KCNQ Kinetic Model
A kinetic model for PIP2 regulation of M/Kv7 channel activity.
Introducing the M-current.
M-type potassium channels (‘M-channels') are subthreshold voltage-gated potassium channels that exert a profound effect on the activity and excitability of neurons throughout the central and peripheral nervous system. The channels are inhibited by several transmitters via receptors that couple to G proteins of the Gq family; this causes membrane depolarization and a dramatic increase in excitability, and contributes to the global effects of (e.g.) acetylcholine and glutamate on brain function. Inhibition is due to hydrolysis of the membrane phospholipid phosphatidylinositol-4'5'-bisphosphate (‘PIP2' ). In some cases channel closure results from a fall in membrane PIP2 (because the channels require PIP2 to open), in other cases through downstream consequences of PIP2 hydrolysis such as increased intracellular calcium or activation of protein kinase C (PKC), either separately or in combination.
Fig.1 . M-channels are composed of four subunits of the Kv7 family of potassium channel proteins ( KCNQ gene
family), principally Kv7.2 and Kv7.3. In arriving at a model that
provides an accurate description of PIP2 regulation of M/Kv7 channel
activity we have focussed on the tetrameric subunit stoichiometry of
potassium channels and assumed that each subunit contributes one PIP2
binding site. For simplicity, the current model is organized without
cooperativity between subunits whether the channel is a homomeric Kv7.2
or Kv7.3, or heteromeric Kv7.2/Kv7.3. On the right is shown a kinetic
scheme for PIP2 activation of Kv7.2/7.3 (M) channels. P=PIP2 ; Q2, Q3 =
KCNQ2 and KCNQ3 (Kv7.2, 7.3) subunits; k, α, β are rate constants.
For a partial update to this model see Telezhkin et al., 2012 (J.Gen.Physiol.,
140, 41-53), at http://jgp.rupress.org/content/140/1/41.full.pdf+html?with-ds=yes
Table 1: Constants for the model in Fig. 1.
Values derived from this model for open and shut time distributions (with component % area), burst-length, maximum Popen and EC50 values for PIP2 are give in Table 2 , together with predicted effects of varying [PIP2] or of altering PIP2 affinity. Relevant reported values for native ganglionic M-channels and expressed Kv7 channels are listed in Table 3.
Table 3: Values for M/Kv7 channel properties.
Predictions from the model.
The model simulations accord with reported M-channel behaviour in many respects, detailed here. In summary:
(1). Open-shut distributions. The model yields 2 distinguishable open time and 3 distinguishable shut time components (Fig. 2) in the steady-state channel open and shut time distributions in agreement with M-channel data from superior cervical ganglion sympathetic neurons and expressed Kv7.2/7.3 channels.
(2). PIP2 activation. Predicted EC50 values for PIP2 -activated open probabilities are 218 μM, 2.64 μM and 44 μM for Kv7.2, 7.3 and 7.2/7.3 respectively, in accordance with experimental values reported for activation of expressed channels by the water-soluble PIP2 analogue diC8-PIP2.
(3). [PIP2 ] and Popen. At saturating PIP2 levels both homomeric and heteromeric channels are predicted to achieve Popen near unity. However, under normal (cell-attached) conditions native M-channels show relatively-low maximum Popen values (between 0.1 and 0.2). This can be replicated in the model by setting [PIP2] at ~21 μM.
(4). Reducing [PIP2 ] . A 75% inhibition of channel activity is obtained by reducing [PIP2 ] from 21 μM to 10 μM. The principal effect is to lengthen the longest shut-time by ~3-fold; open times are unchanged, but the proportion of short openings (presumably reflecting the partially- liganded states) increases, giving an overall shortening of mean open time ( Fig. 2C ). These effects are very different from those associated with voltage-induced changes in Popen, which result from changes in both open and shut times.
(5). Burst length. Our model further predicts that changing [PIP2 ] should also change the burst-length ( Fig. 2D ). This should be reflected in the M-current deactivation kinetics.
(6). Changing PIP2 affinity. Finally our model predicts that the effects of producing an equivalent (~75%) reduction in Popen by reducing PIP2 affinity (by~half, from 44 to 91 μM ) reducing [PIP2] should have a similar effect on channel kinetics (Fig. 2).
Concentration-dependence of PIP2 activation of M-channels.
To investigate the concentration-dependence of M-channel activation by PIP2, the water soluble analogue DiC8-PIP2, is applied in increasing concentrations to the inside face of membrane patches from isolated from CHO cells stably-transfected with Kv7.2/7.3 channels (Fig.3). The results of these experiments show the expected low affinity component of the Popen curve (previously documented for heterologously expressed Kv7.2/7.3 channels) that is comfortably described by the M-channel model illustrated in Fig.1 (Table 1). In addition, a small high-affinity component is evident that requires further evolution of our model to be described. These experiments allow the dependence of channel open probability on [PIP2] to be investigated and identification of membrane patches containing a single channel which can be used for further detailed analysis and model fitting.
Fitting the model to single channel data.
Single channel patch-clamp recordings of Kv7.2/7.3 channel activity are used to estimate the rate constants for PIP2 binding to each channel subunit and the rates of channel opening and closing. The observed sequence of measured open and closed times recorded from each patch using the methods developed by Colquhoun & Hawkes and the software HJCFIT. We start from the concept that, at constant voltage, M-channels behave as multi-subunit ligand-gated ion channels, with PIP2 as the ligand. M-channels appear unable to open in the absence of PIP2, but the number of bound PIP2 molecules needed to cause efficient channel opening is uncertain (though probably >1 given the steepness of their [PIP2] dependence, Fig. 3). The model in Fig.1 generates maximum channel opening when all four subunits have a PIP2 molecule bound and using concentrations of diC8-PIP2 in the mid range of the Popen curve allows definition of the rates for both PIP binding and channel opening and closing. The approach is of value in order to understand how M-channels respond to changes in [PIP2] in the membrane and may give new insights into the significance of the heteromeric structure of neuronal Kv7.2/7.3 channels.
How well the model with fitted rate constants describes the data can be visualised from the distributions of open and closed times (Fig. 4) showing, superimposed, the shape of the distribution predicted for the fitted rate constants when allowance is made for the limited resolution of the recording.