Adjustments and testing for model integration

The stimulation patterns used in the CaMKII ST model are a tetanus of 100 pulses at low- frequency (1, 10 Hz) and high-frequency (100 Hz), respectively. The Ca2+ _{dynamics in the}

dendritic spine ([𝐶𝑎2+_]

𝑐𝑦𝑡𝑜) in response to a stimulation tetanus is governed by

[𝐶𝑎2+_] 𝑐𝑦𝑡𝑜 = [𝐶𝑎2+]𝑟𝑒𝑠𝑡+ 𝐴 ∑ exp (− 𝑖 𝑓𝜏) 𝑛 𝑖=1 (5.1) where [𝐶𝑎2+_]

𝑟𝑒𝑠𝑡 is the cytosolic Ca2+ concentration at the resting level, 𝐴 is the amplitude of Ca2+ _{concentration induced by one stimulation pulse, 𝜏 is the decay time constant, 𝑓 is the}

stimulation frequency and 𝑛 is the total number of the stimulation pulses (Zhabotinsky 2000). The intracellular Ca2+ _{dynamics in response to a 100-pulse tetanus at 100 Hz is in Figure 5.2}

A. The Ca2+ _{level increases with time during the stimulation until it reaches a maximum level}

of about 20 μΜ, and after the last pulse, it decreases exponentially back to the resting level exponentially (τ = 200 ms). We apply a high-frequency presynaptic stimulation (HFS; 100 pulses at 100 Hz) and a high-frequency presynaptic stimulation paired with postsynaptic

140 stimulation (pairing HFS; 100 pulses at 100 Hz) to our Ca2+ _{model, respectively, and the}

results of the Ca2+ _{dynamics are shown in Figure 5.2 B. We use a paired pre/postsynaptic}

stimulation protocol because experimental evidence showed that postsynaptic membrane depolarisation triggered by presynaptic stimulation alone was not sufficient to induce LTP (Pike, Meredith et al. 1999, Mansvelder and McGehee 2000). Paired stimulation at both the presynaptic and postsynaptic neurons are used to create pairing of the EPSP and the bAP, which leads to a large depolarisation and Ca2+ _{elevation by NMDAR in the postsynaptic spine}

head (Caporale and Dan 2008). When simulate the pairing HFS protocol, a 2 ms-delayed bAP is introduced after each presynaptic stimulus pulse (the fomula for bAP was introduced in Chapter 3).

The result produced by Eq. (5.1) did not show any desensitisation of NMDARs (Figure 5.2 A). This may be because of assumptions that NMDARs are not the major Ca2+ _{channels, or}

that NMDARs recover from desensitisation completely between two pulses. Both of these assumptions conflict with the setting of our model that NMDARs are the major Ca2+ _channels

in the spine head and the experimental observation that both NR2A-NMDAR and NR2B- NMDAR will be desensitised under high-frequency stimulation (Erreger, Dravid et al. 2005). The Ca2+ _{response of Ca}2+ _{model to HFS and pairing HFS reaches a peak level, decreases,}

then stays on a plateau at a lower level until the end of stimulation, which reflects the large desensitisation of synaptic NMDAR by high-frequency stimulation (Figure 5.2 B). Under the HFS, the elevation in [𝐶𝑎2+_]

𝑐𝑦𝑡𝑜 in much less than in the original Ca2+ reponse. In contrast, under the pairing HFS, although the peak level of [𝐶𝑎2+_]

𝑐𝑦𝑡𝑜 can be above 40 μM and is higher than in the maximum [𝐶𝑎2+_]

𝑐𝑦𝑡𝑜 fo the original Ca2+ response (around 20 μM), the plateau level (around 5 μM) is much lower than of the original response during the same stimulation time period.

We next compare the levels of the CaMKII-NMDAR complex in the original and our Ca2+

results. Before simulation, we have made several adjustments before connecting the Ca2+

model to the CamKII ST model. In the CaMKII ST model all proteins are in units of particle numbers (#). The time-dependent changes in the concentration of these proteins are calculated in particle numbers and all concentration-based rate constants are in #-1_s-1_{. Therefore, we}

convert the Ca4CaM concentration (in μΜ) from Ca2+ model into particle numbers (in #)

before calculating the translocation of CaMKII. The conversion is according to the following formula

141

𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 = 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 × 𝑁𝐴× 𝑉𝑜𝑙,

where N_A is the Avogadro constant (6.022140857×1023 _mol−1_{) and 𝑉𝑜𝑙 is the volume of the}

spine head (0.1fL).

The rate constants used in the CaMKII ST model are based on 37°C, therefore, we adjust them to 34°C using a Q10 of 2.15 (Chiba, Schneider et al. 2008) to be consistent with the

conditions in the previous chapters. The details of temperature correction on reaction rate constants are in Section 3.2.1. The simulation results of CaMKII ST model show a minor difference in the level of CaMKII-NMDAR complex formation at 34°C and 37°C (Figure 5.2 C).

Furthermore, we adjust the NR2B number in the CaMKII ST model from 20 to 8, which is the standard value based on our previous assumptions in Chapter 3. This decreases the level of the CaMKII-NMDAR complex by CaMKII ST model at t =300s by 1 (Figure 5.2 C). In contrast, the level of the CaMKII-NMDAR complex by our Ca2+ _{model in response to pairing}

HFS is about 0.7 (Figure 5.2 D) lower than in response to the original Ca2+ _{input (Figure 5.2}

C). The difference is because a larger fraction of NMDARs are desensitised during pairing HFS and this leads to fewer Ca2+ _{ions entering the spine than the original input in CaMKII}

ST. There is no CaMKII-NMDAR formation in response to presynaptic HFS alone, because fo the insufficient amount of Ca2+ _{ion entered into the cytosol.}

Moreover, we also use theta-burst stimulation (TBS) as an optional stimulation protocol in this chapter (See Appendix G.1 for the detail of TBS). In a train of TBS, pulses are grouped into several bursts, and the time duration (200 ms) between two bursts allows desensitised NMDARs to partially recover. TBS is considered to be a more physiologically relevant stimulus, which is close to the frequency of the endogenous hippocampal rhythm that triggers LTP (Lee, Barbarosie et al. 2000, Raymond 2007). One train of TBS consists of 10 stimulus bursts at 5 Hz (200 ms separation between bursts) and each burst consists of four pulses at 100 Hz. A 2 ms-delayed bAP is introduced into the model after each presynaptic stimulus pulse. Four trains of TBS are delivered at 0.1 Hz (10 s separation between trains), which is used to induce LTP experimentally (Lee, Barbarosie et al. 2000). The changes of Ca2+ _{level in}

the spine head by four trains of TBS and the corresponding production of CaMKII-NMDAR complex are shown in Figure 5.2 E and Figure 5.2 F, respectively. The level of the CaMKII- NMDAR complex shows a good agreement to that produced by the original Ca2+ _input

142

(A (B

(C) (D)

(E) (F)

Figure 5.2. Ca2+ _{elevation and CaMKII-NMDAR complex formation in the spine head in}

response to presynaptic stimulation. Ca2+ _{dynamics in the spine head in response to Ca}2+

by Eq. (5.1) (A), HFS and paring HFS (B) and 4 trains of TBS (E), respectively, and the coresponding CaMKII-NMDAR complex production (C, D and F).

143

5.2

Computational experiments

In this section, we mimic disturbances in the availability of synaptic NMDAR in AD to investigate the consequential effects on CaMKII ST and study the contribution of NMDARs with different subunit compositions in CaMKII ST. For each experiment, we run the model under 1 s of pairing HFS (100 pulses at 100 Hz) and 4 trains of paring TBS (4 TBS),

respectively. In both stimulation protocols, a 2 ms-delayed bAP is introduced into the model after each presynaptic stimulus pulse. All simulations are run for 300 s.

After each simulation, we collect the Ca2+ _{elevation in the spine head ([Ca}2+_{]spine) and 4 key}

outputs from the downstream events as following:

(1) Numbers of Ca4CaM complexes. This is a determining factor for CaMKII activation and,

subsequently, autophosphorylation.

(2) Numbers of autophosphorylated CaMKII subunits. Because once a CaMKII is

autophosphorylated, its activity is independent from CaM and it shows persistent activity after the removal of stimulation. This is critical for the induction and maintenance of LTP, which requires a much longer time course in comparison with the stimulation.

(3) Numbers of CaMKII in PSD. Because CaMKII needs to be translocated into the PSD to affect its target, AMPAR, and bind to NR2B-NMDAR, once a CaMKII enters into the PSD, its autophosphorylation is suggested to be irreversible (Mullasseril, Dosemeci et al. 2007). The level of translocated CaMKII can be an indicator of the potential ability to form CaMKII-NMDAR complexes.

(4) Numbers CaMKII-NMDAR complex in PSD at time t = 300 s. The persistent localisation of CaMKII in PSD is suggested to be a critical factor for LTP induction and maintenance, and NR2B may play a key role in the synaptic CaMKII maintenance and recruitment (Bayer, LeBel et al. 2006). Therefore, the level of CaMKII-NMDAR complex numbers is an important output that can provide insights into the induction and maintenance of NMDAR-LTP.