抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

/pdf/pattern-formation-outside-of-equilibrium-1601b9znum.pdf

Pattern formation outside of equilibrium

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

A systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering The form of each evolution equation is characterized by the dispersion relation of its associated linearized version and an integro-differential operator A comprehensive presentation of the inverse scattering method is given and general features of the solution are discussed The relationship of the scattering theory and Backlund transformations is brought out In view of the role of the dispersion relation, the comparatively simple asymptotic states, and the similarity of the method itself to Fourier transforms, this theory can be considered a natural extension of Fourier analysis to nonlinear problems

The Inverse scattering transform fourier analysis for nonlinear problems

AACR Centennial Conference: Translational Cancer Medicine-- Nov 4-8, 2007; Singapore

PL02-05 

All cancers are due to abnormalities in DNA. The availability of the human genome sequence has led to the proposal that resequencing of cancer genomes will reveal the full complement of somatic mutations and hence all the cancer genes. To explore the nature of the information that will be derived from cancer genome sequencing we have sequenced the coding exons of the family of 518 protein kinases, ~1.3Mb DNA per cancer sample, in 210 cancers of diverse histological types. Despite the screen being directed toward the coding regions of a gene family that has previously been strongly implicated in oncogenesis, the results indicate that the majority of somatic mutations detected are “passengers”. There is considerable variation in the number and pattern of these mutations between individual cancers, indicating substantial diversity of processes of molecular evolution between cancers. The imprints of exogenous mutagenic exposures, mutagenic treatment regimes and DNA repair defects can all be seen in the distinctive mutational signatures of individual cancers. This systematic mutation screen and others have previously yielded a number of cancer genes that are frequently mutated in one or more cancer types and which are now anticancer drug targets (for example BRAF , PIK3CA , and EGFR ). However, detailed analyses of the data from our screen additionally suggest that there exist a large number of additional “driver” mutations which are distributed across a substantial number of genes. It therefore appears that cells may be able to utilise mutations in a large repertoire of potential cancer genes to acquire the neoplastic phenotype. However, many of these genes are employed only infrequently. These findings may have implications for future anticancer drug development.

Patterns of Somatic Mutation in Human Cancer Genomes

The History of the Soliton Derivation of the Korteweg-de Vries, Nonlinear Schrodinger and Other Important and Canonical Equations of Mathematical Physics Soliton Equation Families and Solution Methods The -Function, the Hirota Method, the Painleve Property and Backlund Transformations for the Korteweg-de Vries Family of Soliton Equations Connecting Links among the Miracles of Soliton Mathematics

Solitons in mathematics and physics

A method of solution for the ’’derivative nonlinear Schrodinger equation’’ i q t =−q x x ±i (q*q 2) x is presented. The appropriate inverse scattering problem is solved, and the one‐soliton solution is obtained, as well as the infinity of conservation laws. Also, we note that this equation can also possess ’’algebraic solitons.’’

An exact solution for a derivative nonlinear Schrödinger equation

The main purpose of this work is to show how a continuous finite bandwidth of modes can be readily incorporated into the description of post-critical Rayleigh-Benard convection by the use of slowly varying (in space and time) amplitudes. Previous attempts have used a multimodal discrete analysis. We show that in addition to obtaining results consistent with the discrete mode approach, there is a larger class of stable and realizable solutions. The main feature of these solutions is that the amplitude and wave-number of the motion is that of the most unstable mode almost everywhere, but, depending on external and initial conditions, the roll couplets in different parts of space may be 180° out of phase. The resulting discontinuities are smoothed by hyperbolic tangent functions. In addition, it is clear that the mechanism for propagating spatial nonuniformities is diffusive in character.

http://geosci.uchicago.edu/~nnn/Dynamics/newell.pdf

Finite bandwidth, finite amplitude convection

We present the inverse scattering method which provides a means of solution of the initial-value problem for a broad class of nonlinear evolution equations. Special cases include the sine-Gordon equation, the sinh-Gordon equation, the Benney-Newell equation, the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, and generalizations.

Alan C. Newell

Papers

The Inverse scattering transform fourier analysis for nonlinear problems

Solitons in mathematics and physics

An exact solution for a derivative nonlinear Schrödinger equation

Finite bandwidth, finite amplitude convection

Nonlinear-evolution equations of physical significance