Kexin Helical Gear's Post

#snsinstitutions #snsdesignthinkers #designthinking Types of Gears Spur Gear: The spur gear has a helix angle of 0°. Worm Gear: Worm gears are found in right angle gearboxes. They “turn a corner.” Helical Gear: This is an angle toothed gear. ... Bevel Gear: Bevel gears tend to have a lower ratio and run at a higher efficiency than worm gears. Gears are classified into 3 categories; parallel axis gears, intersecting axes gears, and nonparallel and nonintersecting axes gears. Spur gears and helical gears are parallel axes gears. Bevel gears are intersecting axes gears. Screw or crossed helical, worm gear and hypoid gears belong to the third category. Gears use the principle of mechanical advantage, which is the ratio of output force to input force in a system. For gears, the mechanical advantage is given by the gear ratio, which is the ratio of the final gear's speed to the initial gear's speed in a

If you are looking for more details, kindly visit Kexin.

Knowledge-informed deep learning of perturbation effects

GEARS is a deep learning-based model that predicts the gene expression outcome of combinatorially perturbing a set of one or more genes (perturbation set). Given unperturbed single-cell gene expression along with the perturbation set being applied (Fig. 1a), the output is the transcriptional state of the cell following the perturbation (Methods).

a, Problem formulation: given unperturbed gene expression (green) and applied perturbation (red), predict the gene expression outcome (purple). Each box corresponds to an individual gene. Arrows indicate change in expression. b, GEARS model architecture. (i) For each gene in the unperturbed state, GEARS initializes a gene embedding vector (green) and a gene perturbation embedding vector (red) (ii). These embedding vectors are assigned as node features in the gene relationship graph and the perturbation relationship graph (iii). A GNN is used to combine information between neighbors in each graph. Each resulting gene embedding is summed with the perturbation embedding of each perturbation in the perturbation set (iv). The output is combined across all genes using the cross-gene layer and fed into gene-specific output layers (v). The final result is postperturbation gene expression; MLP, multilayer perceptron.

Full size image

GEARS introduces a new approach of representing each gene and its perturbation using distinct multidimensional embeddings (arbitrary vectors of numbers used to represent a meaningful concept; Fig. 1b and Supplementary Note 1)30,31. Each gene’s embedding is tuned through the course of training to represent key traits of that gene. Splitting the representation into two multidimensional components gives GEARS additional expressivity for capturing gene-specific heterogeneity of perturbation response. Each gene’s embedding is sequentially combined with the perturbation embedding of each gene in the perturbation set and finally used to predict the postperturbation state for that gene. This prediction is conditioned on a single ‘cross-gene’ embedding vector that captures transcriptome-wide information for each cell.

GEARS is uniquely able to predict the outcomes of perturbation sets that involve one or more genes for which there are no experimental perturbation data. GEARS does this by incorporating prior knowledge of gene–gene relationships using a gene coexpression knowledge graph when learning gene embeddings and a Gene Ontology (GO)-derived knowledge graph when learning gene perturbation embeddings (Methods). This relies on two biological intuitions: (i) genes that share similar expression patterns should likely respond similarly to external perturbations, and (ii) genes that are involved in similar pathways should impact the expression of similar genes after perturbation (Fig. 1b). Different knowledge graphs, such as large context-specific networks, may prove more suitable depending on the gene set of interest32 (Supplementary Note 2). GEARS functionalizes this graph-based inductive bias using a graph neural network (GNN) architecture33.

Predicting single-gene perturbation transcriptional responses

In the case of single-gene perturbations, GEARS was evaluated on the perturbation of genes whose data had been held out at the time of training, and thus those genes had not been seen experimentally perturbed during training (Fig. 2a). We used data from two different genetic perturbation screens consisting of 1,543 (RPE-1 cells) and 1,092 (K562 cells) perturbations, respectively, with each measuring over 170,000 cells (Replogle et al.34; Supplementary Notes 3 and 4). The screens were run using the Perturb-seq assay, which combines a pooled screen with a single-cell RNA-sequencing readout of the entire transcriptome for each cell16. GEARS was trained separately on each dataset. In addition to an existing deep learning-based model (CPA), we designed two alternative baseline models for evaluation of performance. One baseline model (no perturbation) assumes that the perturbation does not result in any change in gene expression. The other baseline model first infers a gene regulatory network20 and then linearly propagates the effects of perturbing a gene along this network (adapted from CellOracle22; Supplementary Notes 6 and 7).

a, Train–test data split for single-gene perturbations. b, The m.s.e. in predicted postperturbation gene expression for single-gene perturbations normalized to the no perturbation case. For each perturbation, the 20 most differentially expressed (DE) genes were considered; perturb, perturbation; GRN, gene regulatory network. c, Pearson correlation between mean predicted postperturbation differential gene expression over control and true values across all genes. d, Fraction of the top 20 differentially expressed genes where the predicted postperturbation differential expression is in the opposite direction of the ground truth. e, Train–test data split categories for two-gene perturbations. f, Normalized m.s.e. in predicted postperturbation gene expression for two-gene perturbations. g, Boxes indicate experimentally measured differential gene expression after perturbing the gene combination FOSB and CEBPB (n = 85). The red symbol shows the mean change in gene expression predicted by GEARS when it has only seen FOSB experimentally perturbed at the time of training. The green dotted line shows mean unperturbed control gene expression. Whiskers represent the last data point within 1.5× interquartile range. h, Jaccard similarity between model-predicted differentially expressed genes and true differentially expressed genes. Throughout the figure, markers correspond to the mean and error bars correspond to 95% confidence intervals computed over predictions made by five models trained using different data splits (n = 5).

Full size image

We tested model performance by measuring the mean squared error (m.s.e.; Fig. 2b) and Pearson correlation (Fig. 2c) between the predicted postperturbation gene expression and true postperturbation expression for the held-out set (Supplementary Table 1). Because the vast majority of genes do not show substantial variation between unperturbed and perturbed states, we restricted our m.s.e. analysis to the harder task of only considering the top 20 most differentially expressed genes (Supplementary Note 8). GEARS significantly outperformed all baselines on both datasets with an m.s.e. improvement of 30–50% (Fig. 2b). When considering all genes using Pearson correlation, GEARS exhibited more than two times better performance in the case of both cell lines (Fig. 2c). Additionally, GEARS displayed a clear improvement in capturing the right direction of change in expression following perturbation (Fig. 2d), which reflects a more accurate representation of regulatory relationships. We consistently observed superior performance of GEARS over baselines across metrics (Supplementary Fig. 1) and across five additional datasets, including a genome-wide perturbation screen16,18,34,35,36 (Supplementary Table 2 and Supplementary Figs. 2 and 3). Furthermore, GEARS scaled to large datasets more effectively than conventional gene regulatory network-based methods (Supplementary Table 3). Beyond transcription levels, GEARS also identified groups of genes that induced similar transcriptional responses to perturbation, even when data for their perturbation had not been seen during training (Extended Data Fig. 1 and Supplementary Note 9).

Predicting multigene perturbation outcomes

GEARS is designed to predict transcriptional outcomes for perturbation sets consisting of multiple genes. We evaluated performance using a Perturb-seq dataset (Norman et al.9) containing 131 two-gene perturbations. When evaluating GEARS on two-gene perturbations, we defined three generalization classes based on how many of the genes we see experimentally perturbed at the time of training (Fig. 2e). The first case is when the model has seen each of the two genes in the combination individually experimentally perturbed in the training data (two-gene perturbation, zero of two unseen). The other cases, which are progressively harder to predict, are when either one of the two perturbed genes (one of two unseen) or both genes (two of two unseen) have not been seen individually perturbed at the time of training (Supplementary Fig. 4 and Supplementary Note 10). GEARS improves performance by more than 30% across all cases (Fig. 2f), with the highest improvement of 53% observed when both perturbed genes in the combination are unseen. Improvements were also observed across other metrics (Supplementary Fig. 5) and on a different dataset (Supplementary Tables 2 and 4)37.

Model performance was also analyzed on a gene-by-gene basis. In the case of predicting the outcome of perturbing FOSB with CEBPB, GEARS correctly captured both the right trend and the magnitude of perturbation across all 20 differentially expressed genes (Fig. 2g) even though one of the perturbed genes (CEBPB) had not been seen experimentally perturbed during training. Moreover, the predictions were different from the transcriptional state observed in the case of the single-gene perturbation (FOSB) that was seen at the time of training the model (Supplementary Fig. 6). Similar performance was observed for several other examples across generalization categories (Supplementary Fig. 7). We also measured 50% greater enrichment in the most significant differentially expressed genes as predicted by GEARS than observed with baseline methods (Fig. 2h, Extended Data Fig. 2 and Supplementary Note 11).

Although the incorporation of knowledge graphs was instrumental in enabling these predictions (Extended Data Fig. 3 and Supplementary Fig. 8), it also limits the ability of GEARS to predict outcomes for perturbing previously unperturbed genes that are not well connected in this graph (Extended Data Fig. 4 and Supplementary Note 12). GEARS makes use of a Bayesian formulation to overcome this challenge by outputting an uncertainty metric that is inversely correlated with model performance (Supplementary Fig. 9).

Predicting non-additive combinatorial perturbation effects

In the case of a two-gene perturbation, if the outcomes of perturbing the two genes independently are already known, then a naive model could simply add the perturbational effects to estimate the effect of the combinatorial perturbation (Fig. 3a,b). However, genes are known to interact with one another to produce non-additive genetic interactions after perturbation. For example, two genes that independently cause a minor loss in cell growth could synergistically interact with one another following combinatorial perturbation to cause cell death.

Contact us to discuss your requirements of Kexin Gear. Our experienced sales team can help you identify the options that best suit your needs.

a, Illustration of an additive interaction between two genes after perturbation. X and Y represent change over the unperturbed state caused by single-gene perturbations. Z is a combinatorial perturbation of both genes. b, Definition of genetic interaction subtypes. c, Mean precision@10 in predicting genetic interactions from 131 two-gene combinations (error bars represent s.d.). A random model performs 1,000 random draws; other models perform three predictions (n = 3). d, Change in gene expression after perturbing the combination PTPN12 and ZBTB25. The gray bars show the true mean postperturbation gene expression change (n = 257). The hatched gray bars show the true change for each of the two single-gene perturbations performed individually (PTPN12 n = 164 and ZBTB25 n = 247), which are summed by the naive additive model. The red bar indicates the prediction made by GEARS (n = 3 trained models). Error bars correspond to 95% confidence interval.

Full size image

We defined five types of genetic interactions (Supplementary Note 15): synergy, suppression, neomorphism, redundancy and epistasis (Supplementary Note 16). When both genes in a two-gene combination had been individually perturbed, the genetic interaction scores predicted by GEARS showed a stronger correlation with the ground truth scores calculated using true expression than existing methods. For instance, the correlation coefficient (R2) was approximately 0.4 for synergy, neomorphism and redundancy, whereas it was only around 0.0 for the same interactions when predicted by CPA (Extended Data Fig. 5).

To identify new genetic interactions, GEARS can recommend pairs of genes that are predicted to have strong genetic interactions. To assess the real-world application of GEARS where the recommended pairs are then experimentally validated, we calculated performance metrics based on the top-ranked predictions. Precision@10 measures the fraction of predicted combinations in the top ten that truly exhibit a specific genetic interaction subtype, as determined by experimentally measured gene expression after perturbation (Supplementary Note 17). When compared to baseline methods, GEARS improved precision@10 by more than 40% for four of five genetic interaction subtypes, and the improvement exceeded 90% for redundancy and epistasis (Fig. 3c). Additionally, GEARS demonstrated a twofold increase in accuracy when predicting the ten strongest interactions for a specific genetic interaction subtype (top ten accuracy; Extended Data Fig. 6b). Further validation using an additional dataset confirmed the effectiveness of GEARS, showing a 20% increase in accuracy across four genetic interaction subtypes. Moreover, the precision–recall curves for all observed genetic interaction subtypes exhibited a higher area under the curve than other methods (Supplementary Fig. 12)37. In scenarios where only one gene had been perturbed previously, GEARS successfully detected synergistic and suppressive interactions (Supplementary Fig. 13).

Different types of genetic interactions can also be evaluated at the level of individual genes. For this, the 20 most affected genes were identified for each two-gene combination (Supplementary Note 18). Based on the m.s.e. for these genes, GEARS was able to capture the effects of different types of genetic interactions more than 40% better than existing methods across three of the five genetic interaction subtypes (Extended Data Fig. 6a). As an example, GEARS predicted the correct non-additive effects across almost all of the top ten non-additively expressed genes following the perturbation of PTPN12 and ZBTB25 (Fig. 3d). This was also observed across other examples belonging to different genetic interaction subtypes (Supplementary Fig. 14).

Predicting new biologically meaningful phenotypes

We applied GEARS to the discovery of new phenotypes by predicting the outcomes of all pairwise combinatorial perturbations of 102 genes from the Norman et al. dataset9 (Fig. 4a). To make this prediction, GEARS was trained using the postperturbational gene expression profiles for both one-gene perturbation outcomes and 128 two-gene perturbation outcomes (Fig. 4b and Supplementary Note 13). The predicted postperturbation expression captured many distinct phenotypic clusters, including those previously identified in Norman et al.9 (Fig. 4c and Supplementary Note 13). Additionally, GEARS predicts a few new phenotypes, including one cluster showing high expression of erythroid markers.

a, Workflow for predicting all pairwise combinatorial perturbation outcomes of a set of genes. b, Low-dimensional representation of postperturbation gene expression for 102 one-gene perturbations and 128 two-gene perturbations used to train GEARS. A random selection is labeled. c, GEARS predicts postperturbation gene expression for all 5,151 pairwise combinations of the 102 single genes seen experimentally perturbed. Predicted postperturbation phenotypes (non-black symbols) are often different from phenotypes seen experimentally (black symbols). Colors indicate Leiden clusters labeled using marker gene expression (Supplementary Information).

Full size image

To ascertain the biological relevance of this newly predicted phenotype, which was not observed in the training data, we compared it with data for proerythroblasts from the Tabula Sapiens cell atlas (Supplementary Fig. 10 and Supplementary Note 14). While this cluster’s distinct high erythroid marker expression has still not been experimentally validated, its identification demonstrates the ability of GEARS to expand the space of postperturbation phenotypes beyond what is observed in perturbational experiments. Moreover, we validated the robustness of this prediction by excluding all phenotypically similar postperturbation outcomes during training (Supplementary Fig. 11).

Mapping combinatorial space of diverse genetic interactions

We extended our analysis to predict genetic interactions among all possible pairwise combinations of 102 genes (Fig. 5a), following CRISPRa-based combinatorial gene activation9. By leveraging the predicted postperturbation gene expression for each of the 5,151 pairwise combinatorial perturbations, we constructed a genetic interaction map that could simultaneously represent five distinct types of genetic interactions: synergy, suppression, neomorphism, redundancy and epistasis. The genetic interaction map revealed a rich and diverse landscape of genetic interactions, with many genes exhibiting strong tendencies toward specific genetic interaction subtypes (Fig. 5b). This effect is most evident in the interactions between functionally related genes, which is in line with previous experimental results15,16,38. For instance, genes involved in early erythroid differentiation pathways (PTPN12, IKZF3 and LHX1) show a consistent trend of strong synergistic interactions with one another. Moreover, the uniqueness of this genetic interaction map is in how it captures a much broader range of interactions than a conventional genetic interaction map, which focuses primarily on synergistic or buffering interactions (Supplementary Fig. 15)15.

a, Workflow for predicting genetic interaction (GI) scores. b, Multidimensional genetic interaction map generated by GEARS for all pairwise combinations of 102 single genes perturbed in Norman et al.9. For each combination, GEARS predicted genetic interaction scores for five different genetic interactions: synergy and suppression (red to blue), neomorphism (green), redundancy (orange) and epistasis (purple).

Full size image

To validate some of these predictions, we used data from a cell fitness screen that perturbed all pairwise combinations of 92 genes9 (Supplementary Note 19). GEARS performed comparably to a real Perturb-seq experiment in capturing the strong interaction effects observed in the cell fitness screen (Extended Data Fig. 7). The distribution of GEARS-predicted genetic interaction scores was significantly higher for perturbations showing synergistic cell fitness effects (P < 0.0013, n = 123; data were analyzed by one-sided t-test comparing the means) and lower for those showing buffering effects (P < 4 × 10−5, n = 69) than those showing approximately additive cell fitness effects. These findings increase our confidence that several strong interactions captured in the genetic interaction map are biologically meaningful even though not all predictions have been experimentally validated. When trained to directly predict cell fitness, GEARS also showed strong performance (R2 between 0.64 and 0.93; Supplementary Figs. 16 and 17 and Supplementary Note 20).

If you are looking for more details, kindly visit Straight Bevel Gear.