A computational method for design of connected catalytic networks in proteins

Computational design of new active sites has generally proceeded by geometrically defining interactions between the reaction transition state(s) and surrounding side‐chain functional groups which maximize transition‐state stabilization, and then searching for sites in protein scaffolds where the specified side‐chain–transition‐state interactions can be realized. A limitation of this approach is that the interactions between the side chains themselves are not constrained. An extensive connected hydrogen bond network involving the catalytic residues was observed in a designed retroaldolase following directed evolution. Such connected networks could increase catalytic activity by preorganizing active site residues in catalytically competent orientations, and enabling concerted interactions between side chains during catalysis, for example, proton shuffling. We developed a method for designing active sites in which the catalytic side chains, in addition to making interactions with the transition state, are also involved in extensive hydrogen bond networks. Because of the added constraint of hydrogen‐bond connectivity between the catalytic side chains, to find solutions, a wider range of interactions between these side chains and the transition state must be considered. Our new method starts from a ChemDraw‐like two‐dimensional representation of the transition state with hydrogen‐bond donors, acceptors, and covalent interaction sites indicated, and all placements of side‐chain functional groups that make the indicated interactions with the transition state, and are fully connected in a single hydrogen‐bond network are systematically enumerated. The RosettaMatch method can then be used to identify realizations of these fully‐connected active sites in protein scaffolds. The method generates many fully‐connected active site solutions for a set of model reactions that are promising starting points for the design of fully‐preorganized enzyme catalysts.     

三种群互惠模型抛物系统解的整体存在与爆破

研究了三种群互惠模型的抛物系统,用上下解方法研究解的整体存在性与爆破问题,并给出了相应的条件.结果表明当种群自身的竞争强时解整体存在,反之则有可能爆破.     

一类互惠生态模型解的周期性和爆破

研究了变系数两种群互惠模型解的周期性和爆破性.首先利用上下解和单调迭代方法研究了互惠模型周期解的存在性、稳定性和吸引性,结果表明种群之间的竞争强于互惠时周期解存在.接着利用比较原理得到了解在有限时刻爆破的充分条件,结果表明种群之间的互惠强于之间的竞争时爆破发生.最后通过数值模拟验证了定理的正确性.     

Predicting Unobserved Exposures from Seasonal Epidemic Data

We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model with a contact rate that fluctuates seasonally. Through the use of a nonlinear, stochastic projection, we are able to analytically determine the lower dimensional manifold on which the deterministic and stochastic dynamics correctly interact. Our method produces a low dimensional stochastic model that captures the same timing of disease outbreak and the same amplitude and phase of recurrent behavior seen in the high dimensional model. Given seasonal epidemic data consisting of the number of infectious individuals, our method enables a data-based model prediction of the number of unobserved exposed individuals over very long times.     

Differentiation of Enamel and Dentine Particles

A method, based on the periodic acid-leucofuchsin reaction, is described, by which dentine particles may be selectively stained with neutral solutions. The method is suitable for pulverized teeth, containing particles with dimensions greater than 1-2μ. It can be applied also to sections. The dentine is stained red by treatment with a buffered neutral solution of periodic acid followed by a dilute solution of unreduced fuchsin; the excess fuchsin being removed by washing with water. The enamel is either unstained or stained a light pink. The loss of material caused by the usual acidic solutions is reduced to negligible proportions.     

一类具有时滞的传染病模型的稳定性分析

研究了一类具有时滞的传染病生物模型．首先研究了该模型的线性稳定性,并给出了一列Hopf分支值,然后利用中心流形定理和正规型方法,给出了确定分支周期解的分支方向与稳定性的计算公式．     

Investigation of Thiazin Dyes as Biological Stains II. Influence of Buffered Solutions on Staining Properties

The effect of buffer solutions of varying reaction upon staining fixed sections with thionin, azures A, B, and C, and methylene blue has been studied. The buffer solutions were employed in one of three different ways: for pre-treatment of the sections, for post-treatment, or as solvents for the dyes. Regardless of the method of employing the buffer solutions it was found that the intensity of staining increased with increasing pH-values (a fact which is generally known to be true in the case of basic dyes). It is not certain whether this effect is due to varying the H-ion concentration or to altering the salt content of the solution, or to both. It was also noticed that there was one point where the staining intensify increased most rapidly. This point was either between pH 5 and pH 6 or between pH 6 and pH 7, its position varying with the method of fixation and of applying the buffer solutions. It was further observed that between pH 5 and pH 7 there were always more pronounced metachromatic effects than with either more acid or more alkaline buffer solutions.     

Investigation of Thiazin Dyes as Biological Stains II. Influence of Buffered Solutions on Staining Properties

The effect of buffer solutions of varying reaction upon staining fixed sections with thionin, azures A, B, and C, and methylene blue has been studied. The buffer solutions were employed in one of three different ways: for pre-treatment of the sections, for post-treatment, or as solvents for the dyes. Regardless of the method of employing the buffer solutions it was found that the intensity of staining increased with increasing pH-values (a fact which is generally known to be true in the case of basic dyes). It is not certain whether this effect is due to varying the H-ion concentration or to altering the salt content of the solution, or to both. It was also noticed that there was one point where the staining intensify increased most rapidly. This point was either between pH 5 and pH 6 or between pH 6 and pH 7, its position varying with the method of fixation and of applying the buffer solutions. It was further observed that between pH 5 and pH 7 there were always more pronounced metachromatic effects than with either more acid or more alkaline buffer solutions.     

The Isolation of Plasma Membrane from Vicia faba Leaves and Pollen Tubes of Luffs cylindrica by the Two-Polymer Phase System

A method for the isolation of plasma membrane enriched fraction from plant sources is described. An aqueous two-phase system is suitable for the isolation of plasma membrane. Purified plasma membrane fractions have been prepared from Vicia faba leaves and pollen tubes of Luffa cylindrica. The determination of marker enzymes shows that the plasma membrane has a high affinity for the polyethylene glycol-rich upper phase, whereas those membranes from mitochondria, chloroplasts and other organelles prefer the dextran-rich lower phase and the interface. The plasma membrane was identified with the aid of silicotungstic acid-chromic acid staining. In the upper phase there are mainly stained elliptical vesicles, whereas in the lower phase there are many differnet kind of unstained vesicles. This result is coincident with the marker enzyme examination. The two-phase method for the isolation of plasma membrane may be widely applied not only to nongreen tissues but also to green tissues of plants.     

Recycling procedure for gold chloride used in neurohistology.

A simple method is described whereby pure chloroauric acid (HAuCl4; "brown gold chloride") is recovered from old solutions used for toning silver-stained sections. The procedure can be carried out in any laboratory and 60 to 80% of the gold initially present in a solution is recovered. The recycled product may be used for toning or for the staining of astrocytes by Cajal's method.     

A rapid method for detecting malformations in rat fetuses

A rapid method for examining rat fetuses is presented. The technique consists of fixing the fetuses in Bouin's solution, serially sectioning the head, neck and lower trunk with a razor blade and doing sagittal sections of the heart after opening the thoracic cavity. Examples of sections from normal 20 day rat fetuses are given as well as some with the following abnormalities: cleft palate produced by chlorcyclizine and eye and heart malformations resulting from anti-adult rat kidney serum.     

Origin of the lower jaw in cephalopods: a biting issue

A survey of serial, histological sections of cephalopod embryos at early and advanced morphogenetic stages provided evidence that always the cutting edge of the lower jaw is first connected, by a thin organic membrane, to the cutting edge of the upper jaw. The lower jaw rudiment does not exhibit any separation of the right from the left half. The evolutionary origin of the lower jaw, which has no obvious homologue in other molluscs, remains a matter of debate.     

一类食饵捕食系统的Hopf分岔及周期解的稳定性

首先建立了具有时滞的三种群食饵捕食模型,并研究了平衡点的存在性,接着应用规范化方法和中心流行定理研究了Hopf分岔以及分岔周期解的稳定性.并举例论证.     

Effect of transport and competition on ligand binding

We present a model to describe the physics of chemoreception in processes determined by competitive ligand binding. Our model describes the competition between various populations, such as ligands vs. blockers and receptors vs. decoys, in protein activation when diffusion is rate-determining. Full spatio-temporal solutions can be obtained numerically. The model structure is kept simple enough as to permit its easy generalization to describe a large subset of the manifold of possible situations occurring in nature. The power and simplicity of the proposed method are exhibited through the solution of several examples which are discussed in detail.     

Seed dispersal in a patchy environment with global age dependence

A model of seed population dynamics proposed by S. A. Levin, A. Hastings, and D. Cohen is presented and analyzed. With the environment considered as a mosaic of patches, patch age is used along with time as an independent variable. Local dynamics depend not only on the local state, but also on the global environment via dispersal modelled by an integral over all patch ages. Basic technical properties of the time varying solutions are examined; necessary and sufficient conditions for nontrivial steady states are given; and general sufficient conditions for global asymptotic stability of these steady states are established. Primary tools of analysis include a hybrid Picard iteration, fixed point methods, monotonicity of solution structure, and upper and lower solutions for differential equations.This work was supported in part by National Science Foundation Grants MCS-7903497 and MCS-790349701     

Cable Theory for Finite Length Dendritic Cylinders with Initial and Boundary Conditions

The cable equation is solved in the Laplace transform domain for arbitrary initial and boundary conditions. The cable potential is expressed directly in terms of the impedance of the terminations and the cable electrotonic length. A computer program is given to invert the transform. Numerical solutions may be obtained for any particular model by inserting expressions describing the terminations and parameter values into the program, without further computation by the modeler. For a finite length cable, sealed at one end, the solution is expressed in terms of the ratio of the termination impedance to the impedance of the finite length cable, a generalization of the steady-state conductance ratio. Analysis of a model of a soma with several primary dendrites shows that the dendrites may be lumped into one equivalent cylinder if they have the same electrotonic length, even though they may vary in diameter. Responses obtained under voltage clamp are conceptually predictable from measurements made under current clamp, and vice versa. The equalizing time constants of an infinite series expression of the solution are the negative reciprocals of the roots of the characteristic equation. Examination of computed solutions shows that solutions which differ theoretically may be indistinguishable experimentally.     

Mathematical modeling and simulation of seated stability

Various methods have been used to quantify the kinematic variability or stability of the human spine. However, each of these methods evaluates dynamic behavior within the stable region of state space. In contrast, our goal was to determine the extent of the stable region. A 2D mathematical model was developed for a human sitting on an unstable seat apparatus (i.e., the “wobble chair”). Forward dynamic simulations were used to compute trajectories based on the initial state. From these trajectories, a scalar field of trajectory divergence was calculated, specifically a finite time Lyapunov exponent (FTLE) field. Theoretically, ridges of local maxima within this field are expected to partition the state space into regions of qualitatively different behavior. We found that ridges formed at the boundary between regions of stability and failure (i.e., falling). The location of the basin of stability found using the FTLE field matched well with the basin of stability determined by an alternative method. In addition, an equilibrium manifold was found, which describes a set of equilibrium configurations that act as a low dimensional attractor in the controlled system. These simulations are a first step in developing a method to locate state space boundaries for torso stability. Identifying these boundaries may provide a framework for assessing factors that contribute to health risks associated with spinal injury and poor balance recovery (e.g., age, fatigue, load/weight, and distribution). Furthermore, an approach is presented that can be adapted to find state space boundaries in other biomechanical applications.     

一类具连续时滞的三种群互助模型正平衡态的渐近稳定性

本文研究了一类具连续时滞的三种群互助模型,利用上、下解方法及相应的单调迭代方法,获得了该系统存在唯一正常数平衡态及该平衡态是全局渐近稳定的结论,为讨论时滞三种群模型提供了一种有效方法,所得结果也适用于二种群互助模型及不含时滞和扩散项的互助模型,因而推广了已有的一些结论．