Mutatais in the Software Libraries Industry

Mutata

The following piece claims to reduce an artist's cognitive overload in graphics design software using a simplified digital compositing node graph aka Pipeline. Proceed at your own risk. Content Overview An Example of Cognitive Overload A Mad Proposal A Mad Comparison to Digital Compositing Node Graph What Changed? Nothing, Really An Insane User Interface Then, things Start to get Crazier Digital Compositing Paradigm in a Pipeline Omg! Advantages. Lol! You must be Mad too An Example of Cognitive Overload Imagine a graphic artist performing a series of photo edits: 1. Apply Disc Blur to an image.
2. Apply Sepia Tone to Disc Blur.
3. Blend the Sepia Tone with the original. The intent of the artist usually consists of a sequence of actions to be translated into operations  carried out with the graphics software. For example, the process of the photo edits above may involve creating a new document, selecting the optimal image options in the application menu, creating Layers to apply a Disc Blur, changing properties in a side panel, bringing up an object dialog box, and repeating the process to add additional layers for the Sepia Tone/Blend to achieve the desired effect. This approach of user interface and when exacerbated with an increasing number of steps results in and . NON-STREAMLINED disrupts the flow of thoughts of the artist Cognitive Overload loss of creative productivity We are OK with the above. What's WRONG? A Mad Proposal We the user interface into a linear sequence of actions that can be compounded or stacked like a digital compositing node graph but with simplification to express how to achieve the desired outcome succinctly, like below: streamline Pipeline

1. Read Image
2. Disc Blur
3. Sepia Tone
4. Blend (2,3) A Pipeline is to the user interface of graphics design software like what Markdown is to HTML. A Mad Comparison to Digital Compositing Node Graph To someone familiar with Digital Compositing, they will immediately recognize that the list of steps, the Pipeline, above is "almost" identical to a digital compositing node graph. A digital compositing node graph is shown below: Read Image
|         |
|         |
|         V
|         Disc Blur
|         |
|         |
|         V
|         Sepia Tone
|         |
|         |
V         V
   Blend What Changed? Nothing, Really A Pipeline is indeed similar to a digital compositing node graph with a subtle yet significant change. Instead of displaying a full node graph graphically, with two lines from the Read Image node and Sepia Tone node connecting to the Blend node. The Pipeline simplifies the node graph by just showing a list of steps and a spreadsheet-like function for the final Blend step. 4. Blend (2,3) This creativity of arranging a digital compositing node graph as a Pipeline enables the intent of the artist to be conveyed as a succinct list of steps, following the artist's flow of thoughts from start to end, without a graphical map. The Pipeline also guides the artist into thinking of what to do next in a streamlined manner. Without using a traditional node graph, more information can be conveyed in a smaller amount of space linearly, providing a larger contextual overview to the creative mind. An Insane User Interface A Pipeline, in software, maps directly to a list and is easy to implement. The list removes the need for a complicated graphical map that may require (scrolling) to identify the right node to work on. The properties screen of a node can also be brought up intuitively and naturally by drilling into the node. panning Pipeline

1. Read Image
2. Disc Blur  ----> Drill into the Properties screen
3. Sepia Tone
4. Blend (2,3) PROTOTYPE - Fits into a mobile phone Then, Things Start to get Crazier No loss of information The important thing to note is the above creativity does not lose any information. The simplified node graph above, the Pipeline, in a mathematical sense, can be fully represented as a node graph (Directed Acyclic Graph) in any manner or form. For example, if we have the following node graph for video processing. Read media Read media 
|          |
V          V
Premult    Color Correction 
|          |
|          V 
|          Transform 
|          |
|          V 
|          Gaussian Blur 
|          | 
V          V 
Merge 
|
V 
Viewer It can be flattened, streamlined, and represented as follows: Read media
|
V
Premult

Read media
|
V
Color Correction
|
V
Transform
|
V
Gaussian Blur

Merge
|
V
Viewer Note the break from the first series after the 'Premult' node and the second break after the 'Gaussian Blur' node. Pipeline

1. Read media         >
2. Premult            >

3. Read media         >
4. Color Correction   >
5. Transform          >
6. Blur               >

7. Merge (2,6)        >
8. Viewer             > The space between node 2 and node 3 represents the break, while the '>' is optional and used to indicate the availability of a properties screen. Digital Compositing Paradigm in a Pipeline The paradigm of node-based digital compositing where we can lay out steps in a progression and make modifications to an earlier step to change the outcome is completely kept. Each node can be easily reused by referencing it with a node number as in Step 7, and if required, used further in a later step, saving time and effort. In the same way that a digital compositing node graph is broken into a series of nodes in a graph, a Pipeline breaks it into a series of actions or steps. A Pipeline, from another angle, is thus like a single-column spreadsheet, a metaphor that many computer users are quite familiar with. Viewing the output of each step: Viewer Cycling The arrangement in a series of steps enables the output of each progression step to be viewed easily, for example, by long pressing on a node on the Pipeline. This enables an artist to step through the progression to reinforce his or her cognitive working memory of what has been performed. Connecting the steps: Auto-Chaining Each node on the Pipeline that requires an input can be assumed to be taking the output of the previous node automatically. For example, the 'Premult' node in Step 2 is assumed to automatically take the output from 'Read Media' in Step 1. Connecting the steps like a node graph: Reverse Compositing The auto-chaining or automatic preceding node referencing behavior can also be altered by enabling the artist to make changes in the properties of a node. For example, in Step 7, the artist can choose from its properties screen any of the previous nodes, such as nodes 2 and 6, for blending. Omg! Advantages. Lol! Modular Extensibility A Pipeline, being almost identical to a digital compositing node graph, enables it to achieve the same modular extensibility in software development. Software developers can think of developing graphical effects, filters, animations, and 3D operations modularly as a node. Each node is accompanied by a properties user interface that does not interfere with other parts of the software. A node and its user interface can thus be developed and tested independently while knowing ultimately that it can be easily integrated into a full node graph, aka the Pipeline, to achieve any complex graphics operation. Such a design will benefit the open-source community greatly where many different developers can build an open-source Pipeline, the Open Pipeline, together in a distributed and collaborative manner. Reduce Information Overload To start using a graphics application, artists usually need to learn the way of achieving it through documentation. Often, the documentation requires an artist to follow a series of screenshots, explaining where and how to click or tap on different parts of the screen using a non-streamlined user interface offered by the graphics application. The non-streamlined user interface makes the information hard for an artist to remember and may require the artist to constantly refer to the documentation. Over time, this introduces an additional cost that, when accumulated, can lead to . Information Overload Succinct Self-Describing Pipeline The Open Pipeline reduces Information Overload as it succinctly describes what needs to be done and allows all necessary details to be shown in context nearby. This significantly benefits documentation: tutorials, articles, or books. Open Pipeline

1. Disc Blur: radius = 8
2. Sepia Tone: intensity = 1
3. Blend (1,2) The details of the radius for Disc Blur are shown as part of the node in the Pipeline. Moreover, besides being , it is common for the above description to supporting screenshots as it is self-explanatory. succinct NOT REQUIRE You must be Mad too If you have followed this article till here, find out more about the author's banishment due to his 'NOT SO' , and where he is living in exile. His ‘BLUFF’ of implementing a node that ‘CAN BE INTEGRATED EASILY’ into the Pipeline. And him performing a MAGIC TRICK. REALLY. He compares himself with the Roman poet Ovid by quoting on ‘how shapes changed into new bodies’ in Metamorphoses: Open Pipeline Photo Curve Photo Fire Effect – OVID In nova fert animus mutatas dicere formas corpora; di, coeptis (nam vos mutastis et illas) adspirate meis primaque ab origine mundi ad mea perpetuum deducite tempora carmen. Sigh, I give up He further mumbles about animating a graphics object with a node. METAMORPHOSIS The lead image for this article was generated by HackerNoon's AI Image Generator via the prompt "cognitive overload".

Revolutionary User Interface Design: Tackling Cognitive Overload in Graphics Software

Insect Adventures by Jean-Henri Fabre and Louise Hasbrouck Zimm, is part of the HackerNoon Books Series. You can jump to any chapter in this book here . THE GEOMETRY OF THE SPIDER’S WEB CHAPTER XXV. THE GEOMETRY OF THE SPIDER’S WEB [This chapter, one of the most wonderful in Fabre’s books, is included in a simplified form in this volume, on account of its interest to such younger readers as have studied geometry.] WHEN we look at the webs of the Garden Spiders, especially those of the Silky Spider and the Banded Spider, we notice first that the spokes or radii are equally spaced; the angles formed by each consecutive pair are of the same value; and this in spite of their number, which in the webs of the Silky Spider sometimes exceeds forty. We know in what a strange way the Spider weaves her web and divides the area of the web into a large number of equal parts or sectors, a number which is almost always the same in the work of each species of Spider. The Spider darts here and there when laying her spokes as if she had no plan, and this irresponsible way of working produces a beautiful web like the rose-window in a church, a web which no designer could have drawn better with compasses. We shall also notice that, in each sector, the various chords, parts of the angular spiral, are parallel to one another and gradually draw closer together as they near the center. With the two radiating lines that frame them they form obtuse angles on one side and acute angles on the other; and these angles remain constant in the same sector, because the chords are parallel. There is more than this: these same angles, the obtuse as well as the acute, do not alter in value, from one sector to another, as far as the eye can judge. Taken as a whole, therefore, the spiral consists of a series of cross-bars intersecting the several radiating lines obliquely at angles of equal value. By this characteristic we recognize what geometricians have named the “logarithmic spiral.” It is famous in science. The logarithmic spiral describes an endless number of circuits around its pole, to which it constantly draws nearer without ever being able to reach it. We could not see such a line, the whole of it, even with our best philosophical instruments. It exists only in the imagination of scientists. But the Spider knows it, and winds her spiral in the same way, and very accurately at that. Another property of this spiral is that if one in imagination winds a flexible thread around it, then unwinds the thread, keeping it taut the while, its free end will describe a spiral similar at all points to the original. The curve will merely have changed places. Jacques Bernouilli, the professor of mathematics who discovered this magnificent theorem, had engraved on his tomb, as one of his proudest titles to fame, the spiral and its double, made by the unwinding of the thread. Written underneath it was the sentence: Eadem mutata resurgo. “I rise again like unto myself.” It was a splendid flight of fancy which showed his belief in immortality. Now is this logarithmic spiral, with its curious properties, merely an idea of the geometricians? Is it a mere dream, an abstract riddle? No, it is a reality in the service of life, a method of construction often employed by animals in their architecture. The Mollusk never makes its shell without reference to the scientific curve. The first-born of the species knew it and put it into practice; it was as perfect in the dawn of creation as it can be to-day. There are perfect examples of this spiral found in the shells of fossils. To this day, the last representative of an ancient tribe, the Nautilus of the Southern Seas, remains faithful to the old design, and still whirls its spiral logarithmically, as did its ancestors in the earliest ages of the world’s existence. Even in the stagnant waters of our grassy ditches, a tiny Shellfish, no bigger than a duckweed, rolls its shell in the same manner. The common snail-shell is constructed according to logarithmic laws. Where do these creatures pick up this science? We are told that the Mollusk is descended from the Worm. One day the Worm, rendered frisky by the sun, brandished its tail and twisted it into a corkscrew for sheer glee. There and then the plan of the future spiral shell was discovered. This is what is taught quite seriously, in these days, as the very last word in science. But the Spider will have none of this theory. For she is not related to the Worm; and yet she is familiar with the logarithmic spiral and uses it in her web, in a simpler form. The Mollusk has years in which to build her spiral, so she makes it very perfectly. The Spider has only an hour at the most to spread her net, so she makes only a skeleton of the curve; but she knows the same line dear to the Snail. What guides her? Nothing but an inborn skill, whose effects the animal is no more able to control than the flower is able to control the arrangement of its petals and stamens. The Spider practices higher geometry without knowing or caring. The thing works of itself and takes its way from an instinct imposed upon creation at the start. The stone thrown by the hand returns to earth describing a certain curve; the dead leaf torn and wafted away by a breath of wind makes its journey from the tree to the ground with a similar curve. The curve is known to science and is called the “parabola.” The geometricians speculate still more about this curve; they imagine it rolling on an indefinite straight line and ask what course the focus of the curve follows. The answer comes that the focus of the parabola describes a “catenary,” a line whose algebraic symbol is so complicated that a numeral will not express it. The nearest it can get is this terrible sum: The geometricians do not attempt to refer to it by this number; they give it a letter, e. Is this line imaginary? Not at all; you may see the catenary frequently. It is the shape taken by a flexible cord when held at each end and relaxed; it is the line that governs the shape of a sail filled out by the wind. All this answers to the number e. What a quantity of abstruse science for a bit of string! Let us not be surprised. A pellet of shot swinging at the end of a thread, a drop of dew trickling down a straw, a splash of water rippling under the kisses of the air, a mere trifle, after all, becomes tremendously complicated when we wish to examine it with the eye of calculation. We need the club of Hercules to crush a fly. Our methods of mathematical investigation are certainly ingenious; we cannot too much admire the mighty brains that have invented them; but how slow and laborious they seem when compared with the smallest actual things! Shall we never be able to inquire into reality in a simpler fashion? Shall we be intelligent enough some day to do without all these heavy formulæ? Why not? Here we have the magic number e reappearing, written on a Spider’s thread. On a misty morning the sticky threads are laden with tiny drops, and, bending under the burden, have become so many catenaries, so many chains of limpid gems, graceful chaplets arranged in exquisite order and following the curve of a swing. If the sun pierce the mist, the whole lights up with rainbow-colored fires and becomes a dazzling cluster of diamonds. The number e is in its glory. Geometry, that is to say, the science of harmony in space, rules over everything. We find it in the arrangement of the scales of a fir-cone, as in the arrangement of a Spider’s sticky snare; we find it in the spiral of a snail-shell, in the chaplet of a Spider’s thread, as in the orbit of a planet; it is everywhere, as perfect in the world of atoms as in the world of immensities. And this universal geometry tells us of a Universal Geometrician, whose divine compass has measured all things. I prefer that, as an explanation of the logarithmic curve of the Nautilus and the Garden Spiders, to the Worm screwing up the tip of its tail. It may not perhaps be in agreement with some latter-day teaching, but it takes a loftier flight. About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. Jean-Henri Fabre and Louise Hasbrouck Zimm (2014). Insect Adventures. Urbana, Illinois: Project Gutenberg. Retrieved October https://www.gutenberg.org/cache/epub/45812/pg45812-images.html This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org , located at https://www.gutenberg.org/policy/license.html .

THE GEOMETRY OF THE SPIDER’S WEB

THE GEOMETRY OF THE EPEIRA’S WEB

SECONDARY SEXUAL CHARACTERS OF MAN

This paper is available on under CC 4.0 license. Arxiv Authors: (1) Md Masud Rana, Department of Mathematics, University of Kentucky; (2) Duc Duy Nguyen, Department of Mathematics, University of Kentucky & ducnguyen@uky.edu. Table of Links Abstract & Introduction Datasets and Results Methods Conclusion, Data and Software Availability, Competing interests, Acknowledgments & References 4 Conclusion The study of protein-protein interactions (PPIs) and the prediction of mutation-induced binding free energy changes are of great importance in understanding the molecular basis of biological processes. The application of geometric graph theory and atom-level graph coloring techniques provides a powerful framework for analyzing biomolecules and capturing their intricate relationships. By utilizing the concept of geometric subgraphs and constructing multi-scale weighted colored geometric subgraphs (MWCGS), we can effectively represent the structural and functional properties of PPIs. The site-specific MWCGS features allow us to extract meaningful patterns and characteristics, shedding light on the effects of mutations and the underlying molecular interactions. In this work, we developed a mutation-induced binding free energy change predictor, called GGL-PPI, by incorporating site-specific MWCGS features for PPIs and gradient-boosting trees. Our method demonstrates superior performance compared to existing methods. The model was validated on three datasets: AB-Bind S645, SKEMPI 1.0 S1131, and SKEMPI 2.0 S4169 and S8338, showcasing its robustness and effectiveness. Furthermore, GGL-PPI was evaluated on a blind test set, the Ssym dataset. To prevent data leakage between the test and training sets, the model was trained on a homology-reduced balanced training set Q3488. This approach ensures the reliability and fairness of the evaluation process. GGL-PPI exhibits the most unbiased and superior performance in predicting binding free energy changes for both direct and reverse mutations, outperforming other existing methods, particularly for reverse mutations. Overall, the results highlight the potential of the GGL-PPI approach in accurately predicting mutation-induced binding free energy changes in protein-protein interactions, providing valuable insights into the molecular mechanisms underlying protein-protein interactions and facilitating drug design and discovery efforts. 5 Data and Software Availability The source code is available at Github: https://github.com/NguyenLabUKY/GGL-Mutation. 6 Competing interests No competing interest is declared. 7 Acknowledgments This work is supported in part by funds from the National Science Foundation (NSF: # 2053284, # 2151802, and # 2245903), and the University of Kentucky Startup Fund. References [1] Dana Chuderland and Rony Seger. 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Mathdl: mathematical deep learning for d3r grand challenge 4. J. Comput. Aided. Mol. Des., 34(2):131–147, 2020. [52] Jerome H Friedman. Greedy function approximation: a gradient boosting machine. Annals of statistics, pages 1189–1232, 2001. This paper is available on under CC 4.0 license. Arxiv

PPIs and the Prediction of Mutation-Induced Binding Free Energy Changes: What It All Means

This paper is available on arxiv under CC 4.0 license. Authors: (1) Md Masud Rana, Department of Mathematics, University of Kentucky; (2) Duc Duy Nguyen, Department of Mathematics, University of Kentucky & ducnguyen@uky.edu. Table of Links Abstract & Introduction Datasets and Results Methods Conclusion, Data and Software Availability, Competing interests, Acknowledgments & References 3 Methods 3.1 Graph Theory and Atom-level Interactions in Biomolecules Graph theory provides a mathematical framework that is widely applied in the study of biomolecules such as proteins, DNA, and RNA. For a biomolecule, a graph G(V, E) is a collection of nodes V and edges E that can represent the connectivity and relationships between different atoms or residues within the molecule. A refinement to this representation is graph coloring, a technique that assigns unique labels to different atom types within the biomolecule. This enriched, colored graph encodes diverse atomic interactions, paving the way for a collective and coarse-grained description of the dataset. In this representation, atoms with assigned labels are organized into subgraphs, and the colored edges between them represent atom-specific interactions. The advantage of using subgraphs lies in their ability to focus on specific regions or components of the biomolecule. By isolating relevant subsets of atoms, subgraphs allow us to identify localized patterns, interactions, or clusters that might not be evident in the global graph representation. This targeted approach provides a more nuanced understanding of the structural and functional properties of biomolecules. To extract atom-level interaction information, we consider specific atom types based on their names in the PDB structure such as carbon alpha (CA), carbon beta (CB), carbon delta-1 (CD1), etc. These atom names serve as identifiers for specific positions within a protein’s three-dimensional structure. They help define the individual atoms that constitute amino acids, the building blocks of proteins, and provide crucial information about their spatial orientation and chemical properties. We consider a total of 37 distinct atom names that are frequently found in protein structures within the PDB database. These atom types are represented by the set A. To simplify the notation, we assume the set A is sorted in alphanumeric order, A = {C, CA, CB, · · · , N, ND1, ND2, · · · , O, OD1, · · · , SD, SG}, serves as a measure of the combined strength of interaction between chosen pairs of atom types, providing valuable insights into the molecular structure and properties. 3.2 Geometric Subgraph Representation of PPIs In the context of studying protein-protein interactions (PPIs) and predicting the effects of mutations on these interactions, it is important to focus on the relevant regions where the interactions occur. While protein-protein complexes can consist of a large number of atoms, the interactions between proteins primarily take place at specific regions known as interfaces. To streamline computational costs and concentrate on pertinent information, it is common practice to consider only the protein atoms near the binding sites. The binding site, in this context, refers to the region within a certain cutoff distance c from the chain where the mutation occurred. By defining the binding site in this way, we can narrow our focus to the specific area where the interaction and subsequent effects of the mutation are most pronounced. Furthermore, when analyzing the effects of mutations, it is crucial to incorporate geometric graph information from the mutation sites and their neighboring regions. The mutation site is defined as the region within a cutoff distance c from the mutated residue, allowing us to capture the structural changes resulting from the mutation. To construct a site-specific multiscale weighted colored geometric subgraph (MWCGS) representation for a PPI, both the wild-type and mutant-type proteins are considered. This leads to four sets of features for each PPI, corresponding to the two sites and the two types of proteins involved. Each set consists of 37 × 37 = 1369 MWCGS features, representing the interactions between the atom types involved in the PPI. These features encompass diverse chemical and biological properties, such as the presence of specific interatomic interactions involving oxygen and nitrogen atoms, the hydrophobic nature of certain regions, and the ability of atoms to undergo polarization, among other relevant molecular characteristics. By utilizing these site-specific MWCGS features, we can uncover valuable insights into the effects of mutations and the underlying molecular interactions, revealing significant information and characteristics embedded within the PPI system. 3.3 Geometric Graph Learning for PPIs Accurately predicting the changes in binding affinity induced by mutations in protein-protein complexes poses a significant challenge due to the complex nature of these systems. The interactions between proteins are highly intricate, and the effects of mutations can be subtle and context-dependent. Machine learning techniques offer a promising approach to tackle this problem by leveraging the power of data-driven models to capture complex patterns and relationships. Machine learning algorithms can aid in predicting mutation-induced binding affinity changes by learning from a set of training examples that consist of protein-protein complexes with known experimental binding affinities. These algorithms can analyze the features extracted from the complexes, such as geometric graph information, to identify relevant patterns and associations between the features and the binding affinities. By learning from these patterns, the algorithms can generalize and make predictions on unseen protein-protein complexes. There are several machine learning algorithms that can be used in combination with geometric graph features to predict binding affinity changes. These algorithms include random forests [49], support vector machines (SVM) [50], neural networks [51], and gradient boosting trees (GBT) [52]. Each algorithm has its strengths and weaknesses, and their performance can vary depending on the specific problem and dataset. Among these algorithms, gradient boosting trees (GBT) have gained significant popularity in recent years [39]. GBT is an ensemble method that builds a sequence of weak learners, typically decision trees, to correct the errors made by the previous learners. By combining these weak learners, GBT can effectively model complex relationships and improve prediction accuracy. One advantage of GBT is its robustness against overfitting, which is especially beneficial when dealing with a moderate number of features. Additionally, GBT models can provide interpretability, allowing us to gain insights into the factors contributing to the binding affinity changes. The implementation of the GBT algorithm in this study utilized the scikit-learn package (v 0.24.1). To optimize the performance of the GBT model for ensemble methods, specific hyperparameters were fine-tuned. The number of estimators was set to 40000, indicating the number of weak learners in the ensemble, while the learning rate was set to 0.001, determining the contribution of each weak learner to the final prediction. Given the large number of features involved in the prediction task, an efficient training process was achieved by limiting the maximum number of features considered to the square root of the descriptor length. This approach helped expedite the training process without compromising the overall performance of the GBT model. To ensure reliable performance evaluation, fifty runs were performed for each feature set, employing different random seeds. By averaging the results obtained from these runs, a more robust and representative performance measure was obtained. Despite the complexity of the prediction task and the involvement of numerous features, the selected parameter settings and multiple runs yielded satisfactory performance results. The GBT approach was chosen for its ability to effectively handle overfitting, exhibit good performance with moderately sized datasets, and provide interpretable models. These characteristics make GBT a suitable and reliable choice for this study, enabling accurate predictions of mutation-induced binding affinity changes in protein-protein complexes using the provided geometric graph features. This paper is available on under CC 4.0 license. Arxiv

The Methods We Used to Predict Mutation-Induced Binding Free Energy Changes

This paper is available on arxiv under CC 4.0 license. Authors: (1) Md Masud Rana, Department of Mathematics, University of Kentucky; (2) Duc Duy Nguyen, Department of Mathematics, University of Kentucky & ducnguyen@uky.edu. Table of Links Abstract & Introduction Datasets and Results Methods Conclusion, Data and Software Availability, Competing interests, Acknowledgments & References Abstract Protein-protein interactions (PPIs) are critical for various biological processes, and understanding their dynamics is essential for decoding molecular mechanisms and advancing fields such as cancer research and drug discovery. Mutations in PPIs can disrupt protein binding affinity and lead to functional changes and disease. Predicting the impact of mutations on binding affinity is valuable but experimentally challenging. Computational methods, including physics-based and machine learning-based approaches, have been developed to address this challenge. Machine learning-based methods, fueled by extensive PPI datasets such as Ab-Bind, PINT, SKEMPI, and others, have shown promise in predicting binding affinity changes. However, accurate predictions and generalization of these models across different datasets remain challenging. Geometric graph learning has emerged as a powerful approach, combining graph theory and machine learning, to capture structural features of biomolecules. We present GGL-PPI, a novel method that integrates geometric graph learning and machine learning to predict mutation-induced binding free energy changes. GGL-PPI leverages atom-level graph coloring and multi-scale weighted colored geometric subgraphs to extract informative features, demonstrating superior performance on three validation datasets, namely AB-Bind, SKEMPI 1.0, and SKEMPI 2.0 datasets. Evaluation on a blind test set highlights the unbiased predictions of GGLPPI for both direct and reverse mutations. The findings underscore the potential of GGL-PPI in accurately predicting binding free energy changes, contributing to our understanding of PPIs and aiding drug design efforts. — geometric graph, machine learning, protein-protein interactions, mutation, binding free energy changes Keywords 1 Introduction Protein-protein interactions (PPIs) play a fundamental role in numerous biological processes, including cell signaling, metabolic pathways, and immune responses [1;2;3]. Understanding PPIs and their dynamics is crucial for unraveling the intricate mechanisms underlying these processes and holds significant implications for various fields, such as cancer research, drug discovery, and personalized medicine [3;4]. The effects of mutations on PPIs have drawn substantial attention due to their potential impact on protein function and cellular behavior [5;6;7;8]. Missense mutations, which involve single amino acid substitutions, can disrupt the binding affinity between proteins and their partners [9;10]. Such alterations can lead to malfunctioning PPI networks, resulting in diseases, drug resistance, or other molecular disorders [11;12;13;14;15;16]. Therefore, accurate prediction of the impact of mutations on binding affinity holds significant importance in understanding disease mechanisms, facilitating therapeutic interventions, and enabling the design of innovative biopharmaceuticals. One of the key parameters used to assess the impact of mutations on PPIs is the binding free energy change (∆∆G). This thermodynamic parameter quantifies the difference in binding affinity between the wild-type and mutant protein complexes. Experimental determination of ∆∆G values, while accurate, can be tedious and costly. Consequently, there has been a surge in the development of computational methods to predict these energy changes. Broadly, these computation approaches fall into two main categories: physics-based and machine learning-based methods. The former, rooted in biophysical principles, delves into protein conformations and offers a rigorous approach [17;18;19]. However, they often demand significant computational resources and are not always scalable. On the other hand, machine learning-based methods have gained popularity due to their scalability and rapid prediction capabilities. Leveraging the wealth of data from PPI datasets such as ASEdb [20], PINT[21], ProTherm[22], SKEMPI [23;24], and others [25;26;27], machine learning models like mCSM28, BindProf 6 , iSEE29, MutaBind [7] , and several others [30;31;32;33] have been developed. These models have shown significant potential in predicting ∆∆Gs. However, challenges such as imbalanced training datasets, generalization across different PPI datasets, and the intricacy of capturing complex sequence-structure-function relationships remain obstacles [34;35;36;37]. This underscores the need for further research to enhance machine learning methodologies, ensuring accurate and efficient ∆∆G predictions. In recent years, geometric graph learning has emerged as a promising approach for analyzing complex biomolecular systems [38;39;40]. By representing proteins and their interactions as graphs, this methodology leverages the power of graph theory and machine learning to capture essential structural and spatial features of the biomolecular complexes. Specifically, the use of geometric subgraphs, which encode local interactions between atoms and residues, offers a rich representation. This not only sheds light on intricate molecular details but also provides insights into their impact on binding affinity [39]. This work presents a novel method, called GGL-PPI (Geometric Graph Learning for Protein-Protein Interactions), which combines the principles of geometric graph learning and machine learning to predict mutation-induced binding free energy changes. The workflow of GGL-PPI is depicted in Figure 1. Central to its methodology, GGL-PPI utilizes atom-level graph coloring and multi-scale weighted colored geometric subgraphs, enabling the extraction of informative features from protein structures and their interactions. These features serve as inputs to a gradient-boosting tree model, which facilitates precise and consistent predictions of binding free energy change upon mutations. When compared with existing models, GGL-PPI consistently outperforms state-of-the-art approaches across all datasets. Further addressing its generalizability, GGL-PPI was evaluated on a blind test set, Ssym dataset [36]. This evaluation was conducted using a homology-reduced balanced training set to avert data leakage, showcasing GGL-PPI’s robust performance and ability to produce unbiased predictions for both direct and reverse mutations. This paper is available on under CC 4.0 license. Arxiv

GGL-PPI: Geometric Graph Learning to Predict Mutation-Induced Binding Free Energy Changes

This paper is available on arxiv under CC 4.0 license. Authors: (1) Matu´s Medo, Department for BioMedical Research, Inselspital, Bern University Hospital, University of Bern, Department of Radiation Oncology, Inselspital, Bern University Hospital, University of Bern and matus.medo@unifr.ch; (2)  Michaela Medova, Department for BioMedical Research, Inselspital, Bern University Hospital, University of Bern, and Department of Radiation Oncology, Inselspital, Bern University Hospital, University of Bern. Table of Links Abstract & Introduction Results Discussion Materials and methods Acknowledgement & References Supporting Information Supporting Information This paper is available on under CC 4.0 license. Arxiv

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