Two theoretical formalisms are widely used in modeling mechanochemical systems such as protein motors: continuum Fokker-Planck models and discrete kinetic models. Both have advantages and disadvantages. Here we present a “finite volume”... more
Two theoretical formalisms are widely used in modeling mechanochemical systems such as protein motors: continuum Fokker-Planck models and discrete kinetic models. Both have advantages and disadvantages. Here we present a “finite volume” procedure to solve Fokker-Planck equations. The procedure relates the continuum equations to a discrete mechanochemical kinetic model while retaining many of the features of the continuum formulation. The resulting numerical algorithm is a generalization of the algorithm developed previously by Fricks, Wang, and Elston through relaxing the local linearization approximation of the potential functions, and a more accurate treatment of chemical transitions. The new algorithm dramatically reduces the number of numerical cells required for a prescribed accuracy. The kinetic models constructed in this fashion retain some features of the continuum potentials, so that the algorithm provides a systematic and consistent treatment of mechanical-chemical responses such as load-velocity relations, which are difficult to capture with a priori kinetic models. Several numerical examples are given to illustrate the performance of the method.
Research Interests: Algorithms, Biophysics, Thermodynamics, Kinetics, Biophysical Chemistry, and 15 moreStochastic processes, Biological Sciences, Computer Simulation, Animals, Physical sciences, Temperature, Molecular motor proteins, FOkker Planck Equation, CHEMICAL SCIENCES, Finite Volume, Theoretical Models, Potential Function, Linear Approximation, Lumping Kinetic Model, and Adenosine Triphosphate
Recent experiments have provided new quantitative measurements of the rippling phenomenon in fields of developing myxobacteria cells. These measurements have enabled us to develop a mathematical model for the ripple phenomenon on the... more
Recent experiments have provided new quantitative measurements of the rippling phenomenon in fields of developing myxobacteria cells. These measurements have enabled us to develop a mathematical model for the ripple phenomenon on the basis of the biochemistry of the C-signaling system, whereby individuals signal by direct cell contact. The model quantitatively reproduces all of the experimental observations and illustrates how
Research Interests:
Many cell movements appear to be driven by the polymerization of actin. Here we show how the force of polymerization can be generated by the thermal motions of the actin filaments near the sites of polymerization. We apply the model to... more
Many cell movements appear to be driven by the polymerization of actin. Here we show how the force of polymerization can be generated by the thermal motions of the actin filaments near the sites of polymerization. We apply the model to explain the observations that the lamellipodial cytoskeleton is organized into an orthogonal network interspersed with filopodial protrusions, and that
Research Interests:
... THE VELIGER © CMS, Inc., 1986 A Model for Shell Patterns Based on Neural Activity by BARD ERMENTROUT ... 28, No.4 a b c Figure 1 Three fundamental classes of shell pigment markings on Bankivia fasciata: a, longitudinal bands; b,... more
... THE VELIGER © CMS, Inc., 1986 A Model for Shell Patterns Based on Neural Activity by BARD ERMENTROUT ... 28, No.4 a b c Figure 1 Three fundamental classes of shell pigment markings on Bankivia fasciata: a, longitudinal bands; b, incremental lines; c, oblique stripes. ...
Three protein motors have been unambiguously identified as rotary engines: the bacterial flagellar motor and the two motors that constitute ATP synthase (F(0)F(1) ATPase). Of these, the bacterial flagellar motor and F(0) motors derive... more
Three protein motors have been unambiguously identified as rotary engines: the bacterial flagellar motor and the two motors that constitute ATP synthase (F(0)F(1) ATPase). Of these, the bacterial flagellar motor and F(0) motors derive their energy from a transmembrane ion-motive force, whereas the F(1) motor is driven by ATP hydrolysis. Here, we review the current understanding of how these protein motors convert their energy supply into a rotary torque.
Research Interests:
Research Interests: Catalysis, Biophysical Chemistry, Biological Sciences, Computer Simulation, Magnesium, and 17 morePhysical sciences, Molecular motor proteins, Hydrogen Bond, CHEMICAL SCIENCES, Hydrogen Bonding, Tight Binding, Protein Conformation, Energy Transfer, Atomic Structure, Energy Source, Protein Binding, Hydrolysis, High Efficiency, Molecular Dynamic Simulation, Conformational Change, Nucleotides, and Adenosine Triphosphate
Human keratinocytes migrate towards the negative pole in DC electric fields of physiological strength. This directional migration is promoted by epidermal growth factor (EGF). To investigate how EGF and its receptor (EGFR) regulate this... more
Human keratinocytes migrate towards the negative pole in DC electric fields of physiological strength. This directional migration is promoted by epidermal growth factor (EGF). To investigate how EGF and its receptor (EGFR) regulate this directionality, we first examined the effect of protein tyrosine kinase inhibitors, including PD158780, a specific inhibitor for EGFR, on this response. At low concentrations, PD158780 inhibited
Research Interests: Cell Migration, Enzyme Inhibitors, Signal Transduction, Biological Sciences, Humans, and 13 moreKeratinocytes, Galvanic Skin Response, Cell, Electromagnetic Fields, Protein Tyrosine Kinase, Phosphorylation, Epidermal Growth Factor, Epidermal Growth Factor Receptor, Growth Factor, Reference Values, Electric Field, Plasma Membrane, and Tyrosine Kinase
Research Interests:
Research Interests:
Research Interests:
We propose that protein translocation across membranes is driven by biased random thermal motion. This "Brownian ratchet" mechanism depends on chemical asymmetries between the cis and trans sides of the membrane. Several... more
We propose that protein translocation across membranes is driven by biased random thermal motion. This "Brownian ratchet" mechanism depends on chemical asymmetries between the cis and trans sides of the membrane. Several mechanisms could contribute to rectifying the thermal motion of the protein, such as binding and dissociation of chaperonins to the translocating chain, chain coiling induced by pH and/or ionic gradients, glycosylation, and disulfide bond formation. This helps explain the robustness and promiscuity of these transport systems.
Research Interests:
The ornate and diverse patterns of seashells testify to the complexity of living systems. Provocative computational explorations have shown that similarly complex patterns may arise from the collective interaction of a small number of... more
The ornate and diverse patterns of seashells testify to the complexity of living systems. Provocative computational explorations have shown that similarly complex patterns may arise from the collective interaction of a small number of rules. This suggests that, although a system may appear complex, it may still be understood in terms of simple principles. It is still debatable whether shell patterns emerge from some undiscovered simple principles, or are the consequence of an irreducibly complex interaction of many effects. Recent work by Boettiger, Ermentrout and Oster on the biological mechanisms of shell patterning has provided compelling evidence that, at least for this system, simplicity produces diversity and complexity.
Research Interests:
The elastic interaction of membrane inclusions provides one of the simplest physical realizations of multibody forces. Here we show how the cross-sectional shape of the inclusion greatly changes the character of the interaction, and... more
The elastic interaction of membrane inclusions provides one of the simplest physical realizations of multibody forces. Here we show how the cross-sectional shape of the inclusion greatly changes the character of the interaction, and illustrates a pattern formation mechanism. The formalism provides a transparent framework for modeling bilayer-inclusion boundary effects on the multibody interaction.
Research Interests:
Research Interests: Algorithms, Water, Molecular Biology, Computational Biology, Catalysis, and 16 moreKinetics, DNA, Molecular, Software, ATPase, Ring, Oxygen, Time Factors, Helicase, Genetic Recombination, Protein Conformation, Protein Binding, Hydrolysis, Protein Transport, DNA primase, and Biochemistry and cell biology
... Sissi, C., Rossi, P., Felluga, F., Formaggio, F., Palumbo, M., Tecilla, P., Toniolo, C. and Scrimin, P. (2001) Dinuclear Zn2+ complexes of synthetic heptapeptides as ... Yang, Q., Xu, JQ, Sun, YS, Li, ZG, Li, YG and Qian, XH (2006)... more
... Sissi, C., Rossi, P., Felluga, F., Formaggio, F., Palumbo, M., Tecilla, P., Toniolo, C. and Scrimin, P. (2001) Dinuclear Zn2+ complexes of synthetic heptapeptides as ... Yang, Q., Xu, JQ, Sun, YS, Li, ZG, Li, YG and Qian, XH (2006) Hydrolysis of plasmid DNA and RNA by amino alkyl ...
Research Interests:
Research Interests: Algorithms, Electrophysiology, Mathematical Biology, Kinetics, Statistical Analysis, and 18 moreNonlinear dynamics, Cell Migration, Linear models, Parameter estimation, Stochastic processes, Biological Sciences, Humans, Mathematical Sciences, Maximum Likelihood, Animals, Chemotaxis, Mathematical, Stochastic differential equation, Acoustic Diffusion Equation Model, Stochastic Model, Electric Field, Nonlinear Diffusion, and Kinesis
Research Interests: Online and ATP synthase
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
We present here a procedure for growing lipid tubules in vitro. This method allows us to grow tubules of consistent shape and structure, and thus can be a useful tool for nano-engineering applications. There are three stages during the... more
We present here a procedure for growing lipid tubules in vitro. This method allows us to grow tubules of consistent shape and structure, and thus can be a useful tool for nano-engineering applications. There are three stages during the tubule growth process: initiation, elongation and termination. Balancing the forces that act on the tubule head shows that the growth of tubules during the elongation phase depends on the balance between osmotic pressure and the viscous drag exerted on the membrane from the substrate and the external fluid. Using a combination of mathematical modelling and experiment, we identify the key forces that control tubule growth during the elongation phase.
Research Interests:
The bacterial flagellar motor (BFM) is responsible for driving bacterial locomotion and chemotaxis, fundamental processes in pathogenesis and biofilm formation. In the BFM, torque is generated at the interface between transmembrane... more
The bacterial flagellar motor (BFM) is responsible for driving bacterial locomotion and chemotaxis, fundamental processes in pathogenesis and biofilm formation. In the BFM, torque is generated at the interface between transmembrane proteins (stators) and a rotor. It is well established that the passage of ions down a transmembrane gradient through the stator complex provides the energy for torque generation. However, the physics involved in this energy conversion remain poorly understood. Here we propose a mechanically specific model for torque generation in the BFM. In particular, we identify roles for two fundamental forces involved in torque generation: electrostatic and steric. We propose that electrostatic forces serve to position the stator, whereas steric forces comprise the actual "power stroke." Specifically, we propose that ion-induced conformational changes about a proline "hinge" residue in a stator α-helix are directly responsible for generating the power stroke. Our model predictions fit well with recent experiments on a single-stator motor. The proposed model provides a mechanical explanation for several fundamental properties of the flagellar motor, including torque-speed and speed-ion motive force relationships, backstepping, variation in step sizes, and the effects of key mutations in the stator.
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Intracellular organelles have characteristic pH ranges that are set and maintained by a balance between ion pumps, leaks, and internal ionic equilibria. Previously, a thermodynamic study by Rybak et al. (Rybak, S., F. Lanni, and R.... more
Intracellular organelles have characteristic pH ranges that are set and maintained by a balance between ion pumps, leaks, and internal ionic equilibria. Previously, a thermodynamic study by Rybak et al. (Rybak, S., F. Lanni, and R. Murphy. 1997. Biophys. J. 73:674-687) identified the key elements involved in pH regulation; however, recent experiments show that cellular compartments are not in thermodynamic equilibrium. We present here a nonequilibrium model of lumenal acidification based on the interplay of ion pumps and channels, the physical properties of the lumenal matrix, and the organelle geometry. The model successfully predicts experimentally measured steady-state and transient pH values and membrane potentials. We conclude that morphological differences among organelles are insufficient to explain the wide range of pHs present in the cell. Using sensitivity analysis, we quantified the influence of pH regulatory elements on the dynamics of acidification. We found that V-ATPase proton pump and proton leak densities are the two parameters that most strongly influence resting pH. Additionally, we modeled the pH response of the Golgi complex to varying external solutions, and our findings suggest that the membrane is permeable to more than one dominant counter ion. From this data, we determined a Golgi complex proton permeability of 8.1 x 10(-6) cm/s. Furthermore, we analyzed the early-to-late transition in the endosomal pathway where Na,K-ATPases have been shown to limit acidification by an entire pH unit. Our model supports the role of the Na,K-ATPase in regulating endosomal pH by affecting the membrane potential. However, experimental data can only be reproduced by (1) positing the existence of a hypothetical voltage-gated chloride channel or (2) that newly formed vesicles have especially high potassium concentrations and small chloride conductance.
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Adsorption of proteins onto membranes can alter the local membrane curvature. This phenomenon has been observed in biological processes such as endocytosis, tubulation, and vesiculation. However, it is not clear how the local surface... more
Adsorption of proteins onto membranes can alter the local membrane curvature. This phenomenon has been observed in biological processes such as endocytosis, tubulation, and vesiculation. However, it is not clear how the local surface properties of the membrane, such as membrane tension, change in response to protein adsorption. In this article, we show that the partial differential equations arising from classical elastic model of lipid membranes, which account for simultaneous changes in shape and membrane tension due to protein adsorption in a local region, cannot be solved for nonaxisymmetric geometries using straightforward numerical techniques; instead, a viscous-elastic formulation is necessary to fully describe the system. Therefore, we develop a viscous-elastic model for inhomogeneous membranes of the Helfrich type. Using the newly available viscous-elastic model, we find that the lipids flow to accommodate changes in membrane curvature during protein adsorption. We show that, at the end of protein adsorption process, the system sustains a residual local tension to balance the difference between the actual mean curvature and the imposed spontaneous curvature. We also show that this change in membrane tension can have a functional impact such as altered response to pulling forces in the presence of proteins.
Research Interests:
The forces that drive sea urchin primary invagination remain mysterious. To solve this mystery we have developed a set of finite element simulations that test five hypothesized mechanisms. Our models show that each of these mechanisms can... more
The forces that drive sea urchin primary invagination remain mysterious. To solve this mystery we have developed a set of finite element simulations that test five hypothesized mechanisms. Our models show that each of these mechanisms can generate an invagination; however, the mechanical properties of an epithelial sheet required for proper invagination are different for each mechanism. For example, we
Research Interests:
Research Interests:
Summary Since the days of van Leeuwenhoek in the 1600s, cell biologists have marveled at how cells crawl. Although much is understood about the contractile forces generated at the leading edge of the crawling cell, little is known about... more
Summary Since the days of van Leeuwenhoek in the 1600s, cell biologists have marveled at how cells crawl. Although much is understood about the contractile forces generated at the leading edge of the crawling cell, little is known about the retraction force at the rear of the ...
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests: Biophysics, Thermodynamics, Energy Conversion, Multidisciplinary, Ion Channels, and 15 moreMovement, Flagella, Molecular motor proteins, Mathematical Model, Theoretical Models, Sodium, Protein Conformation, Torque, Rotation, Proton Motive Force, Cytoplasm, Ions, Molecular Motor, Polystyrenes, and Biomechanical Phenomena
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
The motility of some kinds of bacteria depends on their spiral form, as does the virulence of certain pathogenic species. We propose a novel mechanism for the development of spiral shape in bacteria and the supercoiling of chains... more
The motility of some kinds of bacteria depends on their spiral form, as does the virulence of certain pathogenic species. We propose a novel mechanism for the development of spiral shape in bacteria and the supercoiling of chains ('filaments') of many cells. Recently discovered actin-like proteins lying just under the cell wall form fibers that play a role in maintaining cell shape. Some species have a single actin-like fiber helically wrapped around the cell, while others have two fibers wrapped in the same direction. Here, we show that if these fibers elongate more slowly than growth lengthens the cell, the cell both twists and bends, taking on a spiral shape. We tested this mechanism using a mathematical model of expanding fiber-wound structures and via experiments that measure the shape changes of elongating physical models. Comparison of the model with in vivo experiments on stationary phase Caulobacter crescentus filaments provide the first evidence that mechanical s...
Research Interests:
Research Interests:
Research Interests:
Research Interests: Theoretical biology, Biological Sciences, High Frequency, Protein Structure and Function, Cellular mechanotransduction, and 14 moreHumans, Mathematical Sciences, Diffusion, FOkker Planck Equation, Theoretical, Frequency Dependence, Charge transfer, Experimental Measurement, Membrane Protein, Diffusion Model, Electric Field, Electric Conductivity, Phase Shift, and Kinetic Equation
After a first encounter with most antigens, the immune system responds to subsequent encounters with a faster, more efficient and more strenuous antibody response. The memory of previous antigen contacts is carried by lymphocytes.... more
After a first encounter with most antigens, the immune system responds to subsequent encounters with a faster, more efficient and more strenuous antibody response. The memory of previous antigen contacts is carried by lymphocytes. Expanding on the model developed in Part I of this paper, we examine the optimal strategy available to the immune system for B memory cell production. We again find that the strategy should be of the bang-bang variety.
Research Interests:
Research Interests:
Research Interests: Algorithms, Water, Molecular Biology, Computational Biology, Catalysis, and 16 moreKinetics, DNA, Molecular, Software, ATPase, Ring, Oxygen, Time Factors, Helicase, Genetic Recombination, Protein Conformation, Protein Binding, Hydrolysis, Protein Transport, DNA primase, and Biochemistry and cell biology
Research Interests: Algorithms, Electrophysiology, Mathematical Biology, Kinetics, Statistical Analysis, and 18 moreNonlinear dynamics, Cell Migration, Linear models, Parameter estimation, Stochastic processes, Biological Sciences, Humans, Mathematical Sciences, Maximum Likelihood, Animals, Chemotaxis, Mathematical, Stochastic differential equation, Acoustic Diffusion Equation Model, Stochastic Model, Electric Field, Nonlinear Diffusion, and Kinesis
Research Interests:
Research Interests:
The pentameric ATPase motor gp16 packages double-stranded DNA into the bacteriophage phi29 virus capsid. On the basis of the results of single-molecule experimental studies, we propose a push and roll mechanism to explain how the... more
The pentameric ATPase motor gp16 packages double-stranded DNA into the bacteriophage phi29 virus capsid. On the basis of the results of single-molecule experimental studies, we propose a push and roll mechanism to explain how the packaging motor translocates the DNA in bursts of four 2.5 bp power strokes, while rotating the DNA. In this mechanism, each power stroke accompanies P(i) release after ATP hydrolysis. Since the high-resolution structure of the gp16 motor is not available, we borrowed characterized features from the P4 RNA packaging motor in bacteriophage phi12. For each power stroke, a lumenal lever from a single subunit is electrostatically steered to the DNA backbone. The lever then pushes sterically, orthogonal to the backbone axis, such that the right-handed DNA helix is translocated and rotated in a left-handed direction. The electrostatic association allows tight coupling between the lever and the DNA and prevents DNA from slipping back. The lever affinity for DNA de...
Research Interests: Optical Tweezers, Molecular Biology, Bacteriophages, Single molecule, Stochastic processes, and 11 moreStochastic Simulation, Experimental Study, High Resolution, Mechanical Stress, Dna Packaging, Protein Conformation, Right Handed, Nucleic Acid Conformation, Molecular Motor, Static Electricity, and Biochemistry and cell biology
... 2185 The biophysics of DNA hybridization with immobilized oligonucleotide probes. Vincent Chan, David J. Graves, and Steven E. McKenzie..... ... Knut Debus, Jana Hartmann, Gordan Kilic, and Manfred Lindau..... 2808 ...
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
... If the herbivore is a defoliator, then the parameter function p~ in [2] depends also on ... depend on F(t,a,m). As an illustration of the formulation of plant-herbivore interaction models ... less demonstrable as an infinite... more
... If the herbivore is a defoliator, then the parameter function p~ in [2] depends also on ... depend on F(t,a,m). As an illustration of the formulation of plant-herbivore interaction models ... less demonstrable as an infinite combination of timing, defoliation severity, and fruit attack rates exist ...
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests: Biophysical Chemistry, Anisotropy, Stochastic processes, Biological Sciences, Computer Simulation, and 13 moreViscosity, Physical sciences, ATP synthase, Molecular motor proteins, Friction, CHEMICAL SCIENCES, Tight Binding, Protein Conformation, Energy Transfer, Rotation, Protein Binding, Dimerization, and Adenosine Triphosphate
Research Interests: Biophysical Chemistry, Polymers, Stochastic processes, Biological Sciences, Elasticity, and 13 moreComputer Simulation, Physical sciences, Molecular motor proteins, Motion, CHEMICAL SCIENCES, Protein Complex Detection, Symmetry Breaking, Mechanical Stress, Listeria, Protein Conformation, Microspheres, Experimental Measurement, and Actin Filaments
Research Interests: Kinetics, Membrane Proteins, Crystallization, Biophysical Chemistry, Biological Sciences, and 21 moreElasticity, Computer Simulation, Physical sciences, Endoplasmic Reticulum, Theoretical Analysis, Motion, Free Energy, CHEMICAL SCIENCES, Protein Interaction, Mechanical Stress, Time Dependent, Surface Properties, Molecular Conformation, Protein Conformation, Energy Transfer, Lipid bilayers, Membrane Protein, X Ray Diffraction Analysis, Static Electricity, Membrane Fluidity, and Protein Sorting
Research Interests:
Research Interests:
Research Interests:
Research Interests: Algorithms, Biophysics, Thermodynamics, Kinetics, Biophysical Chemistry, and 15 moreStochastic processes, Biological Sciences, Computer Simulation, Animals, Physical sciences, Temperature, Molecular motor proteins, FOkker Planck Equation, CHEMICAL SCIENCES, Finite Volume, Theoretical Models, Potential Function, Linear Approximation, Lumping Kinetic Model, and Adenosine Triphosphate
Research Interests:
Research Interests: Biophysics, Kinetics, Biophysical Chemistry, Polymers, Entropy, and 16 moreCytoskeleton, Biological Sciences, Animals, Male, Physical sciences, CHEMICAL SCIENCES, Theoretical Models, Listeria, Lumping Kinetic Model, Spermatozoa, Sperm Motility, Cell free System, Experimental Data, Protein Tyrosine Phosphatases, Cell Size, and Yersinia Enterocolitica
Research Interests: Biophysical Chemistry, Biological Sciences, Protein Structure and Function, Computer Simulation, Physical sciences, and 9 moreMolecular motor proteins, CHEMICAL SCIENCES, Mathematical Model, Protein Conformation, Energy Transfer, Torque, Structure activity Relationship, Experimental Data, and Adenosine Triphosphate
Research Interests: Thermodynamics, Membrane Proteins, Biophysical Chemistry, Biological Sciences, Physical sciences, and 14 moreOsmotic pressure, Protein Aggregation, Long Range, Contact angle, Van Der Waals, CHEMICAL SCIENCES, Theoretical Models, Protein Secondary Structure Prediction, Biological Process, Lipid bilayers, Membrane Protein, Gaussian Curvature, Thermodynamic Properties, and Static Electricity
Research Interests: Biophysical Chemistry, Swimming, Molecular Mechanics, Cell Division, Biological Sciences, and 11 moreCellular mechanotransduction, Computer Simulation, Physical sciences, Molecular motor proteins, Spiroplasma, Motion, CHEMICAL SCIENCES, Mechanical Stress, Mycoplasma, Species Specificity, and Conformational Change
Research Interests: Catalysis, Biophysical Chemistry, Biological Sciences, Computer Simulation, Magnesium, and 17 morePhysical sciences, Molecular motor proteins, Hydrogen Bond, CHEMICAL SCIENCES, Hydrogen Bonding, Tight Binding, Protein Conformation, Energy Transfer, Atomic Structure, Energy Source, Protein Binding, Hydrolysis, High Efficiency, Molecular Dynamic Simulation, Conformational Change, Nucleotides, and Adenosine Triphosphate
Research Interests:
Research Interests:
Research Interests:
Prestin is a critical component of the motor complex that generates forces and dimensional changes in cells in response to changes in the cell transmembrane potential. We propose an electro-diffusion model to reveal the frequency and... more
Prestin is a critical component of the motor complex that generates forces and dimensional changes in cells in response to changes in the cell transmembrane potential. We propose an electro-diffusion model to reveal the frequency and voltage dependence of electric charge transfer by prestin. The movement of the combined charge (including chloride ion and protein charges) across the membrane is
Research Interests:
... THE VELIGER © CMS, Inc., 1986 A Model for Shell Patterns Based on Neural Activity by BARD ERMENTROUT ... 28, No.4 a b c Figure 1 Three fundamental classes of shell pigment markings on Bankivia fasciata: a, longitudinal bands; b,... more
... THE VELIGER © CMS, Inc., 1986 A Model for Shell Patterns Based on Neural Activity by BARD ERMENTROUT ... 28, No.4 a b c Figure 1 Three fundamental classes of shell pigment markings on Bankivia fasciata: a, longitudinal bands; b, incremental lines; c, oblique stripes. ...
Research Interests:
The two-headed motor protein kinesin hydrolyzes nucleotide to move unidirectionally along its microtubule track at speeds up to 1000 nm/s (Saxton et al., 1988) and develops forces in excess of 5 pN (Hunt et al., 1994; Svoboda et al., 1... more
The two-headed motor protein kinesin hydrolyzes nucleotide to move unidirectionally along its microtubule track at speeds up to 1000 nm/s (Saxton et al., 1988) and develops forces in excess of 5 pN (Hunt et al., 1994; Svoboda et al., 1 994a). Individual kinesin molecules ...
Research Interests:
MONOGRAPHS IN POPULATION HIOLOGY KDTIT.I) PV ROm.RT M. MAY 1. The Theory of Island Biogeography, by Robert H. MacArthur and Kdward O. \Vilson 2. Involution in Changing Knvironments: Sonic I heorctical Ex- plorations, hy Richard Kevins 3.... more
MONOGRAPHS IN POPULATION HIOLOGY KDTIT.I) PV ROm.RT M. MAY 1. The Theory of Island Biogeography, by Robert H. MacArthur and Kdward O. \Vilson 2. Involution in Changing Knvironments: Sonic I heorctical Ex- plorations, hy Richard Kevins 3. Adaptive Geometry ...