## Martin NilssonAssociate ProfessorWebPage |

# Understanding and Modeling Motor Control in the Central Nervous System

## Neurons connect in microcircuits

In the THE (“The Hand Embodied”) project, we try to understand and model the function of **microcircuits** (fig. 1) involved in motor control in the central nervous system (CNS), including the motor centra, the spinal cord, the cerebellum, and the pre-cerebellar structures. A microcircuit is a combination of a small number of neurons operating together—it can be seen as the next level up, above neurons, in the structural hierarchy of the CNS. We cooperate closely with a group of neurophysiologists led by Dr. Henrik Jörntell at Lund University, Department of Experimental Medical Science, who perform advanced electrophysiological experiments, where physical connectivity and signal transmission between neurons are recorded *in vivo*. Using these data we try to reverse-engineer the circuit function, validate the models, and propose new experiments.

*Fig. 1: Symbolic figure of recurrent lateral inhibition, an example of a common microcircuit.*

N = neuron, a = axon, i = inhibitory synapse, e = excitatory synapse.

N = neuron, a = axon, i = inhibitory synapse, e = excitatory synapse.

## Motor synergies simplify control

One facet of this work is to find out why nature is so successful in controlling motion, despite the many **degrees of freedom** that must be synchronized. One degree of freedom corresponds to one direction of motion; one joint always has at least one, but sometimes many, as exemplified by the shoulder joint. We may think of juggling or virtuoso piano playing as advanced, but even “ordinary” grasping is quite a complex control problem. A single human arm, for instance, has on the order of 30 degrees of freedom! But not all of the degrees of freedom are used equally; nature tends to “favorize” certain combinations of degrees of freedom, which are used particularly often. These are known as **motor synergies**, and an important question is how they are represented, developed, or learnt. Perhaps similar techniques can be used in order to control robots?

## Hand motion uses feedback

Synergies are most often mentioned in the context of motor control, but the motor system of mammals is an intricate system of **feedback control loops** (fig. 2) critically dependent also on sensor feedback. Our working hypothesis is that the motor control system is indeed organized as a system of cascaded control loops, perhaps not too radically different from those used in industrial process control. This idea is not new, but was proposed already more than 40 years ago (*“The cerebellum as a neuronal machine” by Eccles, Ito, and Szentágothai in 1967*). The theory has been elaborated and refined over the years (e.g.* “The Cerebellum and Neural Control” by Ito in 1984; “M**ultiple paired forward and inverse models for motor control” by Wolpert and Kawato in 1998; “The cerebellum and adaptive control” by Barlow in 2002*), but remains excruciatingly difficult to prove.

## But the hardware has limitations

In order not to propose, at best, yet another theory, or at worst, merely handwaving, we attempt to base our model of circuit operation carefully on theoretical detail, instead of only empirically. If this means that we have to go to the molecular level of detail in the analysis of neuronal systems (and in fact, it does!), we do. For instance, the prevalent view is that precision motor control is largely located inside cerebellum, but we believe that many structures outside cerebellum are also involved. In order to demonstrate this, we are trying to show that the core processing elements of the cerebellum and the spinal cord—in the cerebellum, huge neurons called **Purkinje cells** (fig. 3), and in the spinal cord, **spinal interneuron**—have such inherent limitations that the function of the cerebellum as a stand-alone controller is unfeasible, and that of the spinal cord has definite limitations.

*Fig. 3: A Purkinje cell. A: Side view, B: Front view. a = axon.*

(From Piersol, G.A.: Human anatomy, Philadelphia: J. B. Lippincott Company, 1908) II:1091.

(From Piersol, G.A.: Human anatomy, Philadelphia: J. B. Lippincott Company, 1908) II:1091.

*Reproduced with permisson by Clipart ETC, http://etc.usf.edu/clipart.)*

## Haunted by noise

A challenging, but at the same time stimulating aspect of this work is its multidisciplinarity: The research combines neurophysiology, robotics, electronics, control theory, mathematical statistics, and mathematics. The fundamental operation of neurons depends on molecular dynamics, directly affected by thermodynamic **noise**. Although noise in an electronic circuit is normally undesirable, we can clearly recognize that evolution has taken advantage of this in order to ingeniously design robustness into circuit operation! Unfortunately, evolution didn’t consider the poor souls that attempt to analyze these systems mathematically. The crucial function of noise in microcircuits requires a non-trivial mathematical treatment, and the stochastic (i.e., random) models of neuronal activity used have been described as “among the most advanced applications of the theory of stochastic processes in biology” (*“**One-dimensional stochastic diffusion models of neuronal activity and related first passage time problems”, Lansky, Smith, and Ricciardi, 1990*).

## Mathematics can explain neurons and microcircuits

However, we have now developed a model that is successfully validated by the recording data delivered by Lund University. The model is based on a hierarchical description of microcircuits divided into five levels (fig. 4), consisting of a level of description in terms of neuron populations; one in terms of inter-spike interval probability distributions; one in terms of spike trains; one in terms of membrane potential; and one in terms of ion channels. The model can provide detailed theoretical support for most our working hypotheses, and we are now working to publish these results. Our most recent result is a fundamental mathematical relation which both greatly simplifies the theoretical treatment, and accelerates simulation of the model. Forthcoming publications present the mathematical model and how it maps to physical neurons and microcircuits; the validation using experimental data; and the explanation of circuit function using the theoretical model.