Research Project

Defining the principles that govern the neural output for touch receptors

Computational models of skin and neural output

August 26, 2020

Gregory J. Gerling, Lingtian Wan, Benjamin U. Hoffman, Yuxiang Wang, and Ellen A. Lumpkin

Despite past progress, the principles that govern the neural output for touch receptors have not been fully defined. We take an approach of combining computational models with experimental methods. Our work in collaboration of Dr. Ellen A. Lumpkin of Columbia University has sought to define rules in the end organ architecture of the Merkel cells and neurites that are innervated by slowly adapting type I afferents. We have built end organ models to show that the grouping of Merkel cells to heminodes strongly influence the sensitivity function of an afferent. Such computational single-unit models are built for neural afferents, comprising finite elements to capture skin mechanics, differential equations to represent sensory transduction, and integrate-and-fire models to mimic neural dynamics.

Overview of paper

Slowly-adapting type I (SAI) cutaneous afferents help us discriminate fine spatial details. Their physiology and anatomy are distinguished by their slow adaptation in firing to held stimuli and innervation of Merkel cells, respectively. How mechanotransduction currents in Merkel cells and sensory neurons combine to give rise to neural spike firing is unknown. In considering wildtype animals, as well as Atoh1 conditional knockout animals that lack Merkel cells, this effort employs a computational modeling approach constrained by biological measurements.

A computational model of mechanotransduction in the slowly adapting type I cutaneous afferent. Shown is current over a ramp and hold stimulus for multiple sub-components, including a slowly inactivating (SI) current modeled as originating from the Merkel cell and rapidly inactivating (RI) and ultra-slowly inactivating (USI) currents modeled as originating from the neurite terminal. All three currents are included within the generator function, which receives input of compressive stress from a finite element model. The finite element model takes probe force, as shown in the upper panel, as its input. The generated trace of compressive stress interior to the skin’s layers exhibits time-dependent viscoelastic relaxation. The currents that the generator function represents, in modeling one Merkel cell—neurite complex, are summed across a cluster of eight Merkel cell-neurite complexes feeding a heminode. It is this current, upon entering into a leaky integrate and fire model, which gives rise to predicted spike firing times. Note that for the sake of the simulation here, the irregular inter-spike intervals were unimportant so noise was removed from the model.

For the developed generator function to recapitulate firing responses across genotype, a previously unsuspected current source is required that is ultra slowly adapting. Thus, the model makes specific predictions for future experimental studies.

Using computational approaches, constrained by biophysical measurements, we determine that matching the wildtype response requires extending the slowly inactivating (SI) time constant or adding an ultra slowly adapting (USI) decay. As is shown elsewhere in the paper, only the addition of an USI term is feasible in a Atoh1 knockout animal without Merkel cells. I.e., when the SI term is taken away, the remaining rapidly inactivating (RI) channels are far too fast to re-capitulate the Atoh1 knockout response.

An ultra-slowly inactivating (USI) current is essential to drive the slow adaptation in firing in the sustained response. Without the USI component, the output IFF reaches a plateau and does not adapt as is typically observed for SAI afferents. Another potential way to achieve adaptation is to increase the time constant on the SI component of the model from 200 to 570 ms. However, the duration of this time constant is well outside empirically observed bounds.

‍

References

Gerling, G.J., Wan, L., Hoffman, B.U., Wang, Y., and Lumpkin, E.A., Computation predicts rapidly adapting mechanotransduction currents cannot account for tactile encoding in Merkel cell-neurite complexes [DOI][PDF]. Plos Computational Biology, 2018.

‍

Gerling Touch Lab