Biophysical basis of alpha rhythm disruption in Alzheimer’s disease

Alpha is one of the most prominent rhythms (7.5–12.5 Hz) detected in electroencephalography (EEG) during wakeful relaxation with closed eyes. In response to elevated ambient acetylcholine levels, a subclass of thalamic pacemaker cells generate alpha. This rhythm is intrinsic to the cell and is robustly orchestrated by an interplay of hyperpolarization activated cyclic nucleotide gated channels(HCN) and calcium-ion channels. It has been shown that decreased expression of HCN channels is correlated to Alzheimer's Diseased (AD). In early stages of AD, alpha is known to be down-regulated and lowered in coherence. We use this well characterized and quantified rhythm to understand the changes in ion channel properties that lead to disruption of alpha as seen in AD in a biophysically detailed network model of the thalamo-cortical circuit that generates the alpha-rhythm. Our computational model allows us to explore the causal links between alpha rhythms, HCN channels and amyloid-beta aggregation. The most commonly used drugs(acetylcholinesterase inhibitors) in AD increase the duration and level of acetylcholine and provide temporary symptomatic relief in some cases. Our simulations show how increasing acetylcholine can provide rescue for a small range of aberrant HCN expression. We hypothesize that reduced alpha rhythm frequency and coherence is a result of down-regulated HCN expression, rather then compromised cholinergic modulation(as is currently thought). The model predicts that lowering of the alpha-rhythm can modify the network activity in the thalamo-cortical circuit and lead to an increase in the inhibitory drive to the thalamus.

The high-threshold calcium current gets activated around the 90ms mark(dotted line) D) Zoomed in to the the first 10 ms after of activation I T HT . Burst of action potentials are generated driven by membrane depolarization initiated by I H and I T HT in that order. E) The high-threshold calcium current provides the depolarizing impetus that sustains a burst of action potentials . F) The slow decay of the gating variables of the I H as the membrane potential rises above the activation voltage. The gating variables of I T HT slowly deactivate at the high voltages during action potentials.

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Details of ionic currents associated with the neuron, synapses and the 124 network connections in the thalamo-cortical circuit that generates the 125 alpha-rhythm. 126 The model consists of the canonical point-neuron network model of the library written in C++ https://github.com/insilico-lib/insilico to do the simulations.

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The time step of each simulation was taken to be 0.01ms.

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Neurons 136 Thalamo-reticular(RE) neurons Potassium Current : here: where: The m ∞ , τ m , h ∞ and τ h have equations identical to the n ∞ and the τ n of the 143 potassium gate n.

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where: g N a = 100 mS/cm 2 and E N a = 50 mV 146 Calcium Current : where: The first term must be positive, otherwise it is set to zero. g Ca = 2.3mS/cm 2 and the 149 reversal potential for calcium is calculated using the Nernst Equation where: 152 g L = 0.01mS/cm 2 , E L = −73, g KL = 0.07 − 0.08 mS/cm 2 and E KL = −100mV Applied Current :

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The applied current is a train of poisson-distributed excitatory and inhibitory impulses.

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The details of the same will be discussed later.

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Thalamo-cortical(TC) neurons where: 5.0 The first term must be positive, otherwise it is set to zero. 165 g Ca = 2mS/cm 2 , V t = V + 2 and the reversal potential for calcium is calculated using 166 the Nernst Equation

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Leak Current : H-Current : The applied current is a train of poisson-distributed excitatory and inhibitory impulses.

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The details of the same will be discussed later. where: 3.0 The first term must be positive, otherwise it is set to zero. where: H-Current : where: [T] is the transmitter concentration. When a pre-synaptic cell experiences and action [T] is the neuro-transmitter concentration. When a pre-synaptic cell sees an action [T] is the neuro-transmitter concentration. When a pre-synaptic cell sees an action The difference between the impulse times, T 1 , T 2 .....T n is an exponentially distributed 222 random variable with a mean of 10ms for RE cells, which have g s = 0.02mS/cm 2 for 223 EPSPs and g s = 0.015mS/cm 2 for IPSPs. For TC neurons the mean is also 10ms for 224 EPSPs with g s = 1.0mS/cm 2 , but they are not given any IPSPs.

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The HTC cells receive a gaussian distributed white noise through the stochastic 226 Euler-Maruyama integrator: where ξ(t) is drawn from a Gaussian distribution with mean 0 and variance 0.
Before performing the Fourier transformation, we do some basic processing over the 231 LFP trace. We take a simple moving average over a window of 10ms(we use an 232 observation frequency of 2.5kHz) and make it's mean zero.  The lowered coherence of alpha as a result of lower g H can be rescued by increasing acetylcholine levels (78% g H expression needs 20% increase in acetylcholine(III). There appears to be a threshold of ambient acetylcholine levels beyond which entropy(filled diamonds) increases dramatically, suggesting loss in periodicity. The overall entropy also remains high for decreased g H . (B)When I H expression is compromised severely (50% green open circles) lowered frequency of alpha is not rescued by increasing acetylcholine levels. 50% g H expression can only achieve periodicity 9 Hz before complete breakdown of regular firing. This is seen as a sudden rise in entropy (closed red diamonds). (C)Power Spectra corresponding to I, II and III from (A) and IV from (B). can only achieve periodicity 9 Hz before complete breakdown of regular firing. This is 307 seen as a sudden rise in entropy (closed red diamonds).

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Lowering g H can lead to an enhanced GABA activity 310 Several studies have characterized compromised alpha in AD [20]. to dysregulation in the calcium signaling within the cell [23]. We simulate the pathology 337 by changing the high-threshold calcium conductance in the cell (crucial for alpha).  and Tau fibrils, a characteristic feature of AD [24]. While amyloid-beta and tau-fibrils 368 disrupt a wide array of signaling pathways in the brain, that include cell death, we do inhibitors [25,26]. EEG tools that are used to diagnose AD, report a reduction in power  non-AD subjects [17]. Using these observations, the relationships described in the Potential causality between amyloid-beta plaques (Aβ), HCN channels(g H ) and the alpha-rhythm(α). I)HCN expression directly effects the alpha-rhythm: elimination of the possibilities where this is not the case. II): Appearance of beta-amyloid plaques and lowered expression of HCN channels are strongly correlated and therefore not independent pathologies. It has been established that HCN channels activity effects amyloid-beta: elimination of box II possibilities [17]. III) Three remaining possibilities in the causal relationships time has a substantial barrier to cross to reach the threshold. This allows for a robust 450 10 Hz burst to be precisely orchestrated, that is predominantly unaffected by noise.

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Alpha-rhythm relation to overall firing rates and extracellular GABA:

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A recent AD study reports abnormally high levels of the neurotransmitter GABA in the 453 extracellular space [22] implicating enhanced GABAergic drive in the pathology. In  Wellcome DBT India Alliance.