Mathematical models of cellular signaling and supramolecular self-assembly

Synthetic biologists endeavor to predict how the increasing complexity of multi-step signaling cascades impacts the fidelity of molecular signaling, whereby cellular state information is often transmitted with proteins diffusing by a pseudo-one-dimensional stochastic process. We address this problem by using a one-dimensional drift-diffusion model to derive an approximate lower bound on the degree of facilitation needed to achieve single-bit informational efficiency in signaling cascades as a function of their length. We find that a universal curve of the Shannon-Hartley form describes the information transmitted by a signaling chain of arbitrary length and depends upon only a small number of physically measurable parameters. This enables our model to be used in conjunction with experimental measurements to aid in the selective design of biomolecular systems. Another important concept in the cellular world is molecular self-assembly. As manipulating the self-assembly of supramolecular and nanoscale constructs at the single-molecule level increasingly becomes the norm, new theoretical scaffolds must be erected to replace the classical thermodynamic and kinetics-based models. The models we propose use state probabilities as its fundamental objects and directly model the transition probabilities between the initial and final states of a trajectory. We leverage these probabilities in the context of molecular self-assembly to compute the overall likelihood that a specified experimental condition leads to a desired structural outcome. We also investigated a larger complex self-assembly system, the heterotypic interactions between amyloid-beta and fatty acids by an independent ensemble kinetic simulation using an underlying differential equation-based system which was validated by biophysical experiments

Fatty Acid Concentration and Phase Transitions Modulate Aβ Aggregation Pathways

Aggregation of amyloid β (Aβ) peptides is a significant event that underpins Alzheimer disease (AD) pathology. Aβ aggregates, especially the low-molecular weight oligomers, are the primary toxic agents in AD and hence, there is increasing interest in understanding their formation and behavior. Aggregation is a nucleation-dependent process in which the pre-nucleation events are dominated by Aβ homotypic interactions. Dynamic flux and stochasticity during pre-nucleation renders the reactions susceptible to perturbations by other molecules. In this context, we investigate the heterotypic interactions between Aβ and fatty acids (FAs) by two independent tool-sets such as reduced order modelling (ROM) and ensemble kinetic simulation (EKS). We observe that FAs influence Aβ dynamics distinctively in three broadly-defined FAconcentration regimes containing non-micellar, pseudo-micellar or micellar phases. While the non-micellar phase promotes on-pathway fibrils, pseudo-micellar and micellar phases promote predominantly off-pathway oligomers, albeit via subtly different mechanisms. Importantly off-pathway oligomers saturate within a limited molecular size, and likely with a different overall conformation than those formed along the on-pathway, suggesting the generation of distinct conformeric strains of Aβ, which may have profound phenotypic outcomes. Our results validate previous experimental observations and provide insights into potential influence of biological interfaces in modulating Aβ aggregation pathways

A Game-Theoretic Approach to Deciphering the Dynamics of Amyloid-Beta Aggregation Along Competing Pathways

Aggregation of amyloid-β (Aβ) peptides is a significant event that underpins Alzheimer\u27s disease (AD). Aβ aggregates, especially the low-molecular weight oligomers, are the primary toxic agents in AD pathogenesis. Therefore, there is increasing interest in understanding their formation and behaviour. In this paper, we use our previously established results on heterotypic interactions between Aβ and fatty acids (FAs) to investigate off-pathway aggregation under the control of FA concentrations to develop a mathematical framework that captures the mechanism. Our framework to define and simulate the competing on- and off-pathways of Aβ aggregation is based on the principles of game theory. Together with detailed simulations and biophysical experiments, our models describe the dynamics involved in the mechanisms of Aβ aggregation in the presence of FAs to adopt multiple pathways. Specifically, our reduced-order computations indicate that the emergence of off- or on-pathway aggregates are tightly controlled by a narrow set of rate constants, and one could alter such parameters to populate a particular oligomeric species. These models agree with the detailed simulations and experimental data on using FA as a heterotypic partner to modulate the temporal parameters. Predicting spatio-temporal landscape along competing pathways for a given heterotypic partner such as lipids is a first step towards simulating scenarios in which the generation of specific ‘conformer strains’ of Aβ could be predicted. This approach could be significant in deciphering the mechanisms of amyloid aggregation and strain generation, which are ubiquitously observed in many neurodegenerative diseases

A Taxonomic Survey of Physics-Informed Machine Learning

Physics-informed machine learning (PIML) refers to the emerging area of extracting physically relevant solutions to complex multiscale modeling problems lacking sufficient quantity and veracity of data with learning models informed by physically relevant prior information. This work discusses the recent critical advancements in the PIML domain. Novel methods and applications of domain decomposition in physics-informed neural networks (PINNs) in particular are highlighted. Additionally, we explore recent works toward utilizing neural operator learning to intuit relationships in physics systems traditionally modeled by sets of complex governing equations and solved with expensive differentiation techniques. Finally, expansive applications of traditional physics-informed machine learning and potential limitations are discussed. In addition to summarizing recent work, we propose a novel taxonomic structure to catalog physics-informed machine learning based on how the physics-information is derived and injected into the machine learning process. The taxonomy assumes the explicit objectives of facilitating interdisciplinary collaboration in methodology, thereby promoting a wider characterization of what types of physics problems are served by the physics-informed learning machines and assisting in identifying suitable targets for future work. To summarize, the major twofold goal of this work is to summarize recent advancements and introduce a taxonomic catalog for applications of physics-informed machine learning

Benchmarking the communication fidelity of biomolecular signaling cascades featuring pseudo-one-dimensional transport

Synthetic biologists endeavor to predict how the increasing complexity of multi-step signaling cascades impacts the fidelity of molecular signaling, whereby information about the cellular state is often transmitted with proteins that diffuse by a pseudo-one-dimensional stochastic process. This begs the question of how the cell leverages passive transport mechanisms to distinguish informative signals from the intrinsic noise of diffusion. We address this problem by using a one-dimensional drift-diffusion model to derive an approximate lower bound on the degree of facilitation needed to achieve single-bit informational efficiency in signaling cascades as a function of their length. Within the assumptions of our model, we find that a universal curve of the Shannon-Hartley form describes the information transmitted by a signaling chain of arbitrary length and depends upon only a small number of physically measurable parameters. This enables our model to be used in conjunction with experimental measurements to aid in the selective design of biomolecular systems that can overcome noise to function reliably, even at the single-cell level

Cause and Consequence of Aβ: Lipid Interactions in Alzheimer Disease Pathogenesis

Self-templating propagation of protein aggregate conformations is increasingly becoming a significant factor in many neurological diseases. In Alzheimer disease (AD), intrinsically disordered amyloid-β (Aβ) peptides undergo aggregation that is sensitive to environmental conditions. High-molecular weight aggregates of Aβ that form insoluble fibrils are deposited as senile plaques in AD brains. However, low-molecular weight aggregates called soluble oligomers are known to be the primary toxic agents responsible for neuronal dysfunction. The aggregation process is highly stochastic involving both homotypic (Aβ-Aβ) and heterotypic (Aβ with interacting partners) interactions. Two of the important members of interacting partners are membrane lipids and surfactants, to which Aβ shows a perpetual association. Aβ–membrane interactions have been widely investigated for more than two decades, and this research has provided a wealth of information. Although this has greatly enriched our understanding, the objective of this review is to consolidate the information from the literature that collectively showcases the unique phenomenon of lipid-mediated Aβ oligomer generation, which has largely remained inconspicuous. This is especially important because Aβ aggregate “strains” are increasingly becoming relevant in light of the correlations between the structure of aggregates and AD phenotypes. Here, we will focus on aspects of Aβ-lipid interactions specifically from the context of how lipid modulation generates a wide variety of biophysically and biochemically distinct oligomer sub-types. This, we believe, will refocus our thinking on the influence of lipids and open new approaches in delineating the mechanisms of AD pathogenesis. This article is part of a Special Issue entitled: Protein Aggregation and Misfolding at the Cell Membrane Interface edited by Ayyalusamy Ramamoorthy

Propagation of an Aβ Dodecamer Strain Involves a Three-Step Mechanism and a Key Intermediate

Proteinaceous deposits composed of fibrillar amyloid-β (Aβ) are the primary neuropathological hallmarks in Alzheimer disease (AD) brains. The nucleation-dependent aggregation of Aβ is a stochastic process with frequently observed heterogeneity in aggregate size, structure, and conformation that manifests in fibril polymorphism. Emerging evidence indicates that polymorphic variations in Aβ fibrils contribute to phenotypic diversity and the rate of disease progression in AD. We recently demonstrated that a dodecamer strain derived from synthetic Aβ42 propagates to morphologically distinct fibrils and selectively induces cerebral amyloid angiopathy phenotype in transgenic mice. This report supports the growing contention that stable oligomer strains can influence phenotypic outcomes by faithful propagation of their structures. Although we determined the mechanism of dodecamer propagation on a mesoscopic scale, the molecular details of the microscopic reactions remained unknown. Here, we have dissected and evaluated individually the kinetics of macroscopic phases in aggregation to gain insight into the process of strain propagation. The bulk rates determined experimentally in each phase were used to build an ensemble kinetic simulation model, which confirmed our observation that dodecamer seeds initially grow by monomer addition toward the formation of a key intermediate. This is followed by conversion of the intermediate to fibrils by oligomer elongation and association mechanisms. Overall, this report reveals important insights into the molecular details of oligomer strain propagation involved in AD pathology

Capacity estimates of additive inverse Gaussian molecular channels with relay characteristics

Molecular communications is an emergent field that seeks to develop nanoscale communication devices using design principles gleaned from studies of the topology and dynamic properties of biological signaling networks. To understand how these networks function, we must first characterize the functional building blocks that compose them, and the best candidates for those are the topologically distinct subnetworks, or motifs, that appear in a statistically improbable abundance. In transcriptional networks, one of the most prevalent motifs is the feed-forward loop, a three node motif wherein one top-level protein regulates the expression of a target gene either directly or indirectly through an intermediate regulator protein. Currently, no systematic effort has been made to treat an isolated feed-forward loop as a stand-alone signal amplifying/attenuating device and understand its communication capacity in terms of the diffusion of individual molecules. To address this issue, we derive a theorem that estimates the upper and lower bounds of the channel capacity for a relay channel, which structurally corresponds to a feed-forward loop, by using an additive inverse Gaussian noise channel model of protein-ligand binding. Our results are just a first step towards assessing the performance bounds of simplified biological circuits in order to guide the development and optimization of synthetic, bio-inspired devices that can be used as information processing and forwarding units

Multimodal Deep Learning Methods on Image and Textual Data to Predict Radiotherapy Structure Names

Physicians often label anatomical structure sets in Digital Imaging and Communications in Medicine (DICOM) images with nonstandard random names. Hence, the standardization of these names for the Organs at Risk (OARs), Planning Target Volumes (PTVs), and ‘Other’ organs is a vital problem. This paper presents novel deep learning methods on structure sets by integrating multimodal data compiled from the radiotherapy centers of the US Veterans Health Administration (VHA) and Virginia Commonwealth University (VCU). These de-identified data comprise 16,290 prostate structures. Our method integrates the multimodal textual and imaging data with Convolutional Neural Network (CNN)-based deep learning approaches such as CNN, Visual Geometry Group (VGG) network, and Residual Network (ResNet) and shows improved results in prostate radiotherapy structure name standardization. Evaluation with macro-averaged F1 score shows that our model with single-modal textual data usually performs better than previous studies. The models perform well on textual data alone, while the addition of imaging data shows that deep neural networks achieve better performance using information present in other modalities. Additionally, using masked images and masked doses along with text leads to an overall performance improvement with the CNN-based architectures than using all the modalities together. Undersampling the majority class leads to further performance enhancement. The VGG network on the masked image-dose data combined with CNNs on the text data performs the best and presents the state-of-the-art in this domain