The structure is the message: Preserving experimental context through tensor decomposition.

Recent biological studies have been revolutionized in scale and granularity by multiplex and high-throughput assays. Profiling cell responses across several experimental parameters, such as perturbations, time, and genetic contexts, leads to richer and more generalizable findings. However, these multidimensional datasets necessitate a reevaluation of the conventional methods for their representation and analysis. Traditionally, experimental parameters are merged to flatten the data into a two-dimensional matrix, sacrificing crucial experiment context reflected by the structure. As Marshall McLuhan famously stated, "the medium is the message." In this work, we propose that the experiment structure is the medium in which subsequent analysis is performed, and the optimal choice of data representation must reflect the experiment structure. We review how tensor-structured analyses and decompositions can preserve this information. We contend that tensor methods are poised to become integral to the biomedical data sciences toolkit.

Censored Least Squares for Imputing Missing Values in PARAFAC Tensor Factorization.

Tensor factorization is a dimensionality reduction method applied to multidimensional arrays. These methods are useful for identifying patterns within a variety of biomedical datasets due to their ability to preserve the organizational structure of experiments and therefore aid in generating meaningful insights. However, missing data in the datasets being analyzed can impose challenges. Tensor factorization can be performed with some level of missing data and reconstruct a complete tensor. However, while tensor methods may impute these missing values, the choice of fitting algorithm may influence the fidelity of these imputations. Previous approaches, based on alternating least squares with prefilled values or direct optimization, suffer from introduced bias or slow computational performance. In this study, we propose that censored least squares can better handle missing values with data structured in tensor form. We ran censored least squares on four different biological datasets and compared its performance against alternating least squares with prefilled values and direct optimization. We used the error of imputation and the ability to infer masked values to benchmark their missing data performance. Censored least squares appeared best suited for the analysis of high-dimensional biological data by accuracy and convergence metrics across several studies.

Tensor modeling of MRSA bacteremia cytokine and transcriptional patterns reveals coordinated, outcome-associated immunological programs.

Methicillin-resistant Staphylococcus aureus (MRSA) bacteremia is a common and life-threatening infection that imposes up to 30% mortality even when appropriate therapy is used. Despite in vitro efficacy determined by minimum inhibitory concentration breakpoints, antibiotics often fail to resolve these infections in vivo, resulting in persistent MRSA bacteremia. Recently, several genetic, epigenetic, and proteomic correlates of persistent outcomes have been identified. However, the extent to which single variables or their composite patterns operate as independent predictors of outcome or reflect shared underlying mechanisms of persistence is unknown. To explore this question, we employed a tensor-based integration of host transcriptional and cytokine datasets across a well-characterized cohort of patients with persistent or resolving MRSA bacteremia outcomes. This method yielded high correlative accuracy with outcomes and immunologic signatures united by transcriptomic and cytokine datasets. Results reveal that patients with persistent MRSA bacteremia (PB) exhibit signals of granulocyte dysfunction, suppressed antigen presentation, and deviated lymphocyte polarization. In contrast, patients with resolving bacteremia (RB) heterogeneously exhibit correlates of robust antigen-presenting cell trafficking and enhanced neutrophil maturation corresponding to appropriate T lymphocyte polarization and B lymphocyte response. These results suggest that transcriptional and cytokine correlates of PB vs. RB outcomes are complex and may not be disclosed by conventional modeling. In this respect, a tensor-based integration approach may help to reveal consensus molecular and cellular mechanisms and their biological interpretation.

Mixed IgG Fc immune complexes exhibit blended binding profiles and refine FcR affinity estimates.

Immunoglobulin G (IgG) antibodies coordinate immune effector responses by interacting with effector cells via fragment crystallizable γ (Fcγ) receptors. The IgG Fc domain directs effector responses through subclass and glycosylation variation. Although each Fc variant has been extensively characterized in isolation, during immune responses, IgG is almost always produced in Fc mixtures. How this influences effector responses has not been examined. Here, we measure Fcγ receptor binding to mixed Fc immune complexes. Binding of these mixtures falls along a continuum between pure cases and quantitatively matches a mechanistic model, except for several low-affinity interactions mostly involving IgG2. We find that the binding model provides refined estimates of their affinities. Finally, we demonstrate that the model predicts effector cell-elicited platelet depletion in humanized mice. Contrary to previous views, IgG2 exhibits appreciable binding through avidity, though it is insufficient to induce effector responses. Overall, this work demonstrates a quantitative framework for modeling mixed IgG Fc-effector cell regulation.

The NF-κB multidimer system model: A knowledge base to explore diverse biological contexts.

The nuclear factor κB (NF-κB) system is critical for various biological functions in numerous cell types, including the inflammatory response, cell proliferation, survival, differentiation, and pathogenic responses. Each cell type is characterized by a subset of 15 NF-κB dimers whose activity is regulated in a stimulus-responsive manner. Numerous studies have produced different mathematical models that account for cell type-specific NF-κB activities. However, whereas the concentrations or abundances of NF-κB subunits may differ between cell types, the biochemical interactions that constitute the NF-κB signaling system do not. Here, we synthesized a consensus mathematical model of the NF-κB multidimer system, which could account for the cell type-specific repertoires of NF-κB dimers and their cell type-specific activation and cross-talk. Our review demonstrates that these distinct cell type-specific properties of NF-κB signaling can be explained largely as emergent effects of the cell type-specific expression of NF-κB monomers. The consensus systems model represents a knowledge base that may be used to gain insights into the control and function of NF-κB in diverse physiological and pathological scenarios and that describes a path for generating similar regulatory knowledge bases for other pleiotropic signaling systems.

A quantitative view of strategies to engineer cell-selective ligand binding.

A critical property of many therapies is their selective binding to target populations. Exceptional specificity can arise from high-affinity binding to surface targets expressed exclusively on target cell types. In many cases, however, therapeutic targets are only expressed at subtly different levels relative to off-target cells. More complex binding strategies have been developed to overcome this limitation, including multi-specific and multivalent molecules, creating a combinatorial explosion of design possibilities. Guiding strategies for developing cell-specific binding are critical to employ these tools. Here, we employ a uniquely general multivalent binding model to dissect multi-ligand and multi-receptor interactions. This model allows us to analyze and explore a series of mechanisms to engineer cell selectivity, including mixtures of molecules, affinity adjustments, valency changes, multi-specific molecules and ligand competition. Each of these strategies can optimize selectivity in distinct cases, leading to enhanced selectivity when employed together. The proposed model, therefore, provides a comprehensive toolkit for the model-driven design of selectively binding therapies.

A general model of multivalent binding with ligands of heterotypic subunits and multiple surface receptors.

Multivalent cell surface receptor binding is a ubiquitous biological phenomenon with functional and therapeutic significance. Predicting the amount of ligand binding for a cell remains an important question in computational biology as it can provide great insight into cell-to-cell communication and rational drug design toward specific targets. In this study, we extend a mechanistic, two-step multivalent binding model. This model predicts the behavior of a mixture of different multivalent ligand complexes binding to cells expressing various types of receptors. It accounts for the combinatorially large number of interactions between multiple ligands and receptors, optionally allowing a mixture of complexes with different valencies and complexes that contain heterogeneous ligand units. We derive the macroscopic predictions and demonstrate how this model enables large-scale predictions on mixture binding and the binding space of a ligand. This model thus provides an elegant and computationally efficient framework for analyzing multivalent binding.

Tensor-structured decomposition improves systems serology analysis.

Systems serology provides a broad view of humoral immunity by profiling both the antigen-binding and Fc properties of antibodies. These studies contain structured biophysical profiling across disease-relevant antigen targets, alongside additional measurements made for single antigens or in an antigen-generic manner. Identifying patterns in these measurements helps guide vaccine and therapeutic antibody development, improve our understanding of diseases, and discover conserved regulatory mechanisms. Here, we report that coupled matrix-tensor factorization (CMTF) can reduce these data into consistent patterns by recognizing the intrinsic structure of these data. We use measurements from two previous studies of HIV- and SARS-CoV-2-infected subjects as examples. CMTF outperforms standard methods like principal components analysis in the extent of data reduction while maintaining equivalent prediction of immune functional responses and disease status. Under CMTF, model interpretation improves through effective data reduction, separation of the Fc and antigen-binding effects, and recognition of consistent patterns across individual measurements. Data reduction also helps make prediction models more replicable. Therefore, we propose that CMTF is an effective general strategy for data exploration in systems serology.