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Multi-stage models for the failure of complex systems, cascading disasters, and the onset of disease.

ABSTRACT: Complex systems can fail through different routes, often progressing through a series of (rate-limiting) steps and modified by environmental exposures. The onset of disease, cancer in particular, is no different. Multi-stage models provide a simple but very general mathematical framework for studying the failure of complex systems, or equivalently, the onset of disease. They include the Armitage-Doll multi-stage cancer model as a particular case, and have potential to provide new insights into how failures and disease, arise and progress. A method described by E.T. Jaynes is developed to provide an analytical solution for a large class of these models, and highlights connections between the convolution of Laplace transforms, sums of random variables, and Schwinger/Feynman parameterisations. Examples include: exact solutions to the Armitage-Doll model, the sum of Gamma-distributed variables with integer-valued shape parameters, a clonal-growth cancer model, and a model for cascading disasters. Applications and limitations of the approach are discussed in the context of recent cancer research. The model is sufficiently general to be used in many contexts, such as engineering, project management, disease progression, and disaster risk for example, allowing the estimation of failure rates in complex systems and projects. The intended result is a mathematical toolkit for applying multi-stage models to the study of failure rates in complex systems and to the onset of disease, cancer in particular.

SUBMITTER: Webster AJ

PROVIDER: S-EPMC6527192 | biostudies-literature | 2019

REPOSITORIES: biostudies-literature

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Multi-stage models for the failure of complex systems, cascading disasters, and the onset of disease.

Webster Anthony J AJ

PloS one 20190520 5

Complex systems can fail through different routes, often progressing through a series of (rate-limiting) steps and modified by environmental exposures. The onset of disease, cancer in particular, is no different. Multi-stage models provide a simple but very general mathematical framework for studying the failure of complex systems, or equivalently, the onset of disease. They include the Armitage-Doll multi-stage cancer model as a particular case, and have potential to provide new insights into h ...[more]

PMID: 31107895

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Project description:Complex biological systems are organized across various spatiotemporal scales with particular scientific disciplines dedicated to the study of each scale (e.g. genetics, molecular biology and cognitive neuroscience). When considering disease pathophysiology, one must contemplate the scale at which the disease process is being observed and how these processes impact other levels of organization. Historically Alzheimer's disease has been viewed as a disease of abnormally aggregated proteins by pathologists and molecular biologists and a disease of clinical symptoms by neurologists and psychologists. Bridging the divide between these scales has been elusive, but the study of brain networks appears to be a pivotal inroad to accomplish this task. In this study, we were guided by an emerging systems-based conceptualization of Alzheimer's disease and investigated changes in brain networks across the disease spectrum. The default mode network has distinct subsystems with unique functional-anatomic connectivity, cognitive associations, and responses to Alzheimer's pathophysiology. These distinctions provide a window into the systems-level pathophysiology of Alzheimer's disease. Using clinical phenotyping, metadata, and multimodal neuroimaging data from the Alzheimer's Disease Neuroimaging Initiative, we characterized the pattern of default mode network subsystem connectivity changes across the entire disease spectrum (n = 128). The two main findings of this paper are (i) the posterior default mode network fails before measurable amyloid plaques and appears to initiate a connectivity cascade that continues throughout the disease spectrum; and (ii) high connectivity between the posterior default mode network and hubs of high connectivity (many located in the frontal lobe) is associated with amyloid accumulation. These findings support a system model best characterized by a cascading network failure--analogous to cascading failures seen in power grids triggered by local overloads proliferating to downstream nodes eventually leading to widespread power outages, or systems failures. The failure begins in the posterior default mode network, which then shifts processing burden to other systems containing prominent connectivity hubs. This model predicts a connectivity 'overload' that precedes structural and functional declines and recasts the interpretation of high connectivity from that of a positive compensatory phenomenon to that of a load-shifting process transiently serving a compensatory role. It is unknown whether this systems-level pathophysiology is the inciting event driving downstream molecular events related to synaptic activity embedded in these systems. Possible interpretations include that the molecular-level events drive the network failure, a pathological interaction between the network-level and the molecular-level, or other upstream factors are driving both.

Project description:A most important property of biochemical systems is robustness. Static robustness, e.g., homeostasis, is the insensitivity of a state against perturbations, whereas dynamics robustness, e.g., homeorhesis, is the insensitivity of a dynamic process. In contrast to the extensively studied static robustness, dynamics robustness, i.e., how a system creates an invariant temporal profile against perturbations, is little explored despite transient dynamics being crucial for cellular fates and are reported to be robust experimentally. For example, the duration of a stimulus elicits different phenotypic responses, and signaling networks process and encode temporal information. Hence, robustness in time courses will be necessary for functional biochemical networks. Based on dynamical systems theory, we uncovered a general mechanism to achieve dynamics robustness. Using a three-stage linear signaling cascade as an example, we found that the temporal profiles and response duration post-stimulus is robust to perturbations against certain parameters. Then analyzing the linearized model, we elucidated the criteria of when signaling cascades will display dynamics robustness. We found that changes in the upstream modules are masked in the cascade, and that the response duration is mainly controlled by the rate-limiting module and organization of the cascade's kinetics. Specifically, we found two necessary conditions for dynamics robustness in signaling cascades: 1) Constraint on the rate-limiting process: The phosphatase activity in the perturbed module is not the slowest. 2) Constraints on the initial conditions: The kinase activity needs to be fast enough such that each module is saturated even with fast phosphatase activity and upstream changes are attenuated. We discussed the relevance of such robustness to several biological examples and the validity of the above conditions therein. Given the applicability of dynamics robustness to a variety of systems, it will provide a general basis for how biological systems function dynamically.

Project description:Functionally related brain regions are selectively vulnerable to Alzheimer's disease pathophysiology. However, molecular markers of this pathophysiology (i.e., beta-amyloid and tau aggregates) have discrepant spatial and temporal patterns of progression within these selectively vulnerable brain regions. Existing reductionist pathophysiologic models cannot account for these large-scale spatiotemporal inconsistencies. Within the framework of the recently proposed cascading network failure model of Alzheimer's disease, however, these large-scale patterns are to be expected. This model postulates the following: 1) a tau-associated, circumscribed network disruption occurs in brain regions specific to a given phenotype in clinically normal individuals; 2) this disruption can trigger phenotype independent, stereotypic, and amyloid-associated compensatory brain network changes indexed by changes in the default mode network; 3) amyloid deposition marks a saturation of functional compensation and portends an acceleration of the inciting phenotype specific, and tau-associated, network failure. With the advent of in vivo molecular imaging of tau pathology, combined with amyloid and functional network imaging, it is now possible to investigate the relationship between functional brain networks, tau, and amyloid across the disease spectrum within these selectively vulnerable brain regions. In a large cohort (n = 218) spanning the Alzheimer's disease spectrum from young, amyloid negative, cognitively normal subjects to Alzheimer's disease dementia, we found several distinct spatial patterns of tau deposition, including 'Braak-like' and 'non-Braak-like', across functionally related brain regions. Rather than arising focally and spreading sequentially, elevated tau signal seems to occur system-wide based on inferences made from multiple cross-sectional analyses we conducted looking at regional patterns of tau signal. Younger age-of-disease-onset was associated with 'non-Braak-like' patterns of tau, suggesting an association with atypical clinical phenotypes. As predicted by the cascading network failure model of Alzheimer's disease, we found that amyloid is a partial mediator of the relationship between functional network failure and tau deposition in functionally connected brain regions. This study implicates large-scale brain networks in the pathophysiology of tau deposition and offers support to models incorporating large-scale network physiology into disease models linking tau and amyloid, such as the cascading network failure model of Alzheimer's disease.

Dataset Information

Multi-stage models for the failure of complex systems, cascading disasters, and the onset of disease.

Publications

Multi-stage models for the failure of complex systems, cascading disasters, and the onset of disease.

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