Biological Modeling

Computer analysis of biological systems, using approaches such as metabolic control analysis is common. A typical example is a language like Herbert Sauro's SCAMP (Sauro & Fell, 1991), which allows simulations of enzyme systems, and calculation of control coefficients and elasticities. However such systems are motivated by the underlying biochemical theory and often have limitations as programming languages which mean that they can only be applied to particular classes of problems.ABPL (a biochemical programming language) extends these ideas by adding all (...) the facilities of a fully-fledged programming language, together with some of the capabilities of a modern computer algebra system. Syntactically it derives from the programming language LISP, while the underlying functionality is that of iMAP, the successor to SCAMP. (shrink)

This article revisits a reduced model of cardiac electro-physiology which was proposed to understand the genesis of unidirectional block pathology and of ectopic foci. We underline some specificities of the model from the viewpoint of dynamical systems and bifurcation theory. We point out that essentially the same properties are shared by a simpler system more accessible to analysis. With this simpler system, it becomes possible to give a new presentation of the phenomenon in a phase plane with time moving slow (...) manifolds. This presentation can be of interest both for cardiac electro-physiologists and for mathematicians. (shrink)

Building a meaningful model of biological regulatory network is usually done by specifying the components and their interactions, by guessing the values of parameters, by comparing the predicted behaviors to the observed ones, and by modifying in a trial-error process both architecture and parameters in order to reach an optimal fitness. We propose here a different approach to construct and analyze biological models avoiding the trial-error part, where structure and dynamics are represented as formal constraints. We apply the method to (...) Hopfield-like networks, a formalism often used in both neural and regulatory networks modeling. The aim is to characterize automatically the set of all models consistent with all the available knowledge . The available knowledge is formalized into formal constraints. The latter are compiled into Boolean formula in conjunctive normal form and then submitted to a Boolean satisfiability solver. This approach allows to formulate a wide range of queries, expressed in a high level language, and possibly integrating formalized intuitions. In order to explore its potential, we use it to find cycles for 3-nodes networks and to determine the flower morphogenesis regulatory network of Arabidopsis thaliana. Applications of this technique are numerous and concern the building of models from data as well as the design of biological networks possessing specified behaviors. (shrink)

Scientific risk evaluations are constructed by specific evidence, value judgements and biological background assumptions. The latter are the framework-setting suppositions we apply in order to understand some new phenomenon. That background assumptions co-determine choice of methodology, data interpretation, and choice of relevant evidence is an uncontroversial claim in modern basic science. Furthermore, it is commonly accepted that, unless explicated, disagreements in background assumptions can lead to misunderstanding as well as miscommunication. Here, we extend the discussion on background assumptions from basic (...) science to the debate over genetically modified (GM) plants risk assessment. In this realm, while the different political, social and economic values are often mentioned, the identity and role of background assumptions at play are rarely examined. We use an example from the debate over risk assessment of stacked genetically modified plants (GM stacks), obtained by applying conventional breeding techniques to GM plants. There are two main regulatory practices of GM stacks: (i) regulate as conventional hybrids and (ii) regulate as new GM plants. We analyzed eight papers representative of these positions and found that, in all cases, additional premises are needed to reach the stated conclusions. We suggest that these premises play the role of biological background assumptions and argue that the most effective way toward a unified framework for risk analysis and regulation of GM stacks is by explicating and examining the biological background assumptions of each position. Once explicated, it is possible to either evaluate which background assumptions best reflect contemporary biological knowledge, or to apply Douglas' 'inductive risk' argument. (shrink)

This paper aims to identify the key characteristics of model organisms that make them a specific type of model within the contemporary life sciences: in particular, we argue that the term “model organism” does not apply to all organisms used for the purposes of experimental research. We explore the differences between experimental and model organisms in terms of their material and epistemic features, and argue that it is essential to distinguish between their representational scope and representational target. We also examine (...) the characteristics of the communities who use these two types of models, including their research goals, disciplinary affiliations, and preferred practices to show how these have contributed to the conceptualization of a model organism. We conclude that model organisms are a specific subgroup of organisms that have been standardized to fit an integrative and comparative mode of research, and that it must be clearly distinguished from the broader class of experimental organisms. In addition, we argue that model organisms are the key components of a unique and distinctively biological way of doing research using models.Keywords: Experimental organism; Genetics; Model organism; Modeling; Philosophy of biology; Representation. (shrink)

Aggregation methods allow one to replace a large scale dynamical system (micro-system) by a reduced dynamical system (macro-system) governing a small number of global variables. This aggregation of variables can be performed when two time scales exist, a fast time scale and a slow time scale. Perturbation theory allows to obtain an approximated aggregated dynamical system which describes the behaviour of a few number of slow time varying variables which are constants of motion of the fast part of the micro-system. (...) Aggregation methods are applied to the case of the devastation of the great barrier reef by the starfishes. We recall the Antonelli/Kazarinoff model which implies a stable limit cycle for the corals and starfish populations. This prey-predator model describes the interactions between two species of corals and the starfish. Then, we generalize the Antonelli/Kazarinoff model to the case of two spatial patches with a fast part describing the starfish migration on the patches and the human manipulation of the communities by divers and, a slow part describing the growth and the interactions between the populations. We obtain an aggregated model governing the total coral densities on the patches and the total starfish population. This model can exhibit stable limit cycle oscillations and a Hopf bifurcation. The critical value of the bifurcation parameter is expressed in terms of the proportions of coral species and starfish on the two patches. This implies for example that rather than random killing of starfish by the Australian military, it may be better to send teams of divers to outbreaking reefs when they first occur who will then manipulate the community structure to increase protection. (shrink)

Philosophical treatments of scientific controversies usually focus on theory, excluding important practice related aspects. However, scientists in conflict often appeal to extra-theoretical and extra-empirical elements. To understand better the role that non-empirical elements play in scientific controversies, we introduce the notion of borrowed epistemic credibility, illustrating our proposal with a recent controversy in a field of evolutionary biology known as phylogeography. Our analysis shows how scientific controversies that spring from disagreements about methodological issues potentially involve deeperdebates regarding whatconstitutes good science, (...) prompting the re-examination of more general issues, such as the nature of inference, rationality, and objectivity. (shrink)

This paper responds to a recent challenge for the validity of extrapolation of neurobiological knowledge from laboratory animals to humans. According to this challenge, experimental neurobiology, and thus neuroscience, is in a state of crisis because the knowledge produced in different laboratories hardly generalizes from one laboratory to another. Presumably, this is so because neurobiological laboratories use simplified animal models of human conditions that differ across laboratories. By contrast, I argue that maintaining a multiplicity of experimental protocols and simple models (...) is well justified. It fosters rather than precludes the validity of extrapolation of neurobiological knowledge. The discipline is thriving. (shrink)

The aim of this work is to study complex ecological models exhibiting simple dynamics. We consider large scale systems which can be decomposed into weakly coupled subsystems. Perturbation Theory is used in order to get a reduced set of differential equations governing slow time varying global variables. As examples, we study the influence of the individual behaviour of animals in competition and predator-prey models. The animals are assumed to do many activities all day long such as searching for food of (...) different types. The degree of competition as well as the predation pressure are dependent upon these activities. Preys are more vulnerable when doing some activities during which they are very exposed to predators attacks rather than for others during which they are hidden. We study the effect of a change in the average individual behaviour of the animals on interspecific relationships. Computer simulations of the whole sets of equations are compared to simulations of the reduced sets of equations. (shrink)

We present a dynamical model of a multi-site fishery. The fish stock is located on a discrete set of fish habitats where it is catched by the fishing fleet. We assume that fishes remain on fishing habitats while the fishing vessels can move at a fast time scale to visit the different fishing sites. We use the existence of two time scales to reduce the dimension of the model : we build an aggregated model considering the habitat fish densities and (...) the total fishing effort. We explore a regulation procedure, which imposes an average residence time in patches. Several equilibria exist, a Fishery Free Equilibria as well as a Sustainable Fishery Equilibria . We show that the dynamics depends on a threshold which is similar to a basic reproduction ratio for the fishery. When the basic reproduction ratio is less or equal to 1, one of the FFEs is globally asymptotically stable , otherwise one of the SFEs is GAS. (shrink)

The aim of this work is to present aggregation methods of hierarchically organized systems allowing one to replace the initial micro-system by a macro-system described by a few global variables. We also study the relations between the fast micro-dynamics and the slow macro-dynamics which can produce global properties. Emergence corresponds to a bottom-up coupling that is the result effected by a micro-level at a macro-level. As an example, we present prey-predator models with different time scales in an heterogeneous environment. A (...) fast time scale is associated to the migration process on spatial patches and a slow time scale is associated to growth and interactions between the populations. Preys must go on spatial patches where resources are located and where predators can attack them. The efficiency of the predators to catch preys is patch dependent. Perturbation methods allow us to aggregate the initial system of differential equations for the patch sub-populations into a macro-system of two differential equations governing the total population densities. We study the case of density independent and density dependent migrations. In the latter case, we show that different functional responses can emerge in the macro prey-predator model as a result of the coupling between the slow and fast systems. (shrink)

This paper deals with the interrelationship between causal explanation and methodology in a relatively young discipline in biology: epigenetics. Based on cases from molecular and ecological epigenetics, I show that James Woodward’s interventionist account of causation captures essential features about how epigeneticists using highly diverse methods, i.e. laboratory experiments and purely observational studies, think about causal explanation. I argue that interventionism thus qualifies as a useful unifying explanatory approach when it comes to cross-methodological research efforts: It can act as a (...) guiding rationale to link causal models in molecular biology with statistical models derived from observational data analysis and to identify test- criteria for reciprocal transparent studies in different fields of research, which is a shared issue across the sciences. (shrink)

This paper provides an account of the experimental conditions required for establishing whether correlating or causally relevant factors are constitutive components of a mechanism connecting input (start) and output (finish) conditions. I argue that two-variable experiments, where both the initial conditions and a component postulated by the mechanism are simultaneously manipulated on an independent basis, are usually required in order to differentiate between correlating or causally relevant factors and constitutively relevant ones. Based on a typical research project molecular biology, a (...) flowchart model detailing typical stages in the formulation and testing of hypotheses about mechanistic components is also developed. (shrink)

We show how a simple nonlinear dynamical system (the discrete quadratic iteration on the unit segment) can be the basis for modelling the embryogenesis process. Such an approach, even though being crude, can nevertheless prove to be useful when looking with the two main involved processes:i) on one hand the cell proliferation under successive divisions ii) on the other hand, the differentiation between cell lineages. We illustrate this new approach in the case of Caenorhabditis elegans by looking at the early (...) stages of embryogenesis, up to several hundreds of cells (lima bean larval stage). We show how the many results that have been obtained by several groups can be interpreted in terms of values for the parameters controlling the dynamical system. Furthermore, we can extend the model to the cases of genetic mutations. More precisely the teratogenetic and lethal effects are associated with abnormal variation of the control parameters with time. (shrink)

We used computer simulations to study the possible role of the dispersion of cellular coupling, refractoriness or both, in the mechanisms underlying cardiac arrhythmias. Local ischemia was first assumed to induce cell to cell dispersion of the coupling resistance (Case 1), refractory period (Case 2), or both of them (Case 3). Our numerical experiments based on the van Capelle and Durrer model showed that vortices could not be induced by cell to cell variations. With cellular properties dispersed in a patchy (...) way within the ischemic zone, a single activation wave could give rise to abnormal activities. This demonstrates the stability of the wave front under small inhomogeneities. Probabilities of reentry, estimated for the three cases cited above showed that a severe alteration of the coupling resistance may be an important factor in the genesis of reentry. Moreover, use of isochronal maps revealed that vortices were both stable and sustained with an alteration of the coupling alone or combined with a reduction of the action potential duration. Conversely, simulations with reduction of the refractoriness alone, inducing only transient patterns, could exhibit functionally determined reentries. (shrink)

The present work is aimed at investigating the effects of myocardial infarction and ischemia on induction of ventricular fibrillation. Electrophysiologic effects of global and local ischemia (variation of the dispersion of refractory periods as well as conduction velocity) on initiation of reentry mechanisms was studied by means of computer simulations based on a cellular automata model of propagation of activation wave through a ventricular surface element. A local area of ischemia where effects of the dispersion of refractory periods are investigated (...) is then simulated. This is made using a Gaussian distribution characterized by its mean and standard deviation. These simulations show that ischemia is capable of initiating reentry phenomena which propagate through the whole ventricle; they are responsible for ventricular fibrillation which causes sudden cardiac death, even when ischemia only involves limited parts of the myocardium. Statistical study of the probability of reentries as a function of both of the size of ischemic zones and the rate of dispersion of refractory periods shows that the latter parameter is of primary importance in triggering cardiac reentries. (shrink)

Limitations of antiarrhythmic drugs on cardiac sudden death prevention appeared since the early 80's. The "Cardiac Arrhythmia Suppression Trial"(CAST) showed more recently that mortality was significantly higher inpatients treated with some particular antiarrhythmic drugs than in non-treated patients. In this field, our group recently demonstrated that a bolus of a Class 1B antiarrhythmic drug was able to trigger a ventricular fibrillation due to transient blocks induction. The aim of the present work was to systematically study, by use of the van (...) Capelle and Durrer (VCD) model which allows to simulate ventricular activation wave propagation, the link between arrhythmogenic effects and the ability of transient blocks to possibly degenerate in severe arrhythmias. A fragment of the ventricular wall is represented by an array of 16384elements electrically coupled. Effects of induction of one or several transient blocks, as the effects of their size and duration on possible induction of reentries have been studied. Results obtained show that various combinations between these different parameters may trigger reentries, ventricular tachycardia and/or more complex patterns assimilable to ventricular fibrillation. These results clearly evidence the fact that possible induction of transient blocks may directly be related to risk factor associated to arrhythmogenic effects of antiarrhythmic drugs. (shrink)

Despite the burgeoning interest in new and more complex accounts of the organism-environment dyad by biologists and philosophers, little attention has been paid in the resulting discussions to the history of these ideas and to their deployment in disciplines outside biology—especially in the social sciences. Even in biology and philosophy, there is a lack of detailed conceptual models of the organism-environment relationship. This volume is designed to fill these lacunae by providing the first multidisciplinary discussion of the topic of organism-environment (...) interaction. It brings together scholars from history, philosophy, psychology, anthropology, medicine, and biology to discuss the common focus of their work: entangled life, or the complex interaction of organisms and environments. (shrink)

This paper examines the very disparate positions that various actors have taken towards the argument of subversion from within in a set of related debates on group selection, altruism and the handicap principle. Using this set of debates as a case study, this paper argues that different applications of epistemic values were one of the factors behind the disagreements between John Maynard Smith and Amotz Zahavi over a number of important evolutionary issues. The paper also argues that these different applications (...) were connected to important epistemological differences related in part to their disciplinary background. Apart from conflicting evolutionary views concerning the theoretical feasibility of the handicap effect, these antagonists both differed in the confidence they ascribed to mathematical modeling and over the hereditary basis for altruistic behavior. (shrink)

The immune system does not just fight pathogens but also engages in interactions with beneficial microbes and non-immune cells of the body to harmonize their behavior by means of cytokines, antibodies and effector cells (Dinarello, 2007; Moticka, 2015, pp. 217e226, 261e267). However, the importance of these “housekeeping” functions has not been fully appreciated (Cohen, 2000). In his new book Immunity: The Evolution of an Idea Alfred I. Tauber traces the history of fundamental ideas in immunology and refers to recent advances (...) in the field to overturn the notion that immunity is the ability of an autonomous organism to protect itself against pathogens. Indeed, as suggested by the author, the autonomy of the organism is illusive because individuals develop as holobionts: functionally integrated multispecies consortia (p. 98). Similarly, he suggests that pathogenicity also emerges from the lack of subordination of a microbe to social welfare of the holobiont rather than from context-independent properties of this organism (pp. 165, 181). Emphasizing the contextual character of the parasite and the host, Tauber redefines immunity as an active process of coordination of a cellular ecosystem, which allows this collective to navigate through challenges of the environment and to face demands of the communal living (pp. 10e16). From this point of view, the failure to modulate intercellular interactions by the immune system entails mitigating immunity and impairing resistance to infection and disease (pp. 103e104). Immunity is a groundbreaking work establishing a new framework for understanding the function and activity of the immune system. Its value also lies in the fact that it serves as an important stepping-stone towards an integrated philosophical, ecological and immunological study of our embedment in the microbial world. (shrink)

Several key areas in modeling the cardiovascular and respiratory control systems are reviewed and examples are given which reflect the research state of the art in these areas. Attention is given to the interrelated issues of data collection, experimental design, and model application including model development and analysis. Examples are given of current clinical problems which can be examined via modeling, and important issues related to model adaptation to the clinical setting.

Contemporary philosophy of science has seen a growing trend towards a focus on scientific practice over the epistemic outputs that such practices produce. This practice-oriented approach has yielded a clearer understanding of how reductive research strategies play a central role in contemporary scientific inquiry. In parallel, a growing body of work has sought to explore the role of non-reductive, or systems-level, research strategies. As a result, the relationship between reductive and non-reductive scientific practices is becoming of increased importance. In this (...) paper, I provide a framework within which research strategies can be compared. I argue that no strategy is reductive or non-reductive simpliciter, rather strategies are more, or are less, reductive than one another according to a frame of reference. That frame of reference is provided by a continuum of possible ways in which the target system might be conceptualised. I illustrate the utility of the framework by deploying it to analyse a recent debate in cancer research. When set within the framework, a prominent reductive strategy—the somatic mutation theory—and a prominent non-reductive strategy—the tissue organisational field theory—do not stand opposed to one another. Rather, they serve as boundary markers to chart the territory of approaches to carcinogenesis within which most strategies in the field fall. (shrink)

Webb distinguishes two endeavors she calls animal modeling and animat modeling and advocates for the former. I share her preference and point to additional virtues of modeling actual biological mechanisms (animal modeling). As Webb argues, animat modeling should be regarded as modeling of specific, but madeup, biological mechanisms. I contend that modeling made-up mechanisms in situations in which we have some knowledge of the actual mechanisms involved is modeling with one hand—the good one—tied behind one’s back.1 The hand that is (...) used in animat modeling is constructing and evaluating models by whether they behave in the right way—do they exhibit the particular phenomenon one is trying to understand? The good hand that is disavowed seeks to use evidence about the mechanism employed in real living systems both for inspiration in designing the model and for evaluating the model. Denying oneself use of one’s good hand both limits one’s access to valuable evidence for evaluating a model and denies oneself access to a potent discovery strategy. Webb draws attention to one reason to employ the good hand—if models are to be relevant to biology (and not just characterize hypothetical mechanisms), then the component parts and operations specified in the model must in some way map onto those in actual biological organisms. Especially if one accepts the possibility of multiple realizations, then if one only uses behavior to evaluate the model one may well have described an alternative realization than that found in real organisms. To determine that one has modeled the actual realization, it is necessary to compare the proposed mechanism with the actual mechanism—does it.. (shrink)

Over the last decade the modeling and the storage of biological data has been a topic of wide interest for scientists dealing with biological and biomedical research. Currently most data is still stored in text files which leads to data redundancies and file chaos.In this paper we show how to use relational modeling techniques and relational database technology for modeling and storing biological sequence data, i.e. for data maintained in collections like EMBL or SWISS-PROT to better serve the needs for (...) these application domains. (shrink)

Biological processes span several scales in space, from the single molecules to organisms and ecosystems. Multiscale modelling approaches in biology are useful to take into account the complex interactions between different organisation levels in those systems. We review several single- and multiscale models, from the most simple to the complex ones, and discuss their properties from a multiscale point of view. Approaches based on master equations for stochastic processes, individual-based models, hybrid continuous-discrete models and structured PDE models are presented.

A link between biological and human sciences may be established, under the condition that we should admit the existence of reciprocal influences between them. The model for the regulation of agonistic antagonistic couples (MRAAC) is built from the study of biological systems and gives rise to specific types of control. This model can be helpful in decision processes in some human sciences such as management, economical and political strategies. The reason for such an opportunity lies in the fact that MRAAC (...) is a general and phenomenological model able to incorporate the whole of the agonistic antagonistic systems. This type of regulation might be related to the concept of the viability of a system (yet also valid for human science systems) and to a functional and structural pattern which is the basis for agonistic antagonistic networks. (shrink)

A two strain HIV/AIDS model with treatment which allows AIDS patients with sensitive HIV-strain to undergo amelioration is presented as a system of non-linear ordinary differential equations. The disease-free equilibrium is shown to be globally asymptotically stable when the associated epidemic threshold known as the basic reproduction number for the model is less than unity. The centre manifold theory is used to show that the sensitive HIV-strain only and resistant HIV-strain only endemic equilibria are locally asymptotically stable when the associated (...) reproduction numbers are greater than unity. Qualitative analysis of the model including positivity, boundedness and persistence of solutions are presented. The model is numerically analysed to assess the effects of treatment with amelioration on the dynamics of a two strain HIV/AIDS model. Numerical simulations of the model show that the two strains co-exist whenever the reproduction numbers exceed unity. Further, treatment with amelioration may result in an increase in the total number of infective individuals (asymptomatic) but results in a decrease in the number of AIDS patients. Further, analysis of the reproduction numbers show that antiretroviral resistance increases with increase in antiretroviral use. (shrink)

Despite numerous and increasing attempts to define what life is, there is no consensus on necessary and sufficient conditions for life. Accordingly, some scholars have questioned the value of definitions of life and encouraged scientists and philosophers alike to discard the project. As an alternative to this pessimistic conclusion, we argue that critically rethinking the nature and uses of definitions can provide new insights into the epistemic roles of definitions of life for different research practices. This paper examines the possible (...) contributions of definitions of life in scientific domains where such definitions are used most (e.g., Synthetic Biology, Origins of Life, Alife, and Astrobiology). Rather than as classificatory tools for demarcation of natural kinds, we highlight the pragmatic utility of what we call operational definitions that serve as theoretical and epistemic tools in scientific practice. In particular, we examine contexts where definitions integrate criteria for life into theoretical models that involve or enable observable operations. We show how these definitions of life play important roles in influencing research agendas and evaluating results, and we argue that to discard the project of defining life is neither sufficiently motivated, nor possible without dismissing important theoretical and practical research. (shrink)

Cooperation is rife in the microbial world, yet our best current theories of the evolution of cooperation were developed with multicellular animals in mind. Hamilton’s theory of inclusive fitness is an important case in point: applying the theory in a microbial setting is far from straightforward, as social evolution in microbes has a number of distinctive features that the theory was never intended to capture. In this article, I focus on the conceptual challenges posed by the project of extending Hamilton’s (...) theory to accommodate the effects of gene mobility. I begin by outlining the basics of the theory of inclusive fitness, emphasizing the role that the concept of relatedness is intended to play. I then provide a brief history of this concept, showing how, over the past fifty years, it has departed from the intuitive notion of genealogical kinship to encompass a range of generalized measures of genetic similarity. I proceed to argue that gene mobility forces a further revision of the concept. The reason in short is that, when the genes implicated in producing social behaviour are mobile, we cannot talk of an organism’s genotype simpliciter; we can talk only of an organism’s genotype at a particular stage in its life cycle. We must therefore ask: with respect to which stage(s) in the life cycle should relatedness be evaluated? For instance: is it genetic similarity at the time of social interaction that matters to the evolution of social behaviour, or is it genetic similarity at the time of reproduction? I argue that, strictly speaking, it is neither of these: what really matters to the evolution of social behaviour is diachronic genetic similarity between the producers of fitness benefits at the time they produce them and the recipients of those benefits at the end of their life-cycle. I close by discussing the implications of this result. The main payoff is that it makes room for a possible new mechanism for the evolution of altruism in microbes that does not require correlated interaction among bearers of the genes for altruism. The importance of this mechanism in nature remains an open empirical question. (shrink)

As the result of the complexity inherent in nature, mathematical models employed in ecology are often governed by a large number of variables. For instance, in the study of population dynamics we often deal with models for structured populations in which individuals are classified regarding their age, size, activity or location, and this structuring of the population leads to high dimensional systems. In many instances, the dynamics of the system is controlled by processes whose time scales are very different from (...) each other. Aggregation techniques take advantage of this situation to build a low dimensional reduced system from which behavior we can approximate the dynamics of the complex original system.In this work we extend aggregation techniques to the case of time dependent discrete population models with two time scales where both the fast and the slow processes are allowed to change at their own characteristic time scale, generalizing the results of previous studies. We propose a non-autonomous model with two time scales, construct an aggregated model and give relationship between the variables governing the original and the reduced systems. We also explore how the properties of strong and weak ergodicity, regarding the capacity of the system to forget initial conditions, of the original system can be studied in terms of the reduced system. (shrink)

Many biological systems experience a periodic environment. Floquet theory is a mathematical tool to deal with such time periodic systems. It is not often applied in biology, because linkage between the mathematics and the biology is not available. To create this linkage, we derive the Floquet theory for natural systems. We construct a framework, where the rotation of the Earth is causing the periodicity. Within this framework the angular momentum operator is introduced to describe the Earth’s rotation. The Fourier operators (...) and the Fourier states are defined to link the rotation to the biological system. Using these operators, the biological system can be transformed into a rotating frame in which the environment becomes static. In this rotating frame the Floquet solution can be derived. Two examples demonstrate how to apply this natural framework. (shrink)