A General Systems Outlook to the Prediction-Inference Dilemma of Neuroscience Models.
Keywords:general systems theory, model making, computational neuroscience, neural network, portable concepts
As the predictions made by a mathematical model gets validated, the level of confidence on the model grows with every successful prediction. With this rise in confidence one is tempted to make inferences from the more abstract parts of the model. This may result in perceived notion of contradictions or paradoxes. For an ontologically oriented non-general system theorists the relation between model and real-world such that the model results are applied, is a complex one. Let me illustrate this using one of the most famous models in computational neuroscience, the Hodgkin-Huxley model.
Since its unveiling 67 years ago, the system of the four differential equations have successfully modelled other axons and entire neurons based on the modelling schema. For the typical model the equations are such that one is a derivative of the membrane voltage. This is coupled to the remaining three derivatives of the probability that three different ion gates are open. Consider the case of a single channel with four charged particles. And the probability that each charged particle is in a position to open the channel is 0.5. But a real cell membrane has more than one channel of the same type, say ten. Does that mean there are only four charged particles for all the ten channels combined? How can a single channel have four charged particle and at the same time the number of charged particles in the remaining nine channels is also ten?
This contradiction leads to the prediction-inference dilemma. The dilemma that the model makes successful predictions yet, inferences from the model results in inconsistencies. If we waited until someone produced a type of channel with four charged particles and also four charged particles for an arbitrary number of the channel we would not be using the Hodgkin-Huxley model today. This would be like, not using geometry until someone produces a point with no dimension.
From the perspective of a general system theorists the prediction-inference dilemma is resolved. This is because from a general system view, a mathematical model has two facets; principal quantity/ies and secondary quantity/ies or constructs. The principal quantity agrees with the measurable quantity. For instance, membrane voltage variable in the system of equations. The principal quantity and the measured quantity are two different quantities. The model and real-world relation is provided by the agreement between the quantities. Secondary quantities are the result of mathematical abstractions; concepts, operations and symbols of which there are no counterpart in the real-world. This is the Slepian’s two-world view from information theory.
In the interdisciplinary field of neuroscience the role of computational neuroscience (also, theoretical or mathematical neuroscience) is to join the disciplinary rungs of the neuroscience ladder. The computational neuroscientist must therefore be a general system theorists and also be proficient in the science of modelling. This paper will present the solution to the prediction-inference dilemma as an illustration of the general systems approach to the science of modelling in computational neuroscience.