There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This presentation is a case study taken from the travel and holiday industry. Paxport/Multicom, based in UK and Sweden, have recently adopted a recommendation system for holiday accommodation bookings. Machine learning techniques such as Collaborative Filtering have been applied using Python (3.5.1), with Jupyter (4.0.6) as the main framework. Data scale and sparsity present significant challenges in the case study, and so the effectiveness of various techniques are described as well as the performance of Python-based libraries such as Python Data Analysis Library (Pandas), and Scikit-learn (built on NumPy, SciPy and matplotlib). The presentation is suitable for all levels of programmers.

Machine learning with Python

The past several months have witnessed the emergence of SARS-CoV-2 variants with novel spike protein mutations that are influencing the epidemiological and clinical aspects of the COVID-19 pandemic. These variants can increase rates of virus transmission and/or increase the risk of reinfection and reduce the protection afforded by neutralizing monoclonal antibodies and vaccination. These variants can therefore enable SARS-CoV-2 to continue its spread in the face of rising population immunity while maintaining or increasing its replication fitness. The identification of four rapidly expanding virus lineages since December 2020, designated variants of concern, has ushered in a new stage of the pandemic. The four variants of concern, the Alpha variant (originally identified in the UK), the Beta variant (originally identified in South Africa), the Gamma variant (originally identified in Brazil) and the Delta variant (originally identified in India), share several mutations with one another as well as with an increasing number of other recently identified SARS-CoV-2 variants. Collectively, these SARS-CoV-2 variants complicate the COVID-19 research agenda and necessitate additional avenues of laboratory, epidemiological and clinical research.

/pdf/the-biological-and-clinical-significance-of-emerging-sars-4cwn3ih835.pdf

The biological and clinical significance of emerging SARS-CoV-2 variants.

The latest severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variant Omicron (B.1.1.529) has ushered panic responses around the world due to its contagious and vaccine escape mutations. The essential infectivity and antibody resistance of the SARS-CoV-2 variant are determined by its mutations on the spike (S) protein receptor-binding domain (RBD). However, a complete experimental evaluation of Omicron might take weeks or even months. Here, we present a comprehensive quantitative analysis of Omicron’s infectivity, vaccine breakthrough, and antibody resistance. An artificial intelligence (AI) model, which has been trained with tens of thousands of experimental data and extensively validated by experimental results on SARS-CoV-2, reveals that Omicron may be over 10 times more contagious than the original virus or about 2.8 times as infectious as the Delta variant. On the basis of 185 three-dimensional (3D) structures of antibody–RBD complexes, we unveil that Omicron may have an 88% likelihood to escape current vaccines. The U.S. Food and Drug Administration (FDA)-approved monoclonal antibodies (mAbs) from Eli Lilly may be seriously compromised. Omicron may also diminish the efficacy of mAbs from AstraZeneca, Regeneron mAb cocktail, Celltrion, and Rockefeller University. However, its impacts on GlaxoSmithKline’s sotrovimab appear to be mild. Our work calls for new strategies to develop the next generation mutation-proof SARS-CoV-2 vaccines and antibodies.

https://pubs.acs.org/doi/pdf/10.1021/acs.jcim.1c01451

Omicron Variant (B.1.1.529): Infectivity, Vaccine Breakthrough, and Antibody Resistance

Mutations Strengthened SARS-CoV-2 Infectivity.

Advanced mathematics, such as multiscale weighted colored subgraph and element specific persistent homology, and machine learning including deep neural networks were integrated to construct mathematical deep learning models for pose and binding affinity prediction and ranking in the last two D3R Grand Challenges in computer-aided drug design and discovery. D3R Grand Challenge 2 focused on the pose prediction, binding affinity ranking and free energy prediction for Farnesoid X receptor ligands. Our models obtained the top place in absolute free energy prediction for free energy set 1 in stage 2. The latest competition, D3R Grand Challenge 3 (GC3), is considered as the most difficult challenge so far. It has five subchallenges involving Cathepsin S and five other kinase targets, namely VEGFR2, JAK2, p38-α, TIE2, and ABL1. There is a total of 26 official competitive tasks for GC3. Our predictions were ranked 1st in 10 out of these 26 tasks.

/pdf/mathematical-deep-learning-for-pose-and-binding-affinity-uyncctornq.pdf

Mathematical deep learning for pose and binding affinity prediction and ranking in D3R Grand Challenges

The ability to predict protein-protein interactions is crucial to our understanding of a wide range of biological activities and functions in the human body, and for guiding drug discovery. Despite considerable efforts to develop suitable computational methods, predicting protein-protein interaction binding affinity changes following mutation (ΔΔG) remains a severe challenge. Algebraic topology, a champion in recent worldwide competitions for protein-ligand binding affinity predictions, is a promising approach to simplifying the complexity of biological structures. Here we introduce element- and site-specific persistent homology (a new branch of algebraic topology) to simplify the structural complexity of protein-protein complexes and embed crucial biological information into topological invariants. We also propose a new deep learning algorithm called NetTree to take advantage of convolutional neural networks and gradient-boosting trees. A topology-based network tree is constructed by integrating the topological representation and NetTree for predicting protein-protein interaction ΔΔG. Tests on major benchmark datasets indicate that the proposed topology-based network tree is an important improvement over the current state of the art in predicting ΔΔG.

A topology-based network tree for the prediction of protein-protein binding affinity changes following mutation.

Protein–ligand binding is essential to almost all life processes. The understanding of protein–ligand interactions is fundamentally important to rational drug and protein design. Based on large scale data sets, we show that protein rigidity strengthening or flexibility reduction is a mechanism in protein–ligand binding. Our approach based solely on rigidity is able to unveil a surprisingly apparently long-range contribution of apparently four residue layers to protein–ligand binding, which has ramifications for drug and protein design. Additionally, the present work reveals that among various pairwise interactions, the short-range ones within the distance of the van der Waals diameter are most important. It is found that the present approach outperforms all other state-of-the-art scoring functions for protein–ligand binding affinity predictions of two benchmark test sets.

Rigidity Strengthening: A Mechanism for Protein-Ligand Binding.

We present the performances of our mathematical deep learning (MathDL) models for D3R Grand Challenge 4 (GC4). This challenge involves pose prediction, affinity ranking, and free energy estimation for beta secretase 1 (BACE) as well as affinity ranking and free energy estimation for Cathepsin S (CatS). We have developed advanced mathematics, namely differential geometry, algebraic graph, and/or algebraic topology, to accurately and efficiently encode high dimensional physical/chemical interactions into scalable low-dimensional rotational and translational invariant representations. These representations are integrated with deep learning models, such as generative adversarial networks (GAN) and convolutional neural networks (CNN) for pose prediction and energy evaluation, respectively. Overall, our MathDL models achieved the top place in pose prediction for BACE ligands in Stage 1a. Moreover, our submissions obtained the highest Spearman correlation coefficient on the affinity ranking of 460 CatS compounds, and the smallest centered root mean square error on the free energy set of 39 CatS molecules. It is worthy to mention that our method on docking pose predictions has significantly improved from our previous ones.

Menglun Wang

Papers

Mutations Strengthened SARS-CoV-2 Infectivity.

Mathematical deep learning for pose and binding affinity prediction and ranking in D3R Grand Challenges

A topology-based network tree for the prediction of protein-protein binding affinity changes following mutation.

Rigidity Strengthening: A Mechanism for Protein-Ligand Binding.

MathDL: mathematical deep learning for D3R Grand Challenge 4