Computer simulation of the enteric neural circuits mediating an ascending reflex: roles of fast and slow excitatory outputs of sensory neurons

Quantification of CGRP-immunoreactive myenteric neurons in mouse colon

Quantitative data of biological systems provide valuable baseline information for understanding pathology, experimental perturbations, and computational modeling. In mouse colon, calcitonin gene-related peptide (CGRP) is expressed by myenteric neurons with multiaxonal (Dogiel type II) morphology, characteristic of intrinsic primary afferent neurons (IPANs). Analogous neurons in other species and gut regions represent 5-35% of myenteric neurons. We aimed to quantify proportions of CGRP-immunopositive (CGRP+) myenteric neurons. Colchicine-treated wholemount preparations of proximal, mid, and distal colon were labeled for HuC/D, CGRP, nitric oxide synthase (NOS), and peripherin (Per). The pan-neuronal markers (Hu+/Per+) co-labeled 94% of neurons. Hu+/Per- neurons comprised ∼6%, but Hu-/Per+ cells were rare. Thus, quantification was based on Hu+ myenteric neurons (8576 total; 1225 ± 239 per animal, n = 7). CGRP+ cell bodies were significantly larger than the average of all Hu+ neurons (329 ± 13 vs. 261 ± 12 μm² , p < .0001). CGRP+ neurons comprised 19% ± 3% of myenteric neurons without significant regional variation. NOS+ neurons comprised 42% ± 2% of myenteric neurons overall, representing a lower proportion in proximal colon, compared to mid and distal colon (38% ± 2%, 44% ± 2%, and 44% ± 3%, respectively). Peripherin immunolabeling revealed cell body and axonal morphology in some myenteric neurons. Whether all CGRP+ neurons were multiaxonal could not be addressed using peripherin immunolabeling. However, of 118 putatively multiaxonal neurons first identified based on peripherin immunoreactivity, all were CGRP+ (n = 4). In conclusion, CGRP+ myenteric neurons in mouse colon were comprehensively quantified, occurring within a range expected of a putative IPAN marker. All Per+ multiaxonal neurons, characteristic of Dogiel type II/IPAN morphology, were CGRP+.

Modeling experimental recordings of vagal afferent signaling of intestinal inflammation for neuromodulation

OBJECTIVE

Artificial modulation of peripheral nerve signals (neuromodulation) by electrical stimulation is an innovation with potential to develop treatments that replace or supplement drugs. One function of the nervous system that can be exploited by neuromodulation is regulation of disease intensity. Optimal interfacing of devices with the nervous system requires suitable models of peripheral nerve systems so that closed-loop control can be utilized for therapeutic benefit.

APPROACH

We use physiological data to model afferent signaling in the vagus nerve that carries information about inflammation in the small intestine to the brain.

MAIN RESULTS

The vagal nerve signaling system is distributed and complex; however, we propose a class of reductive models using a state-space formalism that can be tuned in a patient-specific manner.

SIGNIFICANCE

These models provide excellent fits to a large range of nerve recording data but are computationally simple enough for feedback control in implantable neuromodulation devices.

Electrical stimulation of gut motility guided by an in silico model

OBJECTIVE

Neuromodulation of the central and peripheral nervous systems is becoming increasingly important for treating a diverse set of diseases-ranging from Parkinson's Disease and epilepsy to chronic pain. However, neuromodulation of the gastrointestinal (GI) tract has achieved relatively limited success in treating functional GI disorders, which affect a significant population, because the effects of stimulation on the enteric nervous system (ENS) and gut motility are not well understood. Here we develop an integrated neuromechanical model of the ENS and assess neurostimulation strategies for enhancing gut motility, validated by in vivo experiments.

APPROACH

The computational model included a network of enteric neurons, smooth muscle fibers, and interstitial cells of Cajal, which regulated propulsion of a virtual pellet in a model of gut motility.

MAIN RESULTS

Simulated extracellular stimulation of ENS-mediated motility revealed that sinusoidal current at 0.5 Hz was more effective at increasing intrinsic peristalsis and reducing colon transit time than conventional higher frequency rectangular current pulses, as commonly used for neuromodulation therapy. Further analysis of the model revealed that the 0.5 Hz sinusoidal currents were more effective at modulating the pacemaker frequency of interstitial cells of Cajal. To test the predictions of the model, we conducted in vivo electrical stimulation of the distal colon while measuring bead propulsion in awake rats. Experimental results confirmed that 0.5 Hz sinusoidal currents were more effective than higher frequency pulses at enhancing gut motility.

SIGNIFICANCE

This work demonstrates an in silico GI neuromuscular model to enable GI neuromodulation parameter optimization and suggests that low frequency sinusoidal currents may improve the efficacy of GI pacing.

Lactobacillus rhamnosus strain JB-1 reverses restraint stress-induced gut dysmotility

BACKGROUND

Environmental stress affects the gut with dysmotility being a common consequence. Although a variety of microbes or molecules may prevent the dysmotility, none reverse the dysmotility.

METHODS

We have used a 1 hour restraint stress mouse model to test for treatment effects of the neuroactive microbe, L. rhamnosus JB-1^™ . Motility of fluid-filled ex vivo gut segments in a perfusion organ bath was recorded by video and migrating motor complexes measured using spatiotemporal maps of diameter changes.

KEY RESULTS

Stress reduced jejunal and increased colonic propagating contractile cluster velocities and frequencies, while increasing contraction amplitudes for both. Luminal application of 10E8 cfu/mL JB-1 restored motor complex variables to unstressed levels within minutes of application. L. salivarius or Na.acetate had no treatment effects, while Na.butyrate partially reversed stress effects on colonic frequency and amplitude. Na.propionate reversed the stress effects for jejunum and colon except on jejunal amplitude.

CONCLUSIONS & INFERENCES

Our findings demonstrate, for the first time, a potential for certain beneficial microbes as treatment of stress-induced intestinal dysmotility and that the mechanism for restoration of function occurs within the intestine via a rapid drug-like action on the enteric nervous system.

Mathematical modelling of enteric neural motor patterns

1. The enteric nervous system modulates intestinal behaviours, such as motor patterns and secretion. Although much is known about different types of neurons and simple reflexes in the intestine, it remains unclear how complex behaviours are generated. 2. Mathematical modelling is an important tool for assisting the understanding of how the neurons and reflexes can be pieced together to generate intestinal behaviours. 3. Models have identified a functional role for slow excitatory post-synaptic potentials (EPSPs) by distinguishing between fast and slow EPSPs in the ascending excitation reflex. These models also discovered coordinated firing of similarly located neurons as emergent properties of feed-forward networks of interneurons in the intestine. A model of the recurrent network of intrinsic sensory neurons identified important control mechanisms to prevent uncontrolled firing due to positive feedback and that the interaction between these control mechanisms and slow EPSPs is necessary for the networks to encode ongoing sensory stimuli. This model also showed that such networks may mediate migrating motor complexes. 4. A network model of vasoactive intestinal peptide neurons in the submucosal plexus found this relatively sparse recurrent network could produce uncontrolled firing under conditions that appear to be related to cholera toxin-induced hypersecretion. 5. Abstract modelling of the intestinal fed-state motor patterns has identified how stationary contractions can arise from a polarized network. 6. These models have also helped predict and/or explained pharmacological evidence for two rhythm generators and the requirement of feedback from contractions in the circular muscle.

Recurrent networks of submucous neurons controlling intestinal secretion: a modeling study

Secretomotor neurons, immunoreactive for vasoactive intestinal peptide (VIP), are important in controlling chloride secretion in the small intestine. These neurons form functional synapses with other submucosal VIP neurons and transmit via slow excitatory postsynaptic potentials (EPSPs). Thus they form a recurrent network with positive feedback. Intrinsic sensory neurons within the submucosa are also likely to form recurrent networks with positive feedback, provide substantial output to VIP neurons, and receive input from VIP neurons. If positive feedback within recurrent networks is sufficiently large, then neurons in the network respond to even small stimuli by firing at their maximum possible rate, even after the stimulus is removed. However, it is not clear whether such a mechanism operates within the recurrent networks of submucous neurons. We investigated this question by performing computer simulations of realistic models of VIP and intrinsic sensory neuron networks. In the expected range of electrophysiological properties, we found that activity in the VIP neuron network decayed slowly after cessation of a stimulus, indicating that positive feedback is not strong enough to support the uncontrolled firing state. The addition of intrinsic sensory neurons produced a low stable firing rate consistent with the common finding that basal secretory activity is, in part, neurogenic. Changing electrophysiological properties enables these recurrent networks to support the uncontrolled firing state, which may have implications with hypersecretion in the presence of enterotoxins such as cholera-toxin.

Computational model of the migrating motor complex of the small intestine

The migrating motor complex (MMC) is a cyclic motor pattern with several phases enacted over the entire length of the small intestine. This motor pattern is initiated and coordinated by the enteric nervous system and modulated by extrinsic factors. Because in vitro preparations of the MMC do not exist, it has not been possible to determine the intrinsic nerve circuits that manage this motor pattern. We have used computer simulation to explore the possibility that the controlling circuit is the network of AH/Dogiel type II (AH) neurons. The basis of the model is that recurrent connections between AH neurons cause local circuits to enter a high-firing-rate state that provides the maximal motor drive observed in phase III of the MMC. This also drives adjacent segments of the network causing slow migration. Delayed negative feedback within the circuit, provided by activity-dependent synaptic depression, forces the network to return to rest after passage of phase III. The anal direction of propagation is a result of slight anal bias observed in projections of AH neurons. The model relates properties of neurons to properties of the MMC cycle: phase III migration speed is governed by neuron excitability, MMC cycle length is governed by the rate of recovery of synaptic efficacy, and phase III duration is governed by duration of slow excitatory postsynaptic potentials in AH neurons. In addition, the model makes experimental predictions that can be tested using standard techniques.

Inhibitory cotransmission or after-hyperpolarizing potentials can regulate firing in recurrent networks with excitatory metabotropic transmission

Recurrent networks of neurons communicating via excitatory connections are common in the nervous system. In the absence of mechanisms to control firing (collectively termed negative feedback), these networks are likely to be bistable and unable to meaningfully encode input signals. In most recurrent circuits, negative feedback is provided by a specialized subpopulation of interneurons, but such neurons are absent from some systems, which therefore require other forms of negative feedback. One such circuit is found within the enteric nervous system of the intestine, where AH/Dogiel type II neurons are interconnected via excitatory synapses acting through metabotropic receptors to produce slow excitatory postsynaptic potentials (slow EPSPs). Negative feedback in this recurrent network may come from either inhibitory postsynaptic potentials arising from the terminals that produce slow EPSPs or from the after hyperpolarizing potentials (AHPs) characteristic of these neurons. We have examined these possibilities using mathematical analysis, based on the Wilson-Cowan model, and computer simulations. Analysis of steady states showed that, under appropriate conditions, both types of negative feedback can provide robust regulation of firing allowing the networks to encode input signals. Numerical simulations were performed using large, anatomically realistic networks with realistic models for metabotropic transmission and suppression of the AHP. In the presence of constant exogenous input, parameters controlling aspects of synaptic events were varied, confirming the analytical results for static stimuli. The simulated networks also responded to time varying inputs in a manner consistent with known physiology. In addition, simulation revealed that neurons in networks with inhibitory contransmission fired in erratic bursts, a phenomenon observed in neurons in unparalysed tissue. Thus, either inhibitory contransmission or AHPs, or both, can allow recurrent networks of AH/Dogiel type II neurons to encode ongoing inputs in a biologically useful way. These neurons appear to be intrinsic primary afferent neurons (IPANs), which implies that the IPANs in a region act in a coordinated fashion.

Participation of endogenous nitric oxide in the effect of hypoxia in vitro on neuro-effector transmission in guinea-pig ileum

The implication of endogenous nitric oxide in the effect of hypoxia on the neurotransmission in the enteric nervous system of guinea-pig ileum was studied in vitro. Three methodological approaches have been used: (i) Stretch-induced phases of peristaltic reflex in ileal segments; (ii) twitch contractions of longitudinal segments, evoked by electrical field stimulation; and (iii) release of [3H]acetylcholine from longitudinal muscle-myenteric plexus preparations, measured by liquid spectrophotometry. The effect of nitric oxide synthase inhibitor N(omega)-nitro-L-arginine (L-NNA, 100 microM) was studied under normoxic conditions. L-NNA did not change significantly the ascending contraction phase of peristaltic reflex and the amplitude of twitch contractions. However, the same concentration of L-NNA increased the stimulation-evoked acetylcholine release. The descending relaxation phase decreased in the presence of L-NNA. In another set of experiments, hypoxia was mimicked by replacement of oxygen from the perfusion medium with nitrogen for a period of 30 min. Hypoxia significantly decreased the ascending contraction phase, the twitch contractions, and the release of acetylcholine from the myenteric plexus. Under hypoxic conditions, pretreatment with L-NNA did not change either the contractile responses, nor the release of acetylcholine. Our results suggest that under conditions of oxygen deprivation, endogenous nitric oxide seems to be inefficient in modulating the cholinergic neurotransmission in guinea-pig ileum.

A computer simulation of recurrent, excitatory networks of sensory neurons of the gut in guinea-pig

Intrinsic sensory neurons of the intestine are connected together to form a recurrent network. They interact by slow excitatory post synaptic potentials (EPSPs), which have a complex dependence on the pattern of input. These networks are unstable and unable to give graded responses to sensory input without some form of inhibition, but inhibitory synaptic potentials are rare in this system. Intrinsic sensory neurons have a characteristic after-hyperpolarization (AHP), but this is depressed during slow EPSPs. To test whether AHPs can provide the inhibition necessary for stability, AHPs, slow EPSPs and their interactions were included in a computer simulation of realistic sensory neuron networks. Residual AHPs as small as 1% of control were found to lead to stable networks capable of giving graded responses.

A parallel algorithm for simulation of large neural networks

The simulation of biologically realistic neural networks requires the numerical solution of very large systems of differential equations. Variables within the system can be changing at rates that vary by orders of magnitude, not only at different times of the solution, but at the same time in different parts of the network. Therefore, an efficient implementation must be able to vary the solution step size, and do so independently in different subsystems. A single processor algorithm is presented in which each neuron can be solved with its own step size by using a priority queue to integrate them in the correct order. But this leaves the problem of how communication and synchronisation between neurons should be managed when executing in parallel. The proposed solution uses an algorithm based on waveform relaxation, which allows groups of neurons on different processors to be solved independently and hence in parallel, for substantial parts of the computation. Realistic test problems were run on a distributed memory parallel computer and results show that speedups of 10 using 16 processors are achievable, and indicate that further speedups may be possible.

A simple mathematical model of second-messenger mediated slow excitatory postsynaptic potentials

We have developed a novel and simple mathematical model of a slow excitatory postsynaptic potential (EPSP) based on an abstraction of the processes of activation, inactivation, and summation of a cAMP, protein kinase A (PKA)-dependent second-messenger cascade. The model describes the activation of receptors, G-proteins, and production of cAMP as the first stage and uses first-order, non-rate-limited kinetics. The second stage corresponds to the release of active, PKA catalytic subunit and can use first- or higher-order kinetics. The third stage represents simple phosphorylation of ion channels and is limited by the number of channels available. The decay of each stage is based on first-order, mass-action kinetics. These equations and some variations were solved numerically and values of the parameters were determined by fitting to a variety of experimental data from myenteric neurons of the guinea-pig ileum. The model produced a slow EPSP with a nonlinear stimulus-response relationship that resulted from the underlying kinetics of the signaling cascade. This system of equations is suitable for incorporation into a large-scale computer simulation, and the methodology should be generalizable to other pathways.

Genesis and role of coordinated firing in a feedforward network: a model study of the enteric nervous system

The enteric nervous system can generate complex motor patterns independently of the central nervous system. The ascending enteric reflex pathway consists of sensory neurons, long chains of a single class of orally directed interneuron and excitatory motor neurons. Because of the importance of this pathway in peristalsis, it was modelled from the firing of sensory neurons through to muscle membrane activation. The model was anatomically realistic in the number of neurons simulated and in the patterns of connections between neurons. The model was also realistic in the simulation of ligand-gated currents in neuron and muscle membrane, current flow in the muscle syncytium and voltage-dependent currents in muscle. Sensory neurons were activated in a manner consistent with a brief mechanical stimulus. Transmission between sensory neurons and first-order interneurons was by slow excitatory transmission, which caused interneurons to fire continuously for several hundred milliseconds. Interneurons then transmitted to higher order interneurons by fast excitatory postsynaptic potentials, each lasting for around 40 ms. As the activity propagated along the pathway, random firing became progressively more synchronized between neurons, until the network as a whole was firing in a coordinated manner. The coordinated firing was a robust phenomenon over a wide range of network and neuron parameters. It is therefore possible that this is a general property of feedforward networks that receive high levels of sustained input. The smooth muscle model indicated that bursting input to the muscle may increase the likelihood of muscle cells firing action potentials when compared with uniform input. In addition, the syncytium model explains how the predicted muscle excitation might be related to current experimental observations.