Multiple firing patterns in deep dorsal horn neurons of the spinal cord: computational analysis of mechanisms and functional implications

Multimodal sensory control of motor performance by glycinergic interneurons of the mouse spinal cord deep dorsal horn

Sensory feedback is integral for contextually appropriate motor output, yet the neural circuits responsible remain elusive. Here, we pinpoint the medial deep dorsal horn of the mouse spinal cord as a convergence point for proprioceptive and cutaneous input. Within this region, we identify a population of tonically active glycinergic inhibitory neurons expressing parvalbumin. Using anatomy and electrophysiology, we demonstrate that deep dorsal horn parvalbumin-expressing interneuron (dPV) activity is shaped by convergent proprioceptive, cutaneous, and descending input. Selectively targeting spinal dPVs, we reveal their widespread ipsilateral inhibition onto pre-motor and motor networks and demonstrate their role in gating sensory-evoked muscle activity using electromyography (EMG) recordings. dPV ablation altered limb kinematics and step-cycle timing during treadmill locomotion and reduced the transitions between sub-movements during spontaneous behavior. These findings reveal a circuit basis by which sensory convergence onto dorsal horn inhibitory neurons modulates motor output to facilitate smooth movement and context-appropriate transitions.

Steering Toward Normative Wide-Dynamic-Range Neuron Activity in Nerve-Injured Rats With Closed-Loop Peripheral Nerve Stimulation

OBJECTIVES

Chronic pain is primarily treated with pharmaceuticals, but the effects remain unsatisfactory. A promising alternative therapy is peripheral nerve stimulation (PNS), but it has been associated with suboptimal efficacy because its modulation mechanisms are not clear and the current therapies are primarily open loop (ie, manually adjusting the stimulation parameters). In this study, we developed a proof-of-concept computational modeling as the first step toward implementing closed-loop PNS in future biological studies. When developing new pain therapies, a useful pain biomarker is the wide-dynamic-range (WDR) neuron activity in the dorsal horn. In healthy animals, the WDR neuron activity occurs in a stereotyped manner; however, this response profile can vary widely after nerve injury to create a chronic pain condition. We hypothesized that if injury-induced changes of neuronal response can be normalized to resemble those of a healthy condition, the pathological aspects of pain may be treated while maintaining protective physiological nociception.

MATERIALS AND METHODS

Using an in vivo electrophysiology data set of WDR neuron recordings obtained in nerve-injured rats and naïve rats, we constructed sets of linear phenomenologic models of WDR firing rate during windup stimulation for both conditions. Then, we applied robust control systems techniques to identify a closed-loop PNS controller, which can drive the dynamics of WDR neuron response in neuropathic pain model into ranges associated with normal physiological pain.

RESULTS

The sets of identified linear models can accurately predict, in silico, nonlinear neural responses to electrical stimulation of the peripheral nerve. In addition, we showed that continuous closed-loop control of PNS can be used to normalize WDR neuron firing responses in three injured cases.

CONCLUSIONS

In this proof-of-concept study, we show how tractable, linear mathematical models of pain-related neurotransmission can be used to inform the development of closed-loop PNS. This new application of robust control to neurotechnology may also be expanded and applied across other neuromodulation applications.

Measuring pain and nociception: Through the glasses of a computational scientist. Transdisciplinary overview of methods

In a healthy state, pain plays an important role in natural biofeedback loops and helps to detect and prevent potentially harmful stimuli and situations. However, pain can become chronic and as such a pathological condition, losing its informative and adaptive function. Efficient pain treatment remains a largely unmet clinical need. One promising route to improve the characterization of pain, and with that the potential for more effective pain therapies, is the integration of different data modalities through cutting edge computational methods. Using these methods, multiscale, complex, and network models of pain signaling can be created and utilized for the benefit of patients. Such models require collaborative work of experts from different research domains such as medicine, biology, physiology, psychology as well as mathematics and data science. Efficient work of collaborative teams requires developing of a common language and common level of understanding as a prerequisite. One of ways to meet this need is to provide easy to comprehend overviews of certain topics within the pain research domain. Here, we propose such an overview on the topic of pain assessment in humans for computational researchers. Quantifications related to pain are necessary for building computational models. However, as defined by the International Association of the Study of Pain (IASP), pain is a sensory and emotional experience and thus, it cannot be measured and quantified objectively. This results in a need for clear distinctions between nociception, pain and correlates of pain. Therefore, here we review methods to assess pain as a percept and nociception as a biological basis for this percept in humans, with the goal of creating a roadmap of modelling options.

Multiscale Computer Model of the Spinal Dorsal Horn Reveals Changes in Network Processing Associated with Chronic Pain

Pain-related sensory input is processed in the spinal dorsal horn (SDH) before being relayed to the brain. That processing profoundly influences whether stimuli are correctly or incorrectly perceived as painful. Significant advances have been made in identifying the types of excitatory and inhibitory neurons that comprise the SDH, and there is some information about how neuron types are connected, but it remains unclear how the overall circuit processes sensory input or how that processing is disrupted under chronic pain conditions. To explore SDH function, we developed a computational model of the circuit that is tightly constrained by experimental data. Our model comprises conductance-based neuron models that reproduce the characteristic firing patterns of spinal neurons. Excitatory and inhibitory neuron populations, defined by their expression of genetic markers, spiking pattern, or morphology, were synaptically connected according to available qualitative data. Using a genetic algorithm, synaptic weights were tuned to reproduce projection neuron firing rates (model output) based on primary afferent firing rates (model input) across a range of mechanical stimulus intensities. Disparate synaptic weight combinations could produce equivalent circuit function, revealing degeneracy that may underlie heterogeneous responses of different circuits to perturbations or pathologic insults. To validate our model, we verified that it responded to the reduction of inhibition (i.e., disinhibition) and ablation of specific neuron types in a manner consistent with experiments. Thus validated, our model offers a valuable resource for interpreting experimental results and testing hypotheses in silico to plan experiments for examining normal and pathologic SDH circuit function.SIGNIFICANCE STATEMENT We developed a multiscale computer model of the posterior part of spinal cord gray matter (spinal dorsal horn), which is involved in perceiving touch and pain. The model reproduces several experimental observations and makes predictions about how specific types of spinal neurons and synapses influence projection neurons that send information to the brain. Misfiring of these projection neurons can produce anomalous sensations associated with chronic pain. Our computer model will not only assist in planning future experiments, but will also be useful for developing new pharmacotherapy for chronic pain disorders, connecting the effect of drugs acting at the molecular scale with emergent properties of neurons and circuits that shape the pain experience.

A Computational Model for Pain Processing in the Dorsal Horn Following Axonal Damage to Receptor Fibers

Computational modeling of the neural activity in the human spinal cord may help elucidate the underlying mechanisms involved in the complex processing of painful stimuli. In this study, we use a biologically-plausible model of the dorsal horn circuitry as a platform to simulate pain processing under healthy and pathological conditions. Specifically, we distort signals in the receptor fibers akin to what is observed in axonal damage and monitor the corresponding changes in five quantitative markers associated with the pain response. Axonal damage may lead to spike-train delays, evoked potentials, an increase in the refractoriness of the system, and intermittent blockage of spikes. We demonstrate how such effects applied to mechanoreceptor and nociceptor fibers in the pain processing circuit can give rise to dramatically distinct responses at the network/population level. The computational modeling of damaged neuronal assemblies may help unravel the myriad of responses observed in painful neuropathies and improve diagnostics and treatment protocols.

Modeling the daily rhythm of human pain processing in the dorsal horn

Experimental studies show that human pain sensitivity varies across the 24-hour day, with the lowest sensitivity usually occurring during the afternoon. Patients suffering from neuropathic pain, or nerve damage, experience an inversion in the daily modulation of pain sensitivity, with the highest sensitivity usually occurring during the early afternoon. Processing of painful stimulation occurs in the dorsal horn (DH), an area of the spinal cord that receives input from peripheral tissues via several types of primary afferent nerve fibers. The DH circuit is composed of different populations of neurons, including excitatory and inhibitory interneurons, and projection neurons, which constitute the majority of the output from the DH to the brain. In this work, we develop a mathematical model of the dorsal horn neural circuit to investigate mechanisms for the daily modulation of pain sensitivity. The model describes average firing rates of excitatory and inhibitory interneuron populations and projection neurons, whose activity is directly correlated with experienced pain. Response in afferent fibers to peripheral stimulation is simulated by a Poisson process generating nerve fiber spike trains at variable firing rates. Model parameters for fiber response to stimulation and the excitability properties of neuronal populations are constrained by experimental results found in the literature, leading to qualitative agreement between modeled responses to pain and experimental observations. We validate our model by reproducing the wind-up of pain response to repeated stimulation. We apply the model to investigate daily modulatory effects on pain inhibition, in which response to painful stimuli is reduced by subsequent non-painful stimuli. Finally, we use the model to propose a mechanism for the observed inversion of the daily rhythmicity of pain sensation under neuropathic pain conditions. Underlying mechanisms for the shift in rhythmicity have not been identified experimentally, but our model results predict that experimentally-observed dysregulation of inhibition within the DH neural circuit may be responsible. The model provides an accessible, biophysical framework that will be valuable for experimental and clinical investigations of diverse physiological processes modulating pain processing in humans.

Human pain sensitivity follows a daily (∼24 hour) rhythm. In particular, humans experience the highest sensitivity to pain in the middle of night and lowest in the afternoon. Patients suffering from neuropathy, a disease resulting from nerve damage leading to an increase in pain sensitivity, experience an approximately 12-hour shift in their rhythmicity such that the highest sensitivity occurs in the afternoon. Neuropathy is a difficult condition to treat since it is often unfeasible to locate the damaged nerve and it is also unclear how this damage causes a shift in rhythmicity and an increase in pain. Understanding the mechanism underlying the shift in rhythmicity may lead to improvements in the knowledge of the transmission of pain from the damaged nerve to the pain-processing center in the spinal cord, and thus better treatment protocols. We have built a population-based model to describe this transmission with a particular focus on daily rhythms. We show that our model reproduces experimentally-observed rhythmicity of both normal pain responses, as well as neuropathic pain. Our model predicts that a potential mechanism underlying the shift in rhythmicity for neuropathic pain is a change in the interaction of the nerve fibers from inhibition to excitation.

Modeling Responses to Peripheral Nerve Stimulation in the Dorsal Horn

Pain is a protective physiological system essential for survival. However, it can malfunction and create a debilitating disease known as chronic pain (CP). CP is primarily treated with drugs that can have negative side effects (e.g., opioid addiction), and lose efficacy after long-term use. Electrical stimulation of the spinal cord or peripheral nerves is an alternative therapy that has great potential to reduce the need for drugs and has fewer negative side effects; but has been associated with suboptimal efficacy because its modulation mechanisms are unknown. Critical to advancing CP treatment is a deeper understanding of how pain is processed in the superficial and deep layers of the dorsal horn (DH), which is the first central relay station for pain processing in the spinal cord. Mechanistic models of the DH have been developed to investigate modulation mechanisms but are non-linear and high-dimensional and thus difficult to analyze. In this paper, we construct a tractable computational model of the DH in rats from LFP recordings of the superficial layer network and spiking activity of WDR neurons in the deep layer. By combining a deterministic linear time-invariant model with a stochastic point process model, we can accurately predict responses of the DH circuit to electrical stimulation of the peripheral nerve. The model is computationally efficient, low-dimensional, and able to capture the stochastic nature of neuronal dynamics in the DH; and is a first step in developing new therapies for CP.

Origin of heterogeneous spiking patterns from continuously distributed ion channel densities: a computational study in spinal dorsal horn neurons

KEY POINTS

Distinct spiking patterns may arise from qualitative differences in ion channel expression (i.e. when different neurons express distinct ion channels) and/or when quantitative differences in expression levels qualitatively alter the spike generation process. We hypothesized that spiking patterns in neurons of the superficial dorsal horn (SDH) of spinal cord reflect both mechanisms. We reproduced SDH neuron spiking patterns by varying densities of KV 1- and A-type potassium conductances. Plotting the spiking patterns that emerge from different density combinations revealed spiking-pattern regions separated by boundaries (bifurcations). This map suggests that certain spiking pattern combinations occur when the distribution of potassium channel densities straddle boundaries, whereas other spiking patterns reflect distinct patterns of ion channel expression. The former mechanism may explain why certain spiking patterns co-occur in genetically identified neuron types. We also present algorithms to predict spiking pattern proportions from ion channel density distributions, and vice versa.

ABSTRACT

Neurons are often classified by spiking pattern. Yet, some neurons exhibit distinct patterns under subtly different test conditions, which suggests that they operate near an abrupt transition, or bifurcation. A set of such neurons may exhibit heterogeneous spiking patterns not because of qualitative differences in which ion channels they express, but rather because quantitative differences in expression levels cause neurons to operate on opposite sides of a bifurcation. Neurons in the spinal dorsal horn, for example, respond to somatic current injection with patterns that include tonic, single, gap, delayed and reluctant spiking. It is unclear whether these patterns reflect five cell populations (defined by distinct ion channel expression patterns), heterogeneity within a single population, or some combination thereof. We reproduced all five spiking patterns in a computational model by varying the densities of a low-threshold (KV 1-type) potassium conductance and an inactivating (A-type) potassium conductance and found that single, gap, delayed and reluctant spiking arise when the joint probability distribution of those channel densities spans two intersecting bifurcations that divide the parameter space into quadrants, each associated with a different spiking pattern. Tonic spiking likely arises from a separate distribution of potassium channel densities. These results argue in favour of two cell populations, one characterized by tonic spiking and the other by heterogeneous spiking patterns. We present algorithms to predict spiking pattern proportions based on ion channel density distributions and, conversely, to estimate ion channel density distributions based on spiking pattern proportions. The implications for classifying cells based on spiking pattern are discussed.

Neurobiological studies of chronic pain and analgesia: Rationale and refinements

Chronic pain is a complex condition for which the need for specialized research and therapies has been recognized internationally. This review summarizes the context for the international call for expansion of pain research to improve our understanding of the mechanisms underlying pain in order to achieve improvements in pain management. The methods for conducting sensory assessment in animal models are discussed and the development of animal models of chronic pain is specifically reviewed, with an emphasis on ongoing refinements to more closely mimic a variety of human pain conditions. Pharmacological correspondences between pre-clinical pain models and the human clinical experience are noted. A discussion of the 3Rs Framework (Replacement, Reduction, Refinement) and how each may be considered in pain research is featured. Finally, suggestions are provided for engaging principal investigators, IACUC reviewers, and institutions in the development of strong partnerships to simultaneously expand our knowledge of the mechanisms underlying pain and analgesia while ensuring the humane use of animals in research.

Modeling effects of spinal cord stimulation on wide-dynamic range dorsal horn neurons: influence of stimulation frequency and GABAergic inhibition

Spinal cord stimulation (SCS) is a clinical therapy for chronic, neuropathic pain, but an incomplete understanding of the mechanisms underlying SCS contributes to the lack of improvement in SCS efficacy over time. To study the mechanisms underlying SCS, we constructed a biophysically based network model of the dorsal horn circuit consisting of interconnected dorsal horn interneurons and a wide-dynamic range (WDR) projection neuron and representations of both local and surround receptive field inhibition. We validated the network model by reproducing cellular and network responses relevant to pain processing including wind-up, A fiber-mediated inhibition, and surround receptive field inhibition. We then simulated the effects of SCS on the activity of the WDR projection neuron and found that the response of the model WDR neuron to SCS depends on the SCS frequency; SCS frequencies of 30–100 Hz maximally inhibited the model WDR neuron, while frequencies under 30 Hz and over 100 Hz excited the model WDR neuron. We also studied the impacts on the effects of SCS of loss of inhibition due to the loss of either GABA or KCC2 function. Reducing the influence of local and surround GABAergic interneurons by weakening their inputs or their connections to the WDR neuron and shifting the anionic reversal potential of the WDR neurons upward each reduced the range of optimal SCS frequencies and changed the frequency at which SCS had a maximal effect. The results of this study provide insights into the mechanisms of SCS and pave the way for improved SCS parameter selection.

Hydrogen sulfide increases excitability through suppression of sustained potassium channel currents of rat trigeminal ganglion neurons

Background

Hydrogen sulfide (H₂S), an endogenous gaseotransmitter/modulator, is becoming appreciated that it may be involved in a wide variety of processes including inflammation and nociception. However, the role and mechanism for H₂S in nociceptive processing in trigeminal ganglion (TG) neuron remains unknown. The aim of this study is to investigate distribution of endogenous H₂S synthesizing enzyme cystathionine-β-synthetase (CBS) expression and role of H₂S on excitability and voltage-gated potassium channels of TG neurons.

Methods

Immunofluorescence studies were carried out to determine whether CBS was co-expressed in Kv1.1 or Kv1.4-positive TG neurons. Whole cell patch clamp recordings were employed on acutely isolated TG neurons from adult male Sprague Dawley rats (6–8 week old). von Frey filaments were used to examine the pain behavioral responses in rats following injection of sodium hydrosulfide.

Results

In rat TG, 77.3±6.6% neurons were immunoreactive for CBS, 85.1±3.8% for Kv1.1 and 97.8±1.1% for Kv1.4. Double staining showed that all CBS labeled cells were Kv1.1 and Kv1.4 positive, but only 92.2±6.1% of Kv1.1 and 78.2±9.9% of Kv1.4 positive cells contained CBS. Application of H₂S donor NaHS (250 μM) led to a significant depolarization of resting membrane potential recorded from TG neurons. NaHS application also resulted in a dramatic reduction in rheobase, hyperpolarization of action potential threshold, and a significant increase in the number of action potentials evoked at 2X and 3X rheobase stimulation. Under voltage-clamp conditions, TG neurons exhibited transient A-type (I_A) and sustained outward rectifier K⁺ currents (I_K). Application of NaHS did suppress I_K density while did not change I_A density of TG neurons (n=6). Furthermore, NaHS, a donor of hydrogen sulfide, produced a significant reduction in escape threshold in a dose dependent manner.

Conclusion

These data suggest that endogenous H₂S generating enzyme CBS was co-localized well with Kv1.1 and Kv1.4 in TG neurons and that H₂S produces the mechanic pain and increases neuronal excitability, which might be largely mediated by suppressing I_K density, thus identifying for the first time a specific molecular mechanism underlying pain and sensitization in TG.

Beyond faithful conduction: short-term dynamics, neuromodulation, and long-term regulation of spike propagation in the axon

Most spiking neurons are divided into functional compartments: a dendritic input region, a soma, a site of action potential initiation, an axon trunk and its collaterals for propagation of action potentials, and distal arborizations and terminals carrying the output synapses. The axon trunk and lower order branches are probably the most neglected and are often assumed to do nothing more than faithfully conducting action potentials. Nevertheless, there are numerous reports of complex membrane properties in non-synaptic axonal regions, owing to the presence of a multitude of different ion channels. Many different types of sodium and potassium channels have been described in axons, as well as calcium transients and hyperpolarization-activated inward currents. The complex time- and voltage-dependence resulting from the properties of ion channels can lead to activity-dependent changes in spike shape and resting potential, affecting the temporal fidelity of spike conduction. Neural coding can be altered by activity-dependent changes in conduction velocity, spike failures, and ectopic spike initiation. This is true under normal physiological conditions, and relevant for a number of neuropathies that lead to abnormal excitability. In addition, a growing number of studies show that the axon trunk can express receptors to glutamate, GABA, acetylcholine or biogenic amines, changing the relative contribution of some channels to axonal excitability and therefore rendering the contribution of this compartment to neural coding conditional on the presence of neuromodulators. Long-term regulatory processes, both during development and in the context of activity-dependent plasticity may also affect axonal properties to an underappreciated extent.