The matching of electrostatic extrema: A useful method in drug design? A study of phosphodiesterase III inhibitors

Summary Ligands which bind to a specific protein binding site are often expected to have a similar electrostatic environment which complements that of the binding site. One method of assessing molecular electrostatic similarity is to examine the possible overlay of the maxima and minima in the electrostatic potential outside the molecules and thereby match the regions where strong electrostatic interactions, including hydrogen bonds, with the residues of the binding site may be possible. This approach is validated with accurate calculations of the electrostatic potential, derived from a distributed multipole analysis of an ab initio charge density of the molecule, so that the effects of lone pair and -electron density are correctly included. We have applied this method to the phosphodiesterase (PDE) III substrate adenosine-3,5-cyclic monophosphate (cAMP) and a range of nonspecific and specific PDE III inhibitors. Despite the structural variation between cAMP and the inhibitors, it is possible to match three or four extrema to produce relative orientations in which the inhibitors are sufficiently sterically and electrostatically similar to the natural substrate to account for their affinity for PDE III. This matching of extrema is more apparent using the accurate electrostatic models than it was when this approach was first applied, using semiempirical point charge models. These results reinforce the hypothesis of electrostatic similarity and give weight to the technique of extrema matching as a useful tool in drug design.     

On the electrostatic and steric similarity of lactam compounds and the natural substrate for bacterial cell-wall biosynthesis

Summary Electrostatic and structural properties of a set of -lactam, -lactam and nonlactam compounds have been analyzed and compared with those of a model of the natural substrate d-alanyl-d-alanine for the carboxy- and transpeptidase enzymes. This first comparison of the electrostatic properties has been based on a distributed multipole analysis of high-quality ab initio wave functions of the substrate and potential antibiotics. The electrostatic similarity of the substrate and active compounds is apparent, and contrasts with the electrostatic properties of the noninhibitors. This has been quantified to give a reasonable correlation with the MIC (Minimum Concentration for Inhibition) and with kinetic data (k₂/K) in accordance with the model for interaction of the lactam compounds with dd-peptidase. These correlations provide a better prediction of antibacterial activity than purely structural criteria.     

Theoretical study of magnetic properties of ammonia molecule in nonuniform magnetic field

The interaction Hamiltonian within the Bloch gauge for the potentials of the electromagnetic field has been used to define magnetic multipole moment operators and operators for the magnetic field of electrons acting on the nuclei of a molecule in the presence of nonhomogeneous external magnetic field. Perturbation theory has been applied to evaluate the induced electronic moments and magnetic field at the nuclei. Multipole magnetic susceptibility and nuclear magnetic shielding tensors have been introduced to describe the contributions arising in nonuniform fields, and their origin dependence has been analyzed. Extended numerical tests on the ammonia molecule in a static, nonuniform magnetic field have been carried out, using the random-phase approximation within the framework of accurate Hartree-Fock zero-order wavefunctions, and allowing for both angular momentum and torque formalisms in the calculation of paramagnetic contributions.     

On the representation of electrostatic fields around ab initio charge distributions

Summary We compare two methods (Mulliken charges and a distributed multipole analysis, DMA) of representing an ab initio charge distribution for calculating the electrostatic field and potential outside the molecule, using pyrimidine and the RNA base uracil as examples. This is done using a 3-D graphical display of the electrostatic fields, which, when used with real-time rotation, zooming and clipping, has many advantages for qualitatively assessing the electrostatic interactions of a molecule. The errors involved in using Mulliken point charges may be of similar magnitude to the total electrostatic field in regions which are important in recognition processes. The DMA representation automatically includes the anisotropic electrostatic effects of non-spherical features in the charge distribution of each atom, and yet the displayed electrostatic fields around the atoms which have lone-pair density do not show marked anisotropy.     

Value function and optimality conditions for semilinear control problems

This paper is concerned with optimal control problems of Mayer and Bolza type for systems governed by a semilinear state equationx(t)=Ax(t) + f(t, x(t), u(t)), u(t) U, whereA is the infinitesimal generator of a strongly continuous semigroup in a Banach spaceX. We prove necessary and sufficient conditions for optimality and then use these conditions to investigate properties of the value function related to superdifferentials. Conversely, we use the value function to obtain criteria for optimality and feedback systems.Work (partially) supported by the Research Project Equazioni di evoluzione e applicazioni fisicomatematiche (M.U.R.S.T.-Italy).     

分布式喇曼光纤放大器在光传输系统中的应用

就分布式喇曼光纤放大器独特的低噪声和灵活的功率调整性质进行了分析，并就它在系统中的应用作了简单的介绍。     

Sampled-data distributed protocol for coordinated aggregation of multi-agent systems subject to communication delays

This paper studies the coordinated aggregation problem of a multi-agent system. Particularly, all the agents reach a consensus within a pre-specified target region. However, only a subset of agents have access to this target region, and each agent merely interacts with its neighbors by communication. Moreover, there exist unknown heterogeneous delays in communication channels. The underlying communication topology is characterized by a digraph. To accommodate the practical digital disposal, a sampled-data distributed protocol is proposed, where the sampling is asynchronous in the sense that the sampling periods of distinct agents are heterogeneous. The resulting closed-loop system from the proposed sampled-data distributed protocol is in a hybrid fashion that the continuous system is fed-back by using discrete states at sampling instants. The convergence performance of this hybrid closed-loop system is analyzed based on the contraction theory. More specifically, it is first shown that all the states are coordinated to aggregate within the target region, i.e., coordinated aggregation. With this result, it is next shown that all the states are coordinated towards a consensus, i.e., state agreement. These together guarantee the fulfillment of the concerned coordinated aggregation objective. Finally, a simulation example is given to validate the theoretical results.     

Synchronization of Takagi–Sugeno fuzzy stochastic discrete-time complex networks with mixed time-varying delays

In this paper, we propose and investigate a new general model of fuzzy stochastic discrete-time complex networks (SDCNs) described by Takagi–Sugeno (T–S) fuzzy model with discrete and distributed time-varying delays. The proposed model takes some well-studied models as special cases. By employing a new Lyapunov functional candidate, we utilize some stochastic analysis techniques and Kronecker product to deduce delay-dependent synchronization criteria that ensure the mean-square synchronization of the proposed T–S fuzzy SDCNs with mixed time-varying delays. These sufficient conditions are computationally efficient as it can be solved numerically by the LMI toolbox in Matlab. A numerical simulation example is provided to verify the effectiveness and the applicability of the proposed approach.     

光频域喇曼反射光纤温度传感器的频域参量设计

研究了功率调制型光频域反射技术空间采样函数的基本特征,得到了频域测量参量对测量距离和空间分辨率的基本限制;用数值计算模拟了功率调制型光频域光纤温度传感器的测量过程,通过比较模拟测量得到的喇曼反射强度空间分布因子对实际喇曼反射强度空间分布因子的再现程度,研究了调制频率范围、频率采样间隔以及起始调制频率对测量结果的影响,得出技术可行的最佳频域测量方案.     

THE EXPONENTIAL STABILIZATION FOR A SEMILINEAR WAVE EQUATION WITH LOCALLY DISTRIBUTED FEEDBACK

This paper considers the exponential decay of the solution to a damped semilinear wave equation with variable coefficients in the principal part by Riemannian multiplier method. A differential geometric condition that ensures the exponential decay is obtained.