This paper explores the diagnostic and therapeutic potential of a new concept of health. Investigations into the nature of health have led to a new definition that explains health as a complex adaptive system (CAS) and is based on five components (a-e). Humans like all biological creatures must satisfactorily respond to (a) the demands of life. For this purpose they need (b) a biologically given potential (BGP) and (c) a personally acquired potential (PAP). These properties of individuals are embedded within (d) social and (e) environmental determinants of health. Between these five components of health there are 10 complex interactions that justify viewing health as a CAS. In each patient, the current state of health as a CAS evolved from the past, will move forward to a new future, and has to be analyzed and treated as an autonomous whole. A diagnostic procedure is suggested as follows: together with the patient, the five components and 10 complex interactions are assessed. This may help patients to better understand their situations and to recognize possible next steps that may be useful in order to evolve toward better health by themselves. In this process mutual trust in the patient-physician interaction is critical. The described approach offers new possibilities for helping patients improve their health prospects. Although the foundations of medicine have evolved since then, the general principles of medical practice have remained the same. Only over the past 20 years has complexity science gradually entered into medicine3. This has become particularly important for the interpretation of health and disease as different states of a complex adaptive system (CAS). The Meikirch model is a new definition of health that exhibits all the features of a CAS4. For such systems the concepts based on Virchow’s pathology ideas are no longer adaquate. An understanding of health and disease now requires appreciation of complexity science which introduces a new dimension for diagnosing and treating patients. It includes the potential of improving health in a way that was hitherto practiced only exceptionally. The purpose of this paper is to summarize the relevant features of the Meikirch model and to spell out in detail how the model and complexity science may be applied for a better understanding of a patient’s disease and its treatment.Individuals consult their physicians when they feel something is out of order, e.g. when they experience pain, fatigue or some other disorder. Physicians then examine them and specifically look for pathological changes. After such an investigation they make a provisional diagnosis and explore their patients further or treat them according to what has been discovered. This approach and type of thinking goes back to the pathologist Rudolf Virchow who, in 1858, used 20 lectures to describe “cellular pathology”, a characterization of different diseasesa toe. The interactions are exhibited as double-edged arrows from1 – 10. A short explanation of the five components and their interactions is presented below. The complete description of the model with its scientific background is given in the previous publications5.The Meikirch model is based on five components  and 10 cBox 1. a. Life's demandsb. Biologically given potential (BGP)c. Personally acquired potential (PAP)d. Social determinantse. Environmental determinantsBox 2. 1. Health is a dynamic state of wellbeing emergent from conducive interactions between an individual's potentials, life's demands, and social and environmental determinants.2. Health results throughout the life course when an individual's potentials and social and environmental determinants suffice to respond satisfactorily to the demands of life. Life's demands can be physiological, psychosocial, and environmental, and vary across individuals and contexts, but in every case unsatisfactory responses lead to disease.life situation6. Physiological, psychosocial and environmental demands vary with time and circumstances.Physiological demands are related to the homeokinetic balance of nutrients, energy and water necessary for maintaining bodily functions including procreation .Psychosocial demands are the individual´s exposure and response to social conditions needed to succeed in social integration and mental, personal and spiritual development. Expectations and roles related to work, family and society as a whole combine with personal aspirations, values and lifestyle in changing settings and contexts. This also includes peace with the fact that every human being must die.Environmental demands include the availability of and immediate or latent threats from living conditions .Each human being must fullfil the demands of his or herbiologically given potential (BGP), and partly acquired during life -personally acquired potential (PAP). At birth the BGP is based on the genetic equipment, epigenetic regulation and quality of the pregnancy. The BGP diminishes throughout life and is zero at the time of death. During the lifetime the BGP may be threatened or damaged by socioeconomic disadvantages, diseases, injuries and/or defects. The PAP results from the entirety of physiological, mental, spiritual and social resources acquired during the lifetime. It may continue to grow when a person cares for it. Social and environmental conditions also influence the growth of the PAP by providing or withholding determinants of health.The potential of an individual to meet the demands of life is partly biological e.g. a gift of nature -Social determinants of health strongly interact with the demands of life and the potentials of the individual4. Equity and equality, social concerns, working conditions, autonomy and social participation affect health and longevity8 and are also major determinants. Likewise,environmental determinants of health are factors in living and working conditions that affect each person. They may sometimes be of global significance like natural resources, catastrophes, population growth and climate change10.5.Based on these five components and their interactions with each other the Meikirch model represents a new definition of health and disease as shown in11. It can take up material and energy from the environment (input), release end products  and do work. Within the system there are many different parts called agents. In2. This effect refers to the image of a butterfly that flaps its wings in South America and induces a hurricane in Texas. Examples of medical conditions where a similar mechanism may lead from minor incidents to major consequences are ventricular fibrillation, epileptic seizures, tantrum, and psychotic states. Every CAS has evolved from a prior condition and autonomously progresses toward an unforeseeable future state. A CAS may be part of a larger CAS or be composed of many CASs. Such structures are called nested CASs.A complex adaptive system is an entity with a more or less permeable boundary between it and its nearby environment 11. It cIn the Meikirch model the five components (a–e) including their subcomponents are regarded as agents . InteracAn entire life is an evolutionary process. Biologically human life originates with the fertilization of an oocyte. This then passes through the stages of embryo and foetus to the maturity needed for birth. At some time during intrauterine life the personality of the individual is created. At least, physicians and midwifes say that in a new-born it is clearly recognizable. From then on the complete Meikirch model is fully operational throughout all the life course phases of each person. Thus evolution from birth to death demonstrates clearly how many adaptive processes occur as part of the different complex interactions described by the model. While the two potentials evolve, the demands of life, the social, and the environmental determinants also vary. Within these limiting and supporting contexts individuals follow an autonomously chosen course of life. Under such conditions it is not surprizing that some adaptations may not be fully successful for some period of time or permanently. Challenging examples are malnutrition, infectious diseases, love deprivation, sexual maturation, pregnancy, genetic defects, professional stress, the raising of children, physical involution, aging, etc. Such changes may lead the health of an individual as a system into a state of crisis. If it is minor, the two potentials may still manage the demands of life and the difficulties may resolve spontaneously after some time. Such situations may represent illnesses, but are not considered as disease or pathological. They may, though, evolve into a chronic state that draws energy from the person and thereby may explain, for instance, insomnia, chronic fatigue, or somatoform symptoms. If the defect becomes more severe it may lead to a disease that requires more medical attention. In the Meikirch model the term “disease” implies that for some reason one or several adaptation processes are not successful enough to empower the two potentials to satisfy the demands of life.To allow for future research, hypothetical consequences of the Meikirch model and of the properties of CASs have been explored with the purpose of better understanding the state of health of patients, particularly in primary care. According to the Meikirch model, health of a healthy individual or of a patient is considered to be a nested CAS, composed of grouped CASs and being embedded in higher CASs. For the analysis of various conditions, the significance of each of the five components and of each interaction within the Meikirch model were visualized. In addition, possibilities of supporting favourable evolutions of the respective CAS and its meaning for the whole person (nested CAS) were analysed. In this process, the deduction (from observation to theory) and induction (from theory to observation) cycles were repeated until coherent results were achieved.1. Minor maladaptations lead either immediately or with varying delays to discomfort (illness) or to signs of a disease. Examples for the former are minor acute infections or tension headaches, and for the latter, overweight, type 2 diabetes, or arterial hypertension.2. A more severe disturbance of the system leads it into a crisis, i.e. it becomes “chaotic”. Such states may be corrected spontaneously, for example, or by behavioural changes, or by interacting with a physician or healer, by medications, or by medical or surgical interventions. Thereafter there may not be an immediate complete recovery to health. The full adaptive evolution may take time and further interventions, i.e., convalescence or rehabilitation, may be needed. These phenomena may lead to complete healing or to healing with remaining defects.3. If a CAS is disturbed continuously for a prolonged time, the CAS may not be able to satisfactorily respond to the demands of life. This represents a chronic disease or invalidity. If the condition is progressive and serious, it may lead to death. Examples are rheumatic or degenerative diseases and different types of neoplasms.4. Considering a disturbed state of health as a maladapted CAS implies that patients cannot simply be healed by the actions of a competent physician. Healing is much rather the result of a process of self-reorganization, enabling the two potentials to again satisfactorily fulfil the demands of life. The task of physicians and other health professionals therefore consists in being competent advisors and fellow human beings that assist the patient in realizing the necessary evolution himself.Disturbances in health and healing follow a pattern that can be described by four categories:It always is appropriate to examine patients with an ordinary medical history and physical examination to which all indicated laboratory tests and imaging procedures are added. Simultaneously it may be purposeful to perform an analysis of the patients´ health as a CAS. In this case the five components and the ten complex interactions of the Meikirch model are assessed by an extended history as exemplified inBox 3. In addition to the five components and the ten complex interactions the energy flow and other patterns of the model also need to be investigated. The questions enumerated are just examples that have to be adapted and complemented further as needed for each patient’s specific problems.Questions related to the components of the model (a–e):a) What specifically are the demands of life to which the patient has to respond?b) How does the patient perceive the evolution of his or her physical health?c) How does the patient feel about him- or herself? Can he or she manage themselves? Does he or she invest in the future?d) How is the patient integrated into family, household, friends, society and government?e) In which type of natural environment does the patient live?Questions about the interactions (1–10)1.   How does the physical body of the patient (past and current) interact with the demands of life?2.   How does the patient deal with his or her physical, psychological and spiritual demands of life?3.   How does the patient interact with him- or herself, especially with the body? Does he or she invest in it?4.   How does the patient interact with family, household, friends, and government etc.?5.   How does the physical body of the patient interact with the society ?6.   How does the society influence the demands of life?7.   What tis the attitude of the patient toward his natural environment?8.   Which are the past, present and future interactions of the natural environment with the patient’s physical body?9.   How does the natural environment modify the patient’s demands of life?10.  How does the society interact with his or her natural environment?Questions about vitality, motivation and purpose in lifeWhat is the source of the patient’s vitality? Is it spontaneous or rather focused on objectives or purposes? Which occasions induce which type of vigour? What is his or her purpose in life?How is the patient’s physical, intellectual, and emotional vitality? How much is hedonistic and how much eudaimonic?What does the patient do with his or her vitality? Is it used mostly in family, profession, or hobbies?What is the energy flow between the patient and the physician like?Questions about temporal patternsWhen did the patient feel completely healthy the last time? When and how did he or she loose health or wellbeing?What were the manifestations of the crisis?How was the time course of the disease up to now? Which factors induced aggravation and which brought about improvements? Which changes within or outside the patient induced which type of changes?What is the explanation of the patient for the current state of health and for the failure to improve it? What does the patient need in order to surmount the present crisis?What are the future plans of the patient? How much sense of purpose do they evoke?Obviously, for all medically diagnosed conditions treatments are to be prescribed as indicated. Yet, in medicine, indications generally leave considerable room for judgements. Thus the findings collected by assessing all the components and interactions of the Meikirch model must be considered and integrated as far as possible. A CAS cannot be manipulated to health. It must be assisted as it reorganizes itself autonomously to a new state, in order to better fulfil the demands of life and hence better health and well-being. The role of the physician, therefore, is to accompany the patient during the process he goes through. Some advice, assistance, or therapeutic intervention may be helpful, but only the patients are in a position to create their new future state for themselves. By analysing their condition as a CAS together with their physician including all components and all interactions of the model they presumably receive many new ideas that they can use to emerge into a healthier state in the future. For example, they may want to make up their mind whether or not they will accept all the conditions that have determined their life in the past. In this respect, a discussion with their physician of alternatives with their consequences may be useful. For many patients it might be constructive to deal with the energy flow in their system, e.g. to speak about the purpose of their lives.The process of reorientation based on the Meikirch model takes time. During this period it may help the patient if they find in their pysician a trustworthy human beeing with whom they can discuss all sorts of alternatives. Ultimately though, patients have to create their own future. It will encourage them if they feel understood, trusted and accompanied by an experienced person with a sincere interest in their wellbeing.In primary care, such as general internal medicine and general practice, there are many patients who come for consultations because they feel ill. Yet, on examination no clear pathology is found. Thus far such complaints have been explained as functional and often were regarded by physicians as unimportant. Patients then received drugs that may be symptomatically beneficial or placebos or, more often than not, harmful or nocebos. Instead of acting with benign neglect, the Meikirch model offers a true and positive alternative approach. In many cases it will help the patients to understand their problems, to readjust their potentials and to advance their readaptation to the demands of life. Thereby patients may again come closer to a state of health and wellbeing.nature of health; it used instead an intuitive notion of wellbeing which did not lead to new insights. In contrast, a rational understanding of health - as given by the Meikirch model - offers innovative opportunities. Today this model is better founded on scientific evidence than other definitions of health. Its ultimate validity, however, will be documented only by using and evaluating it in practice. This must be done with due consideration to the special features of the model. Much further research is urgently needed.At the present time the Meikirch model is a hypothesis grounded on a theoretical and conceptual framework. Yet, up till now much of health care has not been concerned with an understanding of the11. Poorly functioning parts are not simply corrected by appropriate drugs or surgical operations. Instead considerations of the evolution of the patient’s health to its present state, earlier successes in self-management and failures in the handling of his present crises can be evaluated. Here, Antonovsky’s sense of coherence and meaningfulness also may be very helpful12. The necessary changes a patient has to realize must not come top-down from the physician, but rather bottom-up, originating in the patients themselves, e.g., via new insights. For this purpose mutually trusting patient-physician interactions are critical for a successful future: the physician must believe in the patient’s abilities to evolve to a new state and must accompany and support him with loving wisdom in this endeavour.For the past 150 years medicine has been working with methods derived from Newtonian natural science and obviously has achieved major advances. They are based, however, predominantly on materialism and neglect the social and spiritual features of human nature. In addition, until recently medicine has not considered systems theory. It appears that these two aspects offer new opportunities for health care to become even more effective. Systems thinking implies that science based on Newton must be complemented by complexity science. Particularly for the purpose of health care a phenomenological, narrative, and evolutionary holism must be added to analytical reductionism13. He was a psychiatrist and pursued the purpose of “Training General Practitioners in Psychotherapy” to better understand and respond to the needs of their difficult patients. In contrast, the systems theory approach focusses on a new look at a patient’s possible unresolved evolutionary steps, analyses the biological given and personally acquired potentials and offers him an opportunity to progress further in his personal biography. More research is needed to validate the promises and limitations of this methodology.When speaking with older and experienced general practitioners, and when reading about how they managed their difficult patients, it becomes evident, that they knew their patients from the past quite well. In many difficult situations they often had to accompany rather than to treat them. Such patients remained very loyal because they understood what their doctor had contributed to their health. At the same time physicians realized that they had nothing more to offer than their personal support as a professional human being. The Meikirch model offers now a rational approach to such difficult cases and it is hoped that the five components and the ten complex interactions will lead to new opportunities for patients to move toward better health. At the first glance the described system’s approach to patient care is similar to what Michael Balint intended with his groups14. For this purpose it interacts with all components of the system. The PAP is the seat of memory, visions, fantasy, reasoning, attentional control and inhibitory control, and problem solving. Its sustained evolution toward more and more wisdom is critical for the maintenance of health. The PAP can learn to compensate in part for losses of the BGP. This leads to an interesting aspect of the relationship between the two potentials. It may be compared to rider and horse. If the rider wants that his horse serves him well he has to take good care of his horse. It appears that the neglect of the PAP in modern medicine is well perceived by patients and they have turned to complementary or alternative medicine. In fact, much of the success of homeopathy and other methods might be explained by the physician/patient interaction with its effects on the complex adaptive system that expresses the patient’s health. This mechanism may be relevant also for much of the success of other complementary or alternative treatments. It is our opinion, however, that it will be better to work with the CAS in a planned and scientifically justifiable manner based on the Meikirch model than to apply unproven methods. The model would also serve as an excellent framework for a proper practice of evidence based medicine as defined by David L. Sackett: “Evidence-based medicine (EBM) requires the integration of the best research evidence with our clinical expertise and our patient’s unique values and circumstances15.” This applies also to the newly evolving holistic clinical approach “Integrative Medicine and Health” that “reaffirms the importance of the relationship between practitioner and patient, focuses on the whole person, is informed by evidence, and makes use of all appropriate therapeutic and lifestyle approaches, healthcare professionals and disciplines to achieve optimal health”16.The Meikirch model distinguishes two types of very different potentials with which the demands of life must be met, the biologically given potential (BGP) and the personally acquired potential (PAP). The latter is the resource that continuously pilots the adjustment to new life situations. It is the locus of executive functions5. The Meikirch model provides a framework for how this could be achieved.When looking at health as a lifelong and complex evolutionary process, it is not surprising that crises do occur frequently. Throughout human life there are several major and many minor evolutionary steps to be taken. End of breastfeeding, beginning of school, puberty, professional formation and advancement, partnership, family, menopause, and involution of old age are some of the more demanding processes. Today they must be overcome in a society that offers insufficient respect for the personality of each individual. Lack of a motivating purpose in life and insufficient social support have become almost normal. Economic exploitation, power plays, isolation, social neglect and even wars weigh heavy on the demands of life. A culture that is really concerned with the health and wellbeing of its individuals needs to strongly support lifelong human development by investing in life-affirming compassion and truth I would like to thank the authors for their explanations and revisions of the paper: Applying a complex adaptive system's understanding of health to primary care. It is very clear, provides much food for thought in thinking about health and disease in people as complex adaptive systems. The paper provides a framework for considering the variability in how patients adapt to various conditions. It also centers the responses on the patient and their “Healing is much rather the result of a process of self-reorganization, enabling the two potentials to again satisfactorily fulfil the demands of life.” And helps the physician to know that compassion, humanism, creativity and willingness to stand by are legitimate roles.I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. This is an article describing the confluence of two theories, the model of health as defined by the authors in the Meikirch model which appears to be a model developed and published by the authors, and complex adaptive systems.  The authors propose this as a method to better help patients adapt and aim towards improved health. Strengths:  The authors have developed a theory and are proposing this explicit theory can better support patient care.  Primary care is known for its complexity and uncertainty. Thus the system is a good framework for thinking about a holistic approach to patient care and to the variability of adaptation based on the components. The categories of illness and disease would be helpful for learners to understand that not all illness has a desired resolution. The comments on complex adaptive systems as a way of understanding health in individuals and society is useful in reminding us that linear models often ignore the unintended consequences of change. Suggestions: As a family physician, I found the paper both interesting and difficult to follow.  In general the language is clear with minor errors.  I am not an expert on complex adaptive systems but agree with the comment regarding the use of some terms as detracting from the premise of the article.  My main suggestion would be to expand the methods section.  It is not clear to me who was involved in the process, how this was carried out.  I wonder if this would be better as a theoretical proposal rather than a scientific study.  The examples chosen seem to be the opinions of the authors and have not been tested.  Some are quite vague and would require fuller explanation.  I also agree that comparing this theory to others might be useful.  McWhinney is referenced and as a leader in Family Medicine in Canada, the four principles of family medicine and a model we use to teach residents for patient-centered care helps us to provide care in family medicine that is not likely to be enhanced by the model.  The four principles are:The family physician is a skilled clinician.Family medicine is a community-based discipline.The family physician is a resource to a defined practice population.The patient-physician relationship is central to the role of the family physician. It may be that the authors are specialists and thus are less familiar with general/family practice. The idea that “Physicians then examine them and specifically look for pathological changes.” is not the premise for family medicine in Canada.  The four principles address the environment and social determinants of health in situating the patient in the community and family in which they live.  The idea of accompanying the patient resides in the value of continuity of care and the patient-physician relationship. Knowing the patient’s values and past helps to tailor the approach to support the patient in the direction they wish to go. The skilled clinician is a critical thinker who can deal with uncertainty and as a resource to the practice population advocates for the system to better serve the population.    In Canada we teach a model of interviewing that includes the traditional history focused on disease interwoven with the IFFE model. These include the patient’s ideas of what is wrong with them, their fears, how their function is affected and their expectations from the physician/system. These questions are essential to the patient-centered approach and situate the consultation clearly with the patient as the CAS.  In particular, I find the suggestions for taking a history based on the model cumbersome and clearly the language would be challenging for patients. It is also not clear to me how these questions are related to the CAS.  The treatment approach mirrors the patient-centered approach taken in family medicine. We know that patients often do not fill prescriptions and asking patients what might work for them or what they are comfortable with, helps one to support a treatment approach that is right for the particular patient.  Being aware that a patient does not have the resources to access a particular treatment is essential to a collaborative effort for care.in utero does not include the environment overlooks the social determinants of health of the mother and their effect on thein utero environment.  Some of the examples either require more explanation or less linear thinking. The idea that I have been involved in a number of Balint groups and recall reading Michael Balint’s book. The statement “He was psychiatrist and pursued the purpose to train general practitioners in psychotherapy.” does not reflect my experience. My understanding was he focused on Difficult Clinician-patient relationships to help general practitioners interact and “accompany” our patients more effectively. The groups were meant to support physicians in their own context. I did not see this as training in psychotherapy. Minor suggestions “Examples of medical conditions are ventricular fibrillation, epileptic seizures, tantrum, or psychotic states.” This statement needs further explanation.  It is not logical from the discussion if we think of health in a holistic manner.  There may be cultural differences in writing and I appreciate English may not be the first language of the authors; however I find it a poor reflection to refer to all patients and physicians as male. I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. Response to the comments by Dr. Dianne Delvahttp://f1000research.com/articles/5-1672/v1).From Dr. Delva´s critical comments as a family physician we have come to the conclusion that the original title does not completely reflect the content of the paper and may be misinterpreted. We do not intend to challenge any of the established models as applied to family medicine. We rather intended to explore the possible results of applying the principles of complex adaptive system´s thinking in primary patient care, possibly extending the present practice. Therefore, to avoid any misunderstanding, we have changed the title of the paper into “Applying a complex adaptive system´s understanding of health to primary care”. This was also suggested in the review of Dr. Sturmberg  is trained in and practiced general internal medicine (and gastroenterology) and is familiar with Robert Nikolaus Braun´s conceptual frame of family medicine which is prevalent in German speaking countries.In a participatory and integrative approach to the patient, the inclusion of the patient´s ideas, fears, functions and expectations (IFFE model) is indeed essential for any primary encounter between patient and physician. It is also part of the Meikirch model, as can be seen in box 3 on page 6. Dr. Delva finds it cumbersome to take a history based on the Meikirch model and states that it is not clear to her how the questions in box 3 are related to the CAS. Obviously this table contains examples, is not exclusive and must be adjusted to the patient’s specific problems. The purpose of box 3 is to give the physician a tool to make sure that the history he took covers the whole Meikirch model, i.e. is complete in this sense. The questions suggested in box 3, derived from the Meikirch model with its complex interactions, will also be the basis for describing the patient as a CAS. The Meikirch model is in itself based on complex adaptive systems thinking. Dr. Delva, is right in suggesting to use plain language in real life communication with patients.In order to clarify the issue of the situation in utero we believe that the direct environment of a fetus is the uterus of the mother. The environmental and social determinants of the mother have nonetheless an indirect effect on the child´s development in utero as has been pointed out in a previous description of the Meikirch model.Dr. Delva refers to her understanding of Balint groups. We have taken the information given in our paper directly from an original publication by Michael Balint (1896–1970) in the Br Med 1954 (see reference 13). Balint groups may have developed in a direction not intended by Balint himself, and we agree that the term psychotherapy is not well defined and can be understood in many ways in Balint´s original paper. The case reports included in this paper describe complex psychodynamic situations. We have changed our text on page 9 to stay as close to Balint´s original paper as possible.The butterfly effect used as a metaphore on page 4 is now described in more detail to assure a better understanding of our mentioning of ventricular fibrillation, epileptic seizures, tantrum or psychotic states. These conditions, because of their dramatic appearance, are exclusively meant as an illustration of the butterfly effect.Wherever the gender-neutral terms “patient” or “physician” were used in our text we have now avoided to use them in a gender-specific context by either omitting “he” or “she” or using the plural, including in the abstract. Fink, W. & Kamenski, G. Wien Med Wochenschr (2009) 159: 173. doi:10.1007/s10354-009-0666-8 We as authors appreciate the care Dr. Delva has devoted to our paper. It has helped us significantly to improve the manuscript and make it readable for family physicians. Also, we are happy that she recognizes the overall strengths of our contribution. We understand that she appreciated the value of thinking in terms of health and disease as complex adaptive systems (CAS) to embrace uncertainty and a holistic approach to patient care. In order to respond to her concerns with some aspects of our manuscript we would offer the following point by point response. We will also indicate where we have made changes and corrections of the manuscript. Bircher J, Hahn EG: Understanding the nature of health: New perspectives for medicine and public health.F1000Res. 2016;5:167. 27134730 Improved wellbeing at lower costs . 10.12688/f1000research.7849.1 4837984. See page 4 „personally aquired potential“. 1 principally also apply to this paper.This paper is an extension of the authors’ previous paper in this journal and stimulates long overdue debate. My previous comments Two additional points:The paper’s title “Health as a Complex Adaptive System: a new dimension of patient care in internal medicine and general practice” only loosely reflects the content of the paper, I would think that a title similar to “Applying a complex adaptive system’s understanding of health to clinical care” would be stronger and more appropriate. Offering clinicians alternative ways of practicing is certainly most welcome.2 . Even definable pathology is not objective as many studies have shown significant disagreement between experienced clinicians looking at the same “example of disease”. Highlighting the definitional problems and distinctions is especially important for primary care physicians as many people present with unspecific symptoms rather than a “specific diagnosis”3. Diagnoses are socially constructed4  and have become a “tyranny for clinicians”5 . From a complexity perspective thinking about patients’ complaints as “conditions” or “states of being” clearly fosters more creative approaches to patient care and the emergence of more satisfactory outcomes.The paper - implicitly - wrestles to come to terms with the notions of health in relation to the “non-health” terms of illness and disease  I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard.


During the peak of their accretion phase, supermassive black holes in galactic cores are known to emit very high levels of ionizing radiation, becoming visible over intergalactic distances as quasars or active galactic nuclei (AGN). Here, we quantify the extent to which the activity of the supermassive black hole at the center of the Milky Way, known as Sagittarius A* (Sgr A*), may have affected the habitability of Earth-like planets in our Galaxy. We focus on the amount of atmospheric loss and on the possible biological damage suffered by planets exposed to X-ray and extreme ultraviolet (XUV) radiation produced during the peak of the active phase of Sgr A*. We find that terrestrial planets could lose a total atmospheric mass comparable to that of present day Earth even at large distances (~1 kiloparsec) from the galactic center. Furthermore, we find that the direct biological damage caused by Sgr A* to surface life on planets not properly screened by an atmosphere was probably significant during the AGN phase, possibly hindering the development of complex life within a few kiloparsecs from the galactic center. Other studies addressed the effect of ionizing events from transient high-energy sources such as supernovae and gamma ray bursts on their surroundings, including their potential impact on the history of life on Earth6. This led to the identification of regions in the Milky Way  which might be less prone to such potentially life-threatening occurrences.The search for habitable planets beyond Earth is one of the major goals of contemporary astrophysics. This has motivated increased interest in quantifying the astrophysical factors that can make a planet unsuitable for life as we know it. It has long been recognized that prolonged exposition to ionizing radiation from space can hinder habitability by causing atmosphere loss and exposing planetary surfaces to biologically hazardous high-energy fluxes. Most work on the relation between habitability and exposure to ionizing radiation focused on exploring the effect of the activity of the host star on planetary systems, particularly for planets orbiting highly active stars such as M-dwarfs11, and may have lasted between ~107 and 109 years12. Previous studies on the relation between AGN and habitability have focused either on the effect of the activity of Sgr A* on the past environment of Earth13 or, more recently, on the statistical modeling of the effect on planetary atmospheres of generic quasars populations in a cosmological context15. Here, we ask a different, more specific question: was the global habitability of the Milky Way affected by the past history of the supermassive black hole at its core? We address this issue by using plausible scenarios for the accretion history of Sgr A* and estimating the effect of its XUV emission on planetary atmospheres at various distances from the Galactic center. We then quantify the biological damage caused by the ionizing radiation produced by Sgr A* during its peak activity and whether this posed an increased hazard to surface life, particullarly for planets that lacked protection from a substantial gas envelope.From the comparison with observational studies of the global statistical distribution of active galactic nuclei (AGN) with respect to their cosmological redshift and luminosity, we infer that Sgr A* has almost certainly been an important source of ionizing radiation during the peak of its active phase that has likely occured less than 8 Gyrs ago17. The mass loss rate depends on the XUV flux and on the bulk density of the planet. The efficiency of conversion of incident power into atmospheric loss is parameterized by a factor ε (see Methods). The flux received by a planet at distance D from the galactic center also depends on the attenuation of XUV radiation by the torus of material surrounding the supermassive black hole, parameterized by an optical depth τ (see Methods). We made the reasonable assumption that the AGN torus is co-aligned with the Galactic plane and considered two cases of When XUV radiation falls upon a planetary atmosphere, it can cause its evaporation via hydrodynamic escape8 yrs. A lower luminosity would result in a longer duration, and vice versa (see Methods). However, since the fluence would remain the same, the total atmospheric mass lost at the end of the AGN phase . However, the same total dose can result in smaller or even negligible biological damages if it is absorbed over a sufficiently long time, for example because cell repair mechanisms can come into effect. Then, ionizing radiation should exceed some critical flux (i.e. dose rate) in order to pose a significant hazard to living organisms. Furthermore, it is conceivable that extraterrestrial organisms might evolve their own radiation-resistance mechanisms under very different environmental conditions, making it difficult to predict a universal lethal flux threshold. We should also note that even radiation doses smaller than the lethal value could have relevant biological consequences by causing mutations or adding selective pressure to living organisms.Assessing a hazard threshold for life exposed to ionizing radiation is not straightforward. Lethal values in the literature are usually quoted as an absorbed dose, expressed in units of gray, equivalent to 1021, corresponding to fluences ~5 × 105 erg cm−2 and ~5 × 107 erg cm−2, respectively19. We note, however, that the most radiation-resistant known terrestrial prokaryotes, such as Deinococcus radiodurans, can survive to acute doses of order 104 Gray, or fluences21 ~5 × 109 erg cm−2. Since the lethal doses quoted in studies on the resistance of living organisms to radiations were absorbed over periods ranging from days to, at most, about a year, we decided conservatively to adopt a conventional reference value of 1 year to convert from fluence to flux. This results in critical fluxes of 1.6 × 10−2 erg s−1 cm−2 for “complex” life and 1.6 erg s−1 cm−2 for prokaryotes. We then calculated the distance from Sgr A* where a planetary surface was exposed to such fluxes during peak activity. The results are summarized in Table With these caveats in mind, we derived some quantitative indication of the possible biological damage on planetary surface life during the peak activity of Sgr A*. We did so by comparing the XUV flux at various distances from the galactic center to the absorbed dose that proved to be lethal for various terrestrial organisms. We adopted as reference a lethal dose of 1 gray for eukaryotes and multicellular life and of 100 gray for prokaryotesD ≲ 1 kpc) should have been exposed to enough XUV radiation during the AGN phase of Sgr A* to lose a significant fraction of their atmosphere. The total mass loss could be comparable to that of the atmosphere of present day Earth for distances D ≲ 0.5 kpc even for locations close to the galactic plane, where the attenuation from the AGN torus is maximal, assuming values on the higher end of hydrodynamic efficiency. This is basically independent of specific assumptions on the accretion history of the supermassive black hole. This effect may have catastrophically compromised the past and future habitability of planets in the Galactic bulge, unless their atmospheres were regenerated by some planetary processes (e.g. outgassing). As the rate of volcanism and outgassing for exoplanets cannot be easily predicted from general models, we refrain here to incorporate such a source term in Equation A robust conclusion of our study is that rocky planets in the Galactic bulge . This may not have prevented the appearance of life To sum up, our results imply that the inner region of the Milky Way might have remained unhabitable until the end of the AGN phase of its central black hole, and possibly thereafter. This has important consequences in assessing the likelihood of ancient life in the Galaxy, and should be taken into account in future studies of the Galactic habitable zone. It also suggests further investigations on the relation between supermassive black holes in galactic cores and planetary habitability.−1. Using the best estimate for the mass of Sgr A*, 22), would result in a luminosity −1.In order to estimate the luminosity of Sgr A* during the peak of its activity we can first consider the Eddington luminosity defined as 14. The relation between AGN luminosity L and mass accretion rate Macc is L = LEdd, we obtain a mass-independent time-scale of Then, we can estimate the duration of the AGN phase considering the Salpeter time, defined as the time it takes to double the black hole mass during an Eddington accretion phaseLEdd for local Seyfert galaxies23 the AGN phase would be 10 times longer, Δt = 5 × 108 yrs. Considering an even lower luminosity regime of only ~1% LEdd, the timescale would be 100 times longer than Δts. We consider the ~10% LEdd to be the most likely accretion rate during the AGN phase. However, we note that, since the total atmospheric mass lost by a planet depends on the integrated fluence ~LΔt (as explained later), the final result at the end of the AGN phase will not depend on the assumed luminosity.We can consider the Eddington luminosity as an upper limit on the AGN radiative output and therefore the resultant Salpeter time as a lower limit on the timescale of the AGN phase. Considering the most typical luminosity value of ~10% F(λ) = Aλa, where the spectral index is typically236 eV). This is roughly 70% of the total luminosity over the range 0.1–10 6 eV, consistent with population studies which show that the AGN power is mostly released in the XUV band24.Finally, we need an estimate of the amount of XUV radiation emitted during the AGN phase. The AGN broad-band spectral energy distribution is well approximated by a power-law 25 postulates that the accreting supermassive black hole is surrounded by an optically-thick torus at scales of about 1 pc. This would cause an attenuation eτ− of the flux from the AGN: the optical depth τ of the torus is null along the polar direction and it reaches a maximum of 26. Flux attenuation by the interstellar medium in the Galaxy is negligible with respect to the AGN torus because it is always optically thin and it may reach a maximum optical depth27 of only The unified model of AGND from the Galactic center, taking into account also the attenuation of the radiation passing through the AGN torus and the interstellar medium, can be modeled as:τ is the optical depth along the line of sight.Therefore, the incident flux at a given distance 16. The energy-limited mass loss rate is usually modeled by a first-order differential equation28:Fxuv is the incident flux, ρp is the planet density and ε is an efficiency parameter that is estimated29 in the range Lxuv over the AGN lifetime Δt, we can write the total mass lost by a planet at distance D from the galactic center as:ρp, that we expect to be roughly the same of Earth for all rocky planets.When XUV radiation falls upon a planetary atmosphere, it can cause atmosphere loss via hydrodynamic escapeD from the galactic center where a planet loses an atmosphere mass Mostl after a time Δt:ρ⊕ = 5.5 g cm−3 is the density of the Earth.The previous equation can be inverted to obtain an analytic relation for the distance


The NVVC/NHJ publication prizes are named after one of the founding fathers of Dutch Cardiology, professor D. Durrer 1918–1984) who was the chair of the department of Cardiology at the former Wilhelmina Gasthuis in Amsterdam. He was an outstanding pioneer in the field of electrophysiology with classical works on the electric activation of the heart in the 1960s and 1970s [918–1984 The Netherlands Heart Journal, the official journal of the Netherlands Society of Cardiology (NVVC), awarded the Durrer prizes to two outstanding NHJ articles published in 2017. These articles are selected based upon their originality and scientific quality as well as the number of citations. One article is basic oriented and the other article has a clinical focus. The 2 articles are selected out of a total of 114 articles published in the NHJ 2017.2+ sensitive proteins may play a key role in the maladaptive remodelling of the macromolecular protein complex that forms the intercalated disc. The authors emphasise that we need to interpret the evidence from experimental models with caution as we do not have the appropriate models that mimic the end-stage disease in arrhythmogenic cardiomyopathy patients.The best basic-oriented article was entitled ‘Potential new mechanism of pro-arrhythmia in arrhythmogenic cardiomyopathy: focus on calcium sensitive pathways’ . It is aThe best clinical article is entitled ‘Pathophysiology and treatment of atherosclerosis: Current view and future perspective on lipoprotein modification treatment’ . It is aThe first authors of these articles received an educational grant, provided by the NVVC, at the Annual Spring Meeting of the NVVC held at the congress centre Leeuwenhorst at Noordwijkerhout, the Netherlands, on 5 and 6 April 2018. The NHJ would like to congratulate the authors with these awards and thank them for submitting their excellent work to our journal. The editorial board of the NHJ hopes that the Durrer prizes act as a stimulus for authors to send their best paper to our journal.


We discuss the use of planar Hall effect (PHE) in a ferromagnetic GaMnAs film with two in-plane easy axes as a means for achieving novel logic functionalities. We show that the switching of magnetization between the easy axes in a GaMnAs film depends strongly on the magnitude of the current flowing through the film due to thermal effects that modify its magnetic anisotropy. Planar Hall resistance in a GaMnAs film with two in-plane easy axes shows well-defined maxima and minima that can serve as two binary logic states. By choosing appropriate magnitudes of the input current for the GaMnAs Hall device, magnetic logic functions can then be achieved. Specifically, non-volatile logic functionalities such as AND, OR, NAND, and NOR gates can be obtained in such a device by selecting appropriate initial conditions. These results, involving a simple PHE device, hold promise for realizing programmable logic elements in magnetic electronics. Owing to such flexibility for obtaining desired logic functionalities in a magnetically controlled system, various types of magnetic logic devices – such as domain wall logic, chameleon logic, and spin logic8 have been intensively investigated, with an eye on replacing current semiconductor-based logic devices.Devices performing logic functions are key elements in processing information in electronic systems. Currently logic elements are primarily fabricated from semiconductor materials, in which their logic functionality is realized by utilizing the charge of the electron. Recently, however, magnetic devices have attracted a great deal of attention due to the advantages of non-volatility which these devices offer for information storage and processing. The best known such magnetic device is the magnetoresistive random access memory (MRAM), consisting of two ferromagnetic layers. Such MRAM element provides not only an efficient way of constructing memory devices, but also an opportunity to realize logic operations that can be reconfigured into AND, OR, NAND, or NOR gates by changing initial conditions13.In this context the vector characteristics of magnetization provide a new strategy for device design, based on the dependence of the device resistance on the direction of magnetization. For example, it is well known that the anisotropic magnetoresistance (AMR) of a magnetic film changes between maximum and minimum in a periodic fashion as the magnetization rotates in the film plane. Resistance values corresponding to stable magnetization orientations can then be utilized as logic states for storing information. This property of AMR has already been used for realizing a multi-state magnetic memory function by controlling domain structures in a single Hall device, and by manipulating the magnetization alignment in magnetic tunnel junctions14, and use its dependence on the direction of magnetization to achieve logic functionalities. The PHR in a GaMnAs film with a strong biaxial magnetic anisotropy is especially well suited for this purpose, since its value changes abruptly when the magnetization makes a transition between the magnetic easy axes in the film plane. By choosing an appropriate magnitude of the applied current as input signal, we are then able to demonstrate magnetic logic functions on a GaMnAs Hall device, as discussed later in this paper.In the present study we exploit the phenomenon of the planar Hall resistance (PHR) exhibited by GaMnAs films14. The process of these magnetization transitions in our Hall device must be carefully investigated at different current values, since the current flow during the measurement generates significant Joule heating, and thus affects the magnetic anisotropy of the GaMnAs layer, which is a sensitive function of temperature19. Since this feature will play a critical role in the present investigation, we carried out systematic measurements of such Joule heating effects in our device by changing the magnitude of the current over the range from 20 µA to 1 mA.The magnetic logic function in our Hall device, shown schematically in Fig. Figure 20.The black line in Fig. We then repeated the resistance measurement by systematically changing the magnitude of the sensing current while the temperature of the sample holder was set at 3K during the measurement. Resistances measured with different currents are plotted with red solid squares in Fig. 19, it is of critical importance for the present study to determine how the magnetic anisotropy in the GaMnAs layer – and thus of the orientation of its easy axes – depends on the applied current. We have investigated the magnetic anisotropy of our GaMnAs Hall device by measuring the angular dependence of the Hall resistance at several different currents, and have analyzed it in terms of the magnetic free energy given by22HC is the cubic anisotropy field, HU is the uniaxial anisotropy field associated with the φH denotes the direction of the applied magnetic field, and φH is the direction of magnetization in the film. The value of PHR depends directly on the direction of magnetization, and thus its angular dependence observed by rotating the applied field can be fitted to the condition of free energy minimum by using the magnetic anisotropy fields as fitting parameters. This method of analysis is fully described in the literature24 and we have adapted the same procedure to the present study  occur only while the current pulse is applied. As soon as the pulse ends (and the logic operation is completed), the material returns to its original predominantly cubic anisotropy.The free energy density diagrams corresponding to different current values can now be constructed using these anisotropy fields, as illustrated by Fig. 19.We now monitor the process of magnetization reversal in the Hall device at different currents. Figure Because of the shift in the field angle at which the transition of magnetization takes place at different currents, one can find specific field orientations at which the direction of magnetization in the device is different for different current values. To elucidate this, in Fig. 26. Consistent with Fig. We now discuss the application of our Hall device as a logic gate. Typically, logic operations involve two input values , , and  input combinations), the magnetic anisotropy change in the GaMnAs layer due to Joule heating is insufficient for a transition to occur between the two energy minima, so that the magnetization remains at the initial position, as shown in Fig. We now test the AND logic function given in Table st quadrant to the energy minimum in the second quadrant, as shown in Fig. 33, which is comparable to our device size. This indicates that the logic operation in our device can be understood in terms of single-domain structures. The PHR output responses of the device to these input current combinations correspond exactly to the AND logic operation given in Table However, for the current pulse with 400 µA  input combination), the modification of the magnetic anisotropy in the device is sufficient to cause the transition of magnetization from its initial orientation in the 1st quadrant, as shown in Fig. nd quadrant . This initial condition makes the energy minimum in the 2nd quadrant deeper than was the case for the AND function, making the transition of magnetization to the second quadrant easier.We now consider the operation of the Hall device as an OR gate, represented by Table st and 2nd quadrants to enable the magnetization to switch from its initial position, as shown in Fig. nd quadrant and barrier height between the quadrants) becomes sufficient to enable the magnetization transition to the minimum the 2nd quadrant. This transition is shown by the black dotted and red solid circles in Fig. Figure The device can also be operated after the magnetization is initialized by orienting the magnetization at the energy minimum in the second quadrant, which results in the high value of PHR, corresponding to the output logic state “1”. With this initial state, the device can act as a NAND or a NOR gate, depending on the selected direction of the background field. Detailed discussion of the NAND and NOR logic operations is given in Supplementary Information 36. In particular, Zhan et al.37, reported a similar type of PHE magnetic logic device consisting of a piezoelectric transducer and a ferromagnetic Co2FeAl layer37. The Co2FeAl layer has a biaxial magnetic anisotropy in the film plane, that results in two orthogonal in-plane magnetic easy axes, just as in our GaMnAs layer. The magnetic anisotropy of the film in ref. Magnetic logic operation based on the Hall effect has been reported in several articles39 or current-induced spin-orbit fields41, as required by practical requirements. The logic operations discussed in this paper, although achieved at low temperatures, provide important opportunities for investigating “proof-of-concept” device structures in which various logic strategies can be effectively explored.In conclusion, we have investigated the magnetic logic functionality of a GaMnAs Hall device based on the planar Hall effect. The logic operations are achieved through the dependence of the magnetic anisotropy of the device on the applied current. By appropriately choosing the input currents, and detecting PHR as the output, AND, OR, NAND, or NOR magnetic logic functions were achieved using a single-element Hall device simply by setting appropriate initial conditions. For purposes of this study the logic functions are demonstrated by using a global background field. The function of this field can, however, be replaced by other effects, such as exchange biasx1−MnxAs film with x = 0.08 was then grown on top of the GaAs buffer. For investigating the logic functionality based on the planar Hall effect, we patterned a Hall device on the GaMnAs film by photolithography and chemical wet etching, shown schematically in Fig. φH and of magnetization of the GaMnAs film φM are measured counterclockwise (CCW) from the Ferromagnetic GaMnAs layers used in this study were grown by molecular beam epitaxy on (001) GaAs substrates. Prior to the growth of the GaMnAs layer, a 100 nm GaAs buffer layer was deposited on the substrate at 600 °C, followed by deposition of a 2 nm GaAs buffer at 250 °C. A 100 nm GaSupplementary Material - Non-volatile logic gates based on planar Hall effect in magnetic films with two in-plane easy axes


The data presented in this article were the basis for the study reported in the research articles entitled “Statistical assessment of experimental observation on the slug body length and slug translational velocity in a horizontal pipe”  [1] which presents an experimental investigation of the slug velocity and slug body length for air-water tow phase flow in horizontal pipe. Here, in this article, the experimental set-up and the major instruments used for obtaining the computed data were explained in details. This data will be presented in the form of tables and videos. Specifications TableValue of the data•A detailed database for the technical slug two-phase flow characteristics in a horizontal 3 in. pipe diameter.•The significance of this data that it can be used to verify the results of other researcher's models by providing a common benchmark.•This data can be used for validating the numerical CFD results of the slug characteristics and improving the accuracy of different CFD models in the prediction of slug characteristics.•The data can be used by other researchers to develop different image processing techniques from the utilized technique in the analysis of this paper. The utilized image process technique is explained in details by  1The data presented in this article is based on the experimental investigation of the slug two-phase flow in a horizontal circular pipeline  which wa23 capacity using a centrifugal (EBARA 3M 50-125/2.2) pump which capable to supply a maximum flow rate of 1 m3/min. A solenoid valve was used to control the water supply to the loop. The water and air was separated in the inlet section of the pipe to avoid the perturbation and disturbance. The central compressor was used to supply the air to the test section, which can supply 42.5 m3/min of air. The water and air flow were measured using a calibrated ultrasonic flow meter with 70.5% accuracy and a calibrated mass flow controller (Omega FMA-2600A) consecutively. Flow visualization and recording was conducted utilizing a Phantom 9.2 high-speed camera with a recording frequency 1000 frames per second (fps) at the optimum resolution. The recorded videos from the camera was analyzed and processed using a developed in house Matlab code. The test rig utilized to perform the experimental investigations of air–water slug flow is illustrated in . A trans


Gene regulatory networks (GRNs) control cellular function and decision making during tissue development and homeostasis. Mathematical tools based on dynamical systems theory are often used to model these networks, but the size and complexity of these models mean that their behaviour is not always intuitive and the underlying mechanisms can be difficult to decipher. For this reason, methods that simplify and aid exploration of complex networks are necessary. To this end we develop a broadly applicable form of the Zwanzig-Mori projection. By first converting a thermodynamic state ensemble model of gene regulation into mass action reactions we derive a general method that produces a set of time evolution equations for a subset of components of a network. The influence of the rest of the network, the bulk, is captured by memory functions that describe how the subnetwork reacts to its own past state via components in the bulk. These memory functions provide probes of near-steady state dynamics, revealing information not easily accessible otherwise. We illustrate the method on a simple cross-repressive transcriptional motif to show that memory functions not only simplify the analysis of the subnetwork but also have a natural interpretation. We then apply the approach to a GRN from the vertebrate neural tube, a well characterised developmental transcriptional network composed of four interacting transcription factors. The memory functions reveal the function of specific links within the neural tube network and identify features of the regulatory structure that specifically increase the robustness of the network to initial conditions. Taken together, the study provides evidence that Zwanzig-Mori projections offer powerful and effective tools for simplifying and exploring the behaviour of GRNs. Gene regulatory networks are essential for cell fate specification and function. But the recursive links that comprise these networks often make determining their properties and behaviour complicated. Computational models of these networks can also be difficult to decipher. To reduce the complexity of such models we employ a Zwanzig-Mori projection approach. This allows a system of ordinary differential equations, representing a network, to be reduced to an arbitrary subnetwork consisting of part of the initial network, with the rest of the network (bulk) captured by memory functions. These memory functions account for the bulk by describing signals that return to the subnetwork after some time, having passed through the bulk. We show how this approach can be used to simplify analysis and to probe the behaviour of a gene regulatory network. Applying the method to a transcriptional network in the vertebrate neural tube reveals previously unappreciated properties of the network. By taking advantage of the structure of the memory functions we identify interactions within the network that are unnecessary for sustaining correct patterning. Upon further investigation we find that these interactions are important for conferring robustness to variation in initial conditions. Taken together we demonstrate the validity and applicability of the Zwanzig-Mori projection approach to gene regulatory networks. Biological systems are complex, comprising multiple interacting components. In many cases this complexity makes it difficult to identify underlying mechanisms and to understand the function of a system. Gene regulatory networks (GRNs) are an example of this problem . A GRN cAttempts have been made to map large transcriptional networks, yet even for relatively small networks, the number of links and the feedback within the system make intuitive understanding difficult to obtain. Various computational models have been developed to address this. Logical models, which describe regulatory interactions qualitatively, provide a flexible and simplifying formalism to explore and understand the behaviour of a network . Howevera priori and must conform to a particular network structure [a posteriori the effect that this has on the dynamics of the network. This can be helpful to develop intuition, but generally requires the investigation of a large number of combinations of perturbations [Various techniques have been developed to reduce the complexity of models yet preserve specific features of the behaviour of the system. For Boolean networks it is possible to remove specific components while restructuring other parts of the network to conserve the logical structure, but this requires quite specific network topologies . In the tructure . Other mrbations , 12. A frbations . One canrbations . Less forbations . Along srbations .choose a subnetwork, guided by biological relevance or the availability of data; none of the methods described above allow this and instead identify a subnetwork based on their internal criteria.We focus in this paper on reducing model complexity by tracking a subnetwork that is embedded within the remainder—or “bulk”—of a larger system. Analysing the behaviour of the subnetwork and its interaction with the bulk can help reveal and rationalise the properties of the entire network. With any coarse graining approach, including those discussed above, a compromise must be reached between the precision of the method, i.e. how well it captures the dynamics of the full network, and the simplicity and interpretability of the resulting description. For example, the introduction of intermediate species can produce model reductions with high precision but these may not be interpretable , while me.g. [One class of methods that offers the potential to balance accuracy and interpretability are Zwanzig-Mori projections , 18. Orie.g. —these mee.g. , 21. UseEvolving from its original applications to critical dynamics and supercooled liquids near the glass transition , this apx such that it contains the protein concentrations for each gene. We can then generically define the time evolution for any protein concentration, indexed by j, asβj is the decay rate of protein j. We use the summation over n to represent all possible binding conformations for the DNA that produces protein j. The term αj,n) are so-called random forces that arise from the uncertainty about the initial (time t = 0) state of the bulk concentrations. (For the linear dynamics they can be expressed in closed form [Nonlinear projected equations below.)The Zwanzig-Mori method in general starts from the choice of a set of observables for which dynamical equations are to be obtained. Initially we select, as the simplest possible observables, the deviations from steady state of the concentrations of the chosen subnetwork species. For these observables the Zwanzig-Mori projection leads to a set of dynamical equations of the formsed form  but thismemory functionsMji(Δt), which describe how past concentration fluctuations δxj(t′) influence the current time evolution. However, while the projected equations are formally exact, it is in general impossible to evaluate these memory functions explicitly. One scenario where this can be done is a network of unary reactions, where the full reaction equations are linear in the concentrations [Justifying the heuristics: Network expansion). Explicitly, one linearly expands the time evolution eqs yi, i.e. in terms of the deviations δxi = xi − yi. The r.h.s. of δxi since constant terms cancel out because of the steady state condition. One can therefore write the time evolution equations in matrix form [L with entries Lji.The key quantities in the trations . This surix form ∂tδxi=∑jL one can calculate the terms in the (linear) projected dynamics of the subnetwork concentrations from δxi are numbered so that the first Ns are the subnetwork observables while the rest are the bulk observables. The matrix L for the linearised dynamics then separates into blocks according to the different observables:From the matrix Mathematical results). The rate matrix Ω with entries Ωji in the projected L,L as [L describing the linearised dynamics.We use the labels S and B here to represent subnetwork and bulk species respectively, this will be useful once more subnetwork and bulk observables arise (see Sec.  of L as M(Δt)=LSri(t) represents the random forces but in this nonlinear case further characterization would require knowledge of the statistics of the initial bulk fluctuations, which is not generally available. We therefore disregard these terms, making closed system of equations for the time evolution of the subnetwork concentrations. Note that neglecting the random forces is equivalent to assuming that the bulk concentrations are at their steady state values at the initial time. Formally these initial bulk concentrations should be random rather than deterministic to make the Zwanzig-Mori projection well defined; we follow the strategy of [To capture the leading nonlinear corrections to the subnetwork dynamics, it is natural to enlarge the set of subnetwork observables by adding quadratic observables, i.e. products of concentration deviations. The projected equations then becomeategy of  here andategy of . How larategy of .quadratic observables using the product rule gives e.g.δx. These changes are therefore implicitly assumed to be small. Defining a vector z that collects all δx variables and their products such as δx1δx2, one can now again write a matrix form of the time evolution equations:L matrix constructed as explained above. Because the subnetwork block S now contains linear {s} and quadratic observables {ss}, the matrices have the corresponding block structures. The coefficients Ωji are collected in the block Ωs,s, for example, and the Ωjk)i and Mjk)i((Δt) are similarly contained in blocks Ms,s and Mss,s of the memory matrix M.Moving on to the nonlinear memory functions, we are again faced with the difficulty that these cannot in general be evaluated explicitly. However, previous work  has deveation in  neglectslculated  from theδxi, to obtain an effective set of unary and binary reactions. This set defines the matrix L, from which the rate matrix and memory functions can then be found as explained above.To apply the above technique in order to derive nonlinear projected subnetwork equations for GRN dynamics, the obvious heuristic route is again to expand the dynamical x1), and while these can be Taylor expanded they have only finite radius of convergence. Not only does the heuristic method then have to throw away an infinite number of higher order terms when truncating the Taylor expansion after linear or quadratic order, but it may implicitly be using the resulting approximation outside the regime where the expansion is even convergent. In addition, while we have loosely talked about the expanded time evolution equations as representing networks of effective reactions, such an interpretation is in no way assured as there is no underlying mechanistic model and hence no constraints that would ensure an appropriate stoichiometry or even positivity of rate constants.The heuristic method set out above for deriving linear or nonlinear subnetwork equations for GRN dynamics is a useful practical recipe, but its mathematical basis is not obvious. One difficulty is that the thermodynamic GRN expanding the thermodynamic eqs  to make DNA conformation . Here ep is a unit vector whose i-th entry is δip, i.e. a 1 at position p and zeros elsewhere. Similarly the third term on the right of p. The other two terms capture how DNA in conformation  can be lost by these two processes.Our network expansion approach necessitates defining new reaction rates for binding and unbinding of protein to/from DNA that are consistent with the affinities k in the mass action representation w of the thermodynamic form. The rate constants need to be chosen to ensure the QSS individual pair of binding and unbinding reactions between two conformations vanishes. Detailed balance means, in particular, that where there are multiple reaction paths from one DNA conformation to another, which might be distinguished by the order in which the various proteins bind, each path carries zero reaction flux rather than having a preferred forward or backward reaction direction. Balancing in this way the net change from binding of protein p to DNA in conformation  with the reverse unbinding transition, for the QSS concentrations γ and write all rate constants in the form γ → ∞ at fixed γ numerics of γ′ → ∞. Finally, to compensate for the DNA concentration scaling, protein production rates have to be scaled as We next establish the relationship between the rate constants eactions . As therγ → ∞ ensures that the “fast” species, i.e. the DNA concentrations are always in QSS with respect to the “slow” protein concentrations. The limit γ′ → ∞, on the other hand, means that the effects of binding to, and unbinding from, DNA can be neglected in the equations for the protein concentrations. These statements can be shown mathematically along the lines of the arguments in [γ and γ′. In reality the rate for producing a single protein from the appropriate DNA, which is of order γ′, is lower than the DNA binding/unbinding rates, which are O(γ). However, quantifying this would be non-trivial as the model described here simplifies many biological steps into each of the two elementary processes of protein production and binding/unbinding. In any event, for our argument to hold we only need both γ and γ′ to be large, and for simplicity we take then γ = γ′ as was done in [With the above rescalings, the limit ments in . After d done in .γ on the r.h.s. of rate constants for protein production are also fast, of order γ′, but that the resulting changes to protein concentrations are slow because of the low concentration of (protein-producing) DNA.We now proceed to use the expanded network to derive linearised projected equations. After the expansion, this requires us to keep track of deviations from steady state of all protein and DNA concentrations. We label these observables by “s” and “b” for subnetwork and bulk proteins as before, and “a” for DNA. Below we will refer to the DNA species in the system as “fast”, as expressed mathematically by the factor L matrix by placing the DNA in the bulk, such that S = {s} and B = {b, a}, giving the block formγ and the rate constants L in γ → ∞, with the aim of obtaining an expression for the memory function that only involves parameters of the original thermodynamic eqs  memory function for γ → ∞ can be calculated from an effective L-matrix no longer involving the fast degrees of freedom. To state the expression for the effective L, we first isolate the slow piece of our original L:L-matrix that gives us the rate matrix and memory function for γ → ∞ is then of the form Leff = La∖ + ΔLa∖, which written out reads:La∖ from the fast degrees of freedom. The matrix Leff can be inserted directly into  degrees of freedom, effectively setting the r.h.s. of L-matrix Leff defined in As in , the res+δxaTLa,s∂tδxbT=δ+δxaTLa,b∂tδxaT=δxs, xb and xa are generic components of xs, xb and xa, respectively. This expanded description is constructed so that for γ → ∞, when the xa can be replaced by their QSS values xs and xb is defined implicitly byxs:L: for example, Lb,s has entries ∂Rs/∂xb, Ls,a has entries γ ∂Ra/∂xs etc. The QSS coefficients arising from tδxb.So far we have shown that the rate matrix and memory functions for the linearised dynamics can be found by applying standard projection results to a set of time evolution equations for only the slow degrees of freedom. This reduced set of equations is obtained by first expanding the thermodynamic equations into a set of mass-action equations, linearising, and finally eliminating the fast variables using a QSS assumption. We next show that this procedure is equivalent to directly linearising the original thermodynamic equations, for any case where there is a timescale separation. This generalises previous work  that onlProjected equations for linearised dynamics for obtaining linearised projected equations for the dynamics of a subnetwork within a larger GRN written in thermodynamic form: expand the GRN equations to linear order in protein concentrations around a steady state. Then construct from this the matrix Leff and partition this into “s” and “b” blocks according to the chosen subnetwork–bulk split. Finally determine the rate matrix and memory function matrix from  observables. As before, this Leff can be viewed as arising from a QSS elimination of the fast observables. Finally, one can show that this explicit elimination of the fast observables is equivalent to directly expanding the original thermodynamic equations to quadratic order in concentration deviations from the steady state: this justifies the heuristic method given in the Sec. Nonlinear projected equations.To capture more of the nonlinearity inherent in GRNs one can extend the approach described in the previous sections, to include terms that are quadratic in the deviations from a steady state. The memory function then contains fast and slow contributions, with the former being transformed into additional rate matrix terms when L into fast and slow blocks. The final reduction to a quadratic expansion of the thermodynamic equations is more subtle because the projection approach treats quadratic observables as distinct and not directly tied to products of linear observables. We defer the details to Except for the last step, the above chain of argument is analogous to the linearised dynamics case, being based entirely on the identical structure of the partition—compare γ, of typical DNA reaction rates to protein production rates. γ = 10 the predicted time courses of protein concentrations are almost identical to those predicted by the thermodynamic equations. As γ → ∞ the trajectories from the mass action equations and the thermodynamic equations become identical.We applied the Zwanzig-Mori projection method to a cross repressive motif to illustrate our approach. Application to neural tube network. More general projection methods can overcome this limitation as detailed in the Discussion, although it is clear that there are limits of principle here. For example, where the dynamical choice of steady state depends crucially on the initial concentration of a bulk species, this effect cannot be captured by a subnetwork description that by definition does not track this species.We chose to separate the system so that one protein species, g1Prot, is in the subnetwork and the other, g2Prot, is in the bulk. After expanding into protein and DNA species we proceeded to place all DNA species along with g2Prot in the bulk. Because we have performed the expansion around a steady state, the method is more precise when close to the steady state as expected . Note thlinear memory function—where the signal is δx1(t′)—is positive. This makes sense as, in the cross repressive motif, a protein is inhibiting its inhibitor, thus promoting its own production. The second order memory function governs the effects of the signal Next we analyse the memory functions in our cross-repressive example, which can be thought of as describing the strength of a signal returning from the bulk a specific time after the original signal entered the bulk from the subnetwork . The ampReducing part of a network into memory functions offers a way to simplify and analyse the effect of the factors in this bulk part on the remaining subnetwork. To illustrate this approach we chose to analyse a four gene network involved in the embryonic patterning of the vertebrate neural tube , 30. TheMathematical models have been formulated based on the experimental data and these are able to replicate key aspects of cell patterning , 33 Fig. We takeWe first examined the properties of the linear memory functions. These are the most substantial contributions, close to the specific steady states, of the species in the bulk (Pax6 and Irx3) on the temporal changes in the activity of Nkx2.2 and Olig2. We note that the system is multistable  and diffdecompose the memory into contributions from memory signals passing through the two different bulk species (y-axis): the memory of (past) Olig2 on Nkx2.2 is largely dominated by memory through Irx3. The only exception is for steady states that are not reached during normal neural tube patterning  begin to secrete Shh. Shh spreads into the neural tube and neural progenitors respond to the signal. The consequence is that in the ventral neural tube neural progenitors begin responding to Shh at intermediate levels of Pax6 and Irx3. A more appropriate initial condition, representative of the in vivo situation, is for Pax6 and Irx3 to be somewhere between 0 and maximum. Moreover, heterogeneity between cells, as well as variation in the exact timing of developmental events along the rostral-caudal axis of the embryo, means that the precise initial conditions—the levels of Pax6 and Irx3 when cells respond to Shh signalling—will vary. Hence the robustness provided by the Olig2-Pax6 link may play an important role in ensuring reliable pattern formation in the developing neural tube.We have developed a generally applicable method for applying Zwanzig-Mori projections to transcriptional networks that allows the analysis of subnetworks extracted from a larger network. We demonstrated the approach on a simple genetic cross repressive motif, to illustrate the minimal example of a memory function, and on a more complicated, but well-characterised, transcriptional network operating in the ventral part of the vertebrate neural tube. This showed how the method allows the function and importance of specific links within a network to be defined in an intuitive manner. We used these insights to identify structural features of the neural tube network that appear primarily to increase the robustness of the network to initial conditions, rather than maintain its steady state.The projection technique is straightforward to implement using the methodology described, and can be applied to any GRN following the thermodynamic formalism . Further protein-protein interactions could readily be incorporated as these would be represented by simple first order (unary) or second order (binary) interactions. Thus, in addition to gene regulation, nonlinear protein-protein interactions mediated by enzymes such as those found in signal transduction pathways could be included in the analysis . It wouli.e. the relevant rate constant, can then be large while the resulting relative changes to protein concentration are slow. These assumptions allowed us to construct an extended reaction network involving fast molecular (DNA) species and at most binary reactions. This construction is sufficiently general for it to be applicable to other systems with a timescale separation, as long as they satisfy the above conditions for the relevant concentrations and rate constants.In our mathematical treatment we took advantage of an argument of timescale separation for molecular mechanisms operating in transcriptional networks, in which fast processes (DNA-protein interactions) are assumed to be in QSS compared to the slow processes (changes in protein concentration). We also assume the effective concentration of DNA species to be small in comparison to that of protein species. We consider these to be reasonable assumptions because DNA-protein interactions occur at a much faster rate than the changes in protein concentrations produced by transcription and translation . MoreoveAn important component of this Zwanzig-Mori projection method is that the memory functions describe all the behaviours of a system in the vicinity of a steady state. Even though this comes at the cost of predictions becoming increasingly inaccurate the further the system is from the fixed point, the information around the steady state is sufficient to distil relevant properties of the network. We therefore employ the method as a tool for probing the dynamics near a chosen steady state, rather than for tracking dynamics. The benefit is that the resulting memory functions are substantially simpler than the original system. There is no need to perform simulations to analyse memory functions or to test different positions in phase space as a steady state is approached. Moreover, the method can also be applied to an arbitrarily chosen subnetwork of a generic network whereas other model reduction approaches—as discussed in the Introduction—do not allow this, and are also more restrictive as they require specific network motifs or functional forms of the dynamics.The memory functions produced by the Zwanzig-Mori approach allow exploration of the amplitudes and timescales of the interactions between the subnetwork and bulk. This can reveal information that is not otherwise easy to discern from the parameters of the full dynamics or from the functional form of the equations. Each memory function represents the total of the contributions from a given subnetwork component that feeds back to the subnetwork over time after passing through the bulk. This total memory can be decomposed into channels that describe the flow of signals through specific components in the bulk. In this way, the channels that dominate a memory effect can be identified, providing insight into the dynamical mechanisms responsible for achieving and maintaining a steady state. The memory functions thus help to extract features of the dynamics that would not be readily detectable in direct simulations of the time evolution equations.in vivo system. Simulations in the absence of the Olig2-Pax6 repression, compared to the full model, revealed a marked increase in sensitivity to these initial conditions. Comparison of the bifurcation diagrams of the systems, with and without the Pax6-Olig2 link, indicated that the well-defined Nkx2.2 monostable region (p3 domain)—which appears at high levels of Shh signalling in the full system—was replaced by a region of bistability for Nkx2.2 and Olig2 in the absence of the Olig2-Pax6 regulation. In this latter case the steady state induced by high levels of signal therefore depends on the initial concentrations of Pax6 and Irx3. This suggests that, while not necessary to maintain steady states, the Olig2-Pax6 regulation ensures access to the appropriate steady states irrespective of the initial levels of Pax6 and Irx3. As these may differ between cells and at different locations along the rostral-caudal axis of the neural tube, the Olig2-Pax6 regulatory link might make the system less sensitive to these variations. This implies that the primary purpose of Olig2 repression of Pax6 is to increase the robustness of pattern formation.An example of the type of insight provided by the projection method came from our analysis of the neural tube network. We focused on a subnetwork comprising Nkx2.2 and Olig2. Decomposition of the memory functions suggested that an experimentally documented repression of Pax6 by Olig2  plays onAlternative implementations of the Zwanzig-Mori projection –40 have S1 TextNonlinear projected equations.In this Appendix we give the details of the projection method with linear and quadratic observables, applied to an expanded network as outlined in Sec. (PDF)Click here for additional data file.S2 TextIn this Appendix we give additional detail of the wide variety of effects that memory functions contribute to the behaviour of a system. Specifically, we explore the effect of the contributions from nonlinear memory terms and provide an alternative visualisation using a first order time expansion of the effective drift of the system.(PDF)Click here for additional data file.S3 TextEquations and parameters used in model of neural tube patterning network.(PDF)Click here for additional data file.S1 FigA), with only linear memory (B), with linear and nonlinear memory (C), and the full dynamics (D). Trajectories approaching a low Olig2, low Nkx2.2 state in the p2 domain from different initial conditions, with no memory (E), with only linear memory (F), with linear and nonlinear memory (G), and the full dynamics (H). All figures are parametric plots, showing Nkx2.2 and Olig2 concentrations on the x- and y-axis, respectively, with time as curve parameter. The trajectories are coloured to represent the norm of the drift vector of the system as indicated by the colour scale; high values indicate the system is evolving quickly while the opposite is true for low values. Scalebars on the right apply to the corresponding row. Path crossing can be seen in (C–D) & (G–H), illustrating the importance of nonlinear memory terms to reproduce qualitative features of the full thermodynamic equations.Trajectories approaching a high Olig2 state in the pMN domain from a range of initial conditions, with no memory ((TIF)Click here for additional data file.S2 FigA-D) Nonlinear memory amplitudes across neural tube positions within the pMN domain. The plot titles indicate the type of memory, e.g. (C) shows memory of (past) Nkx2.2 squared fluctuation on Olig2. Memory effects of past Olig2-fluctuations in the pMN domain are negligible. (E-H) Nonlinear memory amplitudes across neural tube positions within the p2 domain. Nkx2.2 receives very little quadratic memory influence in this domain. The x-axis represents neural tube position in all plots. Blue and yellow lines indicate the decomposition into Pax6 and Irx3 channels, while green lines indicate the total memory.((TIF)Click here for additional data file.S3 FigA,D) Memoryless drift,  drift with linear memory,  drift with linear and nonlinear memory. The scalebar on the right applies to each entire row. Effective drift norms have been calculated for time t = 0.8.Colour map and contour plots of the norm of the effective drift, in conditions identical to those in (TIF)Click here for additional data file.