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Lipid Bilayer Mechanics
Lipid bilayer mechanics is the study of the physical material properties of lipid bilayers, classifying bilayer behavior with stress (mechanics), stress and strain (materials science), strain rather than biochemical interactions. Local point deformations such as membrane protein interactions are typically modelled with the complex theory of Liquid Crystal#Biological liquid crystals, biological liquid crystals but the mechanical properties of a homogeneous bilayer are often characterized in terms of only three mechanical elastic modulus, elastic moduli: the area expansion modulus Ka, a bending modulus Kb and an edge energy \Lambda. For fluid bilayers the shear modulus is by definition zero, as the free rearrangement of molecules within plane means that the structure will not support shear stresses. These mechanical properties affect several membrane-mediated biological processes. In particular, the values of Ka and Kb affect the ability of proteins and small molecules to insert into th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lipid Bilayers
The lipid bilayer (or phospholipid bilayer) is a thin polar membrane made of two layers of lipid molecules. These membranes are flat sheets that form a continuous barrier around all cell (biology), cells. The cell membranes of almost all organisms and many viruses are made of a lipid bilayer, as are the nuclear envelope, nuclear membrane surrounding the cell nucleus, and biological membrane, membranes of the membrane-bound organelles in the cell. The lipid bilayer is the barrier that keeps ions, proteins and other molecules where they are needed and prevents them from diffusing into areas where they should not be. Lipid bilayers are ideally suited to this role, even though they are only a few nanometers in width, because they are impermeable to most water-soluble (hydrophilic) molecules. Bilayers are particularly impermeable to ions, which allows cells to regulate salt concentrations and pH by transporting ions across their membranes using proteins called Ion transporter, ion pump ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phosphatidylcholine
Phosphatidylcholines (PC) are a class of phospholipids that incorporate choline as a headgroup. They are a major component of biological membranes and can be easily obtained from a variety of readily available sources, such as egg yolk or soybeans, from which they are mechanically or chemically extracted using hexane. They are also a member of the lecithin group of yellow-brownish fatty substances occurring in animal and plant tissues. Dipalmitoyl phosphatidylcholine (a.k.a. lecithin) is a major component of pulmonary surfactant and is often used in the L/S ratio to calculate fetal lung maturity. While phosphatidylcholines are found in all plant and animal cells, they are absent in the membranes of most bacteria, including ''Escherichia coli''. Purified phosphatidylcholine is produced commercially. The name ''lecithin'' was derived from Greek λέκιθος, ''lekithos'' 'egg yolk' by Theodore Nicolas Gobley, a French chemist and pharmacist of the mid-19th century, who appli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Budding
Budding or blastogenesis is a type of asexual reproduction in which a new organism develops from an outgrowth or bud due to cell division at one particular site. For example, the small bulb-like projection coming out from the yeast cell is known as a bud. Since the reproduction is asexual, the newly created organism is a clone and excepting mutations is genetically identical to the parent organism. Organisms such as hydra use regenerative cells for reproduction in the process of budding. In hydra, a bud develops as an outgrowth due to repeated cell division at one specific site. These buds develop into tiny individuals and, when fully mature, detach from the parent body and become new independent individuals. Internal budding or endodyogeny is a process of asexual reproduction, favored by parasites such as ''Toxoplasma gondii''. It involves an unusual process in which two daughter cells are produced inside a mother cell, which is then consumed by the offspring prior to their s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cytoskeleton
The cytoskeleton is a complex, dynamic network of interlinking protein filaments present in the cytoplasm of all cells, including those of bacteria and archaea. In eukaryotes, it extends from the cell nucleus to the cell membrane and is composed of similar proteins in the various organisms. It is composed of three main components, microfilaments, intermediate filaments and microtubules, and these are all capable of rapid growth or disassembly dependent on the cell's requirements. A multitude of functions can be performed by the cytoskeleton. Its primary function is to give the cell its shape and mechanical resistance to deformation, and through association with extracellular connective tissue and other cells it stabilizes entire tissues. The cytoskeleton can also contract, thereby deforming the cell and the cell's environment and allowing cells to migrate. Moreover, it is involved in many cell signaling pathways and in the uptake of extracellular material ( endocytosis), the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecular Dynamics
Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of the system. In the most common version, the trajectories of atoms and molecules are determined by numerically solving Newton's equations of motion for a system of interacting particles, where forces between the particles and their potential energies are often calculated using interatomic potentials or molecular mechanical force fields. The method is applied mostly in chemical physics, materials science, and biophysics. Because molecular systems typically consist of a vast number of particles, it is impossible to determine the properties of such complex systems analytically; MD simulation circumvents this problem by using numerical methods. However, long MD simulations are mathematically ill-conditioned, generating cumulative errors in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isotropy
Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe situations where properties vary systematically, dependent on direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. Mathematics Within mathematics, ''isotropy'' has a few different meanings: ; Isotropic manifolds: A manifold is isotropic if the geometry on the manifold is the same regardless of direction. A similar concept is homogeneity. ; Isotropic quadratic form: A quadratic form ''q'' is said to be isotropic if there is a non-zero vector ''v'' such that ; such a ''v'' is an isotropic vector or null vector. In complex geometry, a line through the origin in the direction of an isotropic vector is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton's Method
In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a single-variable function defined for a real variable , the function's derivative , and an initial guess for a root of . If the function satisfies sufficient assumptions and the initial guess is close, then :x_ = x_0 - \frac is a better approximation of the root than . Geometrically, is the intersection of the -axis and the tangent of the graph of at : that is, the improved guess is the unique root of the linear approximation at the initial point. The process is repeated as :x_ = x_n - \frac until a sufficiently precise value is reached. This algorithm is first in the class of Householder's methods, succeeded by Halley's method. The method can also be extended to complex functions an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrange Multiplier
In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equality constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). It is named after the mathematician Joseph-Louis Lagrange. The basic idea is to convert a constrained problem into a form such that the derivative test of an unconstrained problem can still be applied. The relationship between the gradient of the function and gradients of the constraints rather naturally leads to a reformulation of the original problem, known as the Lagrangian function. The method can be summarized as follows: in order to find the maximum or minimum of a function f(x) subjected to the equality constraint g(x) = 0, form the Lagrangian function :\mathcal(x, \lambda) = f(x) + \lambda g(x) and find the stationary points of \mathcal considered as a function of x and the Lagrange mu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weak Formulation
Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations. In a weak formulation, equations or conditions are no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test vectors" or "test functions". In a strong formulation, the solution space is constructed such that these equations or conditions are already fulfilled. The Lax–Milgram theorem, named after Peter Lax and Arthur Milgram who proved it in 1954, provides weak formulations for certain systems on Hilbert spaces. General concept Let V be a Banach space, V' its dual space, A\colon V \to V', and f \in V'. Finding the solution u \in V of the equation Au = f is equivalent to finding u\in V such that, for all v \in V, uv) = f(v). Here, v is called a test vector or test function. To bring this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kirchhoff–Love Plate Theory
The Kirchhoff–Love theory of plates is a two-dimensional mathematical model that is used to determine the stresses and deformations in thin plates subjected to forces and moments. This theory is an extension of Euler-Bernoulli beam theory and was developed in 1888 by LoveA. E. H. Love, ''On the small free vibrations and deformations of elastic shells'', Philosophical trans. of the Royal Society (London), 1888, Vol. série A, N° 17 p. 491–549. using assumptions proposed by Kirchhoff. The theory assumes that a mid-surface plane can be used to represent a three-dimensional plate in two-dimensional form. The following kinematic assumptions that are made in this theory:Reddy, J. N., 2007, Theory and analysis of elastic plates and shells, CRC Press, Taylor and Francis. * straight lines normal to the mid-surface remain straight after deformation * straight lines normal to the mid-surface remain normal to the mid-surface after deformation * the thickness of the plate does not change ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elasticity Of Cell Membranes
A cell membrane defines a boundary between a cell and its environment. The primary constituent of a membrane is a phospholipid bilayer that forms in a water-based environment due to the hydrophilic nature of the lipid head and the hydrophobic nature of the two tails. In addition there are other lipids and proteins in the membrane, the latter typically in the form of isolated rafts. Of the numerous models that have been developed to describe the deformation of cell membranes, a widely accepted model is the fluid mosaic model proposed by Singer and Nicolson in 1972. In this model, the cell membrane surface is modeled as a two-dimensional fluid-like lipid bilayer where the lipid molecules can move freely. The proteins are partially or fully embedded in the lipid bilayer. Fully embedded proteins are called integral membrane proteins because they traverse the entire thickness of the lipid bilayer. These communicate information and matter between the interior and the exterior of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pore Schematic
Pore may refer to: Biology Animal biology and microbiology * Sweat pore, an anatomical structure of the skin of humans (and other mammals) used for secretion of sweat * Hair follicle, an anatomical structure of the skin of humans (and other mammals) used for secretion of sebum * Canal pore, an anatomical structure that is part of the lateral line sense system of some aquatic organisms * Gonopore, a genital pore present in some invertebrates, particularly insects * Ozopore, the external discharge site of defensive glands in millipedes and some arachnids * An opening across both inner and outer bacterial membranes, a part of many Gram-negative bacterial secretion systems * One of the openings communicating with the skin surface at the terminus of lactiferous ducts in milk-producing mammals Plant and fungal biology * Germ pore, a small pore in the outer wall of a fungal spore through which the germ tube exits upon germination * Stoma, a small opening on a plant leaf used for g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
