1. Modeling the Calcium Dysregulation Hypothesis of Alzheimer's Disease Júlio de Lima do Rêgo Monteiro, Marcio Lobo Netto, Diego Andina, Javier Ropero Pelaez julio.monteiro@poli.usp.br, lobonett@lsi.usp.br, andina@gc.ssr.upm.es, fjavier@usp.br 6th WSEAS International Conference on COMPUTATIONAL INTELLIGENCE, MAN-MACHINE SYSTEMS and CYBERNETICS (CIMMACS '07)‏

2. The Alzheimer's Disease  First observed 100 years ago by Alois Alzheimer, finding plaques and tangles, toxic to nervous tissue provoking cellular death  Associated symptoms:  memory loss  agnosia – perception disturbances  apraxia – motor disfuntion  aphasia – language problems

3. AD – Many Theories  Cholinergic Hypothesis (Shen, 2004)‏  related to acetylcholinesterase failure  Tau Hypothesis (Schmitz et al, 2004)‏  related to Tau protein deformation  Amyloid Hypothesis (Ijima et al, 2004)‏  abnormal amyloid processing  Calcium Dysregulation Hypothesis (O'Day et al, 2004)‏  inefficient Ca 2+ regulation impairs neuronal functioning

4. Calcium Dysregulation Hypothesis (CDH) ‏  Aging and the AD affects brain Ca 2+ regulation  Many critical neuronal processes are calcium-dependent, and are hampered by the CDH: (Thibault et al, 2001)‏  increase in slow after-hyperpolarization  reduction of long-term potentiation  enhancement of long-term depotentiation  impairment of short-term frequency facilitation

5. Simulating the CDH  We present a formal method of simulating the effects of the CDH in an artificial neural network  The focus lies in the effect produced by calcium dysregulation on the dynamics of the neuron’s activation function and in the consequences of this effect on memory and learning

6. Homeostatic Mechanisms of Neuronal Plasticity  Adaptable response for regulating the input stimuli from synapses and the output generated in the soma  This regulation happens by changing the number of ionic channels in different sites of the cellular membrane  Two major forms of regulation:  Synaptic metaplasticity in the synapses  Intrinsic plasticity in the cellular soma

7. Synaptic Metaplasticity  Slows down the process of synaptic weight increment or decrement  Makes more difficult for the neuron to become inactive or saturated

8. Intrinsic Plasticity  Regulates the rightward shift position of the neuron activation function:  High activity shifts the sigmoid right  Low activity shifts the sigmoid left

9.  For synaptic metaplasticity, we utilize the probabilistic equivallent of the incremental version of the Grossberg's pre-synaptic rule: (Minai, 1993)‏ Simulating the Neuronal Plasticity

10. Simulating the Neuronal Plasticity (cont.) ‏  For the intrinsic plasticity model, we model our neuronal activation function as a sigmoid:  The “shift” component at a given time is determined by the following equation: (  is the shifting velocity)‏

11. Simulation: Neural Nets  To better understanding the relationship between calcium dysregulation and cognitive loss, a computational simulation was performed: 1.Consists of an artificial neural network modeled using homeostatic neuronal plasticity 2.The network has inputs that receive fixed patterns to be learned

12. Simulation: Neural Nets 3.The simulation goes on enough time for the network to achieve equilibrium, learning the initial patterns 4.Next, the sigmoid shift velocity is set to zero, simulating the starting point of the disease 5.Finally, the simulation continues on for some more time to measure the results 6.The simulation is run many times to compare between each random net

13. Simulation: Setup  The neural net is formed by 30 randomly connected neuronsin s sparse way, some of them having inhibitory connections  5 of this neurons serve as inputs, receiving 5 sequential patterns at each epoch  After 150 initial epochs, the sigmoid velocity(  ) is set to zero  After that point, the simulation continues for another 150 epochs  The variation of the 30x30 weight matrix is measured after each epoch

14. Simulation: Results 1  In aprox. 80% of the simulation runs, the synaptic weights are seriously disrupted after the sigmoid stall  This represents networks losing the capability to recognize the input patterns that have been memorized

15. Simulation: Results 2  Aprox. 25% of the random simulated networks exhibit an oscilatory burst-like behaviour, which is lost after the sigmoid stall  No bursting network keeps this behavior after the sigmoid stall

16. Simulation: Results 3  Around 20% of the random networks continue behaving as in the initial phase, even after the sigmoid stall  This is consistent with the fact that a reduced number of AD patients do not exhibit memory or learning impairments

17. Conclusions  Calcium dysregulation might be the starting point of a cascade of events leading to the lose of synaptic weight stability and the memories stored in synaptic weights, explaining memory deficits in Alzheimer’s disease  Although in some cases synaptic weights remain stable, in most of the cases they enter in a situation of instability  The results were also confirmed with networks of different sizes with different architecture of connections and with different input patterns  These results show that calcium dysregulation that is correlated to the impairment of intrinsic plasticity, leads to synaptic instability, which is consistent with cognitive deficits in AD