Estimation of self-sustained activity produced by persistent inward currents using firing rate profiles of multiple motor units in humans

Abstract

Persistent inward calcium and sodium currents (I_P) activated during motoneuron recruitment help synaptic inputs maintain self-sustained firing until derecruitment. Here, we estimate the contribution of the I_P to self-sustained firing in human motoneurons of varying recruitment threshold by measuring the difference in synaptic input needed to maintain minimal firing once the I_P is fully activated compared with the larger synaptic input required to initiate firing before full I_P activation. Synaptic input to ≈20 dorsiflexor motoneurons simultaneously recorded during ramp contractions was estimated from firing profiles of motor units decomposed from high-density surface electromyography (EMG). To avoid errors introduced when using high-threshold units firing in their nonlinear range, we developed methods where the lowest threshold units firing linearly with force were used to construct a composite (control) unit firing rate profile to estimate synaptic input to higher threshold (test) units. The difference in the composite firing rate (synaptic input) at the time of test unit recruitment and derecruitment (ΔF = F_recruit - F_derecruit) was used to measure I_P amplitude that sustained firing. Test units with recruitment thresholds 1-30% of maximum had similar ΔF values, which likely included both slow and fast motor units activated by small and large motoneurons, respectively. This suggests that the portion of the I_P that sustains firing is similar across a wide range of motoneuron sizes.NEW & NOTEWORTHY A new method of estimating synaptic drive to multiple, simultaneously recorded motor units provides evidence that the portion of the depolarizing drive from persistent inward currents that contributes to self-sustained firing is similar across motoneurons of different sizes.

Keywords: high-density surface EMG; motoneurons; persistent inward currents; recruitment threshold; tibialis anterior.

Fig. 1.

Synaptic and intracellular persistent inward calcium and sodium current (I_P) activation and self-sustained firing. A: synaptic activation of cat soleus motoneuron by sinusoidal muscle stretch. Ai–Aiii: firing response of the motoneuron to muscle stretch (synaptic input) when spiking was slightly impeded (−1 nA; Ai), not altered (0 nA; Aii), or aided (+1 nA; Aiii) with steady somatic current injection that does not much alter the distal dendritic I_P, as detailed and modified from Bennett et al. (1998b). Self-sustained firing (pink shading) increased as more of the I_P was activated above the firing threshold (Aiii). Aiv: membrane potential response to stretch during hyperpolarization to estimate the synaptic input (gray trace) and membrane potential at rest to estimate the contribution of the I_P (green trace), which here is a plateau potential because spikes are blocked with QX-314 (different cell from in Ai–Aiii, smoothed). Av: membrane potential response to stretch during hyperpolarization to estimate the synaptic input in the same cell as in Ai–Aiii (black trace) and with trace from iv overlaid (gray). Avi: firing response of motoneuron where I_P is activated before recruitment due to prior activation (warm-up). Avii: firing response of tonically firing motoneuron with tonic I_P activation. Firing response is proportional to synaptic stretch input profile (gray trace). Dashed vertical line in Aiv–Avi marks the end of synaptic stretch input. Bi, top trace: membrane potential (V_m) of low-threshold motoneuron during spiking in response to triangular injected current (black trace). I_P activation is marked by small acceleration in potential just before onset of firing. Bottom trace, firing duration marked by purple box where firing starts at higher current and stops at lower current (blue circles; the difference is ΔI). Firing starts after majority of I_P (green trace with depolarizing inward current depicted in downward direction) is activated, producing a small ΔI (length of black arrow). Bii and Biii: likely firing responses of 2 other hypothetical motoneurons (same as in Bi) but with more of the I_P activated during firing (spike threshold lower relative to I_P onset) to produce a larger ΔI. Biv: voltage-clamp command (black trace) and resulting I_P without (green trace) and with (gray trace) sag in I_P, estimated for motoneuron in Bi. [Modified from Li et al. (2004)]. Dashed line indicates turnaround point of current and start of I_P sag. Bv: firing-current response to triangular current injection displaying primary (black), secondary (pink; during I_P activation), and tertiary (green; after I_P activation) firing ranges. [Modified from Li et al. (2004).]

Fig. 2.

Parameters measured from the motor unit firing rate profile. A, top trace: torque profile for a 20% maximum voluntary contraction (MVC) showing recruitment threshold of the motor unit. Second trace, corrected firing rate profile (blue dots) of decomposed motor unit (see below for details) and straight line fit to the secondary (pink) and tertiary (green) firing range. Time of peak firing rate is marked by vertical dashed line and denotes start of lower offset (sag) in firing rate during the descending phase of the contraction. Third trace, uncorrected firing rate profile. The 5th-order polynomial line fit to the firing rate profile is marked with a green line where the coefficient of determination (R²) of the fit was measured. Straight-line fit to the data points on the entire ascending and descending portion of the polynomial line is marked with a dashed pink line from which the ascending (Asc) and descending (Dsc) slope values were measured, respectively. Black downward arrows mark the start and end firing rates measured from the polynomial line. Modulation depth (MoD) is the maximum rate minus the minimum rate measured from the polynomial line. Bottom trace, the train of pulse amplitudes (blue lines) from the decomposition algorithm (marking firing times of the decomposed motor unit) with an accuracy (silouette, SIL) value of 0.94. Red circles mark pulses selected by the blind source algorithm, and black circles mark pulses that were not selected, producing abnormally low firing rate values marked by small black arrows in the firing rate profile of the third trace. Dashed blue arrows point to the reestimated pulses (dotted red circles) following recomputation of the pulse train to include the missed pulses. The resulting corrected firing rate profile after the recalculation/reestimation is plotted in the second trace. Data are from participant 4M. B–D: average number of motor units decomposed from high-density surface electromyography (HDsEMG) per contraction (B), accuracy (silhouette) values (C), and coefficient of determination (R²) of the polynomial line fit to frequency profile (D). Values are averages of the mean values from each of the 7 participants at the 10%, 20%, and 30% MVC trials. Error whiskers are +1 SD. Individual data in Supplemental Table S1.

Fig. 3.

Firing profiles of multiple motor units and self-sustained firing (∆F) calculation. A: firing rate profiles of 19 decomposed motor units during a 22% maximum voluntary contraction (MVC) in participant 1F in ascending order of recruitment threshold over 2 columns (same torque trace over each column). Dashed vertical line marks peak discharge rates at turnaround of torque. Pink and green lines mark secondary and tertiary range firing in units 1 and 10, respectively. Lower green line marks sag during descending phase. Short horizontal colored lines mark 0-Hz baseline for each rate profile. B: overlay of polynomial lines from the 19 motor units in A (participant 1F) using the same color coding (left) and similar polynomial lines from participant 5M during a 30% MVC contraction (right). C: paired unit analysis for units 1 (U1; control) and 2 (U2; test) from A with ∆F of 1.1 Hz (left) and for U1 (control) vs. U9 (test) producing ∆F of 3.7 Hz (right). Dashed vertical lines mark recruitment and derecruitment of test units. D: same as in C but for test U17 paired with control U13 (left) and with control U6 (right) producing ∆F values of −0.3 Hz and 5.3 Hz, respectively. E: ∆F values for each test unit in A, using same rainbow color code, plotted against recruitment threshold. Number of control units paired with each test unit increases with recruitment order to produce progressively larger number of ∆F values. Test units in C and D (U2, U9, and U17) are marked in plot.

Fig. 4.

Ascending (Asc) and descending (Dsc) rate slopes and start, end, and maximum rates. A: group average across all 7 participants for ascending (i) and descending (ii) slope of polynomial line fit through the firing rate profile at all contraction strengths.*P < 0.05 between ascending and descending slope at each contraction level. B: group average of start, end, and maximum (max) rates for each contraction level taken from the fit polynomial line. *P < 0.01 between start and end rates. C, left: slope of the ascending firing rate of a motor unit plotted against its recruitment threshold from all test units for the 6 contractions at the 10%, 20%, and 30% maximum voluntary contraction (MVC) contraction strengths. Red line is the straight-line fit to the data. Right, group average of slope of straight-line fit through the ascending slope vs. recruitment threshold data. D, left: same as in C but for data during the descending phase of the contraction. Average slope values in C and D (right) are all greater than 0 (all P < 0.001) but not different from each other (P > 0.05). Data in C and D (left) are from participant 7F, who on some trials overshot the 20% MVC target by 5%. Error whiskers are +1 SD. Individual participant data in Supplemental Table S1.

Fig. 5.

Self-sustained firing (ΔF) from pairwise and composite control methods. A: ∆F values obtained from the pairwise method plotted against ∆T recruitment times (time difference between when control unit was recruited and time when test unit was recruited) for 10%, 20%, and 30% maximum voluntary contraction (MVC) trials from participant 1F. Red line indicates best fit from exponential rise to maximum. Number of ∆F values (n) indicated in bottom right of each graph. B: same as in A but for ∆F values measured from composite control method. Best-fit straight line in red. C: ΔF values for pairwise (Pair) and composite control (Comp) methods for 10%, 20%, and 30% MVC trials in A and B, respectively. Mean is represented by the red line (which covers the black median line), the 25th and 75th percentiles by the box bounds, and the 95th and 5th percentiles by whiskers. Open circles represent outliers. D: comparison of mean ∆F values across the 7 participants for the pairwise (black bars) and composite control (red bars) methods and composite control without ∆F values from test units having short ascending activation (SA) times (see Fig. 8 for details on SA units). E: coefficient of variation (CoV) for the different mean ∆F values as in D. Error whiskers are +1 SD. *P < 0.005. Individual participant data in Supplemental Table S2.

Fig. 6.

Composite control motor unit profile. A: overlay of firing frequency profiles of unit 1 (pink circles), unit 2 (blue-green circles), and unit 3 (light blue circles) from Fig. 3A. Slope of secondary and tertiary range firing is marked by pink and green lines, respectively. B: same plot as in A but with the frequency points in the secondary range removed. A new 5th-order polynomial line was fit to the edited profile (red line). Removing the frequency points in the secondary range made the slope of the ascending frequency profile (0.74) similar to the slope of the descending frequency profile (−0.72). Slope values were measured from a straight-line fit to the polynomial line. C and D: paired unit analysis using test units U17 and U4 from Fig. 3 paired against the composite control unit profile (Comp). E–H: mean ratio of the ascending and descending firing rate slope for the composite control unit profiles (E), mean R² value of the control rate-test rate plots (F), mean number of motor units in the composite control unit profiles (G), and mean number of total unit pairs across the six contractions in the self-sustained firing (ΔF) analysis (H). Values are averages of mean values from each of the 7 participants for the 10%, 20%, and 30% maximum voluntary contraction (MVC) trials. In F and H, data are displayed for the pairwise (black bars), composite control (red), and composite control without SA test units (green). Error whiskers are+1 SD. Individual participant data in Supplementary Tables S2 and S3.

Fig. 7.

Self-sustained firing (ΔF) and control unit modulation for pairwise and composite control unit methods. Ai: ΔF values of all 6 contractions plotted against control unit modulation (CMod) for the pairwise ΔF method in participant 5M at the 10%, 20%, and 30% maximum voluntary contraction (MVC) trials. Black line marks the line of unity where ΔF = CMod values. Pearson’s product correlation coefficient (r) and the significance of the correlation are indicated at top left of each graph for the ΔF and CMod relationship. Red line denotes straight-line fit to the data. Aii: same as in Ai but for ΔF measured with the composite control unit method. B: maximum firing rate of the composite control unit profile (CMax_comp) measured from the polynomial line at the 10%, 20%, and 30% MVC trials for participant 5M. Median and mean are represented by black and red lines, the 25th and 75th percentiles by the box bounds, and the 95th and 5th percentiles by whiskers. C: same as in B but for the firing rate of the composite control motor unit when the test motor unit was recruited (C_compRT). D: group data for the composite control unit method, including composite control unit modulation depth (CMod; black bars), ΔF values (red bars), maximum rate of the composite control unit profile (CMax; dark green bars), and composite control unit rate when the test unit was recruited (C_RT; light green bars), averaged across the 7 participants for the 10%, 20%, and 30% MVC trials. E: average slope of the straight line fit to the ΔF vs. CMod data (red lines in A) for the pairwise (Pair; black bars) and composite control unit (Comp; red bars) methods across the 7 participants. Error whiskers are +1 SD. *P < 0.025, difference from a slope of 0. Individual participant data for D and E in Supplemental Table S2.

Fig. 8.

Test units with short ascending activation (SA) times. Ai: test units (gray circles) paired with composite control motor unit profile (colored circles) in participant 6M for a 30% maximum voluntary contraction (MVC). The test unit was recruited at 13% MVC (torque, top trace) and discharged for 3.6 s during the ascending phase of the firing rate profile. Self-sustained firing (ΔF) value from this test unit (5.7 Hz) is plotted in B as one of the gray circles because it was activated for >2 s on the ascending phase of the contraction. Aii and Aiii: same as in Ai but for 2 test units (red circles) that were recruited >20% MVC and with durations of firing during the ascending frequency profile that were <2s, i.e., having short ascending activation (SA) times. ΔF values for these 2 test units are plotted with red circles in B. B: all ΔF and recruitment threshold values from the 6 contractions at 30% MVC in participant 6M. C and D: ΔF values from this same participant as in B plotted against recruitment torque at the 20% MVC (C) and 10% MVC trials (D). ΔF values marked with red circles had test units with SA times and ΔF values less than −1 SD. ΔF measures with test units having SA times removed from the average are shown in Figs. 5 and 6.

Fig. 9.

Self-sustained firing (ΔF) and test motor unit recruitment threshold. A: binned averages of ΔF values across the 7 participants plotted against recruitment threshold of the test unit for the 10%, 20%, and 30% maximum voluntary contraction (MVC) data. Bin widths are 2% MVC. Green circles mark ΔF values from composite control unit method, and black circles mark ΔF values from pairwise method. Stars indicate ΔF values that are different from the ΔF value at the 0–2% MVC bin (arrowheads) for the pairwise data (no bins were different in the composite control data). Missing ΔF value for test units having recruitment thresholds between 28% and 30% MVC in the composite 30% MVC data is due to a small number of values for this bin. Test units with short ascending activation (SA) times were removed from data set. B: binned averages for the slope of the ascending firing rate profile of the test motor units. Same format as in A. Gray bars represent the equivalent of every 2 s in time for the 10-s ascending contraction in each of the different contraction strengths. Error whiskers are ±1 SD.

Fig. 10.

Self-sustained firing duration (SSD). A: examples of test-composite control unit pairs from participant 3M during a 30% maximum voluntary contraction (MVC) trial. Ai: test unit with large self-sustained firing duration (SSD) index. Aii: test unit with small SSD. Vertical gray lines mark the time that the estimated synaptic input reached the level that recruited the test unit during the ascending (a) and descending (a¹) phase of the contraction. The duration of a = time of test unit recruitment to time of peak synaptic input (torque), the latter marked by the dashed vertical line. The duration of a¹ is estimated by the duration of a. Solid black vertical line marks time of derecruitment of test unit. Distance between right gray vertical line and solid black line indicates duration of self-sustained firing of unit, i.e., duration of time unit fires below synaptic input initially needed to recruit unit (see calculation in text; d = duration of time the test unit was active on the descending phase). Self-sustained firing (ΔF) values calculated as in Fig. 3. B: SSD of test units averaged for the 7 participants plotted against recruitment threshold at each contraction intensity (10%, 20%, and 30% MVC). Bin width 2% MVC. Missing values in 20% and 30% MVC data are due to small number of samples for the lowest and highest threshold units [many of the lowest threshold units were used as control units and some high-threshold short ascending activation (SA) units were removed]. Stars indicate SSD values that are different from the SSD value at the 0–2% MVC bin or 2–4% MVC bin (arrowhead). Gray bars represent the equivalent of every 2 s in time for the 10-s ascending contraction for the different contraction strengths. Error whiskers are ±1 SD.

Fig. 11.

Persistent inward calcium and sodium current (I_P) activation and contribution of I_P to self-sustained firing (ΔI) in low- and high-threshold motoneurons. A, top: membrane potential (V_m) of hypothetical low-threshold (small) motoneuron (bottom) during spiking in response to triangular injected current, but used to schematically represent firing in our voluntary ramp contractions. Middle, schematic representation of the synaptic input (I_syn; downward depolarizing current) and I_P current (green trace) activated during the contraction. Purple box marks firing duration where firing starts at higher current and stops at lower current (blue circles; the difference is ΔI). A large portion of I_P is activated before cell firing, giving time for the I_P to be warmed up, so the current changes steeply at the onset of firing, leading to only a brief secondary range (light purple rectangle). Only the portion of the I_P activated after firing contributes to the ΔI (length of green arrow). Data adapted from Li et al. (2007) to schematically demonstrate the contribution of the I_P to the self-sustained firing (ΔF) and ΔI. B, top: membrane potential of hypothetical high-threshold (large) motoneuron (bottom) during spiking in response to triangular injected current, as in A; adapted from Li et al. (2007). Middle, firing duration (red box) where firing starts at higher current and stops at lower current (blue circles; the difference is ΔI). I_P (green trace) is at rest before cell firing, and this non-warmed up I_P has a slow onset, leading to a prolonged secondary range after onset of firing. The entire I_P contributes to the ΔI (length of green arrow). Overall I_P in high-threshold motoneuron is smaller than in low-threshold motoneuron, but the amount of the I_P contributing to ΔI (and ΔF) is the same.