Session X35: Critical Transitions in Biological Systems

Detecting early-warning signals of critical transitions for complex systems

Considerable evidence suggests that during the progression of complex diseases, the deteriorations are not necessarily smooth but are abrupt, and may cause a critical transition from one state to another at a tipping point. Here, we develop a model-free method to detect early-warning signals of such critical transitions, even with only a small number of samples. Specifically, we theoretically derive an index based on a dynamical network biomarker (DNB) for biological systems or dynamical network marker (DNM) for general systems that serves as a general early-warning signal indicating an imminent bifurcation or sudden deterioration before the critical transition occurs. Based on theoretical analyses, we show that predicting a sudden transition from small samples is achievable provided that there are a large number of measurements for each sample, e.g., high-throughput data. We employ microarray data of three diseases to demonstrate the effectiveness of our method for detecting "un-occurred" disease state. The relevance of DNBs with the diseases was also validated by related experimental data and functional analysis.   

The evolution of lossy compression

In complex environments, there are costs to both ignorance and perception. An organism needs to track fitness-relevant information about its world, but the more information it tracks, the more resources it must devote to memory and processing. As a first step towards an understanding of this tradeoff, we use rate-distortion theory to study large, unstructured environments with fixed, randomly-drawn penalties for stimuli confusion (``distortions''). We find that two different environments will have nearly identical rate-distortion functions (but very different codebooks) when distortions are drawn from the same distribution, suggesting an interesting weak universality. We further identify two distinct regimes for organisms in these structured environments: a high-fidelity regime where perceptual costs grow linearly with environmental complexity, and a low-fidelity regime where perceptual costs are, remarkably, independent of the number of environmental states. This last result suggests that evolution will drive organisms to the threshold between the high- and low-fidelity regimes. In dynamic environments of rapidly-increasing complexity, well-adapted organisms will find themselves able to make, just barely, the most subtle distinctions in their environment.   

Dynamics of neuroendocrine stress response: bistability, timing, and control of hypocortisolism

The hypothalamic-pituitary-adrenal (HPA) axis is a neuroendocrine system that regulates numerous physiological processes. Disruptions in its activity are correlated with stress-related diseases such as post-traumatic stress disorder (PTSD) and major depressive disorder. We characterize ``normal'' and ``diseased'' states of the HPA axis as basins of attraction of a dynamical system describing the inhibition of peptide hormones, corticotropin-releasing hormone (CRH) and adrenocorticotropic hormone (ACTH), by circulating glucocorticoids such as cortisol (CORT). Our model includes ultradian oscillations, CRH self-upregulation of CRH release, and distinguishes two components of negative feedback by cortisol on circulating CRH levels: a slow direct suppression of CRH synthesis and a fast indirect effect on CRH release. The slow regulation mechanism mediates external stress-driven transitions between the stable states in novel, intensity, duration, and timing-dependent ways. We find that the \textit{timing} of traumatic events may be an important factor in determining if and how the hallmarks of depressive disorders will manifest. Our model also suggests a mechanism whereby exposure therapy of stress disorders may act to normalize downstream dysregulation of the HPA axis.   

Dynamics of blood flow in a microfluidic ladder network

The dynamics of a complex mixture of cells and proteins, such as blood, in perturbed shear flow remains ill-defined. Microfluidics is a promising technology for improving the understanding of blood flow under complex conditions of shear; as found in stent implants and in tortuous blood vessels. We model the fluid dynamics of blood flow in a microfluidic ladder network with dimensions mimicking venules. Interaction of blood cells was modeled using multiagent framework, where cells of different diameters were treated as spheres. This model served as the basis for predicting transition regions, collision pathways, re-circulation zones and residence times of cells dependent on their diameters and device architecture. Based on these insights from the model, we were able to predict the clot formation configurations at various locations in the device. These predictions were supported by the experiments using whole blood. To facilitate platelet aggregation, the devices were coated with fibrillar collagen and tissue factor. Blood was perfused through the microfluidic device for 9 min at a physiologically relevant venous shear rate of 600 s$^{-1}$. Using fluorescent microscopy, we observed flow transitions near the channel intersections and at the areas of blood flow obstruction, which promoted larger thrombus formation. This study of integrating model predictions with experimental design, aids in defining the dynamics of blood flow in microvasculature and in development of novel biomedical devices.   

Identifying driving gene clusters in complex diseases through critical transition theory

A novel approach of looking at the human body using critical transition theory has yielded positive results: clusters of genes that act in tandem to drive complex disease progression. This cluster of genes can be thought of as the first part of a large genetic force that pushes the body from a curable, but sick, point to an incurable diseased point through a catastrophic bifurcation. The data analyzed is time course microarray blood assay data of 7 high risk individuals for Type 1 Diabetes who progressed into a clinical onset, with an additional larger study requested to be presented at the conference. The normalized data is 25,000 genes strong, which were narrowed down based on statistical metrics, and finally a machine learning algorithm using critical transition metrics found the driving network. This approach was created to be repeatable across multiple complex diseases with only progression time course data needed so that it would be applicable to identifying when an individual is at risk of developing a complex disease. Thusly, preventative measures can be enacted, and in the longer term, offers a possible solution to prevent all Type 1 Diabetes.   

Finding the role of time-delays in complex systems

Time delays are omnipresently observed in many nature and artificial systems including physical, biological, and chemical systems. Naturally, two kinds of questions arise: “How to identify the time delays when a certain amount of datasets are obtained from the experiments or real world systems whenever the theoretical model is known or unknown? ” and “How to characterize the intrinsic roles of time delays that are played in the critical transition of coupled network systems” In this talk, we introduce recent works that address the previous two questions, and show the significance of time delays in dealing with various biological systems.   

Detecting critical state before phase transition of complex systems by hidden Markov model

Identifying the critical state or pre-transition state just before the occurrence of a phase transition is a challenging task, because the state of the system may show little apparent change before this critical transition during the gradual parameter variations. Such dynamics of phase transition is generally composed of three stages, i.e., before-transition state, pre-transition state, and after-transition state, which can be considered as three different Markov processes. Thus, based on this dynamical feature, we present a novel computational method, i.e., hidden Markov model (HMM), to detect the switching point of the two Markov processes from the before-transition state (a stationary Markov process) to the pre-transition state (a time-varying Markov process), thereby identifying the pre-transition state or early-warning signals of the phase transition. To validate the effectiveness, we apply this method to detect the signals of the imminent phase transitions of complex systems based on the simulated datasets, and further identify the pre-transition states as well as their critical modules for three real datasets, i.e., the acute lung injury triggered by phosgene inhalation, MCF-7 human breast cancer caused by heregulin, and HCV-induced dysplasia and hepatocellular carcinoma.   

Identification of driving network of cellular differentiation from single sample time course gene expression data.

Methods developed based on bifurcation theory have demonstrated their potential in driving network identification for complex human diseases, including the work by Chen, et al.~ Recently bifurcation theory has been successfully applied to model cellular differentiation.~ However, there one often faces a technical challenge in driving network prediction: time course cellular differentiation study often only contains one sample at each time point, while driving network prediction typically require multiple samples at each time point to infer the variation and interaction structures of candidate genes for the driving network. In this study, we investigate several methods to identify both the critical time point and the driving network through examination of how each time point affects the autocorrelation and phase locking.~ We apply these methods to a high-throughput sequencing (RNA-Seq) dataset of 42 subsets of thymocytes and mature peripheral T cells at multiple time points during their differentiation (GSE48138 from GEO).~ We compare the predicted driving genes with known transcription regulators of cellular differentiation.~ We will discuss the advantages and limitations of our proposed methods, as well as potential further improvements of our methods.   

Experimental and theoretical description of higher order periods in cardiac tissue action potential duration

Much theoretical, experimental, and clinical research has been devoted to investigating the initiation of cardiac arrhythmias by alternans, the first period doubling bifurcation in the duration of cardiac action potentials. Although period doubling above alternans has been shown to exist in many mammalian hearts, little is understood about their emergence or behavior. There currently exists no physiologically correct theory or model that adequately describes and predicts their emergence in stimulated tissue. In this talk we present experimental data of period 2, 4, and 8 dynamics and a mathematical model that describes these bifurcations. This model extends current cell models through the addition of memory and includes spatiotemporal nonlinearities arising from cellular coupling by tissue heterogeneity.   

Theory of advection-driven long range biotic transport

We consider a new reaction-transport framework, and apply it to the problem of advection-driven biotic transport. The are two compartments - the growth layer, coupled to a separate, advective layer. Density fronts propagate in both layers. Crucially, the downwind front speed goes to a finite value as the coupling goes to zero. We next include diffusion in the growth layer, and study the competition between the advective and diffusive transport mechanisms. Advection wins for small diffusion and cannot be ignored, no matter how weak is the coupling. When coupling is not small, both mechanisms work cooperatively, without a clear winner. A further surprise is the existence of a critical diffusion constant at which the front speed is independent of the interlayer coupling.   

Geometric phase transition in the cellular network of the pancreatic islets may underlie the onset of type 1diabetes.

Living systems are characterized by complexity in structure and emergent dynamic orders. In many aspects the onset of a chronic disease resembles phase transition in a dynamic system: quantitative changes accumulate largely unnoticed until a critical threshold is reached, which causes abrupt qualitative changes of the system. In this study we investigate this idea in a real example, the insulin-producing pancreatic islet $\beta $-cells and the onset of type 1 diabetes. Within each islet, the $\beta $-cells are electrically coupled to each other, and function as a network with synchronized actions. Using percolation theory we show how normal islet function is intrinsically linked to network connectivity, and the critical point where the islet cellular network loses site percolation, is consistent with laboratory and clinical observations of the threshold $\beta $-cell loss that causes islet functional failure. Numerical simulations confirm that the islet cellular network needs to be percolated for $\beta $-cells to synchronize. Furthermore, the interplay between site percolation and bond strength predicts the existence of a transient phase of islet functional recovery after disease onset and introduction of treatment, potentially explaining a long time mystery in the clinical study of type 1 diabetes: the honeymoon phenomenon. Based on these results, we hypothesized that the onset of T1D may be the result of a phase transition of the islet $\beta $-cell network. We further discuss the potential applications in identifying disease-driving factors, and the critical parameters that are predictive of disease onset.