Models of Cell Processes are Far from the Edge of Chaos

About the ozone ability in using adaptive chaos to restore a healthy state in the oxygen-ozone adjunct therapy

The action of ozone in medicine is a subject of interest and lively, controversial debates. Its mechanisms of action are still far from fully understood. However, it is possible that ozone triggers a series of dynamics in living organisms related to chaos, multi-stable phenomena, and oscillatory processes. Ozone may be involved in adaptive chaos. Adaptive chaos in health and the reduction of complexity in pathology are interconnected phenomena that describe the functional dynamics of biological systems. Adaptive chaos refers to a state of controlled, complex, and flexible behaviour exhibited by healthy biological systems. It allows for a dynamic balance between order and unpredictability, enabling the system to respond to various internal and external stimuli. In pathological states, the system loses its adaptive chaos, often becoming either too rigid or overly chaotic. This reduction in complexity limits the ability of the system to respond effectively to stimuli, making it prone to dysfunction. This paper addresses the role of ozone in these scenarios.

Improving neuroendocrine tumor treatments with mathematical modeling: lessons from other endocrine cancers

Neuroendocrine tumors (NETs) occur sporadically or as part of rare endocrine tumor syndromes (RETSs) such as multiple endocrine neoplasia 1 and von Hippel-Lindau syndromes. Due to their relative rarity and lack of model systems, NETs and RETSs are difficult to study, hindering advancements in therapeutic development. Causal or mechanistic mathematical modeling is widely deployed in disease areas such as breast and prostate cancers, aiding the understanding of observations and streamlining in vitro and in vivo modeling efforts. Mathematical modeling, while not yet widely utilized in NET research, offers an opportunity to accelerate NET research and therapy development. To illustrate this, we highlight examples of how mathematical modeling associated with more common endocrine cancers has been successfully used in the preclinical, translational and clinical settings. We also provide a scope of the limited work that has been done in NETs and map how these techniques can be utilized in NET research to address specific outstanding challenges in the field. Finally, we include practical details such as hardware and data requirements, present advantages and disadvantages of various mathematical modeling approaches and discuss challenges of using mathematical modeling. Through a cross-disciplinary approach, we believe that many currently difficult problems can be made more tractable by applying mathematical modeling and that the field of rare diseases in endocrine oncology is well poised to take advantage of these techniques.

HHIP's Dynamic Role in Epithelial Wound Healing Reveals a Potential Mechanism of COPD Susceptibility

A genetic variant near HHIP has been consistently identified as associated with increased risk for Chronic Obstructive Pulmonary Disease (COPD), the third leading cause of death worldwide. However HHIP's role in COPD pathogenesis remains elusive. Canonically, HHIP is a negative regulator of the hedgehog pathway and downstream GLI1 and GLI2 activation. The hedgehog pathway plays an important role in wound healing, specifically in activating transcription factors that drive the epithelial mesenchymal transition (EMT), which in its intermediate state (partial EMT) is necessary for the collective movement of cells closing the wound. Herein, we propose a mechanism to explain HHIP's role in faulty epithelial wound healing, which could contribute to the development of emphysema, a key feature of COPD. Using two different Boolean models compiled from the literature, we show dysfunctional HHIP results in a lack of negative feedback on GLI, triggering a full EMT, where cells become mesenchymal and do not properly close the wound. We validate these Boolean models with experimental evidence gathered from published scientific literature. We also experimentally test if low HHIP expression is associated with EMT at the edge of wounds by using a scratch assay in a human lung epithelial cell line. Finally, we show evidence supporting our hypothesis in bulk and single cell RNA-Seq data from different COPD cohorts. Overall, our analyses suggest that aberrant wound healing due to dysfunctional HHIP, combined with chronic epithelial damage through cigarette smoke exposure, may be a primary cause of COPD-associated emphysema.

The Effect of Noise on the Density Classification Task for Various Cellular Automata Rules

Cellular automata (CA) are discrete dynamical systems with a prominent place in the history and study of artificial life. Here, we focus on the density classification task (DCT) in which a 1-dimensional lattice of Boolean (on/off) automata must perform a form of rudimentary quorum sensing. Typically, the ring lattice consists of 149 cells (though we consider other sizes as well) that update their state according to their own state and its six nearest neighbors in the previous time step. The goal is obtaining Boolean CA rules whose dynamics converges to the majority state of the entire lattice for a given initial configuration of the lattice. This is a nontrivial task because cells have access only to local information, and thus need to integrate and coordinate information across the lattice to converge to the correct collective state. Because initial conditions are random, they have very similar proportions of on and off states, which makes the problem very difficult. This problem has hitherto been studied with the assumption that input to each cell is perfectly stable. Since biological systems that solve similar problems (e.g. bacterial quorum sensing) must operate in noisy environments, here we study the impact of noise on DCT accuracy for the 13 highest-accuracy CA rules from the literature. We use cubewalkers, a recently released GPU-accelerated Boolean simulator to conduct large-scale random experiments. We uncover a trade-off between maximum accuracy without noise and robustness to noise among these high-performance CAs. Moreover, there is no significant difference between rules that were human-designed or evolved computationally.

Canalization reduces the nonlinearity of regulation in biological networks

Biological networks, such as gene regulatory networks, possess desirable properties. They are more robust and controllable than random networks. This motivates the search for structural and dynamical features that evolution has incorporated into biological networks. A recent meta-analysis of published, expert-curated Boolean biological network models has revealed several such features, often referred to as design principles. Among others, the biological networks are enriched for certain recurring network motifs, the dynamic update rules are more redundant, more biased, and more canalizing than expected, and the dynamics of biological networks are better approximable by linear and lower-order approximations than those of comparable random networks. Since most of these features are interrelated, it is paramount to disentangle cause and effect, that is, to understand which features evolution actively selects for, and thus truly constitute evolutionary design principles. Here, we compare published Boolean biological network models with different ensembles of null models and show that the abundance of canalization in biological networks can almost completely explain their recently postulated high approximability. Moreover, an analysis of random N-K Kauffman models reveals a strong dependence of approximability on the dynamical robustness of a network.

Biologically meaningful regulatory logic enhances the convergence rate in Boolean networks and bushiness of their state transition graph

Boolean models of gene regulatory networks (GRNs) have gained widespread traction as they can easily recapitulate cellular phenotypes via their attractor states. Their overall dynamics are embodied in a state transition graph (STG). Indeed, two Boolean networks (BNs) with the same network structure and attractors can have drastically different STGs depending on the type of Boolean functions (BFs) employed. Our objective here is to systematically delineate the effects of different classes of BFs on the structural features of the STG of reconstructed Boolean GRNs while keeping network structure and biological attractors fixed, and explore the characteristics of BFs that drive those features. Using $10$ reconstructed Boolean GRNs, we generate ensembles that differ in BFs and compute from their STGs the dynamics' rate of contraction or 'bushiness' and rate of 'convergence', quantified with measures inspired from cellular automata (CA) that are based on the garden-of-Eden (GoE) states. We find that biologically meaningful BFs lead to higher STG 'bushiness' and 'convergence' than random ones. Obtaining such 'global' measures gets computationally expensive with larger network sizes, stressing the need for feasible proxies. So we adapt Wuensche's $Z$-parameter in CA to BFs in BNs and provide four natural variants, which, along with the average sensitivity of BFs computed at the network level, comprise our descriptors of local dynamics and we find some of them to be good proxies for bushiness. Finally, we provide an excellent proxy for the 'convergence' based on computing transient lengths originating at random states rather than GoE states.

A meta-analysis of Boolean network models reveals design principles of gene regulatory networks

Gene regulatory networks (GRNs) play a central role in cellular decision-making. Understanding their structure and how it impacts their dynamics constitutes thus a fundamental biological question. GRNs are frequently modeled as Boolean networks, which are intuitive, simple to describe, and can yield qualitative results even when data are sparse. We assembled the largest repository of expert-curated Boolean GRN models. A meta-analysis of this diverse set of models reveals several design principles. GRNs exhibit more canalization, redundancy, and stable dynamics than expected. Moreover, they are enriched for certain recurring network motifs. This raises the important question why evolution favors these design mechanisms.