A Hybrid Structure-Based Machine Learning Approach for Predicting Kinase Inhibition by Small Molecules

Kinases have been the focus of drug discovery programs for three decades leading to over 70 therapeutic kinase inhibitors and biophysical affinity measurements for over 130,000 kinase-compound pairs. Nonetheless, the precise target spectrum for many kinases remains only partly understood. In this study, we describe a computational approach to unlocking qualitative and quantitative kinome-wide binding measurements for structure-based machine learning. Our study has three components: (i) a Kinase Inhibitor Complex (KinCo) data set comprising in silico predicted kinase structures paired with experimental binding constants, (ii) a machine learning loss function that integrates qualitative and quantitative data for model training, and (iii) a structure-based machine learning model trained on KinCo. We show that our approach outperforms methods trained on crystal structures alone in predicting binary and quantitative kinase-compound interaction affinities; relative to structure-free methods, our approach also captures known kinase biochemistry and more successfully generalizes to distant kinase sequences and compound scaffolds

Predictability of death time is improved by knowledge of key protein concentrations.

<p>(<b>A</b>) Scatter plot of predicted <i>t_MOMP</i> as a function of Bid initial concentration when no other initial protein concentrations are known (left) or when the initial concentrations of the next seven most influential proteins as ranked by R² of <i>t_MOMP</i> are also known with precision within ±12.5% (right). Simulations shown were selected from a series of 10⁵ simulations sampling from a joint distribution for Bax, Bcl-2, Bid, caspase-3 and XIAP (as measured) and independently for all other proteins with non-zero initial concentration. To mimic knowledge of a protein concentration, simulations were randomly selected from those with an initial concentration of mean value ±12.5% for this protein. Black points represent the predicted death times given perfect knowledge of the concentrations of all model species. MSE is the mean squared error relative to perfect knowledge (black points). (<b>B</b>) Graph of the mean squared error in <i>t_MOMP</i> (relative to perfect knowledge, black points in (A)) as a function of the number of proteins whose concentration is “known”; values are the averages from different runs and error bars represent the standard deviations (n = 10). “Known” proteins were added either randomly (blue), by high-to-low R2 for <i>t_MOMP</i> (gray; Figure S10) or <i>t_PARP</i> (yellow; <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002482#pcbi-1002482-g005" target="_blank">Figure 5E</a>), or by high-to-low CV for <i>t_PARP</i> (brown; <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002482#pcbi-1002482-g004" target="_blank">Figure 4C</a>).</p

Variability in cell fate and time-to-death depends on the interplay between multiple factors.

<p>(<b>A</b>) Plots of <i>t_MOMP</i> as a function of Bcl-2 level for three levels of Bax (0.3X [Bax]₀, left, 1X [Bax]₀, center, and 3X [Bax]₀, right) and Bid (0.1X [Bid]₀, blue, 1X [Bid]₀, green, and 10X [Bid]₀, red). Orange shading represents the 5^th and 95^th percentiles of the measured distribution of endogenous Bcl-2 in HeLa cells. (<b>B</b>) Histograms of the <i>t_MOMP</i> distributions in the range of endogenous Bcl-2 (indicated by the orange shading) for varying Bid and Bax levels. For panels A and B, initial concentrations of Bcl-2 were sampled uniformly in the exponent between 10² to 10⁷ molecules per cell and all other proteins concentrations were set at their default mean values (Table S2 in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002482#pcbi.1002482.s003" target="_blank">Text S3</a>).</p

Sensitivity of <i>t_MOMP</i> to changes in protein initial concentrations and measurements of protein variance and co-variance in HeLa cells.

<p>(<b>A</b>) Scatter plots show the simulated relationship between initial protein concentration and <i>t_MOMP</i> (green) or numerically calculated <i>t_MOMP</i> sensitivity (blue; <i>t_MOMP</i> sensitivity is unitless and is calculated using finite-difference approximations of the derivatives, or slopes, of the green curves) following TRAIL addition, for the indicated proteins. The initial concentration for the indicated protein was uniformly sampled in the exponent for values between 10² to 10⁷ proteins per cell while all other initial protein concentrations and rate constants were set at their default value. Vertical bars represent the 5^th and 95^th percentiles of the measured (orange, see panel B–D and Table S2) or assumed (gray) distributions in endogenous protein concentrations for untreated HeLa cells. Shaded regions in the plot for Bid show an example of concentration ranges that were attained experimentally using RNAi knockdown and GFP-fusion protein overexpression <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002482#pcbi.1002482-Spencer1" target="_blank">[15]</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002482#pcbi.1002482-Albeck2" target="_blank">[23]</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002482#pcbi.1002482-Albeck3" target="_blank">[29]</a>. (<b>B</b>) Overlays of endogenous Bcl-2 concentration distributions in untreated HeLa cells as measured by flow cytometry (FACS, blue), or immunofluorescence (IF, green). The FACS data are well fit by a log-normal distribution (Fit, red); a.u., arbitrary units. (<b>C</b>) Scatter plot of anti-Bcl-2 vs. GFP-Bcl-2 signal in GFP-Bcl-2-transfected HeLa cells measured by 2-color flow cytometry. (<b>D</b>) Histograms of the endogenous Bcl-2 concentration distribution in wildtype HeLa cells measured with an anti-Bcl-2 antibody (left) and of the off-diagonal noise distribution for the scatter plot in (B) (right). Both distributions are for mean-centered data to allow comparison of variability; std is the standard deviation and IQR is the interquartile range.</p

The TRAIL-induced signaling network.

<p>(<b>A</b>) Schematic diagram of the TRAIL-induced cell death signaling network including live-cell imaging reporters for MOMP, the inter-membrane space reporter protein (IMS-RP), and for initiator or effector caspase activity (IC-RP or EC-RP, respectively). The features <i>t_PARP</i>, <i>f_PARP</i>, and <i>t_switch</i> can all be evaluated based on EC-RP dynamics and <i>t_MOMP</i> can be measured in live cells using IMS-RP. IC-RP enables measurement of the threshold of cleaved initiator caspase substrate required for MOMP and of an initial rate of caspase activity (<i>k_IC</i>). See also <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002482#pcbi-1002482-g002" target="_blank">Figure 2</a> and Table <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002482#pcbi-1002482-box001" target="_blank">Box 1</a> for description of how reporter dynamics were modeled and for precise definitions of features.</p

Overexpression of Bcl-2 in HeLa cells shows a region of variable fate before a threshold is reached where all cells survive.

<p>(<b>A–B</b>) Scatter plots showing the relationship between <i>t_MOMP</i> and total Bcl-2 amount as measured in HeLa cells treated with 50 ng/ml TRAIL and 2.5 µg/ml cycloheximide (left) or simulated in EARM1.3, sampling linearly in the exponent for GFP-Bcl-2 levels and from a joint distribution for Bax, Bcl-2, Bid, caspase-3 and XIAP and independently for all other non-zero initial protein concentrations (right). Quantitative immunoblotting (Figure S5 in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002482#pcbi.1002482.s001" target="_blank">Text S1</a>) and single-cell fluorescence quantification were combined to derive the absolute levels of GFP-Bcl-2 for each cell, to which the average endogenous Bcl-2 amount (30,000 molecules/cell; experimentally unobservable) was added to convert the <i>x</i>-axis to units of total Bcl-2 molecules per cell. Cells that did not undergo MOMP by 12 hr were assumed to have survived. (<b>C</b>) Boxplots of initial protein concentration distributions for surviving (green) or dying (gray) simulated cells selected for having a range of total Bcl-2 expression where ∼50% died (∼53,000–57,000 molecules/cell). Box edges show the 25^th and 75^th percentiles, notches show the 95% confidence interval for the median (horizontal line), and whiskers extend to the most extreme data points that are not considered outliers. Asterisks indicate proteins for which the surviving and dying simulated cells show significantly different medians for initial concentration (p<0.05), double asterisks mark the distributions for [Bax]₀ which have the most significant difference. (<b>D</b>) Bar graph showing the coefficients of variation (CV) obtained for model output distributions of <i>t_MOMP</i> when using 3×10⁴ Bcl-2/cell as the mean [Bcl-2]₀ (striped bars; reproduced from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002482#pcbi-1002482-g004" target="_blank">Figure 4B</a>), or when the average [Bcl-2]₀ was changed to 6×10⁴ Bcl-2/cell (solid bars). As in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002482#pcbi-1002482-g004" target="_blank">Figure 4</a>, proteins were classified as affecting the pre-MOMP rate of initiator caspase activity (Rate; gray), the MOMP threshold (Threshold; purple) or post-MOMP processes (Post-MOMP; green).</p

Pathways of EGF receptor internalization.

<p>EGF receptor can be internalized via clathrin dependent endocytosis (CDE) and clathrin independent endocytosis (CIE). <b>A</b>) Schematic representation of EGF receptor internalization according to Schmidt-Glenewinkel et al. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0082593#pone.0082593-SchmidtGlenewinkel1" target="_blank">[21]</a>. <b>B</b>) Example trajectory representing class 0 (‘pathway off’) for clathrin dependent EGFR-internalization. <b>C</b>) Example trajectory representing class 1 (‘pathway on’) for clathrin independent EGFR- internalization.</p

Logic-Based Models for the Analysis of Cell Signaling Networks

Computational models are increasingly used to analyze the operation of complex biochemical networks, including those involved in cell signaling networks. Here we review recent advances in applying logic-based modeling to mammalian cell biology. Logic-based models represent biomolecular networks in a simple and intuitive manner without describing the detailed biochemistry of each interaction. A brief description of several logic-based modeling methods is followed by six case studies that demonstrate biological questions recently addressed using logic-based models and point to potential advances in model formalisms and training procedures that promise to enhance the utility of logic-based methods for studying the relationship between environmental inputs and phenotypic or signaling state outputs of complex signaling networks

The impact of variability in protein initial concentrations is feature-specific.

<p>(<b>A</b>) Histograms showing the distributions of initial concentrations of Bcl-2 and XIAP used as inputs to the model (left) and the model output distributions for <i>t_MOMP</i> and <i>t_switch</i> (right). Input distributions were generated by sampling 10,000 times from a log-normal distribution parameterized with measured or assumed mean and CV as listed in Table S2 in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002482#pcbi.1002482.s003" target="_blank">Text S3</a>. Output distributions were calculated from10⁴ simulations where the initial concentration of the indicated protein was sampled from the distributions shown on the left; all others protein concentrations were set to their default value (Table S2 in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002482#pcbi.1002482.s003" target="_blank">Text S3</a>). (<b>B–E</b>) Bar graph showing the coefficients of variation (CV) obtained for model output distributions of <i>t_MOMP</i> (<b>B</b>), <i>t_PARP</i> (<b>C</b>), <i>f_PARP</i> (<b>D</b>), and <i>t_switch</i> (<b>E</b>) from series of 10⁴ simulations where the indicated protein initial concentration is sampled from a log-normal distribution and all other concentrations set to their default value (Table S2 in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002482#pcbi.1002482.s003" target="_blank">Text S3</a>). Proteins were classified as affecting the pre-MOMP rate of initiator caspase activity (Rate; gray), the MOMP threshold (Threshold; purple) or post-MOMP processes (Post-MOMP; green) based on their position in the TRAIL-induced signaling network (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002482#pcbi-1002482-g001" target="_blank">Figure 1</a>). In panels B–E, the black bar (“All”) indicates the variability observed in a series of 10⁴ simulations where all non-zero initial conditions were independently sampled from log-normal protein distributions using the measured CV where available or else CV = 0.25 (as listed in Table S2 in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002482#pcbi.1002482.s003" target="_blank">Text S3</a>).</p

Conditions C1-C3 on initial values of species required for reaching a distinct steady-state class and activation level of clathrin-independent EGFR-internalization according to Schmidt-Glenewinkel et al. [21].

<p>Conditions C1-C3 on initial values of species required for reaching a distinct steady-state class and activation level of clathrin-independent EGFR-internalization according to Schmidt-Glenewinkel et al. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0082593#pone.0082593-SchmidtGlenewinkel1" target="_blank">[21]</a>.</p