Biomedical subjects

Herbert Levine

Publications and source records attributed to Herbert Levine.

At least 19 recordsLinked to original sources

PubMed2006

Effective stochastic dynamics on a protein folding energy landscape.

We present an approach to protein folding kinetics using stochastic reaction-coordinate dynamics, in which the effective drift velocities and diffusion coefficients are determined from microscopic simulation data. The resultant Langevin equation can then be used to directly simulate the folding process. Here, we test this approach by applying it to a toy two-state dynamical system and to a funnellike structure-based (Go-type) model. The folding time predictions agree very well with full simulation results. Therefore, we have in hand a fast numerical tool for calculating the folding kinetic properties, even when full simulations are not feasible. In addition, the local drift and diffusion coefficients provide an alternative way to compute the free energy profile in cases where only local sampling can be achieved.

Chemistry, Physical↗

PubMed2006

Fluctuation-induced instabilities in front propagation up a comoving reaction gradient in two dimensions.

We study two-dimensional (2D) fronts propagating up a comoving reaction rate gradient in finite number reaction-diffusion systems. We show that in a 2D rectangular channel, planar solutions to the deterministic mean-field equation are stable with respect to deviations from planarity. We argue that planar fronts in the corresponding stochastic system, on the other hand, are unstable if the channel width exceeds a critical value. Furthermore, the velocity of the stochastic fronts is shown to depend on the channel width in a simple and interesting way, in contrast to fronts in the deterministic mean-field equation. Thus fluctuations alter the behavior of these fronts in an essential way. These effects are shown to be partially captured by introducing a density cutoff in the reaction rate. Moreover, some of the predictions of the cutoff mean-field approach are shown to be in quantitative accord with the stochastic results.

Journal Article↗

PubMed2006

Directional sensing in eukaryotic chemotaxis: a balanced inactivation model.

Many eukaryotic cells, including Dictyostelium discoideum amoebae, fibroblasts, and neutrophils, are able to respond to chemoattractant gradients with high sensitivity. Recent studies have demonstrated that, after the introduction of a chemoattractant gradient, several chemotaxis pathway components exhibit a subcellular reorganization that cannot be described as a simple amplification of the external gradient. Instead, this reorganization has the characteristics of a switch, leading to a well defined front and back. Here, we propose a directional sensing mechanism in which two second messengers are produced at equal rates. The diffusion of one of them, coupled with an inactivation scheme, ensures a switch-like response to external gradients for a large range of gradient steepness and average concentration. Furthermore, our model is able to reverse the subcellular organization rapidly, and its response to multiple simultaneous chemoattractant sources is in good agreement with recent experimental results. Finally, we propose that the dynamics of a heterotrimeric G protein might allow for a specific biochemical realization of our model.

Animals↗

PubMed2006

Embryonic pattern scaling achieved by oppositely directed morphogen gradients.

Morphogens are proteins, often produced in a localized region, whose concentrations spatially demarcate regions of differing gene expression in developing embryos. The boundaries of gene expression are typically sharp and the genes can be viewed as abruptly switching from on to off or vice versa upon crossing the boundary. To ensure the viability of the organism these boundaries must be set at certain fractional positions within the corresponding developing field. Remarkably this can be done with high precision despite the fact that the size of the developing field itself can vary widely from embryo to embryo. How this scaling is accomplished is unknown but it is clear that a single morphogen gradient is insufficient. Here we show how a pair of morphogens A and B, produced at opposite ends of a one-dimensional developing field, can solve the pattern-scaling problem. In the most promising scenario the morphogens interact via an effective annihilation reaction A + B --> slashed circle and the switch occurs according to the absolute concentration of A or B. We define a scaling criterion and show that morphogens coupled in this way can set embryonic markers across the entire developing field in proportion to the field size. This scaling occurs at developing-field sizes of a few times the morphogen decay length. The scaling criterion is not met if instead the gradients couple combinatorially such that downstream genes are regulated by the ratio A/B of the morphogen concentrations.

Animals↗

PubMed2006

Self-engineering capabilities of bacteria.

Under natural growth conditions, bacteria can utilize intricate communication capabilities (e.g. quorum-sensing, chemotactic signalling and plasmid exchange) to cooperatively form (self-organize) complex colonies with elevated adaptability-the colonial pattern is collectively engineered according to the encountered environmental conditions. Bacteria do not genetically store all the information required for creating all possible patterns. Instead, additional information is cooperatively generated as required for the colonial self-organization to proceed. We describe how complex colonial forms (patterns) emerge through the communication-based singular interplay between individual bacteria and the colony. Each bacterium is, by itself, a biotic autonomous system with its own internal cellular informatics capabilities (storage, processing and assessment of information). These afford the cell plasticity to select its response to biochemical messages it receives, including self-alteration and the broadcasting of messages to initiate alterations in other bacteria. Hence, new features can collectively emerge during self-organization from the intracellular level to the whole colony. The cells thus assume newly co-generated traits and abilities that are not explicitly stored in the genetic information of the individuals.

Adaptation, Physiological↗

PubMed2006

Analytic approach to the evolutionary effects of genetic exchange.

We present an approximate analytic study of our previously introduced model of evolution including the effects of genetic exchange. This model is motivated by the process of bacterial transformation. We solve for the velocity, the rate of increase of fitness, as a function of the fixed population size, N. We find the velocity increases with ln N, eventually saturating at an N which depends on the strength of the recombination process. The analytical treatment is seen to agree well with direct numerical simulations of our model equations.

Journal Article↗

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

Front propagation up a reaction rate gradient.

We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of motion of the front. We study the system via reaction-diffusion equations, using the expedient of a cutoff in the reaction rate below some critical density to capture the essential role of fluctuations in the system. For large density, the velocity is large, which allows for an approximate analytic treatment. We derive an analytic approximation for the dependence of the front velocity on bulk particle density, showing that the velocity indeed diverges in the infinite density limit. The form in which diffusion is implemented, namely nearest-neighbor hopping on a lattice, is seen to have an essential impact on the nature of the divergence.

Journal Article↗

PubMed2005

Membrane-bound Turing patterns.

Motivated by recent observations in biological cells, we study Turing patterns in bounded regions where the nonlinear chemical reactions occur on the boundary and where reagent transport occurs in the bulk. Within a generic model, we formulate the stability problem and discuss the conditions for the occurrence of a Turing instability. By choosing other model parameters to be unequal, we find that Turing patterns exist even in the case of equal diffusion constants. Finally, a recently introduced computation technique is utilized to follow the nascent pattern into the highly nonlinear regime.

Animals↗

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↗