Bela Joos

Spontaneous Excitation Patterns Computed for Axons with Injury-like Impairments of Sodium Channels and Na/K Pumps

In injured neurons, “leaky” voltage-gated sodium channels (Nav) underlie dysfunctional excitability that ranges from spontaneous subthreshold oscillations (STO), to ectopic (sometimes paroxysmal) excitation, to depolarizing block. In recombinant systems, mechanical injury to Nav1.6-rich membranes causes cytoplasmic Na+-loading and “Nav-CLS”, i.e., coupled left-(hyperpolarizing)-shift of Nav activation and availability. Metabolic injury of hippocampal neurons (epileptic discharge) results in comparable impairment: left-shifted activation and availability and hence left-shifted INa-window. A recent computation study revealed that CLS-based INa-window left-shift dissipates ion gradients and impairs excitability. Here, via dynamical analyses, we focus on sustained excitability patterns in mildly damaged nodes, in particular with more realistic Gaussian-distributed Nav-CLS to mimic “smeared” injury intensity. Since our interest is axons that might survive injury, pumps (sine qua non for live axons) are included. In some simulations, pump efficacy and system volumes are varied. Impacts of current noise inputs are also characterized. The diverse modes of spontaneous rhythmic activity evident in these scenarios are studied using bifurcation analysis. For “mild CLS injury”, a prominent feature is slow pump/leak-mediated EIon oscillations. These slow oscillations yield dynamic firing thresholds that underlie complex voltage STO and bursting behaviors. Thus, Nav-CLS, a biophysically justified mode of injury, in parallel with functioning pumps, robustly engenders an emergent slow process that triggers a plethora of pathological excitability patterns. This minimalist “device” could have physiological analogs. At first nodes of Ranvier and at nociceptors, e.g., localized lipid-tuning that modulated Nav midpoints could produce Nav-CLS, as could co-expression of appropriately differing Nav isoforms.

Left-shifted Nav channels in injured bilayer: primary targets for neuroprotective Nav antagonists?

Mechanical, ischemic, and inflammatory injuries to voltage-gated sodium channel (Nav)-rich membranes of axon initial segments and nodes of Ranvier render Nav channels dangerously leaky. By what means? The behavior of recombinant Nav1.6 (Wang et al., 2009) leads us to postulate that, in neuropathologic conditions, structural degradation of axolemmal bilayer fosters chronically left-shifted Nav channel operation, resulting in ENa rundown. This “sick excitable cell Nav-leak” would encompass left-shifted fast- and slow-mode based persistent INa (i.e., Iwindow and slow-inactivating INa). Bilayer-damage-induced electrophysiological dysfunctions of native-Nav channels, and effects on inhibitors on those channels, should, we suggest, be studied in myelinated axons, exploiting INa(V,t) hysteresis data from sawtooth ramp clamp. We hypothesize that (like dihydropyridines for Ca channels), protective lipophilic Nav antagonists would partition more avidly into disorderly bilayers than into the well-packed bilayers characteristic of undamaged, healthy plasma membrane. Whereas inhibitors using aqueous routes would access all Navs equally, differential partitioning into “sick bilayer” would co-localize lipophilic antagonists with “sick-Nav channels,” allowing for more specific targeting of impaired cells. Molecular fine-tuning of Nav antagonists to favor more avid partitioning into damaged than into intact bilayers could reduce side effects. In potentially salvageable neurons of traumatic and/or ischemic penumbras, in inflammatory neuropathies, in muscular dystrophy, in myocytes of cardiac infarct borders, Nav-leak driven excitotoxicity overwhelms cellular repair mechanisms. Precision-tuning of a lipophilic Nav antagonist for greatest efficacy in mildly damaged membranes could render it suitable for the prolonged continuous administration needed to allow for the remodeling of the excitable membranes, and thus functional recovery.

Viscoelasticity near the gel point: a molecular dynamics study.

We report on extensive molecular dynamics simulations on systems of soft spheres of functionality f, i.e., particles that are capable of bonding irreversibly with a maximum of f other particles. These bonds are randomly distributed throughout the system and imposed with probability p. At a critical concentration of bonds, p(c) approximately 0.2488 for f=6, a gel is formed and the shear viscosity eta diverges according to eta approximately (p(c)-p)(-s). We find s approximately 0.7 in agreement with some experiments and with a recent theoretical prediction based on Rouse dynamics of phantom chains. The diffusion constant decreases as the gel point is approached but does not display a well-defined power law.

Stretching effects on the permeability of water molecules across a lipid bilayer

Using a coarse grained molecular dynamics model of a solvent-surfactant system, we study the effects of stretching on the permeability of water across a lipid bilayer. The density profile, free energy profile, diffusion profile, and tail ordering parameter were computed for a set of stretched membranes maintained at constant area. We computed the water permeability across each membrane using the inhomogeneous solubility-diffusion model first proposed by Marrink and Berendsen [J. Phys. Chem. 98, 4155 (1994)]. We find that even though the resistance to permeation profile shows a great deal of qualitative change as the membranes are stretched, the overall permeability remains nearly constant within the relevant range of stretching. This is explained by the fact that the main barrier to permeation, located in the densest section of the tails, is insensitive to increased area per lipid, as a result of competing effects. Expansion leads to thinning and a higher density in the tail region, the latter leading to an increase in the free energy barrier. However, this is compensated by the reduction in the transverse distance to cross and a larger diffusion coefficient due to increased disordering in the chains.

Mechanosensitive Gating of Kv Channels

K-selective voltage-gated channels (Kv) are multi-conformation bilayer-embedded proteins whose mechanosensitive (MS) Popen(V) implies that at least one conformational transition requires the restructuring of the channel-bilayer interface. Unlike Morris and colleagues, who attributed MS-Kv responses to a cooperative V-dependent closed-closed expansion↔compaction transition near the open state, Mackinnon and colleagues invoke expansion during a V-independent closed↔open transition. With increasing membrane tension, they suggest, the closed↔open equilibrium constant, L, can increase >100-fold, thereby taking steady-state Popen from 0→1; “exquisite sensitivity to small…mechanical perturbations”, they state, makes a Kv “as much a mechanosensitive…as…a voltage-dependent channel”. Devised to explain successive g K (V) curves in excised patches where tension spontaneously increased until lysis, their L-based model falters in part because of an overlooked IK feature; with recovery from slow inactivation factored in, their g(V) datasets are fully explained by the earlier model (a MS V-dependent closed-closed transition, invariant L≥4). An L-based MS-Kv predicts neither known Kv time courses nor the distinctive MS responses of Kv-ILT. It predicts Kv densities (hence gating charge per V-sensor) several-fold different from established values. If opening depended on elevated tension (L-based model), standard g K (V) operation would be compromised by animal cells’ membrane flaccidity. A MS V-dependent transition is, by contrast, unproblematic on all counts. Since these issues bear directly on recent findings that mechanically-modulated Kv channels subtly tune pain-related excitability in peripheral mechanoreceptor neurons we undertook excitability modeling (evoked action potentials). Kvs with MS V-dependent closed-closed transitions produce nuanced mechanically-modulated excitability whereas an L-based MS-Kv yields extreme, possibly excessive (physiologically-speaking) inhibition.

Model for gelation with explicit solvent effects: Structure and dynamics

We study a two-component model for gelation consisting of f-functional monomers (the gel) and inert particles (the solvent). After equilibration as a simple liquid, the gel particles are gradually cross linked to each other until the desired number of cross links have been attained. At a critical cross-link density, the largest gel cluster percolates and an amorphous solid forms. This percolation process is different from ordinary lattice or continuum percolation of a single species in the sense that the critical exponents are new. As the cross-link density p approaches its critical value p(c), the shear viscosity diverges: eta(p) approximately (p(c)-p)(-s) with s a nonuniversal concentration-dependent exponent.

Rigidity transition in polymer melts with van der Waals interaction.

We study the onset of rigidity near the glass transition (GT) in a short-chain polymer melt modelled by a bead-spring model, where all beads interact with Lennard-Jones potentials. The properties of the system are examined above and below the GT. In order to minimize high-cooling-rate effects and computational times, equilibrium configurations are reached via isothermal compression. We monitor quantities such as the heat capacity CP, the short-time diffusion constants D, the viscosity eta , and the shear modulus; the time-dependent shear modulus Gt is compared with the shear modulus mu obtained from an externally applied instantaneous shear. We give a detailed analysis of the effects of such shearing on the system, both locally and globally. It is found that the polymeric glass displays long-time rigid behavior only below a temperature T1 , where T1 < TG. Furthermore, the linear and nonlinear relaxation regimes under applied shear are discussed.

The Hv1 proton channel responds to mechanical stimuli.

Hv1 is a voltage-gated proton channel that is composed of two voltage-sensing domains, each of which is permeable to protons. Pathak et al. find that these voltage-sensing domains are mechanosensitive and that membrane stretch results in a long-lived facilitation of Hv1 activation.

ELASTICITY AND STABILITY OF A HELICAL FILAMENT WITH SPONTANEOUS CURVATURES AND ISOTROPIC BENDING RIGIDITY

We derive the shape equations in terms of Euler angles for a uniform elastic rod with isotropic bending rigidity and spontaneous curvature, and study within this model the elasticity and stability of a helical filament under uniaxial force and torque. We find that due to the special requirements on the boundary conditions, a static slightly distorted helix cannot exist in this system except in some special cases. We show analytically that the extension of a helix may undergo a one-step sharp transition. This agrees quantitatively with experimental observations for a stretched helix in a chemically-defined lipid concentrate (CDLC). We predict further that under twisting, the extension of a helix in CDLC may also exhibit similar behavior. We find that a negative twist tends to destabilize a helix.

Relaxation of a simulated lipid bilayer vesicle compressed by an atomic force microscope

Using coarse-grained molecular dynamics simulations, we study the relaxation of bilayer vesicles, uniaxially compressed by an atomic force microscope cantilever. The relaxation time exhibits a strong force dependence. Force-compression curves are very similar to recent experiments wherein giant unilamellar vesicles were compressed in a nearly identical manner.