Dynamic and thermodynamic models of adaptation

A mathematical formula of plasticity: Measuring susceptibility to change in mental health and data science

Plasticity is increasingly recognized as a critical concept in psychiatry and mental health because it allows the reorganization of neural circuits and behavior during the transition from psychopathology to wellbeing. Differences in individual plasticity may explain why therapies, such as psychotherapeutic and environmental interventions, are highly effective in some but not in all patients. Here I propose a mathematical formula to assess plasticity - i.e., the susceptibility to change - to identify, at baseline, which individuals or populations are more likely to modify their behavioral outcome according to therapies or contextual factors. The formula is grounded in the network theory of plasticity so that, when representing a system (e.g., a patient's psychopathology) as a weighed network where the nodes are the system features (e.g., symptoms) and the edges are the connections (i.e., correlations) among them, the network connectivity strength is an inverse measure of the plasticity of the system: the weaker the connectivity, the higher the plasticity and the greater the susceptibility to change. The formula is predicted to be generalizable, measuring plasticity at multiple scales, from the single cell to the whole brain, and can be applied to a wide range of research fields, including neuroscience, psychiatry, ecology, sociology, physics, market and finance.

Identifying the critical state of cancers by single-sample Markov flow entropy

Background

The progression of complex diseases sometimes undergoes a drastic critical transition, at which the biological system abruptly shifts from a relatively healthy state (before-transition stage) to a disease state (after-transition stage). Searching for such a critical transition or critical state is crucial to provide timely and effective scientific treatment to patients. However, in most conditions where only a small sample size of clinical data is available, resulting in failure when detecting the critical states of complex diseases, particularly only single-sample data.

Methods

In this study, different from traditional methods that require multiple samples at each time, a model-free computational method, single-sample Markov flow entropy (sMFE), provides a solution to the identification problem of critical states/pre-disease states of complex diseases, solely based on a single-sample. Our proposed method was employed to characterize the dynamic changes of complex diseases from the perspective of network entropy.

Results

The proposed approach was verified by unmistakably identifying the critical state just before the occurrence of disease deterioration for four tumor datasets from The Cancer Genome Atlas (TCGA) database. In addition, two new prognostic biomarkers, optimistic sMFE (O-sMFE) and pessimistic sMFE (P-sMFE) biomarkers, were identified by our method and enable the prognosis evaluation of tumors.

Conclusions

The proposed method has shown its capability to accurately detect pre-disease states of four cancers and provide two novel prognostic biomarkers, O-sMFE and P-sMFE biomarkers, to facilitate the personalized prognosis of patients. This is a remarkable achievement that could have a major impact on the diagnosis and treatment of complex diseases.

Gradistics: An underappreciated dimension in evolutionary space

The growth of complexity is an unsolved and underappreciated problem. We consider possible causes of this growth, hypotheses testing, molecular mechanisms, complexity measures, cases of simplification, and significance for biomedicine. We focus on a general ability of regulation, which is based on the growing information storage and processing capacities, as the main proxy of complexity. Natural selection is indifferent to complexity. However, complexification can be inferred from the same first principle, on which natural selection is founded. Natural selection depends on potentially unlimited reproduction under limited environmental conditions. Because of the demographic pressure, the simple ecological niches become fulfilled and diversified (due to species splitting and divergence). Diversification increases complexity of biocenoses. After the filling and diversification of simple niches, the more complex niches can arise. This is the 'atomic orbitals' (AO) model. Complexity has many shortcomings but it has an advantage. This advantage is ability to regulatory adaptation, including behavioral, formed in the evolution by means of genetic adaptation. Regulatory adaptation is much faster than genetic one because it is based on the information previously accumulated via genetic adaptation and learning. Regulatory adaptation further increases complexity of biocenoses. This is the 'regulatory advantage' (RA) model. The comparison of both models allows testable predictions. We focus on the animal evolution because of the appearance of higher regulatory level (nervous system), which is absent in other lineages, and relevance to humans (including biomedical aspects).

Spatial-Temporal Genome Regulation in Stress-Response and Cell-Fate Change

Complex functioning of the genome in the cell nucleus is controlled at different levels: (a) the DNA base sequence containing all relevant inherited information; (b) epigenetic pathways consisting of protein interactions and feedback loops; (c) the genome architecture and organization activating or suppressing genetic interactions between different parts of the genome. Most research so far has shed light on the puzzle pieces at these levels. This article, however, attempts an integrative approach to genome expression regulation incorporating these different layers. Under environmental stress or during cell development, differentiation towards specialized cell types, or to dysfunctional tumor, the cell nucleus seems to react as a whole through coordinated changes at all levels of control. This implies the need for a framework in which biological, chemical, and physical manifestations can serve as a basis for a coherent theory of gene self-organization. An international symposium held at the Biomedical Research and Study Center in Riga, Latvia, on 25 July 2022 addressed novel aspects of the abovementioned topic. The present article reviews the most recent results and conclusions of the state-of-the-art research in this multidisciplinary field of science, which were delivered and discussed by scholars at the Riga symposium.

Reimagining Cancer: Moving from the Cellular to the Tissue Level

The current universally accepted explanation of cancer origin and behavior, the somatic mutation theory, is cell-centered and rooted in perturbation of gene function independent of the external environmental context. However, tumors consist of various epithelial and stromal cell populations temporally and spatially organized into an integrated neoplastic community, and they can have properties similar to normal tissues. Accordingly, we review specific normal cellular and tissue traits and behaviors with adaptive temporal and spatial self-organization that result in ordered patterns and structures. A few recent theories have described these tissue-level cancer behaviors, invoking a conceptual shift from the cellular level and highlighting the need for methodologic approaches based on the analysis of complex systems. We propose extending the analytical approach of regulatory networks to the tissue level and introduce the concept of "cancer attractors." These concepts require reevaluation of cancer imaging and investigational approaches and challenge the traditional reductionist approach of cancer molecular biology.

Early Education Application Software Based on Artificial Intelligence VR Technology

In order to solve the problems of restricted classroom and lack of repeated training in good curriculum, the design and development of a school life adaptation curriculum based on VR is proposed. This study identified six life adaptation themes for design and development (recognizing facial expressions, crossing the road, how to get lost, shopping, taking public transport, and job interview) and set the objectives, design principles, specific content, teaching evaluation, and other aspects of virtual reality life adaptation course. Combined with the characteristics of virtual reality, the implementation suggestions and matters needing attention are put forward. The results showed that, in the recognition of human facial expressions, 51 experts thought it was appropriate, 3 experts thought it needed to be modified, and no expert thought it was inappropriate. On the topic of crossing the road, 46 experts thought it was appropriate, eight thought it needed to be modified, and no expert thought it was inappropriate. On the theme of taking public transportation, 48 experts thought it was appropriate, 6 experts thought it needed to be modified, and no expert thought it was inappropriate. For the three major topics of how to get lost, shopping, and job interview, 2-3 experts put forward different opinions and think that the topic is not appropriate mainly because the grade arrangement is not appropriate. Conclusion. The VR-based curriculum for school life adaptation has been reviewed by experts and revised by researchers. It is scientific, interesting, and operable, solves the teaching problems of life adaptation teachers, and provides a safe, reliable, and effective practice channel for students.

A multi-marker integrative analysis reveals benefits and risks of bariatric surgery

Bariatric surgery (BS) is an effective intervention for severe obesity and associated comorbidities. Although several studies have addressed the clinical and metabolic effects of BS, an integrative analysis of the complex body response to surgery is still lacking. We conducted a longitudinal data study with 36 patients with severe obesity who were tested before, 6 and 12 months after restrictive BS for more than one hundred blood biomarkers, including clinical, oxidative stress and metabolic markers, peptide mediators and red blood cell membrane lipids. By using a synthetic data-driven modeling based on principal component and correlation analyses, we provided evidence that, besides the early, well-known glucose metabolism- and weight loss-associated beneficial effects of BS, a tardive, weight-independent increase of the hepatic cholesterol metabolism occurs that is associated with potentially detrimental inflammatory and metabolic effects. Canonical correlation analysis indicated that oxidative stress is the most predictive feature of the BS-induced changes of both glucose and lipids metabolism. Our results show the power of multi-level correlation analysis to uncover the network of biological pathways affected by BS. This approach highlighted potential health risks of restrictive BS that are disregarded with the current practice to use weight loss as surrogate of BS success.

Global genome decompaction leads to stochastic activation of gene expression as a first step toward fate commitment in human hematopoietic cells

When human cord blood-derived CD34+ cells are induced to differentiate, they undergo rapid and dynamic morphological and molecular transformations that are critical for fate commitment. In particular, the cells pass through a transitory phase known as "multilineage-primed" state. These cells are characterized by a mixed gene expression profile, different in each cell, with the coexpression of many genes characteristic for concurrent cell lineages. The aim of our study is to understand the mechanisms of the establishment and the exit from this transitory state. We investigated this issue using single-cell RNA sequencing and ATAC-seq. Two phases were detected. The first phase is a rapid and global chromatin decompaction that makes most of the gene promoters in the genome accessible for transcription. It results 24 h later in enhanced and pervasive transcription of the genome leading to the concomitant increase in the cell-to-cell variability of transcriptional profiles. The second phase is the exit from the multilineage-primed phase marked by a slow chromatin closure and a subsequent overall down-regulation of gene transcription. This process is selective and results in the emergence of coherent expression profiles corresponding to distinct cell subpopulations. The typical time scale of these events spans 48 to 72 h. These observations suggest that the nonspecificity of genome decompaction is the condition for the generation of a highly variable multilineage expression profile. The nonspecific phase is followed by specific regulatory actions that stabilize and maintain the activity of key genes, while the rest of the genome becomes repressed again by the chromatin recompaction. Thus, the initiation of differentiation is reminiscent of a constrained optimization process that associates the spontaneous generation of gene expression diversity to subsequent regulatory actions that maintain the activity of some genes, while the rest of the genome sinks back to the repressive closed chromatin state.

Energy Cost of Dynamical Stabilization: Stored versus Dissipated Energy

Dynamical stabilization processes (homeostasis) are ubiquitous in nature, but the needed energetic resources for their existence have not been studied systematically. Here, we undertake such a study using the famous model of Kapitza’s pendulum, which has attracted attention in the context of classical and quantum control. This model is generalized and rendered autonomous, and we show that friction and stored energy stabilize the upper (normally unstable) state of the pendulum. The upper state can be rendered asymptotically stable, yet it does not cost any constant dissipation of energy, and only a transient energy dissipation is needed. Asymptotic stability under a single perturbation does not imply stability with respect to multiple perturbations. For a range of pendulum–controller interactions, there is also a regime where constant energy dissipation is needed for stabilization. Several mechanisms are studied for the decay of dynamically stabilized states.

Stability and flexibility in psychotherapy process predict outcome

Ten good outcome and ten poor outcome psychotherapy cases were compared to investigate whether or not the temporal stability and flexibility of their process variables can predict their outcomes. Each participant was monitored daily using the Therapy Process Questionnaire (TPQ), which has 43 items and seven sub-scales, and responses over time were analyzed in terms of correlation robustness and correlation variability across the TPQ sub-scales. "Correlation robustness" and "correlation variability" are two basic characteristics of any correlation matrix: the first is calculated as the sum of the absolute values of Pearson correlation coefficients, the second as the standard deviation of Pearson correlation coefficients. The results demonstrated that the patients within the poor outcome group had lower values on both variables, suggesting lower stability and flexibility. Furthermore, a higher number of cycles of increase and decrease in correlation robustness and variability of the TPQ sub-scales was observed within good outcome psychotherapies, suggesting that, these cycles can be considered as process-markers of good-outcomes. These results provide support for the validity of these quantitative process-parameters, correlation robustness and variability, in predicting psychotherapeutic outcomes. Moreover, the results lend support to the common clinical experience of alternating periods of flexibility and integration being beneficial to good psychotherapeutic processes.

Detection of hearing losses (HL) via transient-evoked otoacoustic emissions: towards an automatic classification

Transiently evoked otoacoustic emissions (TEOAEs) are routinely used in the hearing assessment of the auditory periphery. The major contribution of TEOAEs is the early detection of hearing losses in neonates, children, and adults. The evaluation of TEOAE responses by specific signal decomposition techniques offers numerous advantages for current and future research. One methodology, based on recurrence quantification analysis (RQA), can identify adult subjects presenting sensorineural hearing impairments. In two previous papers, the RQA-based approach was succesfully applied in identifying and classifying cases presenting noise and age related hearing losses. The current work investigates further two aspects of the previously proposed RQA-based analysis for hearing loss detection: (i) the reliability of a Training set built from different numbers of ears with normal hearing, and (ii) the threshold set of values of the key hearing loss detecting parameter RAD2D. Results: The Training set built from 158 healthy ears was found to be quite reliable and a similar but slightly minor performance was observed for the training set of 118 normal subjects, used in the past; the proposed ROC-curve method, optimizing the values of RAD2D, shows improved sensibility and specificity in one class discrimination. Conclusions: A complete and simplified procedure, based on the combined use of the traditional TEOAE reproducibility value and on values from the RQA-based RAD2D parameter, is proposed as an improved automatic classifier, in terms of sensitivity and specificity, for different types of hearing losses.

Thermodynamic selection: mechanisms and scenarios

Thermodynamic selection is an indirect competition between agents feeding on the same energy resource and obeying the laws of thermodynamics. We examine scenarios of this selection, where the agent is modeled as a heat-engine coupled to two thermal baths and extracting work from the high-temperature bath. The agents can apply different work-extracting, game-theoretical strategies, e.g. the maximum power or the maximum efficiency. They can also have a fixed structure or be adaptive. Depending on whether the resource (i.e. the high-temperature bath) is infinite or finite, the fitness of the agent relates to the work-power or the total extracted work. These two selection scenarios lead to increasing or decreasing efficiencies of the work-extraction, respectively. The scenarios are illustrated via plant competition for sunlight, and the competition between different ATP production pathways. We also show that certain general concepts of game-theory and ecology-the prisoner's dilemma and the maximal power principle-emerge from the thermodynamics of competing agents. We emphasize the role of adaptation in developing efficient work-extraction mechanisms.

Soft Statistical Mechanics for Biology

The multilevel organization of nature is self-evident: proteins do interact among them to give rise to an organized metabolism and the same hierarchical organization is in action for gene expression, tissue and organ architectures, and ecological systems.The still more common approach to such state of affairs is to think that causally relevant events originate from the lower level in the form of perturbations, that climb up the hierarchy reaching the ultimate layer of macroscopic behavior (e.g., causing a specific disease). Such rigid bottom-up causative model is unable to offer realistic models of many biological phenomena.Complex network approach allows to uncover the nature of multilevel organization, but in order to operationally define the organization principles of biological systems, we need to go further and complement network approach with sensible measures of order and organization. These measures, while keeping their original physical meaning, must not impose theoretical premises not verifiable in biological frameworks. We will show here how relatively simple and largely hypothesis-free multidimensional statistics tools can satisfactorily meet these criteria.

Networks and Islands of Genome Nano-architecture and Their Potential Relevance for Radiation Biology : (A Hypothesis and Experimental Verification Hints)

The cell nucleus is a complex biological system in which simultaneous reactions and functions take place to keep the cell as an individualized, specialized system running well. The cell nucleus contains chromatin packed in various degrees of density and separated in volumes of chromosome territories and subchromosomal domains. Between the chromatin, however, there is enough "free" space for floating RNA, proteins, enzymes, ATPs, ions, water molecules, etc. which are trafficking by super- and supra-diffusion to the interaction points where they are required. It seems that this trafficking works somehow automatically and drives the system perfectly. After exposure to ionizing radiation causing DNA damage from single base damage up to chromatin double-strand breaks, the whole system "cell nucleus" responds, and repair processes are starting to recover the fully functional and intact system. In molecular biology, many individual epigenetic pathways of DNA damage response or repair of single and double-strand breaks are described. How these responses are embedded into the response of the system as a whole is often out of the focus of consideration. In this article, we want to follow the hypothesis of chromatin architecture's impact on epigenetic pathways and vice versa. Based on the assumption that chromatin acts like an "aperiodic solid state within a limited volume," functionally determined networks and local topologies ("islands") can be defined that drive the appropriate repair process at a given damage site. Experimental results of investigations of the chromatin nano-architecture and DNA repair clusters obtained by means of single-molecule localization microscopy offer hints and perspectives that may contribute to verifying the hypothesis.

Toward a Logic of the Organism: A Process Philosophical Consideration

Mathematical models applied in contemporary theoretical and systems biology are based on some implicit ontological assumptions about the nature of organisms. This article aims to show that real organisms reveal a logic of internal causality transcending the tacit logic of biological modeling. Systems biology has focused on models consisting of static systems of differential equations operating with fixed control parameters that are measured or fitted to experimental data. However, the structure of real organisms is a highly dynamic process, the internal causality of which can only be captured by continuously changing systems of equations. In addition, in real physiological settings kinetic parameters can vary by orders of magnitude, i.e., organisms vary the value of internal quantities that in models are represented by fixed control parameters. Both the plasticity of organisms and the state dependence of kinetic parameters adds indeterminacy to the picture and asks for a new statistical perspective. This requirement could be met by the arising Biological Statistical Mechanics project, which promises to do more justice to the nature of real organisms than contemporary modeling. This article concludes that Biological Statistical Mechanics allows for a wider range of organismic ontologies than does the tacitly followed ontology of contemporary theoretical and systems biology, which are implicitly and explicitly based on systems theory.

Permutation Entropy as a Universal Disorder Criterion: How Disorders at Different Scale Levels Are Manifestations of the Same Underlying Principle

What do bacteria, cells, organs, people, and social communities have in common? At first sight, perhaps not much. They involve totally different agents and scale levels of observation. On second thought, however, perhaps they share everything. A growing body of literature suggests that living systems at different scale levels of observation follow the same architectural principles and process information in similar ways. Moreover, such systems appear to respond in similar ways to rising levels of stress, especially when stress levels approach near-lethal levels. To explain such communalities, we argue that all organisms (including humans) can be modeled as hierarchical Bayesian controls systems that are governed by the same biophysical principles. Such systems show generic changes when taxed beyond their ability to correct for environmental disturbances. Without exception, stressed organisms show rising levels of 'disorder' (randomness, unpredictability) in internal message passing and overt behavior. We argue that such changes can be explained by a collapse of allostatic (high-level integrative) control, which normally synchronizes activity of the various components of a living system to produce order. The selective overload and cascading failure of highly connected (hub) nodes flattens hierarchical control, producing maladaptive behavior. Thus, we present a theory according to which organic concepts such as stress, a loss of control, disorder, disease, and death can be operationalized in biophysical terms that apply to all scale levels of organization. Given the presumed universality of this mechanism, 'losing control' appears to involve the same process anywhere, whether involving bacteria succumbing to an antibiotic agent, people suffering from physical or mental disorders, or social systems slipping into warfare. On a practical note, measures of disorder may serve as early warning signs of system failure even when catastrophic failure is still some distance away.

Network Dynamics in Elemental Assimilation and Metabolism

Metabolism and physiology frequently follow non-linear rhythmic patterns which are reflected in concepts of homeostasis and circadian rhythms, yet few biomarkers are studied as dynamical systems. For instance, healthy human development depends on the assimilation and metabolism of essential elements, often accompanied by exposures to non-essential elements which may be toxic. In this study, we applied laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS) to reconstruct longitudinal exposure profiles of essential and non-essential elements throughout prenatal and early post-natal development. We applied cross-recurrence quantification analysis (CRQA) to characterize dynamics involved in elemental integration, and to construct a graph-theory based analysis of elemental metabolism. Our findings show how exposure to lead, a well-characterized toxicant, perturbs the metabolism of essential elements. In particular, our findings indicate that high levels of lead exposure dysregulate global aspects of metabolic network connectivity. For example, the magnitude of each element's degree was increased in children exposed to high lead levels. Similarly, high lead exposure yielded discrete effects on specific essential elements, particularly zinc and magnesium, which showed reduced network metrics compared to other elements. In sum, this approach presents a new, systems-based perspective on the dynamics involved in elemental metabolism during critical periods of human development.

Social stress drives the multi-wave dynamics of COVID-19 outbreaks

The dynamics of epidemics depend on how people's behavior changes during an outbreak. At the beginning of the epidemic, people do not know about the virus, then, after the outbreak of epidemics and alarm, they begin to comply with the restrictions and the spreading of epidemics may decline. Over time, some people get tired/frustrated by the restrictions and stop following them (exhaustion), especially if the number of new cases drops down. After resting for a while, they can follow the restrictions again. But during this pause the second wave can come and become even stronger then the first one. Studies based on SIR models do not predict the observed quick exit from the first wave of epidemics. Social dynamics should be considered. The appearance of the second wave also depends on social factors. Many generalizations of the SIR model have been developed that take into account the weakening of immunity over time, the evolution of the virus, vaccination and other medical and biological details. However, these more sophisticated models do not explain the apparent differences in outbreak profiles between countries with different intrinsic socio-cultural features. In our work, a system of models of the COVID-19 pandemic is proposed, combining the dynamics of social stress with classical epidemic models. Social stress is described by the tools of sociophysics. The combination of a dynamic SIR-type model with the classical triad of stages of the general adaptation syndrome, alarm-resistance-exhaustion, makes it possible to describe with high accuracy the available statistical data for 13 countries. The sets of kinetic constants corresponding to optimal fit of model to data were found. These constants characterize the ability of society to mobilize efforts against epidemics and maintain this concentration over time and can further help in the development of management strategies specific to a particular society.

Parenclitic and Synolytic Networks Revisited

Parenclitic networks provide a powerful and relatively new way to coerce multidimensional data into a graph form, enabling the application of graph theory to evaluate features. Different algorithms have been published for constructing parenclitic networks, leading to the question-which algorithm should be chosen? Initially, it was suggested to calculate the weight of an edge between two nodes of the network as a deviation from a linear regression, calculated for a dependence of one of these features on the other. This method works well, but not when features do not have a linear relationship. To overcome this, it was suggested to calculate edge weights as the distance from the area of most probable values by using a kernel density estimation. In these two approaches only one class (typically controls or healthy population) is used to construct a model. To take account of a second class, we have introduced synolytic networks, using a boundary between two classes on the feature-feature plane to estimate the weight of the edge between these features. Common to all these approaches is that topological indices can be used to evaluate the structure represented by the graphs. To compare these network approaches alongside more traditional machine-learning algorithms, we performed a substantial analysis using both synthetic data with a priori known structure and publicly available datasets used for the benchmarking of ML-algorithms. Such a comparison has shown that the main advantage of parenclitic and synolytic networks is their resistance to over-fitting (occurring when the number of features is greater than the number of subjects) compared to other ML approaches. Secondly, the capability to visualise data in a structured form, even when this structure is not a priori available allows for visual inspection and the application of well-established graph theory to their interpretation/application, eliminating the "black-box" nature of other ML approaches.

Assessment of socio-economic risks by method of extremely critical (threshold) indicators

Method of extremely critical (threshold) indicators of social development, including assessment of socio-economic risks, has been developed in the national sociology, economics, and other social sciences about three decades. For the first time development of the method as a scientific problem was stated in 1994, and there was made an attempt to construct such scale of indicators. Development of the method is going productively. There have been published a series of research works, dissertations that directly or indirectly develop or apply this method, propose different variants of constructing a scale of indicators. We have three basic components of situation diagnosis: the existing social system, the risks (challenges, threats) hampering progressive development of this system, and the extremely critical values of the risk indicators, a certain "red line", going beyond which means an increase in the probability of radical changes and further— collapse of the existing system, its transitional state and reorganization. The research and management tasks are to counteract such risks and to prevent entry of the society into the critical zone; or vice versa, to stimulate transformation of the system. The article provides an assessment of the socio-economic risks by method of extremely critical (threshold) indicators that leads to conclusion about a certain, far from complete and sufficient departure of the Russian society from the critical line of the 90s of the past century, and therefore about a tendency to reduction of the risk of another dismantlement of the existing social system. Along with these positive changes, dangerous disproportions and critical risks remain in many socio-economic indicators, primarily related to demography, population health, standards and quality of life.

Self-organization of whole-gene expression through coordinated chromatin structural transition

The human DNA molecule is a 2-m-long polymer collapsed into the micrometer space of the cell nucleus. This simple consideration rules out any "Maxwell demon"-like explanation of regulation in which a single regulatory molecule (e.g., a transcription factor) finds autonomously its way to the particular target gene whose expression must be repressed or enhanced. A gene-by-gene regulation is still more contrasting with the physical reality when in the presence of cell state transitions involving the contemporary expression change of thousands of genes. This state of affair asks for a statistical mechanics inspired approach where specificity arises from a selective unfolding of chromatin driving the rewiring of gene expression pattern. The arising of "expression waves" marking state transitions related to chromatin structural reorganization through self-organized critical control of whole-genome expression will be described in the present paper. We adopt as a model system the gene expression time course of a cancer cell (MCF-7) population exposed to an efficient stimulus causing a state transition in comparison with an ineffective stimulus. The obtained results will be put into the perspective of biological adaptive systems living on the edge of chaos.