Chapter 1
Multiscale Hierarchical Processes

Träumen wir uns für einen Moment in einen zukünftigen Zustand der Naturwissenschaft, in dem die Biologie ebenso vollständig mit Physik und Chemie verschmolzen sein wird, wie in der heutigen Quantenmechanik Physik und Chemie miteinander verschmolzen sind. Glaubst du, dass die Naturgesetze in dieser gesamten Wissenschaft dann einfach die Gesetze der Quantenmechanik sein werden, denen man noch biologische Begriffe zugeordnet hat, so wie man den Gesetzen der Newtonschen Mechanik noch statistische Begriffe wie Temperatur und Entropie zuordnen kann; oder meinst du, in dieser einheitlichen Naturwissenschaft gelten dann umfassendere Naturgesetze, von denen aus die Quantenmechanik nur als ein spezieller Grenzfall erscheint, so wie die Newtonsche Mechanik als Grenzfall der Quantenmechanik betrachtet werden kann ?

Werner Heisenberg (1901-1976),
Deutscher Physiker (Heisenberg, 1986)

Multiscale hierarchical processes are understood as information transduction in networks which are hierarchically structured. The most simple assumption might be a house which is structured into rooms, rooms are structured into furnishings but also people that move from one room to another. Of course cupboards and chairs, computers and TVs as well as human beings are hierarchically structured in a somehow comparable way. We would call our house a hierarchically structured system. If information flows from one room to another - and everyone would agree that this is the case when people live in that house and move objects or direct information - we can speak about hierarchical processes. These processes might comprise the information conveyed by the parents that the food is prepared which leads to a movement of the children towards the kitchen and the covering of the table by dishes, not to mention all the processes that are correlated with eating and enjoying the wonderful meal.

If we agree that the type of hierarchical structure might additionally vary if elucidated from different aspects we speak about multiscale hierarchical processes. Such different aspects can be aspects of spatial organization as it is the case in our example, the house. But in addition also other, for example temporal, organization principles are possible. To summarize all these organization principles we generalize the hierarchical systems to multiscale hierarchical systems housing the dynamics of multiscale hierarchical processes.

Living systems are always spatially hierarchically organized: in this case molecules are the basic entities that form genes and proteins as an intermediate structure on a mesoscale. The proteins aggregate in a quaternary structure to form higher ordered systems that do not necessarily need to be stable in time. The network of interacting proteins is in its turn forming a metastructure that can be understood as a network formed from single proteins. However, also on the temporal scale multiscale hierarchical processes arise. For example, a reaction scheme may represent the dynamics of the chemical reaction of two compounds on the temporal microscale. However, if a certain threshold of concentration of its output is present, another chemical reaction may start and is therefore triggered by the first reaction scheme. Long-term effects like the active movement of our extremities, circadian rhythms, the growth of an organism and senescence are typical examples of processes that change their appearance over time and are therefore a hierarchical metastructure that arises on the network of microscale processes.

1.1 Coupled Systems, Hierarchy and Emergence

Naturally, coupled systems are generally nonlinear. That is always the case if two compounds form a special reaction pathway that is not possible if only a single compound is present. If two molecules of two different compounds interact, then the reaction is bilinear or bimolecular, which is a nonlinearity. If two molecules (or two photons) of the same kind are able to reach a state that is not accessible by a single molecule (or photon) then the outcome is typically in a nonlinear dependence on the input. One prominent example of nonlinear optics in physics is the two photon absorption where the absorbing state is reached by interaction of two photons with the ground state within a certain time interval. If the photon density is too low for that to happen then the output is zero, but when the photon density increases the probability for the two photon absorption increases with the square of the photon density. Therefore two (or more) photons are needed to activate a state transition. Only spontaneous population and depopulation of certain states, which is not the typical situation for characteristic biochemical reactions, are truly linear. If several molecules of one or several compounds have to interact within a certain time interval, then the reaction scheme is nonlinear and characterized by the typical mathematical problems and challenges of nonlinear systems.

Photosynthesis is a truly nonlinear reaction as at least eight photons have to be absorbed by two different photosystems to split two molecules of water and release one molecule of oxygen. Photon absorption drives an electron transfer in photosynthesis. However, the involved molecules are reduced and/or oxidized by more than one electron and the coupled proton transfer again forms ATP from ADP and phosphate in a nonlinear process. Biochemistry is truly a hierarchy of nonlinear processes.

The "cycles" of nonlinearities that form the overall, hierarchical structure also include loss processes. After photon absorption excitation-energy can be lost and the following electron transfer processes are likewise restricted by loss processes that limit the production of one molecule of oxygen with a demand of at least 11-12 photons. Other sources report 60 photons per molecule glucose (Häder, 1999; Campbell and Reece, 2009) which would equal 10 photons per molecule glucose according to the basic equation of photosynthesis understood as the light-induced chemical reaction of water with carbon dioxide to glucose:

chemical equation 1

The energetic stoichiometry of light and dark reactions in photosynthesis are again discussed in chap. 4.4.1 as well as in the literature (Häder, 1999). This also features discussions of coupled reaction schemes like the proton assisted electron transfer (Renger, 2008, 2012; Renger and Ludwig, 2011). This question shall therefore not be discussed here in more detail. The basic principles of the photosynthetic light reaction are presented in chapter two.

Here we primarily intend to elucidate the highly nonlinear character of photosynthesis. Indeed, the nonlinearity of photosynthesis goes far beyond this discussion. If one regards the hierarchy of the spatiotemporal order of a plant as an overall reaction system, one could ask how many photons are involved in the construction of a new leaf. Analyzing the biomass of a dried leaf, which is strongly dependent on the organism, we might look at, say, 100 mg and find that the fixation of an order of 1021 carbon molecules was necessary with a corresponding nonlinear response of a new "leaf" to more than 1022 absorbed photons. That means absorption of 1022 photons finally leads to the spontaneous appearance of a single "leaf". Of course these photons have to be absorbed within a certain time interval. If illumination stays under a certain threshold, nothing happens, but if bright sunlight, sufficient day length and adequate temperature trigger the mechanisms correctly in spring, leaves might appear proportional to "packages" of 1022 absorbed photons. In this sense, the process might seem to be a linear response, but it is surely not and stops completely after a short growth period when new priorities like the production and storage of biomass take over in summer.

Even if we understand this reaction as a subsequent construction which can be analyzed step by step, it might still be a matter for discussion whether this reductionism leads to the loss of information and prevents our overall understanding of the growth of a plant (Heisenberg, 1986). After all, we have the appearance of one single leaf after the absorption of 1022 photons if we work as a pure phycisist who did not learn the details of biochemistry and does not know anything from gene activation and proteomics.

Our first identified nonlinear system (the water splitting and oxygen evolution) forms the trigger or the "input" for processes that are highly nonlinear themselves since they require several molecules of glucose, ATP or NADH to drive the production of one single further unit like for example a whole cell. We have a complicated spatiotemporal network of nonlinear systems that are coupled to nonlinear networks on the next hierarchically higher "level". In this way, the complexity of the overall system, the plant, arises. However, if only bottom up processes from the molecular interaction on the single molecule level are taken into account, then reductionism will fail to explain the details of the plant's morphology and lifespan.

Therefore it might still be wondered, like Heisenberg did in his book Der Teil und das Ganze (Heisenberg, 1986), whether we can expect that a possible picture of a plant as an organism understood in full detail will still use the language of physics or whether this picture will require that we formulate its propositions with novel approaches. Of course, taking the view of a physicist, the formalism that enables a...