Author

# Charles S. Peskin

Bio: Charles S. Peskin is an academic researcher from Courant Institute of Mathematical Sciences. The author has contributed to research in topics: Euchromatin & Organelle. The author has an hindex of 5, co-authored 7 publications receiving 3780 citations.

Topics: Euchromatin, Organelle, Nuclear membrane, Cell membrane, Chromatin

##### Papers

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TL;DR: This paper is concerned with the mathematical structure of the immersed boundary (IB) method, which is intended for the computer simulation of fluid–structure interaction, especially in biological fluid dynamics.

Abstract: This paper is concerned with the mathematical structure of the immersed boundary (IB) method, which is intended for the computer simulation of fluid–structure interaction, especially in biological fluid dynamics. The IB formulation of such problems, derived here from the principle of least action, involves both Eulerian and Lagrangian variables, linked by the Dirac delta function. Spatial discretization of the IB equations is based on a fixed Cartesian mesh for the Eulerian variables, and a moving curvilinear mesh for the Lagrangian variables. The two types of variables are linked by interaction equations that involve a smoothed approximation to the Dirac delta function. Eulerian/Lagrangian identities govern the transfer of data from one mesh to the other. Temporal discretization is by a second-order Runge–Kutta method. Current and future research directions are pointed out, and applications of the IB method are briefly discussed. Introduction The immersed boundary (IB) method was introduced to study flow patterns around heart valves and has evolved into a generally useful method for problems of fluid–structure interaction. The IB method is both a mathematical formulation and a numerical scheme. The mathematical formulation employs a mixture of Eulerian and Lagrangian variables. These are related by interaction equations in which the Dirac delta function plays a prominent role. In the numerical scheme motivated by the IB formulation, the Eulerian variables are defined on a fixed Cartesian mesh, and the Lagrangian variables are defined on a curvilinear mesh that moves freely through the fixed Cartesian mesh without being constrained to adapt to it in any way at all.

4,164 citations

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01 Dec 2010

TL;DR: The authors provides an introduction to a wide diversity of problems ranging from population phenomena to demographics, genetics, epidemics and dispersal; in physiological processes, including the circulation, gas exchange in the lungs, control of cell volume, the renal counter-current multiplier mechanism, and muscle mechanics; to mechanisms of neural control.

Abstract: Mathematics in Medicine and the Life Sciences grew from lectures given by the authors at New York University, the University of Utah, and Michigan State University. The material is written for students who have had but one term of calculus, but it contains material that can be used in modeling courses in applied mathematics at all levels through early graduate courses. Numerous exercises are given as well, and solutions to selected exercises are included. Numerous illustrations depict physiological processes, population biology phenomena, models of them, and the results of computer simulations. Mathematical models and methods are becoming increasingly important in medicine and the life sciences. This book provides an introduction to a wide diversity of problems ranging from population phenomena to demographics, genetics, epidemics and dispersal; in physiological processes, including the circulation, gas exchange in the lungs, control of cell volume, the renal counter-current multiplier mechanism, and muscle mechanics; to mechanisms of neural control. Each chapter is graded in difficulty, so a reading of the first parts of each provides an elementary introduction to the processes and their models. Materials that deal with the same topics but in greater depth are included later. Finally, exercises and some solutions are given to test the reader on important parts of the material in the text, or to lead the reader to the discovery of interesting extensions of that material.

125 citations

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TL;DR: It is shown that signal inactivation sharpens signals, reducing variability in the arrival time at the nuclear membrane, and can also compensate for an observed slowdown in signal propagation induced by the presence of organelle barriers.

Abstract: For a chemical signal to propagate across a cell, it must navigate a tortuous environment involving a variety of organelle barriers. In this work we study mathematical models for a basic chemical signal, the arrival times at the nuclear membrane of proteins that are activated at the cell membrane and diffuse throughout the cytosol. Organelle surfaces within human B cells are reconstructed from soft X-ray tomographic images, and modeled as reflecting barriers to the molecules' diffusion. We show that signal inactivation sharpens signals, reducing variability in the arrival time at the nuclear membrane. Inactivation can also compensate for an observed slowdown in signal propagation induced by the presence of organelle barriers, leading to arrival times at the nuclear membrane that are comparable to models in which the cytosol is treated as an open, empty region. In the limit of strong signal inactivation this is achieved by filtering out molecules that traverse non-geodesic paths.

17 citations

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TL;DR: The theory suggests that for binding sites in euchromatin there is an optimal level of volume exclusivity that balances a reduction in the volume searched in finding the binding site, with the height of effective potential barriers the protein must cross during the search process.

15 citations

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TL;DR: It is shown that signal inactivation sharpens signals, reducing variability in the arrival time at the nuclear membrane, and can also compensate for an observed slowdown in signal propagation induced by the presence of organelle barriers.

Abstract: For a chemical signal to propagate across a cell, it must navigate a tortuous environment involving a variety of organelle barriers. In this work we study mathematical models for a basic chemical signal, the arrival times at the nuclear membrane of proteins that are activated at the cell membrane and diffuse throughout the cytosol. Organelle surfaces within human B cells are reconstructed from soft X-ray tomographic images, and modeled as reflecting barriers to the molecules’ diffusion. We show that signal inactivation sharpens signals, reducing variability in the arrival time at the nuclear membrane. Inactivation can also compensate for an observed slowdown in signal propagation induced by the presence of organelle barriers, leading to arrival times at the nuclear membrane that are comparable to models in which the cytosol is treated as an open, empty region. In the limit of strong signal inactivation this is achieved by filtering out molecules that traverse non-geodesic paths.

8 citations

##### Cited by

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01 Oct 2006

TL;DR: This book explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition, providing a link between the two disciplines.

Abstract: This book explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology "Dynamical Systems in Neuroscience" presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties The book introduces dynamical systems starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems Each chapter proceeds from the simple to the complex, and provides sample problems at the end The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum - or taught by math or physics department in a way that is suitable for students of biology This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience

3,683 citations

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TL;DR: This work reviews many significant developments over the past decade of the lattice-Boltzmann method and discusses higherorder boundary conditions and the simulation of microchannel flow with finite Knudsen number.

Abstract: With its roots in kinetic theory and the cellular automaton concept, the lattice-Boltzmann (LB) equation can be used to obtain continuum flow quantities from simple and local update rules based on particle interactions. The simplicity of formulation and its versatility explain the rapid expansion of the LB method to applications in complex and multiscale flows. We review many significant developments over the past decade with specific examples. Some of the most active developments include the entropic LB method and the application of the LB method to turbulent flow, multiphase flow, and deformable particle and fiber suspensions. Hybrid methods based on the combination of the Eulerian lattice with a Lagrangian grid system for the simulation of moving deformable boundaries show promise for more efficient applications to a broader class of problems. We also discuss higherorder boundary conditions and the simulation of microchannel flow with finite Knudsen number. Additionally, the remarkable scalability of the LB method for parallel processing is shown with examples. Teraflop simulations with the LB method are routine, and there is no doubt that this method will be one of the first candidates for petaflop computational fluid dynamics in the near future.

1,585 citations

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TL;DR: In this article, an improved method for computing incompressible viscous flow around suspended rigid particles using a fixed and uniform computational grid is presented. But the main idea is to incorporate Peskin's regularized delta function approach into a direct formulation of the fluid-solid interaction force in order to allow for a smooth transfer between Eulerian and Lagrangian representations.

1,399 citations

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TL;DR: In this paper, a new computational method, the immersed boundary-lattice Boltzmann method, is presented, which combines the most desirable features of the lattice Boltzman and immersed boundary methods and uses a regular Eulerian grid for the flow domain and a Lagrangian grid to follow particles contained in the flow field.

804 citations

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Rice University

^{1}TL;DR: The Grigoryan et al. show that natural and synthetic food dyes can be used as photoabsorbers that enable stereolithographic production of hydrogels containing intricate and functional vascular architectures, and establish intravascular and multivascular design freedoms with photopolymerizablehydrogels.

Abstract: A device made from a hydrogel matrix is provided. The hydrogel matrix includes a photoabsorber with a void architecture in the matrix, having a first vessel architecture and a second vessel architecture that are each tubular and branching, wherein the first and second vessel architectures are fluidically independent from each other. A pre-polymerization solution for forming the device, and methods of fabricating such devices are described. A method of fabricating a 3D hydrogel construct is provided. The method includes using a computer-implemented process to create a 3D model of the construct based on a tessellation of polyhedra having a number of faces connected by edges and vertices, generate a first vascular component of the model, generate a second vascular component of the model, and combine the first and second vascular components of the model.

712 citations