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. 2014 May;111(9):1721-35.
doi: 10.1152/jn.00777.2012. Epub 2013 Dec 26.

Modeling activity-dependent changes of axonal spike conduction in primary afferent C-nociceptors

Jenny Tigerholm  1 , Marcus E Petersson, Otilia Obreja, Angelika Lampert, Richard Carr, Martin Schmelz, Erik Fransén
Affiliations

Modeling activity-dependent changes of axonal spike conduction in primary afferent C-nociceptors

Jenny Tigerholm et al. J Neurophysiol. 2014 May.

Abstract

Action potential initiation and conduction along peripheral axons is a dynamic process that displays pronounced activity dependence. In patients with neuropathic pain, differences in the modulation of axonal conduction velocity by activity suggest that this property may provide insight into some of the pathomechanisms. To date, direct recordings of axonal membrane potential have been hampered by the small diameter of the fibers. We have therefore adopted an alternative approach to examine the basis of activity-dependent changes in axonal conduction by constructing a comprehensive mathematical model of human cutaneous C-fibers. Our model reproduced axonal spike propagation at a velocity of 0.69 m/s commensurate with recordings from human C-nociceptors. Activity-dependent slowing (ADS) of axonal propagation velocity was adequately simulated by the model. Interestingly, the property most readily associated with ADS was an increase in the concentration of intra-axonal sodium. This affected the driving potential of sodium currents, thereby producing latency changes comparable to those observed for experimental ADS. The model also adequately reproduced post-action potential excitability changes (i.e., recovery cycles) observed in vivo. We performed a series of control experiments replicating blockade of particular ion channels as well as changing temperature and extracellular ion concentrations. In the absence of direct experimental approaches, the model allows specific hypotheses to be formulated regarding the mechanisms underlying activity-dependent changes in C-fiber conduction. Because ADS might functionally act as a negative feedback to limit trains of nociceptor activity, we envisage that identifying its mechanisms may also direct efforts aimed at alleviating neuronal hyperexcitability in pain patients.

Keywords: activity-dependent slowing; computer modeling; mechano-insensitive nociceptor; recovery cycles.

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Figures

Fig. 1.
Fig. 1.
Model overview: geometry and temperature. A: model consisting of a terminal branch axon and a parent axon, connected via a cone. The branch and parent axons differ in length, diameter, and temperature. B: axon cross-section. The model consists of an intra-axonal space, a periaxonal space, and extracellular fluid (where concentrations are assumed to be unaffected by activity), modeled according to Scriven (1981). D, diameter of axon; θ, width of periaxonal space.
Fig. 2.
Fig. 2.
Currents and concentrations during an action potential. Following a single current injection at the beginning of the branch, an action potential was generated and propagated along the axon. A: membrane potential (Mem. pot., Vm) and ionic currents recorded at the center of the branch (left) and the center of the parent (right). Time frame shown is expanded from simulation shown in B; bottom recording shows currents at a larger time scale. B: intra-axonal (Kin, Nain) and periaxonal (Ksp, Nasp) concentrations, as well as the resulting reversal potentials (K-rev, Na-rev).
Fig. 3.
Fig. 3.
Activity-dependent slowing (ADS) of conduction velocity. Stimulus-evoked action potentials are shown at the start (A) and at the end (B) of the repetitive stimulation (2 Hz; 3 min). Time frame shown is expanded from simulations shown in C and D around the time of the first and last action potential, respectively. C: latency during repetitive stimulation (top: 360 pulses at 2 Hz, 60 pulses at 0.25 Hz; bottom: 20 pulses at 0.125 Hz, 20 pulses at 0.25 Hz, 30 pulses at 0.5 Hz, 20 pulses at 0.25 Hz). D: latency during repetitive stimulation normalized to the initial latency. Relative latency changes for both the high-frequency (top) and low-frequency (bottom) protocols are shown.
Fig. 4.
Fig. 4.
Activity-dependent changes of Vm and ionic currents. First (left) and 360th (right) action potentials during the high-frequency ADS protocol are shown. Vm (A and B) and ionic currents (C and D) are measured at the center of the parent axon. Note the reduction in Vm and current peaks during the 360th action potential compared with the 1st pulse. Also note that the 360th action potential starts from a more hyperpolarized level (due to activity-dependent hyperpolarization).
Fig. 5.
Fig. 5.
ADS is induced by accumulation of intracellular sodium. A: relative latency during the high-frequency protocol (2 Hz), control (blue) and with clamped reversal potentials (black). B: intracellular (intra-axonal) sodium concentration (green) and periaxonal potassium concentration (black). C: reversal potential of sodium. D: latency relative to the initial latency when the reversal potential was held constant, shown separately for NaV1.7 (green) and NaV1.8 (red) vs. control (blue). E: ADS resulting from NaV1.8 slow inactivation. Control condition (when the ADS developed from changes in Na concentration; blue) vs. ADS when sodium and potassium concentrations were held fixed and a slow inactivation transition was added to NaV1.8 (20°C, green; 37°C, red). F: relationship between minimum current injection and degree of latency change (top) and pulse number (bottom). The minimum current injection needed to trigger an action potential was measured over repetitive stimulations. Increased minimum current indicates decreased fiber excitability. Current injection was positioned on the midpoint of the branch segment.
Fig. 6.
Fig. 6.
Modeling recovery cycle velocity changes. The slowing/speeding during the recovery cycle protocol is shown. The frequency is 2 Hz, and the interstimulus interval (ISI) varies between 10 and 250 ms (note that only 3 specimens are represented). A: membrane potential for different ISIs. Top graphs represent the membrane potential at the beginning of the branch axon, and bottom graphs show the membrane potential at the end of parent axon. B: slowing/speeding for different ISIs.
Fig. 7.
Fig. 7.
Model testing by changes of the temperature and ion concentration and by block of ion channels and the ion pump. We have plotted both absolute (top) and relative latency (bottom) in simulations using the ADS protocol. L, absolute latency. A: block of ion channels: h channel (top left), NaV1.8 (top right), NaV1.7 (bottom). Control condition is shown in black, and block is represented by the colors with steps of 10% as indicated (except for h-channel block, where magenta represents full block). B: changes of extracellular ion concentrations. Decreasing concentrations of the periaxonal sodium (Nasp: 10%, blue; 20%, green; 30%, red) vs. control concentration (black). C: changing temperature. Lower temperature (27°C, blue) compared with control temperature (37°C, black).
Fig. A1.
Fig. A1.
Action potential for 1st and 360th pulse. Action potential shapes are shown for the 1st (left) and 360th pulse (right) in the parent axon. Intracellular Vm is plotted on a long (400 ms; top), medium (10 ms; middle), and short time scale (0.6 ms; bottom).
Fig. A2.
Fig. A2.
Net membrane current (Im; sum of all transmembrane currents) for 1st and 360th pulse. Net action potential current is shown for the 1st (left) and 360th pulse (right) in the parent axon. Transmembrane current is plotted on a long (400 ms; top) and medium time scale (10 ms; bottom).
Fig. A3.
Fig. A3.
First-order sensitivity analysis. The relative influence of a range of currents during the AP phases shown in Fig. A1. Influences are shown as first-order sensitivity indexes (Homma and Saltelli 1996; Sobol 1990), the contribution to the variation from a current. To compute the first-order sensitivity index, all ionic conductances were varied by ±20%. See Petersson (2012) for an in-depth discussion. Color legend: NaV1.8, dark blue; NaV1.7, medium blue; h, light blue; pump, turquoise; leak, green; KM, yellow; KA; orange; Kdr, red; KNa, brown. As can be seen, different currents contribute differently to the action potential (short time scale), afterpotential (intermediate time scale), and ADS phenomena (long time scale). Since most phases show contributions from several currents, the model does not show indications of sensitivity. One exception is during a phase of the action potential where NaV1.8 and Kdr together amount to almost all variation, but this is really what is to be expected.
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