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Herbert Levine

Publications and source records attributed to Herbert Levine.

At least 19 recordsLinked to original sources
PubMed2005

Division accuracy in a stochastic model of Min oscillations in Escherichia coli.

Accurate cell division in Escherichia coli requires the Min proteins MinC, MinD, and MinE as well as the presence of nucleoids. MinD and MinE exhibit spatial oscillations, moving from pole to pole of the bacterium, resulting in an average MinD concentration that is low at the center of the cell and high at the poles. This concentration minimum is thought to signal the site of cell division. Deterministic models of the Min oscillations reproduce many observed features of the system, including the concentration minimum of MinD. However, there are only a few thousand Min proteins in a bacterium, so stochastic effects are likely to play an important role. Here, we show that Monte Carlo simulations with a large number of proteins agree well with the results from a deterministic treatment of the equations. The location of minimum local MinD concentration is too variable to account for cell division accuracy in wild-type, but is consistent with the accuracy of cell division in cells without nucleoids. This finding confirms the need to include additional mechanisms, such as reciprocal interactions with the cell division ring or positioning of the nucleoids, to explain wild-type accuracy.

Adenosine Triphosphatases↗
PubMed2005

Protein oligomerization through domain swapping: role of inter-molecular interactions and protein concentration.

Domain swapping has been shown to be an important mechanism controlling multiprotein assembly and has been suggested recently as a possible mechanism underlying protein aggregation. Understanding oligomerization via domain swapping is therefore of theoretical and practical importance. By using a symmetrized structure-based (Gō) model, we demonstrate that in the free-energy landscape of domain swapping, a large free-energy barrier separates monomeric and domain-swapped dimeric configurations. We investigate the effect of finite monomer concentration, by implementing a new semi-analytical method, which involves computing the second virial coefficient, a thermodynamic indicator of inter-molecular interactions. This method, together with the symmetrized structure-based (Gō) model, minimizes the need for expensive many-protein simulations, providing a convenient framework to investigate concentration effect. Finally, we perform direct simulations of domain-swapped trimer formation, showing that this modeling approach can be used for higher-order oligomers.

Dimerization↗
PubMed2005

Excitation-contraction coupling gain and cooperativity of the cardiac ryanodine receptor: a modeling approach.

During calcium-induced calcium-release, the ryanodine receptor (RyR) opens and releases large amounts of calcium from the sarcoplasmic reticulum into the cytoplasm of the myocyte. Recent experiments have suggested that cooperativity between the four monomers comprising the RyR plays an important role in the dynamics of the overall receptor. Furthermore, this cooperativity can be affected by the binding of FK506 binding protein, and hence, modulated by adrenergic stimulation through the phosphorylating action of protein kinase A. This has important implications for heart failure, where it has been hypothesized that RyR hyperphosphorylation, resulting in a loss of cooperativity, can lead to a persistent leak and a reduced sarcoplasmic-reticula content. In this study, we construct a theoretical model that examines the cooperativity via the assumption of an allosteric interaction between the four subunits. We find that the level of cooperativity, regulated by the binding of FK506 binding-protein, can have a dramatic effect on the excitation-contraction coupling gain and that this gain exhibits a clear maximum. These findings are compared to currently available data from different species and allows for an evaluation of the aforementioned heart-failure scenario.

Allosteric Site↗
PubMed2005

Fluctuation-regularized front propagation dynamics in reaction-diffusion systems.

We introduce and study a new class of fronts in finite particle-number reaction-diffusion systems, corresponding to propagating up a reaction-rate gradient. We show that these systems have no traditional mean-field limit, as the nature of the long-time front solution in the stochastic process differs essentially from that obtained by solving the mean-field deterministic reaction-diffusion equations. Instead, one can incorporate some aspects of the fluctuations via introducing a density cutoff. Using this method, we derive analytic expressions for the front velocity dependence on bulk particle density and show self-consistently why this cutoff approach can get the correct leading-order physics.

Biological Evolution↗
PubMed2005

Recombination dramatically speeds up evolution of finite populations.

We study the role of recombination, in the form of bacterial transformation, in speeding up Darwinian evolution. This is done by adding a new process to a previously studied Markov model of evolution on a smooth fitness landscape; this new process allows alleles to be exchanged with those in the surrounding medium. Our results, both numerical and analytic, indicate that, for a wide range of intermediate population sizes, recombination dramatically speeds up the rate of evolutionary advance.

Bacteria↗
PubMed2005

Structure of infectious prions: stabilization by domain swapping.

A candidate structure for the minimal prion infectious unit is a recently discovered protein oligomer modeled as a beta-helical prion trimer (BPT); BPTs can stack to form cross-beta fibrils and may provide insight into protein aggregates of other amyloid diseases. However, the BPT lacks a clear intermonomer binding mechanism. Here we propose an alternative domain-swapped trimeric prion (DSTP) model and show with molecular dynamics (MD) that the DSTP has more favorable intermonomer hydrogen bonding and proline dihedral strain energy than the BPT. This new structural proposal may be tested by lysine and N terminus fluorescent resonance energy transfer (FRET) either directly on recombinant prion protein amyloid aggregates or on synthetic constructs that contain the proline/lysine-rich hinge region critical for domains to swap. In addition, the domain swapping may provide 1) intrinsic entanglement, which can contribute to the remarkable temperature stability of the infectious prion structure and help explain the absence of PrP(Sc) monomers, 2) insight into why specific prolines are potentially relevant to three inherited forms of prion disease, and 3) a simple explanation of prion strains assuming the strain is encoded in the monomer number of the oligomers.

Amyloid↗
PubMed2004

Domain swapping is a consequence of minimal frustration.

The same energy landscape principles associated with the folding of proteins into their monomeric conformations should also describe how these proteins oligomerize into domain-swapped conformations. We tested this hypothesis by using a simplified model for the epidermal growth factor receptor pathway substrate 8 src homology 3 domain protein, both of whose monomeric and domain-swapped structures have been solved. The model, which we call the symmetrized Gō-type model, incorporates only information regarding the monomeric conformation in an energy function for the dimer to predict the domain-swapped conformation. A striking preference for the correct domain-swapped structure was observed, indicating that overall monomer topology is a main determinant of the structure of domain-swapped dimers. Furthermore, we explore the free energy surface for domain swapping by using our model to characterize the mechanism of oligomerization.

Binding Sites↗
PubMed2004

Dynamic instabilities of fracture under biaxial strain using a phase field model.

We present a phase-field model of the propagation of fracture under plane strain. This model, based on simple physical considerations, is able to accurately reproduce the different behavior of cracks (the principle of local symmetry, the Griffith and Irwin criteria, and mode-I branching). In addition, we test our model against recent experimental findings showing the presence of oscillating cracks under biaxial load. Our model again reproduces well observed supercritical Hopf bifurcation and is therefore the first simulation which does so.

Journal Article↗
PubMed2004

Analytical study of the effect of recombination on evolution via DNA shuffling.

DNA shuffling is an evolutionary protocol wherein cycles of selection, recombination, mutation, and amplification are employed to evolve proteins and DNA sequences. Experiments have shown its superiority to traditional protocols which do not employ recombination. Motivated by DNA shuffling, we investigate a multilocus evolutionary model that incorporates selection, recombination, and point mutations. Due to simplicity of the model, for the case of an infinite population we can obtain a full analytical treatment of both its dynamical and equilibrium properties, and study the benefit of recombination explicitly and quantitatively. We also briefly discuss finite-population size corrections.

Animals↗
PubMed2004

Bacterial linguistic communication and social intelligence.

Bacteria have developed intricate communication capabilities (e.g. quorum-sensing, chemotactic signaling and plasmid exchange) to cooperatively self-organize into highly structured colonies with elevated environmental adaptability. We propose that bacteria use their intracellular flexibility, involving signal transduction networks and genomic plasticity, to collectively maintain linguistic communication: self and shared interpretations of chemical cues, exchange of chemical messages (semantic) and dialogues (pragmatic). Meaning-based communication permits colonial identity, intentional behavior (e.g. pheromone-based courtship for mating), purposeful alteration of colony structure (e.g. formation of fruiting bodies), decision-making (e.g. to sporulate) and the recognition and identification of other colonies - features we might begin to associate with a bacterial social intelligence. Such a social intelligence, should it exist, would require going beyond communication to encompass unknown additional intracellular processes to generate inheritable colonial memory and commonly shared genomic context.

Adaptation, Physiological↗
PubMed2004

Cooperativity can reduce stochasticity in intracellular calcium dynamics.

The opening of inositol (1,4,5)-triphosphate (IP(3)) receptors, clustered at discrete sites on the endoplasmic reticulum, can lead to large-scale intracellular calcium waves. Recent experiments in Xenopus oocytes have shown that the inter-wave intervals for these waves have a standard deviation that is much smaller than their mean and that the background calcium concentration exhibits a slow rise during the interwave interval. Using a simple mathematical model, we examine the possibility that this slow rise increases the cooperativity between the openings of the clusters. We find that our model, coupled to the usual assumption that the pumps on the endoplasmic reticulum are activated instantaneously, is unable to explain the observed data: the clusters are found to fire independently and the inter-wave interval distribution is a Poisson distribution with a standard deviation that is approximately equal to its mean. On the other hand, we find that incorporating pumps that slowly activate leads to a slow increase in the background calcium concentration which makes global events progressively more likely to occur. We show that this cooperativity results in much smaller standard deviations and inter-wave interval distributions that are clearly not Poisson distributions.

Animals↗
PubMed2004

Physical schemata underlying biological pattern formation-examples, issues and strategies.

Biological systems excel at building spatial structures on scales ranging from nanometers to kilometers and exhibit temporal patterning from milliseconds to years. One approach that nature has taken to accomplish this relies on the harnessing of pattern-forming processes of non-equilibrium physics and chemistry. For these systems, the study of biological pattern formation starts with placing a biological phenomenon of interest within the context of the proper pattern-formation schema and then focusing on the ways in which control is exerted to adapt the pattern to the needs of the organism. This approach is illustrated by several examples, notably bacterial colonies (diffusive-growth schema) and intracellular calcium waves (excitable-media schema).

Animals↗
PubMed2003

Wave nucleation rate in excitable systems in the low noise limit.

Motivated by recent experiments on intracellular calcium dynamics, we study the general issue of fluctuation-induced nucleation of waves in excitable media. We utilize a stochastic Fitzhugh-Nagumo model for this study, a spatially extended nonpotential pair of equations driven by thermal (i.e., white) noise. The nucleation rate is determined by finding the most probable escape path via minimization of an action related to the deviation of the fields from their deterministic trajectories. Our results pave the way both for studies of more realistic models of calcium dynamics as well as of nucleation phenomena in other nonequilibrium pattern-forming processes.

Journal Article↗
PubMed2003

Computational approach for modeling intra- and extracellular dynamics.

We introduce a phase-field approach for diffusion inside and outside a closed cell with damping and with source terms at the stationary interface. The method is compared to exact solutions (where possible) and the more traditional finite element method. It is shown to be very accurate, easy to implement, and computationally inexpensive. We apply our method to a recently introduced model for chemotaxis by Rappel et al. [Biophys. J. 83, 1361 (2002)].

Journal Article↗
PubMed2003

Does the continuum theory of dynamic fracture work?

We investigate the validity of the linear elastic fracture mechanics approach to dynamic fracture. We first test the predictions in a lattice simulation, using a formula of Eshelby for the time-dependent stress intensity factor. Excellent agreement with the theory is found. We then use the same method to analyze the experiment of Sharon and Fineberg. The data here are not consistent with the theoretical expectation.

Journal Article↗
PubMed2003

Dynamics of competitive evolution on a smooth landscape.

We study competitive DNA sequence evolution directed by in vitro protein binding. The steady-state dynamics of this process is well described by a shape-preserving pulse which decelerates and eventually reaches equilibrium. We explain this dynamical behavior within a continuum mean-field framework. Analytical results obtained on the motion of the pulse agree with simulations. Furthermore, finite population correction to the mean-field results are found to be insignificant.

Binding, Competitive↗
PubMed2002

Spectral mixing of rhythmic neuronal signals in sensory cortex.

The ability to compute the difference between two frequencies depends on a nonlinear operation that mixes two periodic signals. Behavioral and psychophysical evidence suggest that such mixing is likely to occur in the mammalian nervous system as a means to compare two rhythmic sensory signals, such as occurs in human audition, and as a means to lock an intrinsic rhythm to a sensory input. However, a neurological substrate for mixing has not been identified. Here we address the issue of nonlinear mixing of neuronal activity in the vibrissa primary sensory cortex of rat, a region that receives intrinsic as well as sensory-driven rhythmic input during natural whisking. In our preparation, the intrinsic signal originates from cortical oscillations that were induced by anesthetics, and the extrinsic input is introduced by periodic stimulation of vibrissae. We observed that the local extracellular current in vibrissa primary sensory cortex contained oscillatory components at the sum and difference of the intrinsic and extrinsic frequencies. In complementary experiments, we observed that the simultaneous stimulation of contralateral and ipsilateral vibrissae at different frequencies also led to current flow at the sum and difference frequencies. We show theoretically that the relative amplitudes of the observed mixture terms can be accounted for by a threshold nonlinearity in the input-output relation of the underlying neurons. In general, our results provide a neurological substrate for the modulation and demodulation of rhythmic neuronal signals for sensory coding and feedback stabilization of motor output.

Animals↗