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2.  Electrical Polarization of Titanium Surfaces for the Enhancement of Osteoblast Differentiation 
Bioelectromagnetics  2013;34(8):599-612.
Electrical stimulation has been used clinically to promote bone regeneration in cases of fractures with delayed union or nonunion, with several in vitro and in vivo reports suggesting its beneficial effects on bone formation. However, the use of electrical stimulation of titanium (Ti) implants to enhance osseointegration is less understood, in part because of the few in vitro models that attempt to represent the in vivo environment. In this article, the design of a new in vitro system that allows direct electrical stimulation of osteoblasts through their Ti substrates without the flow of exogenous currents through the media is presented, and the effect of applied electrical polarization on osteoblast differentiation and local factor production was evaluated. A custom-made polycarbonate tissue culture plate was designed to allow electrical connections directly underneath Ti disks placed inside the wells, which were supplied with electrical polarization ranging from 100 to 500 mV to stimulate MG63 osteoblasts. Our results show that electrical polarization applied directly through Ti substrates on which the cells are growing in the absence of applied electrical currents may increase osteoblast differentiation and local factor production in a voltage-dependent manner.
PMCID: PMC4009505  PMID: 23996899
electrical stimulation; current; osseointegration of metal implants; bone; Ti surface properties; polarization
3.  Slow Noise in the Period of a Biological Oscillator Underlies Gradual Trends and Abrupt Transitions in Phasic Relationships in Hybrid Neural Networks 
PLoS Computational Biology  2014;10(5):e1003622.
In order to study the ability of coupled neural oscillators to synchronize in the presence of intrinsic as opposed to synaptic noise, we constructed hybrid circuits consisting of one biological and one computational model neuron with reciprocal synaptic inhibition using the dynamic clamp. Uncoupled, both neurons fired periodic trains of action potentials. Most coupled circuits exhibited qualitative changes between one-to-one phase-locking with fairly constant phasic relationships and phase slipping with a constant progression in the phasic relationships across cycles. The phase resetting curve (PRC) and intrinsic periods were measured for both neurons, and used to construct a map of the firing intervals for both the coupled and externally forced (PRC measurement) conditions. For the coupled network, a stable fixed point of the map predicted phase locking, and its absence produced phase slipping. Repetitive application of the map was used to calibrate different noise models to simultaneously fit the noise level in the measurement of the PRC and the dynamics of the hybrid circuit experiments. Only a noise model that added history-dependent variability to the intrinsic period could fit both data sets with the same parameter values, as well as capture bifurcations in the fixed points of the map that cause switching between slipping and locking. We conclude that the biological neurons in our study have slowly-fluctuating stochastic dynamics that confer history dependence on the period. Theoretical results to date on the behavior of ensembles of noisy biological oscillators may require re-evaluation to account for transitions induced by slow noise dynamics.
Author Summary
Many biological phenomena exhibit synchronized oscillations in the presence of noise and heterogeneity. These include brain rhythms that underlie cognition and spinal rhythms that underlie rhythmic motor activity like breathing and locomotion. A two oscillator system was constructed in which most of the circuit was implemented in a computer model, and was therefore completely known and under the control of the investigators. The one biological component was an oscillator in which an apparently novel manifestation of biological noise was identified, dynamical noise in the period of the oscillator itself. This study quantifies how much noise and heterogeneity this simple two oscillator system can tolerate before desynchronizing. More complicated systems of oscillators may follow similar principles.
PMCID: PMC4022488  PMID: 24830924
4.  Dynamics of neuromodulatory feedback determines frequency modulation in a reduced respiratory network: A computational study 
Neuromodulators, such as amines and neuropeptides, alter the activity of neurons and neuronal networks. In this work, we investigate how neuromodulators, which activate Gq-protein second messenger systems, can modulate the bursting frequency of neurons in a critical portion of the respiratory neural network, the pre-Bötzinger complex (preBötC). These neurons are a vital part of the ponto-medullary neuronal network, which generates a stable respiratory rhythm whose frequency is regulated by neuromodulator release from the nearby Raphe nucleus. Using a simulated 50-cell network of excitatory preBötC neurons with a heterogeneous distribution of persistent sodium conductance and Ca2+, we determined conditions for frequency modulation in such a network by simulating interaction between Raphe and preBötC nuclei. We found that the positive feedback between the Raphe excitability and preBötC activity induces frequency modulation in the preBötC neurons. In addition, the frequency of the respiratory rhythm can be regulated via phasic release of excitatory neuromodulators from the Raphe nucleus. We predict that the application of a Gq antagonist will eliminate this frequency modulation by the Raphe and keep the network frequency constant and low. In contrast, application of a Gq agonist will result in a high frequency for all levels of Raphe stimulation. Our modeling results also suggest that high [K+] requirement in respiratory brain slice experiments may serve as a compensatory mechanism for low neuromodulatory tone.
PMCID: PMC3647346  PMID: 23202052
Central pattern generator; Endogenous bursting; Pre-Bötzinger complex; preBötC
6.  Conflicting effects of excitatory synaptic and electric coupling on the dynamics of square-wave bursters 
Using two-cell and 50-cell networks of square-wave bursters, we studied how excitatory coupling of individual neurons affects the bursting output of the network. Our results show that the effects of synaptic excitation vs. electrical coupling are distinct. Increasing excitatory synaptic coupling generally increases burst duration. Electrical coupling also increases burst duration for low to moderate values, but at sufficiently strong values promotes a switch to highly synchronous bursts where further increases in electrical or synaptic coupling have a minimal effect on burst duration. These effects are largely mediated by spike synchrony, which is determined by the stability of the in-phase spiking solution during the burst. Even when both coupling mechanisms are strong, one form (in-phase or anti-phase) of spike synchrony will determine the burst dynamics, resulting in a sharp boundary in the space of the coupling parameters. This boundary exists in both two cell and network simulations. We use these results to interpret the effects of gap-junction blockers on the neuronal circuitry that underlies respiration.
PMCID: PMC3190594  PMID: 21584773
Pacemaker neuron; Square-wave bursting; Synchronization; Bifurcation analysis
7.  Synaptic and Intrinsic Determinants of the Phase Resetting Curve for Weak Coupling 
A phase resetting curve (PRC) keeps track of the extent to which a perturbation at a given phase advances or delays the next spike, and can be used to predict phase locking in networks of oscillators. The PRC can be estimated by convolving the waveform of the perturbation with the infinitesimal PRC (iPRC) under the assumption of weak coupling. The iPRC is often defined with respect to an infinitesimal current as zi(ϕ), where ϕ is phase, but can also be defined with respect to an infinitesimal conductance change as zg(ϕ). In this paper, we first show that the two approaches are equivalent. Coupling waveforms corresponding to synapses with different time courses sample zg(ϕ) in predictably different ways. We show that for oscillators with Type I excitability, an anomalous region in zg(ϕ) with opposite sign to that seen otherwise is often observed during an action potential. If the duration of the synaptic perturbation is such that it effectively samples this region, PRCs with both advances and delays can be observed despite Type I excitability. We also show that changing the duration of a perturbation so that it preferentially samples regions of stable or unstable slopes in zg(ϕ) can stabilize or destabilize synchrony in a network with the corresponding dynamics.
PMCID: PMC3059351  PMID: 20700637
8.  High Frequency Stimulation Selectively Blocks Different Types of Fibers in Frog Sciatic Nerve 
Conduction block using high frequency alternating current (HFAC) stimulation has been shown to reversibly block conduction through various nerves. However, unlike simulations and experiments on myelinated fibers, prior experimental work in our lab on the sea-slug, Aplysia, found a nonmonotonic relationship between frequency and blocking thresholds in the unmyelinated fibers. To resolve this discrepancy, we investigated the effect of HFAC waveforms on the compound action potential of the sciatic nerve of frogs. Maximal stimulation of the nerve produces a compound action potential consisting of the A-fiber and C-fiber components corresponding to the myelinated and unmyelinated fibers’ response. In our study, HFAC waveforms were found to induce reversible block in the A-fibers and C-fibers for frequencies in the range of 5–50 kHz and for amplitudes from 0.1–1 mA. Although the A-fibers demonstrated the monotonically increasing threshold behavior observed in published literature, the C-fibers displayed a nonmonotonic relationship, analogous to that observed in the unmyelinated fibers of Aplysia. This differential blocking behavior observed in myelinated and unmyelinated fibers during application of HFAC waveforms has diverse implications for the fields of selective stimulation and pain management.
PMCID: PMC3308706  PMID: 21859632
Compound action potential; A-fiber; C-fiber; selective stimulation; pain
9.  Two types of independent bursting mechanisms in inspiratory neurons: an integrative model 
The network of coupled neurons in the pre-Bötzinger complex (pBC) of the medulla generates a bursting rhythm, which underlies the inspiratory phase of respiration. In some of these neurons, bursting persists even when synaptic coupling in the network is blocked and respiratory rhythmic discharge stops. Bursting in inspiratory neurons has been extensively studied, and two classes of bursting neurons have been identified, with bursting mechanism depends on either persistent sodium current or changes in intracellular Ca2+, respectively. Motivated by experimental evidence from these intrinsically bursting neurons, we present a two-compartment mathematical model of an isolated pBC neuron with two independent bursting mechanisms. Bursting in the somatic compartment is modeled via inactivation of a persistent sodium current, whereas bursting in the dendritic compartment relies on Ca2+ oscillations, which are determined by the neuromodulatory tone. The model explains a number of conflicting experimental results and is able to generate a robust bursting rhythm, over a large range of parameters, with a frequency adjusted by neuromodulators.
PMCID: PMC3065506  PMID: 20838868
Respiratory rhythm; Dendritic bursting; Ca2+ oscillations; Pre-Bötzinger complex; Intrinsic burster; Endogenous neurotransmitters
10.  Causes of Transient Instabilities in the Dynamic Clamp 
The dynamic clamp is a widely used method for integrating mathematical models with electrophysiological experiments. This method involves measuring the membrane voltage of a cell, using it to solve computational models of ion channel dynamics in real-time, and injecting the calculated current(s) back into the cell. Limitations of this technique include those associated with single electrode current clamping and the sampling effects caused by the dynamic clamp. In this study, we show that the combination of these limitations causes transient instabilities under certain conditions. Through physical experiments and simulations, we show that dynamic clamp instability is directly related to the sampling delay and the maximum simulated conductance being injected. It is exaggerated by insufficient electrode series resistance and capacitance compensation. Increasing the sampling rate of the dynamic clamp system increases dynamic clamp stability; however, this improvement, is constrained by how well the electrode series resistance and capacitance are compensated. At present, dynamic clamp sampling rates are justified solely on the temporal dynamics of the models being simulated; here we show that faster rates increase the stable range of operation for the dynamic clamp system. In addition, we show that commonly accepted levels of resistance compensation nevertheless significantly compromise the stability of a dynamic clamp system.
PMCID: PMC2748832  PMID: 19228559
Action potential; biological cells; control systems; nervous system

Results 1-10 (10)