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Sten marked it as to-read Nov 04, Edelsteinn Eric added it Apr 21, Kaiser rated it it was amazing Aug 03, As a result, there has been much resurgent interest in, and a huge expansion of, the fields collectively called mathematical biology.
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But opting out of some of these cookies may have an effect on your browsing experience. Necessary cookies are absolutely essential for the website to function properly. Van The subject S takes, in view of the purpose both models and data, 2 model fitting to Fraassen, an innovative advocate of this P, the entity M as a model for the proto- data, 3 mechanism identification account- semantic view remarked: type T.
Apostel, , p. Such facets are here models directly, without paying any atten- The pragmatic view includes syntax explored using a recent exchange between tion to questions of axiomatizability, in and semantics, and explores assumptions two groups of mathematical modelers in any special language, however relevant or and functions of models.
Scientific debate can arise simple or logically interesting that might from different philosophies of modeling. And if the theory as such, is to be iden- Four functions of mathematical tified with anything at all — if theories are modeling Philosophy of science and models to be reified — then a theory should be The pragmatic view helps us focus Three distinct philosophical perspectives identified with its class of models.
Van on the functions of mathematical models, Fraassen, , p. Each illuminates Van Fraassen, , p. The observations. For instance, Darwin unified issue with nineteenth century German ide- tion i.
In mathematical modeling, logical language L e. The lan- assumptions in scientific theory sumption relation allowing for the unifica- guage L consisted of inference rules e. Sentences could be of two forms 1 Practices, instruments, and experi- Model fitting — either theoretical i. Although fitting is essential for containing no theoretical vocabulary and taxes — mathematics, diagrams, narra- model verification, models can be over fitted acquiring meaning only from experimental tives, simulations, and programs, etc.
Put Mechanism identification et al. Comparative analysis of dis- ous strategies, including i analysis i. Mathematical models assist al. For instance, every identification Winther, Because e. In and Prusinkiewicz and Coen of these trade-offs, different researchers this sense, an excellent prediction is surpris- adopt differing but complementary perspec- make distinct claims about which func- ing, validating, and correct.
Indeed, a simple unifying model ers of their own abstractions Levins and The possibility of collaboration rather than has significant virtues, even if it is difficult Lewontin, , p. Mitchell, ; Winther, The philo- The models Now, Prusinkiewicz et al. If it were, there would be no need to write articles like this one. Aspects of a theory of the organism that cannot be dealt with from a phenomenological point of view make it necessary to introduce two further, non-phenomenologically oriented levels of the phenomenal analysis of the organism.
Nevertheless, the phenomenological access to the organism precedes them logically and temporally. The physicochemical processes inside the living being generate its material parts and during morphogenesis e. However, two things should be noted: First, in contrast to inorganic beings, an organism does not suffer its permanent spatiotemporal changes passively, but rather causes and controls them actively. Second, the persistence of an organism does not result automatically, but is an achievement of its special processuality, which is why it can be lost—organisms are precarious beings.
Organisms are continu- ants because they actively resist their decay and repeatedly create the conditions for their continued existence. By emphasizing the exchange of matter, the second level of phenomenal analysis elevates metabolism to the most essential feature of the organism. Nevertheless, the question arises whether inanimate self-organized systems that exchange matter with their environment can also be assigned a form of metabolism.
Is the following statement true, which draws a sharp line between organisms and inanimate systems? In contemporary physics and chemistry, the energetic and material openness of inorganic systems is considered a necessary condition for self-organization. The BZ reaction generates a spatiotemporal pattern of molecular concentration, which has often been compared to biological pattern formation or morphogenesis. However, the passive dependence of inorganic self-organized systems on conditions imposed on them externally stays in a sharp contrast to the essential ability of any living being to autonomously generate nearly all conditions that the maintenance and steering of its metabolism require, as we will see in the exposition of the third level of phenomenal analysis.
Often, this most fundamental ability of all intact organisms is attributed to their capacity to process genetic and other forms of molecular information and, in the case of animals, neuronal information, which inorganic systems cannot.
But this widespread opinion lacks a reliable theoretical basis, since the use of the concept of information in biology is problematic. All forms of biological information have semantic aspects, the understanding of which is necessarily tied to philosophical concepts such as purpose, teleology, meaning, and value.
However, there is currently no information theory that adequately incorporates these terms, so that information theory cannot bridge this gap between organisms and inorganic self-organized systems. Understanding metabolism also requires addressing another central question in con- temporary theory of the organism: Do the spatial boundaries of an organism coincide with its morphological ones?
The answer to this question, which raises the issue of what exactly belongs to the body of an organism, is essential for a deeper understanding of the phenomenon of metabolism, as this occurs between the spatial boundaries of the organism and its environment. This question is not trivial because, according to some biologists, the morphological boundaries of some organisms do not coincide with their functional ones.
This distinction between the two types of boundaries is based on two different understand- ings of organisms: First, the organism is a morphologically coherent unit that is separated from its environment by a continuous material boundary such as skin or membrane. Sec- ond, the organism is a physiological-functional unit of causally dependent objects that do not all belong to the same spatial continuum. This applies even to processes that take place outside the body of the organism, but are central to its life.
The undoubtedly central problem of the discrepancy between the visible morpholog- ical and abstract physiological-functional boundaries of some organisms cannot be dealt with in this article. Here we must be content with the observation that in most organisms their morphological unit coincides with their physiological-functional unit. The problem of the boundaries of the organism is directly related to the issue of the relationship between the organism and its environment.
This question in turn has to do with the problem of the autonomy of the organism, since organisms, unlike inanimate objects, regulate their relationship to their environment autonomously.
The incomparable autonomy of organisms is the subject of the third level of phenomenal analysis. In recent decades, however, the concept of the organism has moved ever closer to the center of biological thinking. As mentioned earlier, this development is also due to the increasing awareness of the ability of organisms to act on their genomes.
Living cells and multicellular organisms have a huge number of ways to reorganize their DNA [13—16]. One of the leading geneticists, James A. At present, there is a rapidly growing number of publications in the fields of genetics, epigenetics, and developmental plasticity that demonstrate the ability of organisms not only to reorganize their own phenotype but also their genomes [13—15].
The following examples demonstrate the ability of organisms to radically transform their morphological, genetic, and physiological structure: i There are many notable examples demonstrating the striking ontogenetic plasticity of multicellular organisms.
The well-known theoretical biologist Mary Jane West- Eberhard is noted for arguing that phenotypic and developmental plasticity play a seminal role in animal evolution and speciation. This ability enables ontogenetic development to respond to challenges imposed by the conditions of life as well as to genetic challenges. The clinical autopsy revealed many morphological changes in its innervation, musculature, and skeleton, such as enlarged hind legs, a curved spine, an unusually large neck, a thorax similar to that found in kanga- roos, and a wide sternum resembling that of an orangutan [17] p.
Then the fly larvae were fed with food contaminated with a toxic concentration of the drug. The flies would only then survive if the gene were expressed in additional tissues. Indeed, after a developmental delay, the promoter activity had been extended over other tissues, so that the resistance gene was expressed in the gut and other organs, thus enabling the larvae to tolerate the otherwise lethal dose [18].
This resulted to the immediate abortion of all the placentas inside the uterus so that only the placenta that was grafted on the intestine survived and came to term. This gives rise to serious problems, such as the disruption of the usual pattern of gene expression and the improper forma- tion of chromosome pairs during meiosis. In addition, as it will be shown in Section 3 of the present article, there is an impressive body of evidence that the shape modification of a cell plays a crucial role in governing metabolic and functional processes [22] p.
Other than the second level of phenomenal analysis of organisms, the third level does not underscore the centrality of metabolism for the understanding of organisms. Rather, it emphasizes the various fundamental organismic processes that enable the metabolism to continue even under extremely adverse conditions.
In contrast to metabolism, which is a phenomenon familiar to the lay observer, those processes can only be revealed and addressed by scientific exploration.
Thus, the present analysis requires a higher level of abstraction above the admittedly essential insight that organisms maintain or law- fully vary their material form despite the permanent and complete exchange of their material constituents. All the examples described above demonstrate that cells and multicellular organisms can autonomously manipulate their morphology and physiology up to the molecular and even genetic level of the latter.
This makes obvious that neither the dynamics of an organism nor the autonomy of its processuality can be reduced to its genome. In addition—and this is more essential—the intensity of the internally and autonomously performed reorganization of organisms down to the molecular structure of their body is a unique biological ability that is unparalleled in the inorganic realm. This highly fundamental biological faculty, which is ubiquitous in the realm of life, clearly transcends the abilities of all inorganic self-organizing systems: Organisms do not simply react to external gradients of matter and energy but manipulate the inner conditions of the formation and maintenance of their morphological structure and their physiological and genetic dynamics in a way that enables the continuation and, if necessary, the purposeful modification of their metabolism.
The autonomous manipulation of the inner- organismic conditions, which determine the internal functions and external actions of the organisms, identifies the distinctiveness of the organismic mode of being. This ability often allows organisms to modify their environment in a way that serves the preservation and steering of their metabolism.
This means, however, that the autonomy and depth of organismic self-organization cannot even approximately be attained by the most complex examples of physical or chemical self-organization of inanimate matter.
Thus, there are good reasons to expect that 21st century biology will be erected around the insight that the explanation of biological phenomena demands a sound theory of the organism. In the opinion of this author, the arising of such a theory requires the elaboration of a logic of organismic causality that meets two conditions: First, it does justice to the radical autonomy of organismic processuality, which is evidenced by all the above mentioned examples.
Second, it occupies a middle position between the phenomenal analysis and the causal-ontological analysis. Nonetheless, the explanation of organismic phenomenality can be achieved only by the causal-ontological analysis of the organism. This subject will be addressed immediately. The Causal-Ontological Analysis of the Organism Scientific explanations presuppose specific ontologies. They are implicitly and more rarely explicitly underlain by metaphysical assumptions about the nature and essential properties of entities, the interactions of which give rise to the phenomena requiring an explanation.
Those philosophical assumptions are the most fundamental theoretical propositions that many if not all natural sciences of a particular historic era share. The history and present state of Western thought shows that both the biological sciences and their philosophical foundation have been grounded on three main ontological traditions succeeding one another. The Substance-Ontological Approach For over two thousand years, between the era of Socrates and the birth of mechanistic physics in the 17th century, the metaphysics of substance was the backbone of occidental philosophy and science.
The substance of a particular being, understood as its essence, is the atemporal, and thus eternal, reason of all its features, which must be attributed to it in order to distinguish it from other beings [24] p. Under the influence of Aristotelian substance ontology, the concept of essence became the main principle of reasoning about nature.
It is the essence or nutritive soul of a growing organism that determines its metabolism and directs growth toward a particular final state. Thus, in sharp contrast to contemporary materialistic biosciences, an essential feature of Aristotelian biology is that the formation and maintenance of an organism are determined by an immaterial causal factor. The central role of essence in the explanation of organism formation and persistence makes it the primary common element in the biological thought of ancient, medieval, and early modern times.
The System-Ontological Approach and the Logic of Systems Biological Mechanisms The decline of Aristotelian ontology was due to the scientific revolution initiated by the introduction of the Copernican heliocentric system in the Renaissance. In the 17th century, philosophers and physicists replaced Aristotelian causality with mechanical contact-forces Bacon, Galileo, Hobbes, Descartes or action-at-a-distance-forces Newton. Systems ontology totally reverses the main principle of Aristotelian philos- ophy of nature by reducing essential features of any actual being to its material elements and their relations or interactions.
Thus, for principal reasons, since its very origin, this ontology rejects any form of explanation of natural phenomena based on the concept of essence. However, systems ontology is not free from overlapping with substance ontology. In the 17th century, Newton succeeded in describing the dynamics of the solar system without using any Aristotelian form of explanation.
Newtonian mechanics provided the example of mechanistic systems ontology par excellence. In French physiologist Claude Bernard introduced a considerably more synthetic view of the organism, according to which living beings consist of diverse material processes that determine each other synergistically [30] p.
Due to his emphasis on synergism, Bernard may be considered the first non-Cartesian materialistic physiologist. After a short revival of substance ontology in the neo-vitalistic biology of the early 20th century, the establishment of mathematical theoretical biology in the s and especially the rise of molecular biology twenty years later facilitated the final breakthrough of materialistic interpretations of the organism.
In the last twenty years, due to the emergence of synthetic and systems biology, theorization of the organism came under the strong influence of mathematically formulated systems-theories.
In the wake of that development—which was anticipated by pioneers of mathematical biology, such as Ludwig von Bertalanffy, Conrad Waddington, Stuart Kauffman, and Brian Goodwin [28,31—35]—organisms are considered complex dynamical systems of nonlinearly interacting biomolecules.
Leading biologists today regard systems biology as supporting the renaissance of the concept of organism. This assessment reflects the fact that systems biology is antagonistic to gene-centered molecular biology in one important respect, as it supports a change in attention from DNA to a systems-theoretical consideration of organismic processes.
One of the central tasks of systems biology is the study of complex cellular processes. Influenced by the paradigm of complexity and self-organization, contemporary theoretical- and systems biologists consider organisms energetically and materially open self-organizing dynamic systems that operate far from thermodynamic equilibrium.
The properties of this function reflect the causal relationships at work between the elements of the system. The set of state variables x1 t , x2 t , The development of a dynamic system—which is usually represented by trajectories in the state space—is not only the result of the function F but depends also on a group of externally set control parameters.
In most cases F is a system of coupled nonlinear differential equations. In the last formula, the letter p represents a set of control parameters. During a process of calculating the variables, the control parameters are usually kept constant and their values are determined by the modelers.
It deserves special attention that in systems biology the values of the control param- eters are determined by the modelers, as this reveals a crucial aspect of this discipline. In carrying this out, a single method was applied: dynamic systems were represented by systems of equations solved under certain control parameters, the values of which were dictated by the nature of the elements of the system under ex- amination.
In contrast, the criterion of quality of systems biological models is not whether they faithfully represent the real nature of organisms and biological processes but whether they facilitate the further medical and biological research by enabling predictions and formulating new hypotheses.
Therefore, a large number of different methods can be used at the same time in systems biology if this helps to outline a formalism and the control parameters under which this formalism enables the desired predictions [37]. Utility rather than theoretical stringency is the criterion for assessing adequacy in systems biology. Thus, systems biology should be seen as being closer to engineering than to science. Therefore, systems biological models of organismic processes should be considered as models for predicting the behavior and not as models for explaining the real causal relations between the parts of an organism.
Due to the essential role of control parameters in systems biological modeling, later in this section special attention is paid to the parameter determination by the modelers. The practical meaning of their research often forces life scientists to find ways to manipulate the course of biological processes—any form of successful medical therapy is mainly a desirable artificial phenomenon. In sciences, real or hypothetical causal structures that produce or predict the course and outcome of natural or artificial phenomena are generally referred to as mechanisms.
Due to the commitment of systems biology to the practical service of the life sciences, much of its research can be understood as the discovery, description, and creation of mechanisms. All mechanisms are mechanisms for something [41] p. They state, however, that entities and activities determine each other, for they are interdependent correlatives [42] p.
In systems biology it is always a computer simulation that shows how the explanan- dum results from a mathematical model consisting usually of differential equations [43] p.
The same applies to simulations, the aim of which is not to explain an observed phenomenon, but to predict a new phenomenon that would occur under specifically ma- nipulated conditions. At present, computer simulations of both small and large systems of equations are considered mechanistic explanations [44] p. Mathematics has become indispensable in contemporary biological explanations. Therefore, in systems biology mech- anisms are always mathematical models. In order to understand how systems biologists operate with mechanisms in their research we must look at mathematical models.
What we will find out about the general logic of systems biological mechanisms is valid no matter which of the possible definitions of mechanism that were introduced above underlies a particular mechanism. In systems biology, depending on the problem to be solved, a variety of different methods can be employed [37] p. Systems biologists, who model organismic pro- cesses as systems of differential equations, often focus on the modeling of the dynamics of genetic, metabolic and signal pathways [48—53].
They also study the behavior of larger network systems constituted by coupling these pathways [45,54], such as might occur in embryogenesis. From the perspective of the theory of dynamic systems, the final-state- directedness of embryogenesis, cell cycles, and other final-state-directed phenomena are thereby reduced to the dynamics of an enormously complex system of positively and negatively coupled biomolecular reactions, represented by positive and negative feedback loops in the corresponding mechanisms.
In order to demonstrate how this approach works, an exemplary case of the mathemat- ical analysis of a biological system, implemented with differential equations, is presented. Their final values to be calculated by the model are the explanandum, i. The thirteen quantities k1 to k13 are the control parameters whose constant value was determined by the modelers and therefore cannot be varied by the calculated system dynamics during the computer simulation.
In other words, the self-organization of this small system of three dynamical quantities vari- ables requires the determination of thirteen static quantities control parameters.
A few years ago van Hoek suggested a metabolic pathway model for the behavior of the bacterium Escherichia coli.
Following the same methodology as that of the authors presented above, he used ten coupled differential equations that calculated the values of the same number of variables for the solution of which he used 58 control parameters [48] pp. In the last few decades several research groups have carried out computer simulations of whole cells.
The model consisting of the three equations introduced above is part of a larger model of the yeast cell cycle that operates with differential equations and was published in the same article [54]. In this model the yeast cell is reduced to 36 state variables, for the computation of which the model makers use control parameters. Thus, on average, for the computation of one variable they use four control parameters. This is also reflected in the models of self-organized behavior, in which dif- ferent sets of control parameters generate different forms of trajectories that, in dependence of the initial conditions, may be directed toward one or more final states or oscillate around a particular area of the state space [55] p.
In systems biological modeling some control parameters represent the degree of activity of specific molecules, while others represent the rate coefficient of reactions in chemical kinetics.
Other control parameters represent constraints, such as the boundary conditions of the system—in other words, they represent the matter and energy that the system imports and exports. Control parameters are preset by the model makers and are held constant during a computer simulation. Of course, with each new simulation, the modelers can vary the val- ues of the parameters. In more philosophical terms, the control parameters are an important part of the explanans. In biological modeling, control parameters are either experimentally derived or estimated or simply taken from the literature [56] pp.
But the last quotation also leads to a further discussion about the ontological status of both the models and the mathematical mechanisms employed in them. This statement is in full agreement with some of the ideas of one of the leading proponents of the New Mechanical Philosophy: Carl F. The constructivity of models, which are based on the interests pursued by certain researchers, is also reflected in the fact that sometimes new, simpler models are derived from original models.
Transtrum and his co-authors report on the reduction of an initial model consisting of 29 differential equations and 48 parame- ters to a model consisting of 6 differential equations and 12 parameters [59] p.
The constructivity of control parameters, which sometimes results in some of them being eliminated, indicates that the control parameters that will be incorporated into the final model, while empirically adjusted factors often do not correspond to actual facts in real organisms [61] p. Both the dependence of models on the subjective perspective of the researchers and the diverse ways in which control parameters are constructed indicate that systems biology modeling has a much higher heuristic than ontological value.
The presence of this expression in the title is justified by the implicit and unconscious ontologization of systems-theoretical access to organisms by most systems biologists and scientists in general.
How else can one interpret the fact that organisms are often treated as if they could be nothing more than dynamic systems of nonlinear molecular interactions? This development has some clearly philosophical overtones, as the biologists who pursue it attribute to the theory of self-organized dynamic systems-ontological and not just heuristic relevance for biology. Such an ontologiza- tion of systems biological mechanisms is not only unjustified, but also highly misleading, especially since in the opinion of this author real organisms obey a completely different logic than our scientific mechanisms, as it will be claimed in Section 3 of this study.
The question of whether systems biology models are assigned a heuristic or ontological value is less important for the present study than the realization that all these models have their most important property in common: They are based on the same implicit assumption about the role of various causal factors in the dynamics of biological systems, as shown below.
They are the time-dependent values of the variables. In the above system of equations, the changing values of M, D, and W are the only intrinsic factors and the control parameters k1 to k13 are the only extrinsic factors.
Those systems of equations are relationships between the less complex factors, i. In contemporary formalisms, the systems of equations are not influenced by the changes of the state of the system. They are inde- pendent of the dynamics of the system, which clearly qualifies them as extrinsic factors.
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