Modeling the Calcium Modeling the Calcium Dysregulation Hypothesis Dysregulation Hypothesis of Alzheimer's Diseaseof Alzheimer's Disease

Júlio de Lima do Rêgo Monteiro, Marcio Lobo Netto,Júlio de Lima do Rêgo Monteiro, Marcio Lobo Netto,Diego Andina, Javier Ropero PelaezDiego 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 on6th WSEAS International Conference onCOMPUTATIONAL INTELLIGENCE, MAN-MACHINE SYSTEMS COMPUTATIONAL INTELLIGENCE, MAN-MACHINE SYSTEMS

and CYBERNETICS (CIMMACS '07)and CYBERNETICS (CIMMACS '07)

The Alzheimer's DiseaseThe Alzheimer's Disease

First observed 100 years ago by Alois First observed 100 years ago by Alois Alzheimer, finding plaques and tangles, toxic to Alzheimer, finding plaques and tangles, toxic to nervous tissue provoking cellular deathnervous tissue provoking cellular death

Associated symptoms:Associated symptoms: memory lossmemory loss agnosia – perception disturbancesagnosia – perception disturbances apraxia – motor disfuntionapraxia – motor disfuntion aphasia – language problemsaphasia – language problems

AD – Many TheoriesAD – Many Theories

Cholinergic Hypothesis Cholinergic Hypothesis (Shen, 2004)(Shen, 2004)

related to acetylcholinesterase failurerelated to acetylcholinesterase failure

Tau Hypothesis Tau Hypothesis (Schmitz et al, 2004)(Schmitz et al, 2004)

related to Tau protein deformationrelated to Tau protein deformation

Amyloid Hypothesis Amyloid Hypothesis (Ijima et al, 2004)(Ijima et al, 2004)

abnormal amyloid processingabnormal amyloid processing

Calcium Dysregulation Hypothesis Calcium Dysregulation Hypothesis (O'Day et al, (O'Day et al, 2004)2004)

inefficient Cainefficient Ca2+2+ regulation impairs neuronal functioning regulation impairs neuronal functioning

Calcium Dysregulation Calcium Dysregulation Hypothesis (CDH)Hypothesis (CDH)

Aging and the AD affects brain CaAging and the AD affects brain Ca2+2+ regulationregulation

Many critical neuronal processes are Many critical neuronal processes are calcium-dependent, and are hampered calcium-dependent, and are hampered by the CDH:by the CDH:(Thibault et al, 2001)(Thibault et al, 2001)

increase in slow after-hyperpolarizationincrease in slow after-hyperpolarization reduction of long-term potentiationreduction of long-term potentiation enhancement of long-term depotentiationenhancement of long-term depotentiation impairment of short-term frequency impairment of short-term frequency

facilitationfacilitation

Simulating the CDHSimulating the CDH

We present a formal method of simulating We present a formal method of simulating the effects of the CDH in an artificial the effects of the CDH in an artificial neural networkneural network

The focus lies in the effect produced by The focus lies in the effect produced by calcium dysregulation on the dynamics of calcium dysregulation on the dynamics of the neuron’s activation function and in the the neuron’s activation function and in the consequences of this effect on memory consequences of this effect on memory and learningand learning

Homeostatic Mechanisms Homeostatic Mechanisms of Neuronal Plasticityof Neuronal Plasticity

Adaptable response for regulating the input Adaptable response for regulating the input stimuli from synapses and the output stimuli from synapses and the output generated in the somagenerated in the soma

This regulation happens by changing the This regulation happens by changing the number of ionic channels in different sites of number of ionic channels in different sites of the cellular membranethe cellular membrane

Two major forms of regulation:Two major forms of regulation: Synaptic metaplasticitySynaptic metaplasticity in the synapses in the synapses Intrinsic plasticityIntrinsic plasticity in the cellular soma in the cellular soma

Synaptic MetaplasticitySynaptic Metaplasticity

Slows down the Slows down the process of synaptic process of synaptic weight increment or weight increment or decrementdecrement

Makes more Makes more difficult for the difficult for the neuron to become neuron to become inactive or inactive or saturatedsaturated

Intrinsic PlasticityIntrinsic Plasticity

Regulates the Regulates the rightward shift rightward shift position of the position of the neuron activation neuron activation function:function: High activity shifts High activity shifts

the sigmoid rightthe sigmoid right Low activity shifts Low activity shifts

the sigmoid leftthe sigmoid left

For synaptic metaplasticity, we utilize the For synaptic metaplasticity, we utilize the probabilistic equivallent of the incremental probabilistic equivallent of the incremental version of the Grossberg's pre-synaptic version of the Grossberg's pre-synaptic rule: rule: (Minai, 1993)(Minai, 1993)

Simulating the Neuronal Simulating the Neuronal PlasticityPlasticity

jiij IOPw /

Simulating the Neuronal Simulating the Neuronal

Plasticity (cont.)Plasticity (cont.) For the intrinsic plasticity model, we model For the intrinsic plasticity model, we model

our neuronal activation function as a our neuronal activation function as a sigmoid:sigmoid:

The “shift” component at a given time is The “shift” component at a given time is determined by the following equation:determined by the following equation:

(( is the shifting velocity) is the shifting velocity)

shiftaeO

251

1

1

11 ttt

shiftOshift

Simulation: Neural NetsSimulation: Neural Nets

To better understanding the relationship To better understanding the relationship between calcium dysregulation and between calcium dysregulation and cognitive loss, a computational cognitive loss, a computational simulation was performed:simulation was performed:

1.1. Consists of an artificial neural network Consists of an artificial neural network modeled using homeostatic neuronal modeled using homeostatic neuronal plasticityplasticity

2.2. The network has inputs that receive fixed The network has inputs that receive fixed patterns to be learnedpatterns to be learned

Simulation: Neural NetsSimulation: Neural Nets

3.3. The simulation goes on enough time for The simulation goes on enough time for the network to achieve equilibrium, the network to achieve equilibrium, learning the initial patternslearning the initial patterns

4.4. Next, the sigmoid shift velocity is set to Next, the sigmoid shift velocity is set to zero, simulating the starting point of the zero, simulating the starting point of the diseasedisease

5.5. Finally, the simulation continues on for Finally, the simulation continues on for some more time to measure the resultssome more time to measure the results

6.6. The simulation is run many times to The simulation is run many times to compare between each random netcompare between each random net

Simulation: SetupSimulation: Setup

The neural net is formed by 30 randomly The neural net is formed by 30 randomly connected neuronsin s sparse way, some of connected neuronsin s sparse way, some of them having inhibitory connectionsthem having inhibitory connections

5 of this neurons serve as inputs, receiving 5 5 of this neurons serve as inputs, receiving 5 sequential patterns at each epoch sequential patterns at each epoch

After 150 initial epochs, the sigmoid velocity(After 150 initial epochs, the sigmoid velocity() ) is set to zerois set to zero

After that point, the simulation continues for After that point, the simulation continues for another 150 epochsanother 150 epochs

The variation of the 30x30 weight matrix is The variation of the 30x30 weight matrix is measured after each epochmeasured after each epoch

Simulation: Results 1Simulation: Results 1

In aprox. 80% of the simulation runs, the synaptic In aprox. 80% of the simulation runs, the synaptic weights are seriously disrupted after the sigmoid stallweights are seriously disrupted after the sigmoid stall

This represents networks losing the capability to This represents networks losing the capability to recognize the input patterns that have been memorizedrecognize the input patterns that have been memorized

Simulation: Results 2Simulation: Results 2

Aprox. 25% of the random simulated networks exhibit Aprox. 25% of the random simulated networks exhibit an oscilatory burst-like behaviour, which is lost after the an oscilatory burst-like behaviour, which is lost after the sigmoid stallsigmoid stall

No bursting network keeps this behavior after the No bursting network keeps this behavior after the sigmoid stallsigmoid stall

Simulation: Results 3Simulation: Results 3

Around 20% of the random networks continue Around 20% of the random networks continue behaving as in the initial phase, even after the sigmoid behaving as in the initial phase, even after the sigmoid stallstall

This is consistent with the fact that a reduced number This is consistent with the fact that a reduced number of AD patients do not exhibit memory or learning of AD patients do not exhibit memory or learning impairmentsimpairments

ConclusionsConclusions

Calcium dysregulation might be the starting point of a Calcium dysregulation might be the starting point of a cascade of events leading to the lose of synaptic weight cascade of events leading to the lose of synaptic weight stability and the memories stored in synaptic weights, stability and the memories stored in synaptic weights, explaining memory deficits in Alzheimer’s diseaseexplaining memory deficits in Alzheimer’s disease

Although in some cases synaptic weights remain stable, in Although in some cases synaptic weights remain stable, in most of the cases they enter in a situation of instabilitymost of the cases they enter in a situation of instability

The results were also confirmed with networks of different The results were also confirmed with networks of different sizes with different architecture of connections and with sizes with different architecture of connections and with different input patternsdifferent input patterns

These results show that calcium dysregulation that is These results show that calcium dysregulation that is correlated to the impairment of intrinsic plasticity, leads to correlated to the impairment of intrinsic plasticity, leads to synaptic instability, which is consistent with cognitive deficits synaptic instability, which is consistent with cognitive deficits in ADin AD