Computational Models of Cerebellar Long-Term Memory

Computational Models of Cerebellar Long-Term Memory Hideaki Ogasawara and Mitsuo Kawato

Introduction Our brain is capable of learning new things while maintaining old memory. Retention of information requires stability, and new learning requires plasticity. As a memory device, neurons have to meet these contradictory requirements (the “stability versus plasticity dilemma” [1]), but stochastic noise makes this duty still more difficult. The dendritic spine, the key unit of neuronal information processing, is very small (∼1 µm or less in diameter) and contains only a limited number of each molecular species. For instance, the number of α-amino-3-hydroxy-5-methylisoxazole-4-propionic acid (AMPA)-type glutamate receptors (AMPARs) in a parallel fiber (PF)–Purkinje cell (PC) synapse is as small as 4 to 73 [2]. In such a minute environment, stochastic fluctuations come into play and, affect the signaling pathways underlying memory formation and maintenance. How do neurons handle the stability versus plasticity dilemma without being overwhelmed by the noise? In this chapter, we address this issue by reviewing several theoretical studies of cerebellar long-term depression (LTD) and simulating simple models.

Cerebellar LTD The main neurons and wirings in the cerebellar cortex include PCs, PFs, and climbing fibers (CFs). PCs provide the sole output from the cortex, and each PC receives two types of excitatory inputs: one from hundreds of thousands of PFs and the other from a single CF. Marr-Albus-Ito theory [3–5] states that their neuronal circuit underlies

H. Ogasawara National Institute of Information and Communications Technology. 2-2-2, Hikaridai, Seika, Kyoto, 619-0288, Japan H. Ogasawara and M. Kawato ATR Computational Neuroscience Laboratories, 2-2-2 Hikaridai, Seika, Kyoto 619-0288, Japan

S. Nakanishi et al. (eds.), Systems Biology, DOI:10.1007/978-4-431-87704-2_18, © Springer 2009

169

170

H. Ogasawara and M.Kawato

supervised learning of the cerebellum. In this theory, PFs provide a sensorimotor context to PCs, while CFs carry teaching signals that modify PF-PC synapses in an associative manner. In fact, the transmission efficacy of a PF–PC synapse is reduced when the CF and PF are repetitively and synchronously activated (cerebellar LTD). The molecular mechanisms are comprehensively reviewed elsewhere [6–11]. Briefly, PF firing induces production of inositol 1,4,5-trisphosphate (IP3) through the mGluR1 metabotropic glutamate receptor pathway. CF firing depolarizes the PC and induces Ca2+ influx through voltage-gated calcium channels (Fig. 1a). Therefore, [IP3] and [Ca2+] represent PF and CF activities, respectively (In this chapter, [substance] stands for the concentration of the substance.) Synergistic increase of [IP3] and [Ca2+] activates IP3 receptors (IP3Rs) located in a calcium store of the dendritic spine and results in an enormous Ca2+ release. Ca2+ activates protein kinase C (PKC), which in turn phosphorylates the GluR2 subunit of AMPARs. Phosphorylated receptors are removed from the postsynaptic membrane through endocytosis.

PF NO

Glu

P

AMPAR

AMPAR

mGluR1

sGC cGMP PKG G-substrate PP2A

Gq protein PKC MAPKKK MAPK-PKC Positive Feedback Loop MAPKK

AA

DAG

PLC PIP2

Ca2+ IP3 PLA2

IP3R

MAPK Ca2+

Calcium store

b

a VGCC Depolarization CF

Fig. 1 Schematic view of signaling cascades in cerebellar long-term depression (LTD). Reactions surrounded by the bold gray line take place inside the dendritic spine. a Parallel fiber–climbing fiber (PF-CF) coincidence detection mechanisms (light gray area; right side) [14]. Glu, glutamate; PKG, cGMP-dependent protein kinase; PIP2, phosphatidylinositol bisphosphate. b The mitogen-activated protein kinase (MAPK)–PKC positive feedback loop [13] and its peripherals (dark gray area; left side). AA, arachidonic acid; AMPA, α-amino-3-hydroxy-5-methylisoxazole4-propionic acid; AMPAR, AMPA-type glutamate receptor; DAG, diacyl glycerol. (From [15], with permission of S. Karger AG, Basel)

Computational Models of Cerebellar Long-Term Memory

171

Essential molecules for LTD include mitogen-activated protein kinase (MAPK), MAPK kinase (MAPKK), MAPKK kinase (MAPKKK), PKC, phospholipases A2 (PLA2) and C (PLC), arachidonic acid (AA), IP3, and many others [6–11].

Models to Explain Cerebellar LTD In numerous situations such as development and cell-cycle progression, cells take discrete states and jump from one to another, avoiding intermediate states. For example, frog eggs are either mature or immature, and there is no half-mature egg [12]. This kind of switch-like behavior is termed “bistability.” Bistability is particularly important in neurobiology because it is implicated in the storage of cellular information. Previous studies have shown that Ca2+-induced Ca2+ release (CICR) and the MAPK-PKC positive feedback loop in the PC are among many bistable dynamics of the cell (Fig. 1) [13,14] (reviewed in [15]).

Calcium Dynamics Model Calcium release via IP3Rs is a supralinear function of calcium influx; the greater an input stimulus (calcium influx) is, the much more greater the output signal (calcium release) is. Doi et al. [14] simulated the molecular mechanism and demonstrated that a positive feedback loop Ca2+ → IP3Rs → Ca2+ is responsible for the supralinearity of calcium release. They also showed that the optimal PF-CF delay (∼100 ms) for calcium release and LTD is attributable to the slow mGluR1 pathway that takes time to biochemically produce IP3, rather than to calcium kinetics and the binding properties of the receptor [16] (see also comments in [17]).

MAPK-PKC Positive Feedback Loop Kuroda et al. [13] modeled the intracellular signaling cascade of cerebellar LTD (Fig. 1b). Their model predicted that MAPK and PKC form a bistable positive feedback loop, which mediates the intermediate phase (