Impact on backpropagation of the spatial heterogeneity of sodium channel kinetics in the axon initial segment.

In a variety of neurons, action potentials (APs) initiate at the proximal axon, within a region called the axon initial segment (AIS), which has a high density of voltage-gated sodium channels (NaVs) on its membrane. In pyramidal neurons, the proximal AIS has been reported to exhibit a higher proportion of NaVs with gating properties that are "right-shifted" to more depolarized voltages, compared to the distal AIS. Further, recent experiments have revealed that as neurons develop, the spatial distribution of NaV subtypes along the AIS can change substantially, suggesting that neurons tune their excitability by modifying said distribution. When neurons are stimulated axonally, computational modelling has shown that this spatial separation of gating properties in the AIS enhances the backpropagation of APs into the dendrites. In contrast, in the more natural scenario of somatic stimulation, our simulations show that the same distribution can impede backpropagation, suggesting that the choice of orthodromic versus antidromic stimulation can bias or even invert experimental findings regarding the role of NaV subtypes in the AIS. We implemented a range of hypothetical NaV distributions in the AIS of three multicompartmental pyramidal cell models and investigated the precise kinetic mechanisms underlying such effects, as the spatial distribution of NaV subtypes is varied. With axonal stimulation, proximal NaV availability dominates, such that concentrating right-shifted NaVs in the proximal AIS promotes backpropagation. However, with somatic stimulation, the models are insensitive to availability kinetics. Instead, the higher activation threshold of right-shifted NaVs in the AIS impedes backpropagation. Therefore, recently observed developmental changes to the spatial separation and relative proportions of NaV1.2 and NaV1.6 in the AIS differentially impact activation and availability. The observed effects on backpropagation, and potentially learning via its putative role in synaptic plasticity (e.g. through spike-timing-dependent plasticity), are opposite for orthodromic versus antidromic stimulation, which should inform hypotheses about the impact of the developmentally regulated subcellular localization of these NaV subtypes.

The Donnan-dominated resting state of skeletal muscle fibers contributes to resilience and longevity in dystrophic fibers.

Duchenne muscular dystrophy (DMD) is an X-linked dystrophin-minus muscle-wasting disease. Ion homeostasis in skeletal muscle fibers underperforms as DMD progresses. But though DMD renders these excitable cells intolerant of exertion, sodium overloaded, depolarized, and spontaneously contractile, they can survive for several decades. We show computationally that underpinning this longevity is a strikingly frugal, robust Pump-Leak/Donnan (P-L/D) ion homeostatic process. Unlike neurons, which operate with a costly "Pump-Leak-dominated" ion homeostatic steady state, skeletal muscle fibers operate with a low-cost "Donnan-dominated" ion homeostatic steady state that combines a large chloride permeability with an exceptionally small sodium permeability. Simultaneously, this combination keeps fiber excitability low and minimizes pump expenditures. As mechanically active, long-lived multinucleate cells, skeletal muscle fibers have evolved to handle overexertion, sarcolemmal tears, ischemic bouts, etc.; the frugality of their Donnan dominated steady state lets them maintain the outsized pump reserves that make them resilient during these inevitable transient emergencies. Here, P-L/D model variants challenged with DMD-type insult/injury (low pump-strength, overstimulation, leaky Nav and cation channels) show how chronic "nonosmotic" sodium overload (observed in DMD patients) develops. Profoundly severe DMD ion homeostatic insult/injury causes spontaneous firing (and, consequently, unwanted excitation-contraction coupling) that elicits cytotoxic swelling. Therefore, boosting operational pump-strength and/or diminishing sodium and cation channel leaks should help extend DMD fiber longevity.

A model for studying the energetics of sustained high frequency firing.

Regulating membrane potential and synaptic function contributes significantly to the energetic costs of brain signaling, but the relative costs of action potentials (APs) and synaptic transmission during high-frequency firing are unknown. The continuous high-frequency (200-600Hz) electric organ discharge (EOD) of Eigenmannia, a weakly electric fish, underlies its electrosensing and communication. EODs reflect APs fired by the muscle-derived electrocytes of the electric organ (EO). Cholinergic synapses at the excitable posterior membranes of the elongated electrocytes control AP frequency. Based on whole-fish O2 consumption, ATP demand per EOD-linked AP increases exponentially with AP frequency. Continual EOD-AP generation implies first, that ion homeostatic processes reliably counteract any dissipation of posterior membrane ENa and EK and second that high frequency synaptic activation is reliably supported. Both of these processes require energy. To facilitate an exploration of the expected energy demands of each, we modify a previous excitability model and include synaptic currents able to drive APs at frequencies as high as 600 Hz. Synaptic stimuli are modeled as pulsatile cation conductance changes, with or without a small (sustained) background conductance. Over the full species range of EOD frequencies (200-600 Hz) we calculate frequency-dependent "Na+-entry budgets" for an electrocyte AP as a surrogate for required 3Na+/2K+-ATPase activity. We find that the cost per AP of maintaining constant-amplitude APs increases nonlinearly with frequency, whereas the cost per AP for synaptic input current is essentially constant. This predicts that Na+ channel density should correlate positively with EOD frequency, whereas AChR density should be the same across fish. Importantly, calculated costs (inferred from Na+-entry through Nav and ACh channels) for electrocyte APs as frequencies rise are much less than expected from published whole-fish EOD-linked O2 consumption. For APs at increasingly high frequencies, we suggest that EOD-related costs external to electrocytes (including packaging of synaptic transmitter) substantially exceed the direct cost of electrocyte ion homeostasis.

Calculating the Consequences of Left-Shifted Nav Channel Activity in Sick Excitable Cells.

Two features common to diverse sick excitable cells are "leaky" Nav channels and bleb damage-damaged membranes. The bleb damage, we have argued, causes a channel kinetics based "leakiness." Recombinant (node of Ranvier type) Nav1.6 channels voltage-clamped in mechanically-blebbed cell-attached patches undergo a damage intensity dependent kinetic change. Specifically, they experience a coupled hyperpolarizing (left) shift of the activation and inactivation processes. The biophysical observations on Nav1.6 currents formed the basis of Nav-Coupled Left Shift (Nav-CLS) theory. Node of Ranvier excitability can be modeled with Nav-CLS imposed at varying LS intensities and with varying fractions of total nodal membrane affected. Mild damage from which sick excitable cells might recover is of most interest pathologically. Accordingly, Na+/K+ ATPase (pump) activity was included in the modeling. As we described more fully in our other recent reviews, Nav-CLS in nodes with pumps proves sufficient to predict many of the pathological excitability phenomena reported for sick excitable cells. This review explains how the model came about and outlines how we have used it. Briefly, we direct the reader to studies in which Nav-CLS is being implemented in larger scale models of damaged excitable tissue. For those who might find it useful for teaching or research purposes, we coded the Nav-CLS/node of Ranvier model (with pumps) in NEURON. We include, here, the resulting "Regimes" plot of classes of excitability dysfunction.

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.

The Hv1 proton channel responds to mechanical stimuli.

The voltage-gated proton channel, Hv1, is expressed in tissues throughout the body and plays important roles in pH homeostasis and regulation of NADPH oxidase. Hv1 operates in membrane compartments that experience strong mechanical forces under physiological or pathological conditions. In microglia, for example, Hv1 activity is potentiated by cell swelling and causes an increase in brain damage after stroke. The channel complex consists of two proton-permeable voltage-sensing domains (VSDs) linked by a cytoplasmic coiled-coil domain. Here, we report that these VSDs directly respond to mechanical stimuli. We find that membrane stretch facilitates Hv1 channel opening by increasing the rate of activation and shifting the steady-state activation curve to less depolarized potentials. In the presence of a transmembrane pH gradient, membrane stretch alone opens the channel without the need for strong depolarizations. The effect of membrane stretch persists for several minutes after the mechanical stimulus is turned off, suggesting that the channel switches to a "facilitated" mode in which opening occurs more readily and then slowly reverts to the normal mode observed in the absence of membrane stretch. Conductance simulations with a six-state model recapitulate all the features of the channel's response to mechanical stimulation. Hv1 mechanosensitivity thus provides a mechanistic link between channel activation in microglia and brain damage after stroke.

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 gK(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 gK(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.

Stimulation-induced ectopicity and propagation windows in model damaged axons.

Neural tissue injuries render voltage-gated Na+ channels (Nav) leaky, thereby altering excitability, disrupting propagation and causing neuropathic pain related ectopic activity. In both recombinant systems and native excitable membranes, membrane damage causes the kinetically-coupled activation and inactivation processes of Nav channels to undergo hyperpolarizing shifts. This damage-intensity dependent change, called coupled left-shift (CLS), yields a persistent or "subthreshold" Nav window conductance. Nodes of Ranvier simulations involving various degrees of mild CLS showed that, as the system's channel/pump fluxes attempt to re-establish ion homeostasis, the CLS elicits hyperexcitability, subthreshold oscillations and neuropathic type action potential (AP) bursts. CLS-induced intermittent propagation failure was studied in simulations of stimulated axons, but pump contributions were ignored, leaving open an important question: does mild-injury (small CLS values, pumps functioning well) render propagation-competent but still quiescent axons vulnerable to further impairments as the system attempts to cope with its normal excitatory inputs? We probe this incipient diffuse axonal injury scenario using a 10-node myelinated axon model. Fully restabilized nodes with mild damage can, we show, become ectopic signal generators ("ectopic nodes") because incoming APs stress Na+ / K+ gradients, thereby altering spike thresholds. Comparable changes could contribute to acquired sodium channelopathies as diverse as epileptic phenomena and to the neuropathic amplification of normally benign sensory inputs. Input spike patterns, we found, propagate with good fidelity through an ectopically firing site only when their frequencies exceed the ectopic frequency. This "propagation window" is a robust phenomenon, occurring despite Gaussian noise, large jitter and the presence of several consecutive ectopic nodes.

Membrane order parameters for interdigitated lipid bilayers measured via polarized total-internal-reflection fluorescence microscopy.

Incorporating ethanol in lipid membranes leads to changes in bilayer structure, including the formation of an interdigitated phase. We have used polarized total-internal-reflection fluorescence microscopy (pTIRFM) to measure the order parameter for Texas Red DHPE incorporated in the ethanol-induced interdigitated phase (LßI) formed from ternary lipid mixtures comprising dioleoylphosphatidylcholine, cholesterol and egg sphingomyelin or dipalmitoylphosphatidylcholine. These lipid mixtures have 3 co-existing phases in the presence of ethanol: liquid-ordered, liquid-disordered and LßI. pTIRFM using Texas Red DHPE shows a reversal in fluorescence contrast between the LßI phase and the surrounding disordered phase with changes in the polarization angle. The contrast reversal is due to changes in the orientation of the dye, and provides a rapid method to identify the LßI phase. The measured order parameters for the LßI phase are consistent with a highly ordered membrane environment, similar to a gel phase. An acyl-chain labeled BODIPY-FL-PC was also tested for pTIRFM studies of ethanol-treated bilayers; however, this probe is less useful since the order parameters of the interdigitated phase are consistent with orientations that are close to random, either due to local membrane disorder or to a mixture of extended and looping conformations in which the fluorophore is localized in the polar headgroup region of the bilayer. In summary, we demonstrate that order parameter measurements via pTIRFM using Texas Red-DHPE can rapidly identify the interdigitated phase in supported bilayers. We anticipate that this technique will aid further research in the effects of alcohols and other additives on membranes.

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 I(Na-window). A recent computation study revealed that CLS-based I(Na-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 E(Ion) 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.

Extrusion of small vesicles through nanochannels: a model for experiments and molecular dynamics simulations.

We propose a model that predicts the final sizes of lipid bilayer vesicles produced by pressure extrusion through nanochannels and we conduct large-scale coarse-grained molecular dynamics simulations of the phenomenon. We show that, to a first approximation independent of pressure, vesicle size can be predicted by a simple geometrical argument that considers an invariable inner vesicle volume enclosed by a finitely extensible lipid bilayer. The pressure dependence is then incorporated in our model by arguing that the effective channel radius decreases with increasing pressure due to a thickening of the lubrication layer between the vesicles and the channel wall. We fit our model to the experimental data of Patty and Frisken [Biophys. J. 85, 996 (2003)]. We predict that at high pressure, vesicle size significantly depends on channel length and, therefore, flow rate. The CGMD simulations reproduce the physical principles of the model. They also show the build-up of the stress in the vesicle, and typical rupture scenarios as the pressure gradient is increased.

Perturbed voltage-gated channel activity in perturbed bilayers: implications for ectopic arrhythmias arising from damaged membrane.

The ceaseless opening and closing of the voltage-gated channels (VGCs) underlying cardiac rhythmicity is controlled, in each VGC, by four mobile voltage sensors embedded in bilayer. Every action potential necessitates extensive packing/repacking of voltage sensor domains with adjacent interacting lipid molecules. This renders VGC activity mechanosensitive (MS), i.e., energetically sensitive to the bilayer's mechanical state. Irreversible perturbations of sarcolemmal bilayer such as those associated with ischemia, reperfusion, inflammation, cortical-cytoskeleton abnormalities, bilayer-disrupting toxins, diet aberrations, etc, should therefore perturb VGC activity. Disordered/fluidized bilayer states that facilitate voltage sensor repacking, and thus make VGC opening too easy could, therefore, explain VGC-leakiness in these conditions. To study this in membrane patches we impose mechanical blebbing injury during pipette aspiration-induced membrane stretch, a process that modulates VGC activity irreversibly (plastic regime) and then, eventually, reversibly (elastic regime). Because of differences in sensor-to-gate coupling among different VGCs, their responses to stretch fall into two major categories, MS-Speed, MS-Number, exemplified by Nav and Cav channels. For particular VGCs in perturbed bilayers, leak mechanisms depend on whether or not the rate-limiting voltage-dependent step is MS. Mode-switch transitions might also be mechanosensitive and thus play a role. Incorporated mathematically in axon models, plastic-regime Nav responses elicit ectopic firing behaviors typical of peripheral neuropathies. In cardiomyocytes with mild bleb damage, Nav and/or Cav leaks from irreversible MS modulation (MS-Speed, MS-Number, respectively) could, similarly, foster ectopic arrhythmias. Where pathologically leaky VGCs reside in damaged bilayer, peri-channel bilayer disorder/fluidity conditions could be an important "target feature" for anti-arrhythmic VGC drugs.

Coupled left-shift of Nav channels: modeling the Na⁺-loading and dysfunctional excitability of damaged axons.

Injury to neural tissue renders voltage-gated Na⁺ (Nav) channels leaky. Even mild axonal trauma initiates Na⁺-loading, leading to secondary Ca²âº-loading and white matter degeneration. The nodal isoform is Nav1.6 and for Nav1.6-expressing HEK-cells, traumatic whole cell stretch causes an immediate tetrodotoxin-sensitive Na⁺-leak. In stretch-damaged oocyte patches, Nav1.6 current undergoes damage-intensity dependent hyperpolarizing- (left-) shifts, but whether left-shift underlies injured-axon Nav-leak is uncertain. Nav1.6 inactivation (availability) is kinetically limited by (coupled to) Nav activation, yielding coupled left-shift (CLS) of the two processes: CLS should move the steady-state Nav1.6 "window conductance" closer to typical firing thresholds. Here we simulated excitability and ion homeostasis in free-running nodes of Ranvier to assess if hallmark injured-axon behaviors--Na⁺-loading, ectopic excitation, propagation block--would occur with Nav-CLS. Intact/traumatized axolemma ratios were varied, and for some simulations Na/K pumps were included, with varied in/outside volumes. We simulated saltatory propagation with one mid-axon node variously traumatized. While dissipating the [Na⁺] gradient and hyperactivating the Na/K pump, Nav-CLS generated neuropathic pain-like ectopic bursts. Depending on CLS magnitude, fraction of Nav channels affected, and pump intensity, tonic or burst firing or nodal inexcitability occurred, with [Na⁺] and [K⁺] fluctuating. Severe CLS-induced inexcitability did not preclude Na⁺-loading; in fact, the steady-state Na⁺-leaks elicited large pump currents. At a mid-axon node, mild CLS perturbed normal anterograde propagation, and severe CLS blocked saltatory propagation. These results suggest that in damaged excitable cells, Nav-CLS could initiate cellular deterioration with attendant hyper- or hypo-excitability. Healthy-cell versions of Nav-CLS, however, could contribute to physiological rhythmic firing.

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 E(Na) rundown. This "sick excitable cell Nav-leak" would encompass left-shifted fast- and slow-mode based persistent I(Na) (i.e., I(window) and slow-inactivating I(Na)). 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 I(Na)(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.

Entropic elasticity of dilated and contorted idealized circular chains.

Thermal energy provides random motion to particles that leads to the well-known entropic force, which favors the clumping of linear and circular molecules. We evaluate the entropic force which resists the radial dilation and subsequent twisting out of plane of circular polymers by developing mechanical models and performing molecular dynamics simulations. We find that dilating a circular chain is analogous to stretching its linear counterpart. We also find that the torque applied to an already dilated ring and the resulting twist out of plane are related by a linear relationship for a wide range of deformed configurations and, using this result, we are able to predict the angular fluctuations of such a macromolecule.

Mechanosensitive closed-closed transitions in large membrane proteins: osmoprotection and tension damping.

Multiconformation membrane proteins are mechanosensitive (MS) if their conformations displace different bilayer areas. Might MS closed-closed transitions serve as tension buffers, that is, as membrane "spandex"? While bilayer expansion is effectively instantaneous, transitions of bilayer-embedded MS proteins are stochastic (thermally activated) so spandex kinetics would be critical. Here we model generic two-state (contracted/expanded) stochastic spandexes inspired by known bacterial osmovalves (MscL, MscS) then suggest experimental approaches to test for spandex-like behaviors in these proteins. Modeling shows: 1), spandex kinetics depend on the transition state location along an area reaction coordinate; 2), increasing membrane concentration of a spandex right-shifts its midpoint (= tension-Boltzmann); 3), spandexes with midpoints below the activating tension of an osmovalve could optimize osmovalve deployment (required: large midpoint, barrier near the expanded state); 4), spandexes could damp bilayer tension excursions (required: midpoint at target tension, and for speed, barrier halfway between the contracted and expanded states; the larger the spandex Delta-area, the more precise the maintenance of target tension; higher spandex concentrations damp larger amplitude strain fluctuations). One spandex species could not excel as both first line of defense for osmovalve partners and tension damper. Possible interactions among MS closed-closed and closed-open transitions are discussed for MscS- and MscL-like proteins.

Disordered, stretched, and semiflexible biopolymers in two dimensions.

We study the effects of intrinsic sequence-dependent curvature for a two-dimensional semiflexible biopolymer with short-range correlation in intrinsic curvatures. We show exactly that when not subjected to any external force, such a system is equivalent to a system with a well-defined intrinsic curvature and a proper renormalized persistence length. We find the exact expression for the distribution function of the equivalent system. However, we show that such an equivalent system does not always exist for the polymer subjected to an external force. We find that under an external force, the effect of sequence disorder depends upon the averaging order, the degree of disorder, and the experimental conditions, such as the boundary conditions. Furthermore, a short to moderate length biopolymer may be much softer or has a smaller apparent persistent length than what would be expected from the "equivalent system." Moreover, under a strong stretching force and for a long biopolymer, the sequence disorder is immaterial for elasticity. Finally, the effect of sequence disorder may depend upon the quantity considered.

Sequence-dependent effects on the properties of semiflexible biopolymers.

Using a path integral technique, we show exactly that for a semiflexible biopolymer in constant extension ensemble, no matter how long the polymer and how large the external force, the effects of short-range correlations in the sequence-dependent spontaneous curvatures and torsions can be incorporated into a model with well-defined mean spontaneous curvature and torsion as well as a renormalized persistence length. Moreover, for a long biopolymer with large mean persistence length, the sequence-dependent persistence lengths can be replaced by their mean. However, for a short biopolymer or for a biopolymer with small persistence lengths, inhomogeneity in persistence lengths tends to make physical observables very sensitive to details and therefore less predictable.

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.

Pore formation in a lipid bilayer under a tension ramp: modeling the distribution of rupture tensions.

The rupture of fluid membrane vesicles with a steady ramp of micropipette suction has been shown to produce a distribution of breakage tensions, with a mean that rises rapidly with tension rate. Starting from a lattice model that incorporates the essential features of the lipid bilayers held together with hydrophobic forces, and developing it to handle varying tension rates, we reproduce the main features of the experimental results. In essence, we show that the rupture kinetics are driven by the nucleation and growth of pores, with two limiting kinetics-growth-limited and nucleation-limited. The model has been extended to address the role of peptides in solution that can adsorb and insert themselves into the bilayer. At concentrations below those required to spontaneously rupture the membrane, the effect of the peptides is to lower the rupture tensions systematically for all tension rates.