Mechanisms of the end-plate potential noise and its implication for the neuromuscular junction anatomy.

We construct a compact model to mimic the membrane voltage response to the concentration of acetylcholine ([ACh]) which is mediated by the stochastic gating of acetylcholine (ACh) receptors. The patterns of the voltage depolarization against [ACh] as well as the accompanying voltage noises are presented. The mechanism of the voltage fluctuation that caused by the stochastic gating of receptors is explained. We consider that our results explain the frequently observed "end-plate (potential) noise" in physiology and electromyographic literature. These results, together with the requirements of evolution pressure on the motor units, explain reasonably the anatomical structure of the neuromuscular junction.

The voltage-depolarization performance vs the free energy cost of a single nACh receptor.

The depolarization of the postsynaptic membrane potential in neuromuscular junction, which is conducted by the (stochastic) opening of nicotinic acetylcholine (nACh) receptors distributed in postsynaptic folds, is an inevitable stage in transmitting the electric signals from neural ends to muscle fibers. To perform this work, free energy must be dissipated. Being the first step in understanding the speech-accuracy-energy trade-off, we calculate the energy dissipation of a tiny membrane system that contains a single nACh receptor, i which firstly the stationary distribution of voltage is calculated based on our new method on solving the high-dimensional ODEs with variable coefficients. The ratio of the extent of depolarized-potential to the dissipated power is used to characterize the energy consuming efficiency of the system.

Characterizing the voltage fluctuations driven by a cluster of ligand-gated channels.

In this paper we present the properties of the voltage fluctuations driven by a cluster of ligand-gated channels. First, the second-order moment of the voltage is expressed in form of the integrated resistance and the random force. Then the power spectrum of the voltage noise is obtained analytically, and it is proved to have the 1/ω^{4}-form. Its mechanism lies in that the randomness of the voltage fluctuation is weaker than channel (conductance) noise, which can be approximately described by the Ornstein-Ulenbeck process.

Tristability in mitochondrial permeability transition pore opening.

Mitochondrial permeability transition pore (PTP), a key regulator of cell life and death processes, is triggered by calcium ions (Ca2+) and potentiated by reactive oxygen species (ROS). Although the two modes of PTP opening, i.e., transient and persistent, have been identified for a long time, its dynamical mechanism is still not fully understood. To test a proposed hypothesis that PTP opening acts as a tristable switch, which is characterized by low, medium, and high open probability, we develop a three-variable model that focused on PTP opening caused by Ca2+ and ROS. For the system reduced to two differential equations for Ca2+ and ROS, both the stability analysis and the potential landscape feature that it exhibits tristability under standard parameters. For the full system, the bifurcation analysis suggests that it can achieve tristability over a wide range of input parameters. Furthermore, parameter sensitivity analysis demonstrates that the existence of tristability is a robust property. In addition, we show how the deterministic tristable property can be understood within a stochastic framework, which also explains the PTP dynamics at the level of a single channel. Overall, this study may yield valuable insights into the intricate regulatory mechanism of PTP opening.

The power spectrum of the membrane voltage driven by a single nACh receptor.

Being the primary mean of translating the chemical signal into the electric signal in neuromuscular junction, the nACh receptor is the first kind of ligand-gated channel that its kinetic structure has been known clearly. The next problem is to know quantitatively how it works in a living system. In this paper, we construct a piece-wise deterministic process to mimic the membrane voltage fluctuation driven by a single nACh receptor. The power spectrum of the voltage fluctuation is solved analytically, which reveals the 1/ω4-type noise.

Non-adiabatic membrane voltage fluctuations driven by two ligand-gated ion channels.

In this paper, we construct a piecewise deterministic Markov process to model the membrane voltage fluctuations driven by two ligand-gated channels. The series-solution method is applied to the third-order ordinary differential equations to get its general solutions. Also, the stationary probability density function (PDF) is just the special solution that satisfies certain boundary conditions. The bifurcation conditions of the PDF at the boundary are obtained analytically. As an application, the PDF is used to calculate the power dissipation of the ionic currents in the (nonequilibrium) steady states.

Free energy dissipation of the spontaneous gating of a single voltage-gated potassium channel.

Potassium channels mainly contribute to the resting potential and re-polarizations, with the potassium electrochemical gradient being maintained by the pump Na+/K+-ATPase. In this paper, we construct a stochastic model mimicking the kinetics of a potassium channel, which integrates temporal evolving of the membrane voltage and the spontaneous gating of the channel. Its stationary probability density functions (PDFs) are found to be singular at the boundaries, which result from the fact that the evolving rates of voltage are greater than the gating rates of the channel. We apply PDFs to calculate the power dissipations of the potassium current, the leakage, and the gating currents. On a physical perspective, the essential role of the system is the K+-battery charging the leakage (L-)battery. A part of power will inevitably be dissipated among the process. So, the efficiency of energy transference is calculated.

Analytical solution of the steady membrane voltage fluctuation caused by a single ion channel.

An analytical steady-state solution of the stochastic model describing the integrated dynamics of the membrane voltage and the gating of a single channel is presented. The voltage density function experiences bifurcation in the parameter space, and the threshold is determined by the comparison between the rates of the voltage evolution and that of the channel gating. It is singular at the reversal potential if the voltage evolves faster than the channel gating. As an application, the entropy production rate associated with the gating currents is calculated; its variation tendency in parameter space is consistent to that of the number of transitions counted from the sample paths. The analysis in this paper identifies the values of parameters that justify the formation of the voltage pulse and the efficient energy cost, which is associated with the singularity of the voltage density functions.

TGF-ß1 related inflammation in the posterior longitudinal ligament of cervical spondylotic myelopathy patients.

AIM: This study aimed to elucidate the pathogenesis of posterior longitudinal ligament (PLL) hypertrophy. METHODS: Cervical PLL specimens were collected from CSM patients during surgery (n = 30) and during routine autopsy (n = 14), and processed for histological examination (HE staining and Masson's Trichrome staining) and IHC (CD3, CD68, CD31, TGF-ß1 and collagen II). In addition, the mRNA expression of collagen I was detected in cervical PLL specimens from 16 CSM patients (n = 16) and from routine autopsy (n = 16) by RT-PCR. RESULTS: Obvious fibrosis, cartilage metaplasia and calcification were found in the cervical PLL of CSM patients. In the degenerated PLL, CD68(+) macrophages were frequently identified, CD3(+) T lymphocytes were occasionally found, and many newly generated small vessels were also present. In the degenerated PLL, of the number of TGF-ß1 positive cells increased markedly when compared with control group. IHC indicated TGF-ß1 was secreted by macrophages. RT-PCR showed a significantly lower mRNA expression of collagen I in the PLL of CSM patients as compared to control group. CONCLUSIONS: Macrophages are the major type of inflammatory cells involved in the cervical PLL degeneration, and TGF-ß1 is related to the cervical PLL degeneration. TGF-ß1 is mainly secreted by macrophages. Anti-inflammation may serve as an alternative non-surgical treatment and prophylactic strategy for PLL degeneration.

Circular stochastic fluctuations in SIS epidemics with heterogeneous contacts among sub-populations.

The conceptual difference between equilibrium and non-equilibrium steady state (NESS) is well established in physics and chemistry. This distinction, however, is not widely appreciated in dynamical descriptions of biological populations in terms of differential equations in which fixed point, steady state, and equilibrium are all synonymous. We study NESS in a stochastic SIS (susceptible-infectious-susceptible) system with heterogeneous individuals in their contact behavior represented in terms of subgroups. In the infinite population limit, the stochastic dynamics yields a system of deterministic evolution equations for population densities; and for very large but finite systems a diffusion process is obtained. We report the emergence of a circular dynamics in the diffusion process, with an intrinsic frequency, near the endemic steady state. The endemic steady state is represented by a stable node in the deterministic dynamics. As a NESS phenomenon, the circular motion is caused by the intrinsic heterogeneity within the subgroups, leading to a broken symmetry and time irreversibility.

Survival and differentiation of neuroepithelial stem cells following transplantation into the lateral ventricle of rats.

Neuroepithelial stem cells (NEPs) demonstrate a high potential for self-renewal and differentiation during embryonic development. To explore the survival and differentiation of NEPs in vivo, we isolated NEPs from green fluorescence protein (GFP) transgenic embryos and transplanted into the lateral ventricle of rats. In vitro culture, NEPs proliferated into neurospheres and differentiated into both neurons and glia. When transplanted into the lateral ventricle of rats, these GFP positive NEPs (GFP+ NEPs) survived and attached to the wall of ventricle. Moreover, grafted cells differentiated into neuron-specific enolase (NSE) positive neurons and glial fibrillary acidic protein (GFAP) positive astrocytes and migrated into the host brain. Thus, our results indicate that NEPs can survive and differentiate into neurons and astrocytes in the lateral ventricle following transplantation.