Fig 1.
One example each from different sAP shapes observed from a typical detrusor smooth muscle cell during an electrophysiological recording session.
The four key features—1) foot convexity, 2) after hyperpolarization (AHP) 3) afterdepolarization (ADP), and 4) slow AHP—which distinguish the shape differences are also indicated.
Fig 2.
Schematic figure depicting the hypothesis that the variations in AP shape is caused by an underlying sEJP [16].
Note that when the amplitude of the underlying sEJP is larger (left) the resultant AP has a taller foot, larger afterdepolarization and no afterhyperpolarization.
Fig 3.
A schematic diagram showing the attenuation of the AP foot convexity and after depolarization amplitude based on distance from the varicosity.
The smooth muscle cells, connected via the gap junctions allow the unattenuated active transmission of APs (shown in black trace). The underlying sEJP (shown in blue trace) is passive signal and is attenuated with distance. The reduced amplitude of the underlying sEJP over distance is visible in the foot and the ADP amplitude (indicated by the arrows) of the observed sAP. At a sufficiently large distance, the underlying sEJP disappears and the observed AP attains the shape of the native AP.
Fig 4.
Features and terminology used in the work indicated on a sample AP.
Fig 5.
One example each for AP signals displaying (left) slow afterhyperpolarization (sAHP) and (right) very slow afterhyperpolarization (vsAHP).
Note the difference in amplitudes and time spans of the hyperpolarization. The presence of slow AHP in an AP cannot be explained by the underlying-sEJP hypothesis, indicating the presence of more components.
Fig 6.
One example each for AP signals of Group 0 (G0, left) and Group 1 (G1, right) categories.
Note the absence of the slow AHP component (marked using * in right panel) in G0 AP, aiding our assumption that such APs consist of only two components—sEJPs and native APs.
Fig 7.
Amplification of the observed sEJP (solid lower trace, blue) to estimate the sEJP underlying AP. The amplification is determined by minimizing the distance measure. The amplified curves for equally weighted distance measure (solid upper trace, red) and the differentially weighted distance measure (solid middle trace, green) is also shown. The dotted line is the AP under consideration. The foot where the distance measurement was taken is shown in a box.
Fig 8.
The extraction of slow AHP signal from a typical G1 AP.
(a) The G1 AP from which the sAHP is to be extracted. The onset and end of first repolarization (EoFR) of the AP are marked. (b) The set of G0 APs which are peak aligned with G1 AP in (a) and matched against the Onset-EoFR window of G1 AP. The best matching AP is shown in a thicker trace. (c) The estimate of the sAHP component contained in the G1 AP obtained by subtracting the best matching G0 AP from the G1 AP.
Fig 9.
Schematic figure showing the synthesis of the AP using linear combination of the underlying components.
The signals named S, A, H1, and H2, represent the sEJP, nAP, sAHP, and vsAHP components respectively. nd is the time delay provided to the sEJP component relative to the other components. a, b, c, and d are the amplification factors assigned to each of the components. Y represents the output AP shape that is synthesized. n1 and n2 represent the time instants at which the onset and peak of the output AP occurs. In all practical cases, the condition nd ∈ [n1, n2] holds true.
Fig 10.
Overlapped plots of matching APs for two APs belonging to different classes.
It can be observed that the variations in the matching APs given in the left panel is higher as compared to those in right. This difference is expressed in the root mean square error (RMSE) values given in the legend.
Table 1.
The pooled summary of different types of signals available in the cell recordings used in the study.
Table 2.
The comparison of standard features of signals observed from the training and test sets.
The sAP (Type A only) amplitudes exhibit smaller amplitudes in the test set compared to the training set (p < 0.01—marked ‘**’ in the table), the reason for which is explained in the text. Rest of the parameters have comparable values for training and test sets (p > 0.05). The parameter values are given as mean ± SD. Number of signals used in Training set: 2487 sEJPs and 1013 sAPs; in Test set: 477 sEJPs and 453 sAPs.
Fig 11.
Top: Overlaid plots of cell wise sEJP (a) and nAP (b) templates obtained from the shortlisted sEJP-AP pairs belonging to individual cells. Only the cells with more than 4 shortlisted sEJP-AP pairs are shown. Bottom: The sEJP (c) and nAP (d) templates derived from all the sEJP-AP pairs shortlisted from the training set.
Fig 12.
The sAHP (left) and vsAHP (right) templates derived from all the shortlisted AP-AP pairs observed from the training set.
Fig 13.
The examples of good replications of the experimentally obtained intracellular sAPs obtained using the proposed 4-component model.
The traces in blue are the recorded signals, and the green traces are the synthesized signals. Only the sAPS belonging to the Test set are shown.
Table 3.
The replication efficiencies obtained for different data sets used in the study.
Fig 14.
An example instance where the amplitudes of the sAHP of an sAP signal is comparable to that of the vsAHP component of another sAP.
Both sAPs are recorded from the same cell. This indicates that the vsAHP component is not merely a prolonged version of the sAHP component.
Fig 15.
Overlaid plots of a typical Type B sAP (solid line) and the native AP template obtained from the Type A sAP decomposition (dashed line).
The amplitudes are normalized and the peaks aligned at time = 0 ms. Note the slow ramp component which is a signature component of Type B sAP.