applied with the following hyperparameters, chosen through grid search to distinguish between closely related S. aureus strains in a pilot dataset: two hidden layers, 64 nodes per layer, five latent variables, a dropout rate of 0.1, and with a zero-inflated negative binomial gene likelihood (other hyperparameters maintained as defaults). Denoised expression values based on the scVI model were obtained using the scVI function “get_normalized_expression”.Initial demultiplexing of barcodes, alignment, and feature quantification was performed using the analysis pipeline described in θc relative to the origin between x and y coordinates in a two-dimensional UMAP embedding of the data as tan1(x / y), similar to the ZAVIT method our lab has described previously71. scVI-denoised expression values were first log2-transformed then converted to z-scores. Embeddings were computed by averaging these z-scores within bins according to chromosomal location , and then performing two-dimensional UMAP analysis using the umap-learn v0.5.1 library in Python (https://umap-learn.readthedocs.io/en/latest/) with the ‘correlation’ distance metric. These embeddings were then mean-centered . To fit this relationship, a custom Bayesian regression analysis was developed according to the following model partially adapted from72, with both θg and D standardized to the range −π to π:While there was a strong relationship between origin distance ect to D  . The parameter ɣ can be interpreted as the gradient of D with respect to θg after standardizing both variables to to the range −π to π. The inverse of ɣ, 1/ɣ, is the gradient of θg with respect to D (after range standardization) and therefore is the fraction of the origin-terminus distance covered within a single span of θg. Therefore, 1 – 1/ɣ is the fraction of D during which the next round of replication has already initiated, referred to as the “overlap fraction” in ɣ is constrained to be positive by the lognormal prior distribution (θg are reversed (i.e. 360 - θg when θg is in degrees) if during analysis this relationship shows a negative trend. This can occur because the directionality of PCs used to calculate θg is arbitrary. Posterior distributions for the parameters were obtained by Hamiltonian Monte-Carlo sampling using Rstan v2.21.373. Fitted values for θg based on D (θg-pred) were calculated by determining θg-pred for all sampled parameter values and then calculating the mean value of θg-pred as tan−1(mean(sin(θg-pred)) / mean(cos(θg-pred))).The von Mises probability distribution is a circular probability distribution here parameterized by ribution , which iɣ, of the gene angle-origin distance model to calculate statistics of the replication pattern. The parameter ɣ can be interpreted as the gradient of D with respect to θg after standardizing both variables to to the range −π to π. To convert the gradient to °/Mb , sin(θc), cos(θg), and sin(θg). All interactions and combinations of these terms up to a fourth degree polynomial were constructed using the scikit-learn PolynomialFeatures function. The untransformed θc and θg values in radians were also included as features. These features were then used to fit a Ridge regression model (ɑ = 10). The model was trained on scVI expression z scores averaged first in 100 bins by θc then in 100 bins by θg . We then determined the value of θc giving the minimum predicted expression, reasoning that if increased expression in this model is responsive to a doubling of copy number, the doubling event should occur at the expression minimum. Therefore, we determined this angle, θ0 to be the most likely value of θc at which replication initiation occurs, rotating the angles by the operation (θc - θ0) mod 360 to set this point as 0°. This interpretation is roughly in accordance with the estimated timing of replication initiation as determined directly from smFISH data . We normalized raw counts for library size , then to reduce sparsity while retaining cycle information, we averaged counts across 20 bins by θc. Next, we log2-transformed the data . We observed a negative overall relationship between the mean and variance of genes in log-transformed data  to “correct” for the effect of replication, and then calculated the standard deviation of this replication-corrected value, σcorrected. A high σcorrected indicates that the dynamics behave differently from that expected based on replication alone. Thresholds for σcorrected  were determined manually based on inspection of the relationship between σcorrected across two datasets and choosing a value above which the correlation between datasets was stronger . To calculate peak/trough fold changes in expression, normalized gene expression derived from scVI was averaged into 100 bins by θc and then the ratio between the fourth highest and fourth lowest values were calculated .Next, to quantify divergence from the replication model, we subtracted the replication-predicted expression from the scVI-derived expression stronger  & I (beltan−1(sin(θg − θg-pred) / cos(θg − θg-pred)) where θg and θg-pred are the observed and predicted gene angles in radians, respectively. For operon annotations, E. coli transcription units from Biocyc78 (https://biocyc.org/) were used. To investigate the relationship between gene distance from transcriptional start sites and angle difference in E. coli, all genes in polycistrons (transcription units with more than one gene) were included. The distance was measured from the annotated transcription unit start site to the midpoint of each gene. Where genes were in multiple transcription units, the longest distance from a start site was taken. Angle difference was converted into time by dividing the angle by 360° then multiplying by the doubling time in seconds. For S. aureus, operon annotation was obtained from AureoWiki79 . Since this provided only the genes within an operon and not its start, the first base of the first gene was taken as the transcriptional start site.We identified the excess of genes with a “delayed” expression profile by calculating the angle difference as nuo operon  and averaged in 10 bins by θc. For the plots in θc so that 0° is the predicted minimum expression of nuoA, the first gene in the operon, so that θc corresponds to the approximate time elapsed since the locus was replicated. Analysis of the mraZ-ftsZ locus was carried out as for the nuo operon except that θc was recentered so that 0° is the predicted minimum expression of mraZ.To analyze per-nucleotide coverage of the o operon  & E, we o operon  and remoθc-min, predicted for each gene. Profiles of gene expression by cell angle (averaged in 100 bins by θc as used elsewhere) are then rotated so that θc = 0 corresponds to this new minimum by the transformation (θc - θc-min) mod 360 to give the cell angle relative to the predicted timing of a gene (θc-rep). Gene expression profiles are then divided by their mean to center them, but they are not scaled (so that amplitude differences are preserved). These profiles are used to generate the k-means clusters described.To align cell cycle gene expression profiles as displayed in E. coli B/r8). For each simulation, we generated 1,000 cells. Cells were initiated one at a time to yield an unsynchronized population, then the simulation was run for a further 1,000 steps with the whole population. We then normalized expression by total counts and calculated Spearman correlations across all genes. In order to simulate specific doubling times, the rate μ was calculated as μ = (n × td)/tc. where n is the number of genes in the longest replication unit , td is the doubling time, and tc is the C-period . The td/tc ratio represents the fraction of one round of chromosomal replication that can take place in one cell cycle. Finally, for simulation of cells with additional origins of replication, genes were split into replication units according to the following assumptions: a) all origins initiate replication simultaneously; b) replication stops at the termination site ter, which is halfway along the chromosome; c) genes are replicated by the nearest origin (unless the replication fork must pass through ter to reach that gene).We predicted the gene-gene correlation patterns arising from DNA replication using a simulation written in Python see  as follo15 (https://www.ncbi.nlm.nih.gov/geo/) under accession ID GSE46915. Counts were size factor-normalized with DESeq2 v1.32.083, then data were standardized to z-scores and averaged into 100 kb bins by chromosomal position. Spearman correlations of binned values across all time points and replicates are shown.For the analysis of bulk RNA-seq from15 , we acce84. Briefly, we first designed seven sets of antisense DNA oligonucleotide probes. Six probe sets were against E. coli mRNAs dnaA, nrdA, nemA, metN, rho, and cspA, and another against bacteriophage lambda cI mRNA . All oligos were synthesized with a 3’ amine modification (LGC Biosearch Technologies). The oligos against a given gene (oligo set) were pooled and covalently linked to 5-Carboxytetramethylrhodamine succinimidyl ester  and purified using ethanol precipitation. Probe sequences are listed in Our smFISH protocol was described previouslyAn inverted microscope , equipped with motorized stage control , a universal specimen holder, an LED lamp (X-Cite XYLIS), a CMOS camera , and a ×100, NA 1.45, oil-immersion phase-contrast objective  was used for imaging. The following fluorescent filter sets were used: DAPI  and Cy3 .E. coli cells were grown as described in Section “34. The coverslip was then lodged in an Attofluor Cell Chamber (Invitrogen), which was then placed onto the microscope’s slide holder and the cells were visually located using the phase-contrast channel. Images were taken in the following order: phase-contrast , Cy3 , and DAPI  . Snapshots were taken at seven z-positions  with steps of 300 nm. Images were acquired at multiple positions on the slide, to image a total of 500–2000 cells per sample .84. Briefly, we first defined the “in-focus” z-slice in every image stack by finding the one with the highest variance among pixels. We then used U-Net, a convolutional network for image segmentation85, previously trained on our E. coli images, to recognize all pixels that are within any given cell. Finally, the segmentation results were manually inspected, with poorly segmented cells manually corrected or removed.Cells were identified in the phase-contrast channel, as described previouslyA was first measured by counting the number of pixels within the cell, and the cell length L by calculating the length of its long axis. Approximating the bacterial cell as a spherocylinder86, we estimated the cell width d and cell volume V using the equations below:To estimate the dimensions of each cell, the cell area V is used when measuring mRNA concentrations in each cell .The estimated cell volume Section “”, and thFollowing cell segmentation Section “”, we est84. Briefly, we used the Spätzcells software34 to identify the spots in the fluorescent images. The software fits the fluorescence intensity profile near each spot to a two-dimensional elliptical Gaussian. The fitting results yielded the properties of each spot, including the position, spot area, peak height (amplitude of the fitted Gaussian), and spot intensity (integrated volume under the fitted Gaussian), used in the subsequent analysis.Spot recognition and the subsequent mRNA quantification were done as described previously84. Briefly, we compared the 2D scatter plots of peak height versus spot area for all detected spots in the experimental samples to that from the negative control  as measured by smFISH with the estimated abundance obtained by scRNA-seq showed that the two methods were highly correlated, and the value found  was consistent with the estimate in Section “L0) to a level similar to that at cell birth (length of L0), as expected.We first examined the cell cycle dependence of mRNA concentration, since we reasoned that those values would correspond closely to the mRNA fraction measured in scRNA-seq. For this purpose, we followed the approach oforiC replication to next oriC replication). Aligning the two signals was done as follows. We first linearly converted the cell length to a parameter β within the range 0 to 2π:To directly compare cell cycle patterns between smFISH and scRNA-seq, we needed to correct for differences in both amplitude and phase of the two signals. In particular, whereas the smFISH pattern is aligned by cell length, hence the bacterial birth-to-division cycle, the scRNA-seq data is aligned, through the cell angle, to the timing of genome replication  correspond to this simple scenario, we first binned the smFISH-measured mRNA numbers based on cell length   is well described by this expression, with the fitted n2 close to 2 as expected . In contrast, two of the three divergent genes (dnaA and nrdA) exhibit a noticeable deviation from the expected form. In particular, mRNA levels appear to overshoot, consistent with our previous observation10.In this expression, the parameter oriC replication (which was estimated to take place at cell length of ~5.2 μm). Whereas in Section “When comparing the cell cycle expression patterns obtained by scRNA-seq and smFISH Section “”, we aliT, TC, TD the cell doubling time, duration of genome replication, and the time between replication termination to cell division82. We specifically consider the case max < T < (TC + TD)/2 where genome replication initiates at cell age 3T − TC − TD89. Under these assumptions, the cellular DNA contents  as a function of cell length . In particular, a 3-fold jump in slope takes place at the cell cycle age (length) when oriC replicates. We use this constraint to fit our experimental data. We first plotted the single-cell DAPI fluorescence against cell length. We then determined the two-fold range of cell length containing most cells . The imperfect agreement between this estimate and the one obtained from scRNA-seq/smFISH alignment (5.2 μm) reflects multiple sources of error. Most notably, the analyses above assumed a simple linear mapping from both cell angle (scRNA-seq) and cell length (smFISH) to cell age, but the relation between observables is in fact nonlinear and subject to stochastic effects. These conceptual errors are likely compounded by experimental ones, for example, the distortion of cell length during fixation, and heterogeneity in DAPI staining.90, which integrates at the SaPI1 chromosomal attachment (attC) site. The vector was linearized with restriction enzymes SphI and XbaI (New England Biolabs) and insertion fragments were amplified using Q5 polymerase (New England Biolabs). For the GbaA-L promoter, the intergenic region of the GbaA regulon (130 bp upstream of the SAUSA300_RS13955 start codon) amplified from USA300 LAC genomic DNA using primers-5’CCGTATTACCGCCTTTGAGTGAGCTGGCGGCCGCTGCATGGATTACACCTACTTAAAATTCTCTAAAATTGACAAACGG-3’ and 5’-AGTTCTTCTCCTTTGCTCATTATCAACACTCTTTTCTTTTATGATATTTAATAGTTATTGCAAATTCA-3’. S. aureus codon-optimized sGFP was amplified from the genomic DNA of S. aureus USA300 LAC previously transformed with the pOS1 plasmid (VJT67.6391) using primers 5’-AAAAGAAAAGAGTGTTGATAATGAGCAAAGGAGAAGAACTTTTCACTG-3’ and 5’-ATAGGCGCGCCTGAATTCGAGCTCGGTACCCGGGGATCCTTTAGTGGTGGTGGTGGTGGTGGG-3’. Fragments were assembled using the NEBuilder HiFi assembly kit (New England Biolabs) and transformed into competent E. coli DH5ɑ (New England Biolabs). The plasmid was purified and then electroporated into RN9011 , and positive chromosomal integrants were selected with 0.1 mM CdCl2. Finally, this strain was lysed using bacteriophage 80ɑ and the lysate was used to transduce JE2 and JE2 gbaA− strains, selecting for transduction on 0.3 mM CdCl2.For generation of the reporter construct, we modified the pJC1111 vector1


Scientifc Reports 10.1038/s41598-021-00857-8, published online 12 November 2021Correction to: The original version of this Article contained an error, where Reference 36 was incorrectly cited. As a result, in the Introduction,36.”“In a survey of 133 college students, 47% of individuals reported engaging with memes as a way of alleviating psychiatric symptomsnow reads:40.”“In a survey of 133 college students, 47% of individuals reported engaging with memes as a way of alleviating psychiatric symptomsThe original Article has been corrected.


There was no significant change in the TG and TC concentrations. Subgroup analysis showed that the LA intake was significantly reduced in blood lipid profiles compared with saturated fatty acids. The effect of LA on lipids was not found to be dependent on the timing of supplementation. LA supplementation in an excess of 20 g/d could be an effective dose for lowering lipid profiles. The research results provide further evidence that LA intake may play a role in reducing LDL-C and HDL-C, but not TG and TC.Th aim of this meta-analysis was to elucidate whether dietary linoleic acid (LA) supplementation affected blood lipid profiles, including triglycerides (TG), total cholesterol (TC), high-density lipoprotein cholesterol (HDL-C), and low-density lipoprotein cholesterol (LDL-C), compared with other fatty acids. Embase, PubMed, Web of Science and the Cochrane Library databases, updated to December 2022, were searched. The present study employed weighted mean difference (WMD) and a 95% confidence interval (CI) to examine the efficacy of the intervention. Out of the 3700 studies identified, a total of 40 randomized controlled trials (RCTs), comprising 2175 participants, met the eligibility criteria. Compared with the control group, the dietary intake of LA significantly decreased the concentrations of LDL-C (WMD: −3.26 mg/dL, 95% CI: −5.78, −0.74, I Abundant epidemiologic studies have demonstrated that cardiovascular disease (CVD) is one of the primary underlying causes of mortality worldwide . DyslipiLinoleic acid (LA) is classified as an essential fatty acid for humans, and the average intake of LA in many countries around the world far exceeds the estimated minimum requirement . LA is wBased on epidemiological findings, previous studies have confirmed a link between LA supplementation and a reduced risk of CVD and atherosclerosis ,12,13. CA previous systematic review suggested that increasing n-6 fatty acids reduces blood TC by six percent for at least one year, and may make little or no difference to TG, HDL or LDL . The resThis systematic review and meta-analysis were designed and analyzed based on the guidelines of the PRISMA statement. The systematic review was registered in the PROSPERO database under the number CRD42020196824. The Embase, PubMed, Web of Science and the Cochrane Library databases were systematically searched, through to December 2022, using the following keywords in titles and abstracts:  AND (“lipid” OR “lipemia” OR “lipidemia” OR “hyperlipemia” OR “hyperlipidemia” OR “dyslipidemia” OR “lipoprotein” OR “dyslipoproteinemia” OR “TG” OR “triglyceride” OR “hypertriglyceridemia” OR “TC” OR “cholesterol” OR “hypercholesterolemia” OR “HDL” OR “high density lipoprotein” OR “HDL-Cholesterol” OR “HDL-C” OR “LDL” OR “low-density lipoprotein” OR “LDL-Cholesterol” OR “LDL-C”) AND  NOT . Moreover, a manual reference check was conducted for the references of the related trials and previous related reviews in order to find further relevant studies.Relevant studies that met the following inclusion criteria were selected: (1) randomized parallel/crossover trials only that investigated the effects of linoleic acid on lipid profiles; (2) an intervention duration of at least 4 weeks on individuals aged 18 years or more, with pregnant women excluded; and (3) the intervention group was provided with LA either through their diet or supplements, with only differences in fatty acid intake compared to the control group. Moreover, publications were excluded if they (1) included LA supplementation in combination with other interventions; (2) were animal or in vitro studies, or involved parenteral nutrition; (3) did not provide a sufficient outcome for both the baseline and the end of study; and (4) focused on increased conjugated linoleic acid (CLA), eicosapentaenoic acid (EPA), DHA, or docosapentaenoic acid (DPA) levels.Data extraction and bias assessment were conducted independently by two researchers (WQ and ZH), in accordance with the Cochrane Handbook of Systematic Reviews. Any discrepancy or disagreement was discussed and resolved by the third investigator (JQ). Relevant data, including the first author’s name and the participant demographics, such as country, age, sex, health status and body mass index (BMI), were extracted from each article. The study design, intervention duration, intervention type and dose, mean change in blood lipid levels between the baseline and endpoint (with standard deviations provided where available) were also recorded. When the effect sizes were measured multiple times at different stages of the trial, the effect size after the longest duration of the intervention was used in the present meta-analysis. The quality of each article was assessed based on the following criteria: (1) random sequence generation; (2) allocation concealment; (3) blinding of participants and personnel; (4) blinding of outcome assessment; (5) incomplete outcome data; (6) selective outcome reporting; and (7) other potential sources of bias. The risk of bias in each item was rated as three categories: low risk, high risk or unclear risk.change = square root [(SDpre-treatment)2 + (SDpost-treatment)2 – (2R × SDpre-treatment × SDpost-treatment)] (R = 0.5) [2 index and the p-value obtained from the Q-test. Substantial heterogeneity was defined as an I2 value over 50%. In order to investigate the impact of the dietary intake of LA on blood lipids, a pre-planned subgroup analysis was conducted based on age, BMI, supplementation duration, health status, and LA source. To assess internal sensitivity, a leave-one-out analysis was conducted, where one study was omitted from the analysis at a time. Egger’s regression asymmetry test and Begg’s rank correlation test were used to assess the possible publication bias. STATA SE 16.0  was used to conduct the statistical analyses. p < 0.05 was considered statistically significant.The pooled effect size was determined using the mean change and standard deviation (SD) of TC, HDL-C, LDL-C, and TG levels. When the SD was not reported directly, it were estimated using the following formulas: SD = SEM × square root (n); SD = IQR ÷ 1.35; SD = square root (n) × (upperlimit – lowerlimit) ÷ 3.92; SDR = 0.5) ,27. All The flow diagram screening and process of selecting the articles is illustrated in 2 [2 [The general characteristics of each study conducted between 1990 and 2022 are illustrated in 2  and 34.12 [2 ,57, and 2 [2  and 72 y2 [2 . The sel2 [2  and 50.72 [2  approximA summary of the risk-of-bias assessment is provided in p = 0.17, I2 = 80.8%). As shown in 2 .Among the eligible studies, there was no significant change in TC concentration after LA intake, showing high levels of heterogeneity , with moderate levels of heterogeneity among the studies . Considering the control groups with different types of fatty acids, LA intake had pronounced effects on the HDL-C concentration compared to SFA intake . With doses of 0–10 g/d and a duration of <12 weeks, the beneficial effect of LA was attenuated regarding HDL-C levels.As shown in p = 0.01). A moderate level of heterogeneity was observed across studies . As shown in p < 0.01, I2 = 75.8%). The subgroup analysis found that LA supplementation resulted in a greater reduction in blood LDL-C than that found in the SFA group . LDL-C levels were significantly reduced by −3.74 in subjects with normal lipids , 4.11 in those with a BMI of < 30 kg/m2 , and 2.56 in those supplemented with sunflower oil . Interestingly, LA supplementation at doses greater than 20 g/d induced a significant decrease in TC and LDL-C levels, while doses of 0–20 g/d had no significant effect.In comparison to the control group, the pooled results demonstrated that LA supplementation led to a noteworthy reduction in blood LDL-C concentration by 3.26 mg/dL . There was significant heterogeneity across the trials . In p = 0.01, I2 = 0.0%). Furthermore, the reduction in blood TG was significantly lower for the LA consumption group compared to the n-3 PUFA consumption group . After categorizing the studies based on the type of intervention, TG was significantly decreased for LA supplementation using corn oil. Meanwhile, LA consumption using soybean oil had reduced serum TG significantly less. In terms of dose difference, the overall trend was that the effect of LA intake decreased with dose, and that significant differences were found regarding the ratio of TG in the studies stratified by dose (p for meta regression =0.027) using meta-regression analysis , TNF , IL-6 , or sICAM-1 .As summarized in p = 0.002, Egger’s test and p = 0.142, Begg’s test). There were no missing studies were evaluated for the effect of LA consumption on TG by the “trim and fill” method. Sensitivity analysis performed that no study had a significant effect on the overall effect sizes of blood lipids profiles , thereby reducing liver adipogenesis . It was 2.In conclusion, this systematic review is the first to comprehensively synthesize the results of LA regulation on lipids from randomized controlled trials. This meta-analysis suggested that a dietary intake of LA significantly decreased blood LDL-C and HDL-C concentrations. The subgroup analysis provided evidence that a dietary intake of LA can significantly decrease blood lipid profiles compared to the SFA. LA supplementation in excess of 20 g/d may be an effective dose for lowering lipid profiles. The effect of LA was more evident among young healthy people and those with a BMI of less than 30 kg/m


As-prepared Fe-rich microwires with perfectly rectangular hysteresis loops present magnetization reversal through fast domain wall propagation, while the giant magnetoimpedance (GMI) effect in Fe-rich microwires is rather low. However, the lower cost of Fe-rich microwires makes them attractive for magnetic sensors applications. We studied the effect of conventional (furnace) annealing and Joule heating on magnetic-propertied domain wall (DW) dynamics and the GMI effect in two Fe microwires with different geometries. We observed that magnetic softness, GMI effect and domain wall (DW) dynamics can be substantially improved by appropriate annealing. Observed experimental results are discussed considering the counterbalance between the internal stresses relaxation and induced magnetic anisotropy associated with the presence of an Oersted magnetic field during Joule heating. Magnetic wires with amorphous and nanocrystalline structures have attracted considerable attention due to an unusual combination of magnetic properties, such as magnetic bistability, fast domain wall (DW) propagation and the giant magnetoimpedance (GMI) effect, suitable for numerous applications in magnetic and/or magnetoelastic sensors and devices ,5,6,7,8.Initially, it was thought that diameters of the metallic nucleus of such glass-coated microwires were limited to 5–30 µm; however, preparation of glass-coated microwires from 0.2 to 100 µm has recently been achieved and reported ,23.δ of a magnetic conductor on applied magnetic fields /2) are different.It is worth noting that both studied samples had rather similar lsewhere ,14,15, tH. For better comparison of the samples with different diameters and chemical compositions, the hysteresis loops were represented in terms of the normalized magnetization M/oM (oM being the magnetic moment of the sample at maximum magnetic field amplitude oH), dependent on magnetic field H.The hysteresis loops of both samples were measured using the fluxmetric method at 114 Hz. As previously reported , such a v is evaluated from the electromotive force EMF signals, induced by the propagating single DW in three pick-up coils surrounding the microwire, separated by the same distance, l, and placed coaxially inside the magnetizing coil. In this case, the v value can be estimated from the time difference ∆t, at which the EMF signals are detected in each pick-up coil as [The DW propagation (dependence of DW velocity on applied magnetic field H) was studied using a modified Sixtus–Tonks method . To brie coil as ,44:v = lZ, and its dependence on magnetic field H, were measured from the reflection coefficient S11, evaluated by the vector network analyzer (VNA) N5230A, as described elsewhere [Z (H) dependence in a frequency range up to 1 GHz [Z values obtained for different H values, we evaluated the magnetic field dependences of the GMI ratio ∆Z/Z, as defined from Equation (1).The impedance lsewhere ,33,34,35to 1 GHz . From Z Z/maxZ, defined as the maximum ∆Z/Z value obtained for each given measurement frequency f, was also evaluated.The frequency dependence of the maximum GMI ratio ∆annT) 300, 400 and 500 °C for annealing time (annt) 1 and 3 h. Additionally, we studied the samples subjected to Joule heating, flowing the DC current with the current values and annt previously employed for such microwires [We evaluated as-prepared samples as well as the samples annealed in the furnace at annealing temperatures   d. Some mr 3 min) a. Howevennealing a–c. The nnealing c. Crystaications ,36. WhilCH values after various thermal treatments is provided in A summary of the observed tendencies in the modification of the annT as well as by Joule heating. However, from previous publications it is known that annealing can substantially affect both DW dynamics and GMI effect performance [As can be concluded from the experimental results provided above, hysteresis loops of both studied samples were slightly affected by annealing at moderate formance ,35,36.Therefore, below we provide our experimental results on the effect of annealing on DW dynamics and GMI effect in both studied samples.v on magnetic field H can be roughly represented as a linear dependence:S is the DW mobility, and H0 is the critical propagation field.The most relevant experimental results of annealing on DW dynamics for both studied samples are provided in v and S values was observed for the “thick” Fe72B13Si11Nb3Ni1 microwire after thermal treatment. Although the increase in maximum v values from 500 to 700 m/s can be appreciated from S values increased only slightly from 4.3 to 5 m2/As.As can be appreciated from 75B9Si12C4 microwire. In this sample, an increase in maximum v values from 750 m/s to 1050 m/s was observed, while the S values increased from 7 to 12 m2/As upon conventional annealing , while the S value remained about 13 m2/As The GMI ratio of “thick” samples was rather large even in as-prepared samples;(ii)Z/Z values was observed after the process;In both studied samples, for almost all annealing conditions, an increase in ∆(iii)Z/Z(H) dependence at high enough frequencies. Usually, these double-peak ∆Z/Z(H) dependencies are reported for Co-rich microwires [Z/Z(H) dependencies with ∆Z/Z maximum at H = 0 are predicted for microwires with axial magnetic anisotropy, such as ours (which is confirmed by the hysteresis loops’ character) [Z/Z(H) dependence was observed in “thick” samples annealed at high enough temperatures  . Such siures see .There were several features of the GMI effect, including:Z/Z(H) is the presence of a transverse magnetic anisotropy domain in the outer area of the metallic core of the studied microwires [The most probable cause for the double-peak ∆crowires ,43.maxZ/Z ratio (~100%), higher than that of “thin” ones (~50%) (Z/Zmax ratio from 50% to 100% in “thin” microwires and from 100% to a bit less than 160% for “thick” ones (As-prepared “thick” samples showed a relatively high ∆s (~50%) . Howeverck” ones .Z/maxZ are provided in Z/maxZ of “thick” and “thin” microwires, respectively.Frequency dependencies of the ∆Z/maxZ (f) dependencies of both studied samples, it became obvious that thicker microwires yield higher ∆Z/maxZ values in the whole frequency range, as the highest ∆Z/maxZ ratios achieved in annealed “thin” samples did not surpass those of the “thick” as-prepared sample.When comparing ∆Z/maxZ ratios of both microwires. A more detailed analysis revealed some more complex behavior. As such, conventional annealing at 300 °C of the Fe72B13Si11Nb3Ni1 microwire resulted in the highest ∆Z/maxZ values of the sample for both 1 and 3 h of processing, while annealing at 400 °C started to lower said values to levels similar to that of the as-prepared sample. The addition of current annealing after these processes yielded a negative effect in most cases as the GMI ratios values became lower, with the exception of the annealing with 400 and 500 °C for 1 h each, which resulted in an enhancement comparable to the one obtained at 300 °C.However, it is relevant that the annealing provided an enhancement in the ∆The results shown in circH (associated to the DC current I flowing through the microwire), also known as the Oersted field, given as [I is the current value, r—radial distance and R—microwire metallic nucleus radius.As discussed elsewhere, the peculiarity of Joule heating is the presence of an Oersted magnetic field produced by the passing of an electrical current through the microwire ,51,52. Tgiven as :Hcirc = circH varies from zero on the microwire axis to the maximum value on the surface.Accordingly, I values were selected to avoid the crystallization of the studied microwires. From previous studies, it is known that the current density is the main parameter that affects the sample temperature during the Joule heating [j = 30–45 A/mm2 can produce the heating of amorphous materials up to 400 °C [j ≈ 20 A/mm2. For the studied microwires (with r ≈ 7.6 and 23.95 µm), Equation (7) gives circH ≈ 315 and 265 A/m on the surface of the metallic nucleus for I = 15 mA and 40 mA, respectively. These circH values were superior to the cH values . However, annealing allows considerable improvement of both GMI effect and single DW dynamics.Current annealing may prove to be a decent alternative to heat annealing as, with only some minutes of treatment, a more substantial magnetic softening can be achieved. The combination of both thermal treatments yields a further reduction in coercivity values, especially in thicker microwires.Higher domain wall velocity values can be achieved in thinner Fe-rich microwires after appropriate annealing. However, even in thicker microwires, an improvement in DW dynamics upon annealing is observed.Conventional annealing of both types of microwires at 300 °C for 1 h has been shown to yield the highest values of GMI ratios. Generally, the highest GMI ratios have been achieved in thicker microwires. While Joule heating used after conventional annealing is mostly detrimental, for specific cases, the GMI ratio values are once again enhanced after their lowering due to excessive annealing temperatures or times. This might prove to be an interesting option to “repair” the sensitivity of microwires used in magnetic sensing technologies at high temperatures.Appropriate postprocessing of Fe-rich microwires is a relevant tool for making Fe-rich microwires suitable for magnetic sensor and devices applications.


They also fragment the organometallic compounds via various competitive reaction channels that occur at higher energies via dissociative electron attachment. The reported data may contribute to a better understanding of the physical chemistry underlying the electron–molecule interactions, which is crucial for potential applications of these molecular systems in the deposition of nanoscale structures.Nowadays, organometallic complexes receive particular attention because of their use in the design of pure nanoscale metal structures. In the present work, we present results obtained from a series of studies on the degradation of metal(II) bis(acetylacetonate)s induced by low-energy electrons. These slow particles induce the formation of the acetylacetonate anion, [acac] Nowadays, organometallic compounds are used in many applications. They receive great interest in the field of nanoscale technologies –3. For eMetal bis(acetylacetonate) complexes are of interest for many thin film fabrication techniques  and the acetylacetonate ligand, respectively. Previous reports were only dedicated to the mechanism and the energetics for the production of the two predominant species, that is, the parent [ML2]− anion and the ligand [L]− anion − anion –19. In a2  produces the parent anion [ML2]− and the fragment anion [L]− as the predominant species . The precursor anion may also survive for a sufficiently long time, that is, before the electron autodetachment process takes place, through the fast redistribution of the excess energy carried by the attaching electron. The formation of TNIs follows different mechanisms. Briefly, the electron may be trapped into a usually unfilled molecular valence orbital  [2]− anion via the core-excited resonance occurs in NiL2 and ZnL2 at around 5 and 8 eV, respectively  . Such a sonance) –19 for tsonance) . This prsonance) . The forectively . Such “hzability –19, whic2 and ZnL2  = C − ΔHsub/T), where C is a constant. Taking into account the sublimation enthalpy, ΔHsub, for MnL2 and CoL2  electron attachment cross sections to compare the experimentally measured ratio between CoL2− anions and MnL2− anions, via Nion = ε·Ne·Nneutral·σion·L, where ε is the ion detection efficiency, Ne and Nneutral are the number of colliding electrons (intensity of the electron current) and the density of the neutral precursor targets, respectively, L is the collision length, and σion is the cross section for the ion production. The experimental estimate of NCoL2−/NMnL2− from 2]− is comparable.At first glance, the formation of the precursor anion is very effective for the Co-, Ni- and Cu-containing organometallic complexes, in contrast to MnLand ZnL2 . These eectively –19. As tectively ), and th2]−, observed for electron attachment to copper hexafluoroacetylacetone, has been suggested to arise from the isomerization from the planar to the tetrahedral configuration − [2]− anion configuration is lower in energy than the neutral configuration − anion prevents the dissociation of the TNI and, hence, the production of [L]− near 0 eV. Furthermore, the formation enthalpy of this fragment has been calculated to be 2.01, 1.72, 0.95, 1.54, and 1.74 eV for Mn, Co, Ni, Cu, and Zn complexes, respectively − –19. Accoguration –19. It h 2.026 Å . As a coectively –19. Henc ligands , may als ligands . Thus, wothermic –19.2]#− anion results in a wide variety of negatively charged species. They arise from the decomposition of one of the ligands into X species, whereas the second ligand still binds to the metal, for example, [MLX]. The loss of C3H3 from one of the ligands, that is, (L-C3H3), is observed for CoL2 (2 (2 (3H3)]− anion  or not 2]#− TNI decomposes into the negative fragments [L]−, [L-C3H3]−, and [C3H3]− at ca. 2.6 eV , in plasma applications, or possibly in radiation therapy as radiosensitizers.The interaction of low-energy electrons with metal(II) bis(acetylacetonate) complexes produces mainly the parent anion [ML2, in a crossed-beam arrangement. According to the description given in [17−8 mbar. A well-defined electron beam generated from a trochoidal electron monochromator (resolution approx. 210 meV FWHM), orthogonally intersects an effusive molecular beam of ML2. The latter emanates from a vessel containing approximately 1 mg of ≥98% purity powder (products purchased from Alfa Aesar) heated by two in vacuo halogen bulbs. The materials were used as received without further purification. The lamps also maintain all of the electrostatic lenses and plates at oven temperature to prevent powder condensation, which otherwise may lead to undesirable changes in contact potentials during the measurements. The present experiments were carried out at temperatures typically 10–20 K below the temperatures for which the decomposition of the molecules has been observed from thermochemistry methods [2, CoL2, NiL2, CuL2, and ZnL2, respectively. At these temperatures, it is very likely that the compounds are evaporated intact for collision experiments. Negative ions that are produced in the reaction area after the electron–molecule interaction are extracted from the collision area by a small draw-out field (ca. 0.5 V·cm−1), then analyzed by the QMA and finally detected using a single-pulse counting technique. The electron energy scale was calibrated using a flow of SF6 gas through the oven that produced the well-known SF6− resonance near 0 eV. The measurements were performed without the presence of the calibration gas, avoiding potentially unwanted reactions such as dissociative electron transfer with the investigated molecules producing an additional signal near 0 eV [We performed electron collision experiments with several metal acetylacetonate compounds, MLgiven in –1729, th methods –34. Thusear 0 eV .