Fluid-gel coexistence in lipid membranes under differential stress

A widely conserved property of many biological lipid bilayers is their asymmetry. In addition to having distinct compositions on its two sides, a membrane can also exhibit different tensions in its two leaflets, a state known as differential stress. Here, we examine how this stress can influence the phase behavior of the constituent lipid monolayers of a single-component membrane. For temperatures sufficiently close to, but still above, the main transition, molecular dynamics simulations show the emergence of finite gel domains within the compressed leaflet. We describe the thermodynamics of this phenomenon by adding two empirical single-leaflet free energies for the fluid-gel transition, each evaluated at its respective asymmetry-dependent lipid density. Finite size effects arising in simulation are included in the theory through a geometry-dependent interfacial term. Our model reproduces the phase coexistence observed in simulation. It could therefore be used to connect the “hidden variable” of differential stress to experimentally observable properties of the main phase transition. These ideas could be generalized to any first-order bilayer phase transition in the presence of asymmetry, including liquid-ordered/liquid-disordered phase separation.     

A chemical flow system mimics waves of gene expression during segmentation

The early vertebrate developmental process of somitogenesis involves bands of gene expression that form periodically at the posterior end of the presomitic mesoderm (PSM) and traverse it with decreasing width and velocity. We have constructed a chemical flow system that, based on the novel flow-distributed oscillator (FDO) mechanism of wave pattern formation, reproduces key physical features of the PSM and observe concentration waves having similar spatio-temporal behavior. This suggests that the gene expression waves can be understood qualitatively in terms of phase dynamics in an open flow of a self-oscillating medium and that chemical flow systems can be used to mimic and model biological pattern formation during axial growth. In fact, expressions for wavelength and wave velocity derived from phase dynamics are found to be in quantitative agreement with measurements from both the biological and the chemical systems. This indicates that they, despite their significant differences, have common dynamics.     

Simultaneous modeling of phase and calorimetric behavior in an amphiphilic peptide/phospholipid model membrane

Differential scanning calorimetry (DSC) experiments have been performed on the amphiphilic peptide/1,2-bis(perdeuteriopalmitoyl)-sn-glycero-3-phosphocholine system for which partial phase diagrams have been measured by deuterium nuclear magnetic resonance. The solute concentration dependence of the transition enthalpy in such systems is often interpreted in terms of an annulus of lipid withdrawn, by the solvent, from participation in the transition while the bulk lipid melts with its fully enthalpy. This idea is equivalent to postulating ideal mixing between the lipid and the peptide/lipid complex, and there is little justification for such an assumption. Adaptation of regular solution theory to this system demonstrates that the peptide concentration dependence of the transition enthalpies can be incorporated into a thermodynamic model which reproduces the observed phase behavior fairly well without postulating that a complexing annulus of lipid around the peptide be withdrawn from participating in the chain-melting transition. The model parameters determined by simultaneous fitting of the phase behavior and transition enthalpies are used to simulate the DSC scan shapes. The asymmetry of the calorimetric scans for chi 2 less than or equal to 0.02 is reproduced by the model, but a broad component observed for higher concentration is not. In light of the results presented here, previous analyses of the calorimetric behavior of two-component systems in terms of symmetric transitions which do not account for the possible extent of a region of two-phase equilibrium must be questioned.     

Coarse-grained molecular dynamics simulations of phase transitions in mixed lipid systems containing LPA, DOPA, and DOPE lipids

The mechanisms that mediate biomembrane shape transformations are of considerable interest in cell biology. Recent in vitro experiments show that the chemical transformation of minor membrane lipids can induce dramatic shape changes in biomembranes. Specifically, it was observed that the addition of DOPA to DOPE has no effect on the stability of the bilayer structure of the membrane. In contrast, the addition of LPA to DOPE stabilizes the bilayer phase of DOPE, increasing the temperature of a phase transition from the bilayer to the inverted hexagonal phase. This result suggests that the chemical conversion of DOPA to LPA is sufficient for triggering a dramatic change in the shape of biomembranes. The LPA/DOPA/DOPE mixture of lipids provides a simple model system for understanding the molecular events driving the shape change. In this work, we used coarse-grained molecular dynamics simulations to study the phase transitions of this lipid mixture. We show that despite the simplicity of the coarse-grained model, it reproduces the experimentally observed phase changes of: 1), pure LPA and DOPA with respect to changes in the concentration of cations; and 2), LPA/DOPE and DOPA/DOPE mixtures with respect to temperature. The good agreement between the model and experiments suggests that the computationally inexpensive coarse-grained approach can be used to infer macroscopic membrane properties. Furthermore, analysis of the shape of the lipid molecules demonstrates that the phase behavior of single-lipid systems is consistent with molecular packing theory. However, the phase stability of mixed lipid systems exhibits significant deviations from this theory, which suggests that the elastic energy of the lipids, neglected in the packing theory, plays an important role.     

The role of stimulus structure in spatial hyperacuity

In spatial hyperacuity the subjects discriminate a stimulus feature relative to a reference, with an accuracy significantly better than the grain of the retinal mosaic. We show that the normalized thresholds have a dichotomous behavior; they are either insensitive to the spatial parameter in the experiment or increase very steeply with it. This behavior is explained by the involvement in the processing of pixel (receptor) accuracy information about the structure of the stimulus. A computational model employing optimal filtering reproduces the experimental data and suggests that processing of spatial hyperacuity tasks in the human visual system is optimal.     

Excitation dynamics: insights from simplified membrane models

Excitable nerve membranes and models for their electrical activity exhibit a broad repertoire of dynamic behavior. To reveal these behaviors the theoretician seeks a model that is simple enough to analyze yet one that retains adequate biophysical realism. Here we strike such a balance by describing a two-variable simplification of the Hodgkin-Huxley (HH) model, which exhibits many membrane phenomena and reproduces, with good agreement, many HH responses. Comparisons and illustrations are presented for the single spike response, repetitive firing (and its cessation by a brief current pulse), and bistable behavior for increased extracellular K+ concentrations.     

Model referenced method of evoked potential analysis

We have described a method for identifying component wave forms of evoked potentials by reference to a model of the dynamic behavior of neuronal systems. The method parsimoniously reproduces measured data and provides a means for utilizing a priori information from sets of experimental data to discriminate between experimental variables. The method appears successful in quantifying the physiologic variability in the amplitude, shape and latency of EP component wave forms.     

The wild-type circadian period of Neurospora is encoded in the residual network of the null frq mutants

We model theoretically the response of the widely studied circadian oscillator of Neurospora crassa to inactivation of the frq gene. The resulting organism has been termed "arrhythmic" under constant conditions. Under entrainment to periodic temperature cycles Roenneberg, Merrow and coworkers have shown that the phase angle at which spore formation occurs depends on the entrainment period, curiously even in the null frq mutants (frq9 and frq10). We show that such a response does not imply the presence of a self-sustained free-running oscillator. We derive a simple candidate model (a damped harmonic oscillator) for the null frq mutants that successfully reproduces the observed phase angle response. An endogenous period of 21 h for the damped harmonic oscillator coincides with the endogenous period of wild-type Neurospora. This suggests that the (noise driven) "residual system" present in the mutants may have a significant timekeeping role in the wild-type organism. Our model (with no change of parameters) was then used to investigate spore formation patterns under constant conditions and reproduces the corresponding experimental data of Aronson et al. (Proc. Natl. Acad. Sci. USA 91 (1994) 7683.)     

Nocardia-like mutants of a soil coryneform bacterium

Summary A rod-shaped, morphologically stable coryneform soil isolate, strain 9b, gives rise to filamentous and nocardioform mycelial mutants when submitted to mutagenic treatment. Stepwise selection for increasing average length of the rods appears to be necessary to obtain the mycelial form. The mycelial mutant reproduces by fragmentation of the mycelium in the stationary phase of growth and the rough variant exhibits aerial hyphae.     

Dynamical changes in neurons during seizures determine tonic to clonic shift

A tonic-clonic seizure transitions from high frequency asynchronous activity to low frequency coherent oscillations, yet the mechanism of transition remains unknown. We propose a shift in network synchrony due to changes in cellular response. Here we use phase-response curves (PRC) from Morris-Lecar (M-L) model neurons with synaptic depression and gradually decrease input current to cells within a network simulation. This method effectively decreases firing rates resulting in a shift to greater network synchrony illustrating a possible mechanism of the transition phenomenon. PRCs are measured from the M-L conductance based model cell with a range of input currents within the limit cycle. A large network of 3000 excitatory neurons is simulated with a network topology generated from second-order statistics which allows a range of population synchrony. The population synchrony of the oscillating cells is measured with the Kuramoto order parameter, which reveals a transition from tonic to clonic phase exhibited by our model network. The cellular response shift mechanism for the tonic-clonic seizure transition reproduces the population behavior closely when compared to EEG data.     

A stochastic model of kinetochore-microtubule attachment accurately describes fission yeast chromosome segregation

In fission yeast, erroneous attachments of spindle microtubules to kinetochores are frequent in early mitosis. Most are corrected before anaphase onset by a mechanism involving the protein kinase Aurora B, which destabilizes kinetochore microtubules (ktMTs) in the absence of tension between sister chromatids. In this paper, we describe a minimal mathematical model of fission yeast chromosome segregation based on the stochastic attachment and detachment of ktMTs. The model accurately reproduces the timing of correct chromosome biorientation and segregation seen in fission yeast. Prevention of attachment defects requires both appropriate kinetochore orientation and an Aurora B-like activity. The model also reproduces abnormal chromosome segregation behavior (caused by, for example, inhibition of Aurora B). It predicts that, in metaphase, merotelic attachment is prevented by a kinetochore orientation effect and corrected by an Aurora B-like activity, whereas in anaphase, it is corrected through unbalanced forces applied to the kinetochore. These unbalanced forces are sufficient to prevent aneuploidy.     

Modelling spatiotemporal olfactory data in two steps: from binary to Hodgkin-Huxley neurones

Network models of synchronously updated McCulloch-Pitts neurones exhibit complex spatiotemporal patterns that are similar to activities of biological neurones in phase with a periodic local field potential, such as those observed experimentally by Wehr and Laurent (1996, Nature 384, 162-166) in the locust olfactory pathway. Modelling biological neural nets with networks of simple formal units makes the dynamics of the model analytically tractable. It is thus possible to determine the constraints that must be satisfied by its connection matrix in order to make its neurones exhibit a given sequence of activity (see, for instance, Quenet et al., 2001, Neurocomputing 38-40, 831-836). In the present paper, we address the following question: how can one construct a formal network of Hodgkin-Huxley (HH) type neurones that reproduces experimentally observed neuronal codes? A two-step strategy is suggested in the present paper: first, a simple network of binary units is designed, whose activity reproduces the binary experimental codes; second, this model is used as a guide to design a network of more realistic formal HH neurones. We show that such a strategy is indeed fruitful: it allowed us to design a model that reproduces the Wehr-Laurent olfactory codes, and to investigate the robustness of these codes to synaptic noise.     

A neural circuit model of flexible sensorimotor mapping: learning and forgetting on multiple timescales

Volitional behavior relies on the brain's ability to remap sensory flow to motor programs whenever demanded by a changed behavioral context. To investigate the circuit basis of such flexible behavior, we have developed a biophysically based decision-making network model of spiking neurons for arbitrary sensorimotor mapping. The model quantitatively reproduces behavioral and prefrontal single-cell data from an experiment in which monkeys learn visuomotor associations that are reversed unpredictably from time to time. We show that when synaptic modifications occur on multiple timescales, the model behavior becomes flexible only when needed: slow components of learning usually dominate the decision process. However, if behavioral contexts change frequently enough, fast components of plasticity take over, and the behavior exhibits a quick forget-and-learn pattern. This model prediction is confirmed by monkey data. Therefore, our work reveals a scenario for conditional associative learning that is distinct from instant switching between sets of well-established sensorimotor associations.     

A spike generator mechanism model simulates utricular afferents response to sinusoidal vibrations

Using a model of spike generator mechanism (SGM) with a variable threshold we simulate the responses of utricular afferents to sinusoidal vibrations. It reproduces the phase locking characteristics (bifurcations diagrams) and the stimulus frequency firing rate relationships of different types of utricular afferents. We estimate the model parameters selecting the values which best fit the experimental results and we compare them with those from basic mechanisms involved in utricular codification.     

Equilibrium and Kinetics of DNA Overstretching Modeled with a Quartic Energy Landscape

It is well known that the dsDNA molecule undergoes a phase transition from B-DNA into an overstretched state at high forces. For some time, the structure of the overstretched state remained unknown and highly debated, but recent advances in experimental techniques have presented evidence of more than one possible phase (or even a mixed phase) depending on ionic conditions, temperature, and basepair sequence. Here, we present a theoretical model to study the overstretching transition with the possibility that the overstretched state is a mixture of two phases: a structure with portions of inner strand separation (melted or M-DNA), and an extended phase that retains the basepair structure (S-DNA). We model the double-stranded DNA as a chain composed of n segments of length l, where the transition is studied by means of a Landau quartic potential with statistical fluctuations. The length l is a measure of cooperativity of the transition and is key to characterizing the overstretched phase. By analyzing the different values of l corresponding to a wide spectrum of experiments, we find that for a range of temperatures and ionic conditions, the overstretched form is likely to be a mix of M-DNA and S-DNA. For a transition close to a pure S-DNA state, where the change in extension is close to 1.7 times the original B-DNA length, we find l ≈ 25 basepairs regardless of temperature and ionic concentration. Our model is fully analytical, yet it accurately reproduces the force-extension curves, as well as the transient kinetic behavior, seen in DNA overstretching experiments.     

Dynamics of the cell cycle: checkpoints, sizers, and timers

We have developed a generic mathematical model of a cell cycle signaling network in higher eukaryotes that can be used to simulate both the G1/S and G2/M transitions. In our model, the positive feedback facilitated by CDC25 and wee1 causes bistability in cyclin-dependent kinase activity, whereas the negative feedback facilitated by SKP2 or anaphase-promoting-complex turns this bistable behavior into limit cycle behavior. The cell cycle checkpoint is a Hopf bifurcation point. These behaviors are coordinated by growth and division to maintain normal cell cycle and size homeostasis. This model successfully reproduces sizer, timer, and the restriction point features of the eukaryotic cell cycle, in addition to other experimental findings.     

Slower Visuomotor Corrections with Unchanged Latency are Consistent with Optimal Adaptation to Increased Endogenous Noise in the Elderly

We analyzed age-related changes in motor response in a visuomotor compensatory tracking task. Subjects used a manipulandum to attempt to keep a displayed cursor at the center of a screen despite random perturbations to its location. Cross-correlation analysis of the perturbation and the subject response showed no age-related increase in latency until the onset of response to the perturbation, but substantial slowing of the response itself. Results are consistent with age-related deterioration in the ratio of signal to noise in visuomotor response. The task is such that it is tractable to use Bayesian and quadratic optimality assumptions to construct a model for behavior. This model assumes that behavior resembles an optimal controller subject to noise, and parametrizes response in terms of latency, willingness to expend effort, noise intensity, and noise bandwidth. The model is consistent with the data for all young (n = 12, age 20–30) and most elderly (n = 12, age 65–92) subjects. The model reproduces the latency result from the cross-correlation method. When presented with increased noise, the computational model reproduces the experimentally observed age-related slowing and the observed lack of increased latency. The model provides a precise way to quantitatively formulate the long-standing hypothesis that age-related slowing is an adaptation to increased noise.     

Equilibrium and Kinetics of DNA Overstretching Modeled with a Quartic Energy Landscape

It is well known that the dsDNA molecule undergoes a phase transition from B-DNA into an overstretched state at high forces. For some time, the structure of the overstretched state remained unknown and highly debated, but recent advances in experimental techniques have presented evidence of more than one possible phase (or even a mixed phase) depending on ionic conditions, temperature, and basepair sequence. Here, we present a theoretical model to study the overstretching transition with the possibility that the overstretched state is a mixture of two phases: a structure with portions of inner strand separation (melted or M-DNA), and an extended phase that retains the basepair structure (S-DNA). We model the double-stranded DNA as a chain composed of n segments of length l, where the transition is studied by means of a Landau quartic potential with statistical fluctuations. The length l is a measure of cooperativity of the transition and is key to characterizing the overstretched phase. By analyzing the different values of l corresponding to a wide spectrum of experiments, we find that for a range of temperatures and ionic conditions, the overstretched form is likely to be a mix of M-DNA and S-DNA. For a transition close to a pure S-DNA state, where the change in extension is close to 1.7 times the original B-DNA length, we find l ≈ 25 basepairs regardless of temperature and ionic concentration. Our model is fully analytical, yet it accurately reproduces the force-extension curves, as well as the transient kinetic behavior, seen in DNA overstretching experiments.