Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

The 4-dimensional nature of living molecular systems
Maurício Vieira Kritz

Last modified: 2014-06-09


Natural phenomena arise from a collection of interacting “things”. Interactions change attributes we observe. Traditionally, “things” reside in Galilean spaces, attributes in phase spaces and time registers changes. Depending on our queries, “things” can be particles, bodies, fields, substances, individuals, populations, communities etc. Such terms encompass paradigms for inspecting natural phenomena, each with its own formal treatment. Particles “occupy” single points — their attributes attach to a point in space. Body’s attributes spread over a region; body-interactions occur at their boundaries. Fields interact at any point in the region they occupy. Individuals are particles that make decisions.


Living-things are space-time organisations.


In physics, every “thing” interacts freely with every other “thing”. Under this view “living-things” appear as protean open systems, barely non-homogenised by self-organisation. Despite chemical constrains, interactions evoke a kaleidoscopic dance of attributes presenting swift patterns difficult to discern. Biologists handle these difficulties abstracting from time and space and representing “living-things” as static objects: networks, organelles and “architectures” (organisations). Although acknowledging the permanent reconstruction of organisations by bio-chemical processes, biological arguments seldom make use of them to explain the living; since we still miss a widely accepted conceptual framework to address the entailment of organisations.


Nevertheless, there are things essential for cell subsistence — like flagella, chaperone aggregates, or biochemical cycles — whose existence, identity and “function” can only be recognised along time; by collapsing several snapshots along the time axis. Modifications in biomolecules’ conformation do change their possibilities of interaction, while biologically relevant events, like mitosis, are entailed to special architectural (con)formations. Organisation, nor mass, nor energy, is ubiquitously recognisable and conserved in living phenomena. Organisations are independent of the elements instantiating them. Portions of DNA are replaced by the SOS system preserving its organisation; cell organelles are repaired by substitution of defective parts.


An alternative view of living phenomena is discussed where: “things” may spread in time and space; interactions are organised; and “things” may dynamically re-organise into other “things”. Under this view, living-things are organisations in 4-dimensions: i.e., organisations imbedded in space-time. Biochemical networks and cycles are 4D entities interacting with different cycles and networks. Cellular components are sub-organisations that continuously  substitute their parts; cycles and generic compounds are organisations that store mass and energy. Time has then two major roles: reckon attribute changes and give “existence” to things.

This view is grounded on a framework for representing organisations and their changes, that possesses predicates and operators, such as: equality, sameness, binding and uniting. It promotes the definition of organised volumes and a concept of “in-formation” that accounts for interactions and organisation changes. This framework is based on hypergraphs and recursion; develops along ideas of NRashevsky and RRosen but is not aligned with them. It is not centred on biological functions, mapping straightforwardly onto living phenomena via molecules as organisations. Interaction graphs tie organisations to dynamics.

This reasoning allows us to consider viral infection as reorganisations of “normal” functions caused by signals — the viruses.


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