Local signaling with molecular diffusion as a decoder of Ca2|[plus]| signals in synaptic plasticity

doi:doi:10.1038/msb4100035

Subject Categories: Simulation and data analysis | Neuroscience

Molecular Systems Biology 1 Article number: 2005.0027 doi:10.1038/msb4100035
Published online: 13 December 2005
Citation: Molecular Systems Biology 1:2005.0027

Local signaling with molecular diffusion as a decoder of Ca²⁺ signals in synaptic plasticity

Honda Naoki¹, Yuichi Sakumura¹ & Shin Ishii¹

Graduate School of Information Science, Nara Institute of Science and Technology, Takayama, Ikoma, Nara, Japan

Correspondence to: Shin Ishii¹ Graduate School of Information Science, Nara Institute of Science and Technology, 8916-5 Takayama, Ikoma, Nara 630-0192, Japan. Tel.: +81 743 72 5984; Fax: +81 743 72 5989; E-mail: Email: ishii@is.naist.jp

Received 17 May 2005; Accepted 25 October 2005; Published online 13 December 2005

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Article highlights

Calmodulin (CaM) activation in the vicinity of Ca2+ influxes relates inversely to the diffusion coefficient of CaM itself
Calmodulin diffusing within the local area, the "local CaM diffusion system", works as a dual decoder of both the frequency and shape of input Ca2+ current pulses.
Dual decoding by the local CaM diffusion system is underlies the frequency-dependent and receptor-specific regulation of synaptic plasticity.

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Synopsis

Calcium ions (Ca²⁺) play fundamental roles in various neural processes, such as synaptic plasticity and vesicle releases at presynaptic terminals. In dendritic spines and dendrites, the spatiotemporal regulation of Ca²⁺ signaling ranges from local (<1 m) to global (>100 m). Thus, elucidating the differences between local and global Ca²⁺ signaling is important for understanding the spatial regulation of signal transduction pathways.

It is thought that the frequency of synaptic inputs, and hence the frequency of Ca²⁺ influxes through NMDA receptors, dictates the direction and the strength of synaptic plasticity (Dudek and Bear, 1992; Markram et al, 1997; Johnston et al, 2003). Recent studies, however, reported that the direction of synaptic plasticity is also governed by NMDAR subtypes (NR2A- and NR2B-containing NMDARs), implying a 'receptor-specific regulation' of synaptic plasticity (Liu et al, 2004a; Massey et al, 2004). How the frequency-dependent and receptor-specific regulation of synaptic plasticity is realized simultaneously has yet to be clarified.

With respect to global Ca²⁺ signaling within an entire dendritic spine, there is a potential problem with receptor-specific regulation. Because Ca²⁺ diffusion is very rapid and the volume of dendritic spines is relatively small (<1 m³), the Ca²⁺ concentration should, in effect, become instantaneously uniform within a spine. If so, downstream signals originating from different Ca²⁺ sources are likely to become entangled. This problem could be avoided if the downstream signals work specifically in the so-called Ca²⁺ nano-domain, a local elevation of Ca²⁺ levels localized near Ca²⁺ channels (Augustine et al, 2003). Local Ca²⁺ signaling has been observed in some experimental studies, and has been associated with changes in synaptic weight (Hoffman et al, 2002; Yasuda et al, 2003).

In this article, we focus on the functions of local Ca²⁺ signaling. In local signaling, the effects of constrained molecular diffusion due to the abundance of actin filaments and PSD-95 (a scaffolding protein) under synaptic membranes (Kennedy, 2000; Matus, 2000) must be taken into account. Suppression of molecular diffusion has indeed been observed in vivo (Popov and Poo, 1992; Luby-Phelps et al, 1995). This impedance may underlie the local molecular regulation of synaptic plasticity.

To examine the functional contributions of local reactions in the Ca²⁺ nano-domain and the impeded diffusion of a Ca²⁺ sensor molecule (calmodulin; CaM) to the regulation of synaptic plasticity, we constructed a mathematical model of spatial Ca²⁺ signaling in a dendritic spine (Figure 1). The model includes Ca²⁺ influx through NMDARs, Ca²⁺ uptake by pumps, leakage through the membrane, and buffering by Ca²⁺-binding proteins. Because CaM is a primary transducer that mediates Ca²⁺-regulated induction of synaptic plasticity (Xia and Storm, 2005), we focused on local CaM activation near NMDARs.

Figure 1

A scheme of a model spine and a local Ca²⁺ profile. (A) The model spine is composed of hemispherical elements and has a volume of 1 m³. Ca²⁺ ions were injected through NMDARs as a point source located at the center of the spine (red arrow). Diffusing molecules were assumed to diffuse radially from the NMDARs. Ca²⁺ influx, Ca²⁺ uptake by pumps, leakage from the membrane, and buffering by Ca²⁺-binding proteins were all incorporated into the model. To compare local and global signaling, we focused on the concentrations of Ca²⁺ and CaM in the local and global areas as indicators of the degree of signaling activity at the PSD and in the whole spine, respectively. (B) The spatiotemporal Ca²⁺ profile when a sequence of 10 Ca²⁺ influxes was injected at 50 Hz (upper panel) into the model. Each injected current was biologically realistic (amplitude=9 pA, Ca²⁺ fraction=11%, period=10 ms) (Pina-Crespo and Gibb, 2002; Nimchinsky et al, 2004). The horizontal axis denotes the elapsed time from the onset of current injection, and the vertical axis denotes the distance from the site of the NMDARs (lower panel).

Full figure and legend (81K)Figures & Tables index

Using our spatial signaling model, we found that local CaM activation relates inversely to the diffusion coefficient of CaM, suggesting that CaM must diffuse at a moderate rate, as has been observed in vivo (Luby-Phelps et al, 1995), to be activated and controlled in the local space. Thus, the activation of local Ca²⁺ signaling is significantly dependent on molecular diffusion. Signal transduction may therefore be regulated by the local structure of the cytoskeleton, which will affect molecular diffusion. We also found that, as long as CaM can diffuse, local Ca²⁺ signaling was able to decode different features of synaptic inputs (Figure 5): the frequency of Ca²⁺ influxes and the shapes of postsynaptic currents generated by two distinct NMDA receptor subtypes (Erreger et al, 2005). Moderate CaM diffusion enables local Ca²⁺ signaling to be a 'dual decoder' to translate these features into the degree of CaM activity. This 'local CaM diffusion system' not only reproduces both the frequency-dependent (Markram et al, 1997; Johnston et al, 2003) and NMDAR subtype-specific (Liu et al, 2004a; Massey et al, 2004) regulations of synaptic plasticity, but also explains the developmental shift from long-term depression to long-term potentiation (Puyal et al, 2003) and meta-plasticity (Fujii et al, 1991; O'Dell and Kandel, 1994; Mockett et al, 2002).

Figure 5

The ability of Ca²⁺ and CaM to decode the frequency and the influx rate of Ca²⁺ influxes. (A, B) Decoding by Ca²⁺ (A) and CaM (B) of the frequency of Ca²⁺ influxes. (C, D) Decoding by Ca²⁺ (C) and CaM (D) of the influx rate of the Ca²⁺ influxes. The horizontal axis denotes the amplitude of the rectangular current. The influx rate is characterized as the current amplitude. The duration of the current varied inversely with the amplitude of the current to keep the total quantity of Ca²⁺ ions. (A, C) Peak plots of the Ca²⁺ concentration in the local area (left panel) and in the global area (>350 nm from the NMDARs) (right panel). (B, D) Peak plots of the CaM-4Ca²⁺ concentration in the local area for the nondiffusible CaM model (left panel) and the diffusible CaM model using the CaM diffusion coefficient observed in vivo (Luby-Phelps et al, 1995) (right panel). Red lines indicate the cases in which the affinity dependence of CaM for Ca²⁺ on CaM effector proteins was considered, as shown in (F). (E) A summary of the decoding abilities of Ca²⁺ and CaM. If the peak response correlated linearly with the frequency or the influx rate, decoding is regarded as success (an open circle), otherwise, as failure (a filled circle). Correspondence to subfigures is also shown; for example, 'A, left' means this decoding success can be observed in the left panel of subfigure (A). (F) Dose–response curve of CaM for Ca²⁺. This curve is derived from kinetic parameters of CaM using CaM4Ca=CaM_totalK₁K₂K₃K₄ Ca⁴/(1+K₁ Ca¹+K₁K₂ Ca²+K₁K₂K₃ Ca³+K₁K₂K₃K₄ Ca⁴), K_i=K_{f_i}/K_{b_i} (i=1–4). Black and red lines indicate the cases without and with the kinetic parameter values of backward reaction in the third and fourth binding of Ca²⁺ being one-tenth; the red-colored condition represents the increase in the affinity of CaM for Ca²⁺ due to the interaction with CaM effector proteins.

Full figure and legend (166K)Figures & Tables index

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Acknowledgements

We thank Dai Keyakidani for valuable discussion. This work was supported by the 21st Century COE Program and Special Coordination Funds Promoting Science and Technology both from the MEXT (Ministry of Education, Culture, Sports, Science, and Technology), Japan.

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Synopsis