A review of dynamical systems approaches for the detection of chaotic attractors in cancer networks

The chaotic dynamics and behavior of prey-predator interaction: Insights into complex ecological systems and epidemic modeling

This study and the literature have shown that the emergence of chaotic behavior has been attributed mostly to predator-prey and competitive dynamics. This is also observed in pandemics, as well as in cancer models, where deterministic chaos or chaotic dynamics can lead to complex oscillations and nonlinear interactions between cell populations. It is important to note that COVID-19 displays the key characteristics of a chaotic system and is one of the deadliest pandemics in recent history.

Research trends, hotspots and future directions of tertiary lymphoid structures in cancer: a comprehensive informatics analysis and visualization study

Many studies have reported the presence of tertiary lymphoid structures (TLSs) in cancer, but the research progress of TLSs in cancer has not been systematically analyzed. Therefore, we analyzed the global scientific knowledge in the field using informatics methods. The results showed that TLSs in cancer have received increasing attention since the 21st century, with an annual publication growth rate of 27.86%. Unsupervised hierarchical clustering based on machine learning further categorized the research features into four clusters, with the cluster related to immunotherapy being considered an emerging cluster. TLSs and immunotherapy were identified as the top two hotspots with the highest occurrence frequency and total link strength. The Walktrap algorithm indicated that "TLSs, carcinoma, prognostic value" and "high endothelial venules, germinal-centers, node-like structures" are important to TLSs but remain underexplored, representing promising research directions. These findings suggest that cancer-related TLSs have brought new insights into antitumor immunity, and targeting TLSs has the potential to transform the landscape of antitumor immunotherapy.

A method for in silico exploration of potential glioblastoma multiforme attractors using single-cell RNA sequencing

We presented a method to find potential cancer attractors using single-cell RNA sequencing (scRNA-seq) data. We tested our method in a Glioblastoma Multiforme (GBM) dataset, an aggressive brain tumor presenting high heterogeneity. Using the cancer attractor concept, we argued that the GBM's underlying dynamics could partially explain the observed heterogeneity, with the dataset covering a representative region around the attractor. Exploratory data analysis revealed promising GBM's cellular clusters within a 3-dimensional marker space. We approximated the clusters' centroid as stable states and each cluster covariance matrix as defining confidence regions. To investigate the presence of attractors inside the confidence regions, we constructed a GBM gene regulatory network, defined a model for the dynamics, and prepared a framework for parameter estimation. An exploration of hyperparameter space allowed us to sample time series intending to simulate myriad variations of the tumor microenvironment. We obtained different densities of stable states across gene expression space and parameters displaying multistability across different clusters. Although we used our methodological approach in studying GBM, we would like to highlight its generality to other types of cancer. Therefore, this report contributes to an advance in the simulation of cancer dynamics and opens avenues to investigate potential therapeutic targets.

Integrating frontiers: a holistic, quantum and evolutionary approach to conquering cancer through systems biology and multidisciplinary synergy

Cancer therapy is facing increasingly significant challenges, marked by a wide range of techniques and research efforts centered around somatic mutations, precision oncology, and the vast amount of big data. Despite this abundance of information, the quest to cure cancer often seems more elusive, with the "war on cancer" yet to deliver a definitive victory. A particularly pressing issue is the development of tumor treatment resistance, highlighting the urgent need for innovative approaches. Evolutionary, Quantum Biology and System Biology offer a promising framework for advancing experimental cancer research. By integrating theoretical studies, translational methods, and flexible multidisciplinary clinical research, there's potential to enhance current treatment strategies and improve outcomes for cancer patients. Establishing stronger links between evolutionary, quantum, entropy and chaos principles and oncology could lead to more effective treatments that leverage an understanding of the tumor's evolutionary dynamics, paving the way for novel methods to control and mitigate cancer. Achieving these objectives necessitates a commitment to multidisciplinary and interprofessional collaboration at the heart of both research and clinical endeavors in oncology. This entails dismantling silos between disciplines, encouraging open communication and data sharing, and integrating diverse viewpoints and expertise from the outset of research projects. Being receptive to new scientific discoveries and responsive to how patients react to treatments is also crucial. Such strategies are key to keeping the field of oncology at the forefront of effective cancer management, ensuring patients receive the most personalized and effective care. Ultimately, this approach aims to push the boundaries of cancer understanding, treating it as a manageable chronic condition, aiming to extend life expectancy and enhance patient quality of life.

Unveiling the Dynamics behind Glioblastoma Multiforme Single-Cell Data Heterogeneity

Glioblastoma Multiforme is a brain tumor distinguished by its aggressiveness. We suggested that this aggressiveness leads single-cell RNA-sequence data (scRNA-seq) to span a representative portion of the cancer attractors domain. This conjecture allowed us to interpret the scRNA-seq heterogeneity as reflecting a representative trajectory within the attractor's domain. We considered factors such as genomic instability to characterize the cancer dynamics through stochastic fixed points. The fixed points were derived from centroids obtained through various clustering methods to verify our method sensitivity. This methodological foundation is based upon sample and time average equivalence, assigning an interpretative value to the data cluster centroids and supporting parameters estimation. We used stochastic simulations to reproduce the dynamics, and our results showed an alignment between experimental and simulated dataset centroids. We also computed the Waddington landscape, which provided a visual framework for validating the centroids and standard deviations as characterizations of cancer attractors. Additionally, we examined the stability and transitions between attractors and revealed a potential interplay between subtypes. These transitions might be related to cancer recurrence and progression, connecting the molecular mechanisms of cancer heterogeneity with statistical properties of gene expression dynamics. Our work advances the modeling of gene expression dynamics and paves the way for personalized therapeutic interventions.

A logic-incorporated gene regulatory network deciphers principles in cell fate decisions

Organisms utilize gene regulatory networks (GRN) to make fate decisions, but the regulatory mechanisms of transcription factors (TF) in GRNs are exceedingly intricate. A longstanding question in this field is how these tangled interactions synergistically contribute to decision-making procedures. To comprehensively understand the role of regulatory logic in cell fate decisions, we constructed a logic-incorporated GRN model and examined its behavior under two distinct driving forces (noise-driven and signal-driven). Under the noise-driven mode, we distilled the relationship among fate bias, regulatory logic, and noise profile. Under the signal-driven mode, we bridged regulatory logic and progression-accuracy trade-off, and uncovered distinctive trajectories of reprogramming influenced by logic motifs. In differentiation, we characterized a special logic-dependent priming stage by the solution landscape. Finally, we applied our findings to decipher three biological instances: hematopoiesis, embryogenesis, and trans-differentiation. Orthogonal to the classical analysis of expression profile, we harnessed noise patterns to construct the GRN corresponding to fate transition. Our work presents a generalizable framework for top-down fate-decision studies and a practical approach to the taxonomy of cell fate decisions.

Finite-Time Lyapunov Exponents of Deep Neural Networks

We compute how small input perturbations affect the output of deep neural networks, exploring an analogy between deep feed-forward networks and dynamical systems, where the growth or decay of local perturbations is characterized by finite-time Lyapunov exponents. We show that the maximal exponent forms geometrical structures in input space, akin to coherent structures in dynamical systems. Ridges of large positive exponents divide input space into different regions that the network associates with different classes. These ridges visualize the geometry that deep networks construct in input space, shedding light on the fundamental mechanisms underlying their learning capabilities.

Modelling and Controlling System Dynamics of the Brain: An Intersection of Machine Learning and Control Theory

The human brain, as a complex system, has long captivated multidisciplinary researchers aiming to decode its intricate structure and function. This intricate network has driven scientific pursuits to advance our understanding of cognition, behavior, and neurological disorders by delving into the complex mechanisms underlying brain function and dysfunction. Modelling brain dynamics using machine learning techniques deepens our comprehension of brain dynamics from a computational perspective. These computational models allow researchers to simulate and analyze neural interactions, facilitating the identification of dysfunctions in connectivity or activity patterns. Additionally, the trained dynamical system, serving as a surrogate model, optimizes neurostimulation strategies under the guidelines of control theory. In this chapter, we discuss the recent studies on modelling and controlling brain dynamics at the intersection of machine learning and control theory, providing a framework to understand and improve cognitive function, and treat neurological and psychiatric disorders.

Mitochondria Transfer from Mesenchymal Stem Cells Confers Chemoresistance to Glioblastoma Stem Cells through Metabolic Rewiring

Glioblastomas (GBM) are heterogeneous tumors with high metabolic plasticity. Their poor prognosis is linked to the presence of glioblastoma stem cells (GSC), which support resistance to therapy, notably to temozolomide (TMZ). Mesenchymal stem cells (MSC) recruitment to GBM contributes to GSC chemoresistance, by mechanisms still poorly understood. Here, we provide evidence that MSCs transfer mitochondria to GSCs through tunneling nanotubes, which enhances GSCs resistance to TMZ. More precisely, our metabolomics analyses reveal that MSC mitochondria induce GSCs metabolic reprograming, with a nutrient shift from glucose to glutamine, a rewiring of the tricarboxylic acid cycle from glutaminolysis to reductive carboxylation and increase in orotate turnover as well as in pyrimidine and purine synthesis. Metabolomics analysis of GBM patient tissues at relapse after TMZ treatment documents increased concentrations of AMP, CMP, GMP, and UMP nucleotides and thus corroborate our in vitro analyses. Finally, we provide a mechanism whereby mitochondrial transfer from MSCs to GSCs contributes to GBM resistance to TMZ therapy, by demonstrating that inhibition of orotate production by Brequinar (BRQ) restores TMZ sensitivity in GSCs with acquired mitochondria. Altogether, these results identify a mechanism for GBM resistance to TMZ and reveal a metabolic dependency of chemoresistant GBM following the acquisition of exogenous mitochondria, which opens therapeutic perspectives based on synthetic lethality between TMZ and BRQ.

Significance

Mitochondria acquired from MSCs enhance the chemoresistance of GBMs. The discovery that they also generate metabolic vulnerability in GSCs paves the way for novel therapeutic approaches.

Cell Adaptive Fitness and Cancer Evolutionary Dynamics

Genome instability of cancer cells translates into increased entropy and lower information processing capacity, leading to metabolic reprograming toward higher energy states, presumed to be aligned with a cancer growth imperative. Dubbed as the cell adaptive fitness, the proposition postulates that the coupling between cell signaling and metabolism constrains cancer evolutionary dynamics along trajectories privileged by the maintenance of metabolic sufficiency for survival. In particular, the conjecture postulates that clonal expansion becomes restricted when genetic alterations induce a sufficiently high level of disorder, that is, high entropy, in the regulatory signaling network, abrogating as a result the ability of cancer cells to successfully replicate, leading to a stage of clonal stagnation. The proposition is analyzed in the context of an in-silico model of tumor evolutionary dynamics to illustrate how cell-inherent adaptive fitness may predictably constrain clonal evolution of tumors, which would have significant implications for the design of adaptive cancer therapies.

Evidence of self-organized criticality in time series by the horizontal visibility graph approach

Determination of self-organized criticality (SOC) is crucial in evaluating the dynamical behavior of a time series. Here, we apply the complex network approach to assess the SOC characteristics in synthesis and real-world data sets. For this purpose, we employ the horizontal visibility graph (HVG) method and construct the relevant networks for two numerical avalanche-based samples (i.e., sand-pile models), several financial markets, and a solar nano-flare emission model. These series are shown to have long-temporal correlations via the detrended fluctuation analysis. We compute the degree distribution, maximum eigenvalue, and average clustering coefficient of the constructed HVGs and compare them with the values obtained for random and chaotic processes. The results manifest a perceptible deviation between these parameters in random and SOC time series. We conclude that the mentioned HVG's features can distinguish between SOC and random systems.

Antifragile Control Systems: The Case of an Anti-Symmetric Network Model of the Tumor-Immune-Drug Interactions

A therapy’s outcome is determined by a tumor’s response to treatment which, in turn, depends on multiple factors such as the severity of the disease and the strength of the patient’s immune response. Gold standard cancer therapies are in most cases fragile when sought to break the ties to either tumor kill ratio or patient toxicity. Lately, research has shown that cancer therapy can be at its most robust when handling adaptive drug resistance and immune escape patterns developed by evolving tumors. This is due to the stochastic and volatile nature of the interactions, at the tumor environment level, tissue vasculature, and immune landscape, induced by drugs. Herein, we explore the path toward antifragile therapy control, that generates treatment schemes that are not fragile but go beyond robustness. More precisely, we describe the first instantiation of a control-theoretic method to make therapy schemes cope with the systemic variability in the tumor-immune-drug interactions and gain more tumor kills with less patient toxicity. Considering the anti-symmetric interactions within a model of the tumor-immune-drug network, we introduce the antifragile control framework that demonstrates promising results in simulation. We evaluate our control strategy against state-of-the-art therapy schemes in various experiments and discuss the insights we gained on the potential that antifragile control could have in treatment design in clinical settings.

Executable models of immune signaling pathways in HIV-associated atherosclerosis

Atherosclerosis (AS)-associated cardiovascular disease is an important cause of mortality in an aging population of people living with HIV (PLWH). This elevated risk has been attributed to viral infection, anti-retroviral therapy, chronic inflammation, and lifestyle factors. However, the rates at which PLWH develop AS vary even after controlling for length of infection, treatment duration, and for lifestyle factors. To investigate the molecular signaling underlying this variation, we sequenced 9368 peripheral blood mononuclear cells (PBMCs) from eight PLWH, four of whom have atherosclerosis (AS+). Additionally, a publicly available dataset of PBMCs from persons before and after HIV infection was used to investigate the effect of acute HIV infection. To characterize dysregulation of pathways rather than just measuring enrichment, we developed the single-cell Boolean Omics Network Invariant Time Analysis (scBONITA) algorithm. scBONITA infers executable dynamic pathway models and performs a perturbation analysis to identify high impact genes. These dynamic models are used for pathway analysis and to map sequenced cells to characteristic signaling states (attractor analysis). scBONITA revealed that lipid signaling regulates cell migration into the vascular endothelium in AS+ PLWH. Pathways implicated included AGE-RAGE and PI3K-AKT signaling in CD8+ T cells, and glucagon and cAMP signaling pathways in monocytes. Attractor analysis with scBONITA facilitated the pathway-based characterization of cellular states in CD8+ T cells and monocytes. In this manner, we identify critical cell-type specific molecular mechanisms underlying HIV-associated atherosclerosis using a novel computational method.

ZNF92, an unexplored transcription factor with remarkably distinct breast cancer over-expression associated with prognosis and cell-of-origin

Tumor phenotype is shaped both by transforming genomic alterations and the normal cell-of-origin. We identified a cell-of-origin associated prognostic gene expression signature, ET-9, that correlates with remarkably shorter overall and relapse free breast cancer survival, 8.7 and 6.2 years respectively. The genes associated with the ET-9 signature are regulated by histone deacetylase 7 (HDAC7) partly through ZNF92, a previously unexplored transcription factor with a single PubMed citation since its cloning in 1990s. Remarkably, ZNF92 is distinctively over-expressed in breast cancer compared to other tumor types, on a par with the breast cancer specificity of the estrogen receptor. Importantly, ET-9 signature appears to be independent of proliferation, and correlates with outcome in lymph-node positive, HER2+, post-chemotherapy and triple-negative breast cancers. These features distinguish ET-9 from existing breast cancer prognostic signatures that are generally related to proliferation and correlate with outcome in lymph-node negative, ER-positive, HER2-negative breast cancers. Our results suggest that ET-9 could be also utilized as a predictive signature to select patients for HDAC inhibitor treatment.

Emotion Regulation Flexibility and Electronic Patient-Reported Outcomes: A Framework for Understanding Symptoms and Affect Dynamics in Pediatric Psycho-Oncology

Simple Summary

The individual’s ability to conceive and regulate the broad spectrum of their human emotions is closely linked to their mental health. The implications of a serious disease such as cancer represent an extraordinary burden to these internal coping mechanisms, especially in the case of young patients. Regarding their well-being and support, it is therefore of particular interest for caregivers to be able to follow the dynamics of the patient’s emotional world and perceptions. Technical progress enables new possibilities for data collection through tools for digital patient self-reports while simultaneously creating new challenges. Within the scope of this article, we provide an overview of the literature on this topic, outlining the current strengths and weaknesses and possible perspectives on digital aids, especially in terms of capturing the flexibility, fluctuations and early detection of symptom changes.

Abstract

Emotion dysregulation is regarded as a driving mechanism for the development of mental health problems and psychopathology. The role of emotion regulation (ER) in the management of cancer distress and quality of life (QoL) has recently been recognized in psycho-oncology. The latest technological advances afford ways to assess ER, affective experiences and QoL in child, adolescent and young adult (CAYA) cancer patients through electronic patient-reported outcomes (ePRO) in their daily environment in real-time. Such tools facilitate ways to study the dynamics of affect and the flexibility of ER. However, technological advancement is not risk-free. We critically review the literature on ePRO in cancer existing models of ER in pediatric psycho-oncology and analyze strength, weaknesses, opportunities and threats of ePRO with a focus on CAYA cancer research and care. Supported by personal study-based experiences, this narrative review serves as a foundation to propose a novel methodological and metatheoretical framework based on: (a) an extended notion of ER, which includes its dynamic, adaptive and flexible nature and focuses on processes and conditions rather than fixed categorical strategies; (b) ePRO as a means to measure emotion regulation flexibility and affect dynamics; (c) identifying early warning signals for symptom change via ePRO and building forecasting models using dynamical systems theory.

Evolution-based mathematical models significantly prolong response to abiraterone in metastatic castrate-resistant prostate cancer and identify strategies to further improve outcomes

Background

Abiraterone acetate is an effective treatment for metastatic castrate-resistant prostate cancer (mCRPC), but evolution of resistance inevitably leads to progression. We present a pilot study in which abiraterone dosing is guided by evolution-informed mathematical models to delay onset of resistance.

Methods

In the study cohort, abiraterone was stopped when PSA was <50% of pretreatment value and resumed when PSA returned to baseline. Results are compared to a contemporaneous cohort who had >50% PSA decline after initial abiraterone administration and met trial eligibility requirements but chose standard of care (SOC) dosing.

Results

17 subjects were enrolled in the adaptive therapy group and 16 in the SOC group. All SOC subjects have progressed, but four patients in the study cohort remain stably cycling (range 53-70 months). The study cohort had significantly improved median time to progression (TTP; 33.5 months; p<0.001) and median overall survival (OS; 58.5 months; hazard ratio, 0.41, 95% confidence interval (CI), 0.20-0.83, p<0.001) compared to 14.3 and 31.3 months in the SOC cohort. On average, study subjects received no abiraterone during 46% of time on trial. Longitudinal trial data demonstrated the competition coefficient ratio (αRS/αSR) of sensitive and resistant populations, a critical factor in intratumoral evolution, was two- to threefold higher than pre-trial estimates. Computer simulations of intratumoral evolutionary dynamics in the four long-term survivors found that, due to the larger value for αRS/αSR, cycled therapy significantly decreased the resistant population. Simulations in subjects who progressed predicted further increases in OS could be achieved with prompt abiraterone withdrawal after achieving 50% PSA reduction.

Conclusions

Incorporation of evolution-based mathematical models into abiraterone monotherapy for mCRPC significantly increases TTP and OS. Computer simulations with updated parameters from longitudinal trial data can estimate intratumoral evolutionary dynamics in each subject and identify strategies to improve outcomes.

Funding

Moffitt internal grants and NIH/NCI U54CA143970-05 (Physical Science Oncology Network).

Generalized Full Order Observer Subject to Incremental Quadratic Constraint (IQC) for a Class of Fractional Order Chaotic Systems

In this paper, we used Lyapunov theory and Linear Matrix Inequalities (LMI) to design a generalized observer by adding more complexity in the output of the dynamic systems. Our designed observer is based on the optimization problem, minimizing error between trajectories of master and slave systems subject to the incremental quadratic constraint. Moreover, an algorithm is given in our paper used to demonstrate a method for obtaining desired observer and gain matrixes, whereas these gain matrixes are obtained with the aid of LMI and incremental multiplier matrix (IMM). Finally, discussion of two examples are an integral part of our study for the explanation of achieved analytical results using MATLAB and SCILAB.

Intrinsically Disordered Proteins: Critical Components of the Wetware

Despite the wealth of knowledge gained about intrinsically disordered proteins (IDPs) since their discovery, there are several aspects that remain unexplored and, hence, poorly understood. A living cell is a complex adaptive system that can be described as a wetware─a metaphor used to describe the cell as a computer comprising both hardware and software and attuned to logic gates─capable of "making" decisions. In this focused Review, we discuss how IDPs, as critical components of the wetware, influence cell-fate decisions by wiring protein interaction networks to keep them minimally frustrated. Because IDPs lie between order and chaos, we explore the possibility that they can be modeled as attractors. Further, we discuss how the conformational dynamics of IDPs manifests itself as conformational noise, which can potentially amplify transcriptional noise to stochastically switch cellular phenotypes. Finally, we explore the potential role of IDPs in prebiotic evolution, in forming proteinaceous membrane-less organelles, in the origin of multicellularity, and in protein conformation-based transgenerational inheritance of acquired characteristics. Together, these ideas provide a new conceptual framework to discern how IDPs may perform critical biological functions despite their lack of structure.

Can Systems Biology Advance Clinical Precision Oncology?

Precision oncology is perceived as a way forward to treat individual cancer patients. However, knowing particular cancer mutations is not enough for optimal therapeutic treatment, because cancer genotype-phenotype relationships are nonlinear and dynamic. Systems biology studies the biological processes at the systems' level, using an array of techniques, ranging from statistical methods to network reconstruction and analysis, to mathematical modeling. Its goal is to reconstruct the complex and often counterintuitive dynamic behavior of biological systems and quantitatively predict their responses to environmental perturbations. In this paper, we review the impact of systems biology on precision oncology. We show examples of how the analysis of signal transduction networks allows to dissect resistance to targeted therapies and inform the choice of combinations of targeted drugs based on tumor molecular alterations. Patient-specific biomarkers based on dynamical models of signaling networks can have a greater prognostic value than conventional biomarkers. These examples support systems biology models as valuable tools to advance clinical and translational oncological research.