Biological macro-molecules come in a large variety of complexes. Representation and modelling their structures are essential to provide a computational analogue of experimentally determined structures. In this work, the authors propose a representational scheme for biomolecules with the aid of approximate cell decomposition and a nano-robotic schema. The kino-chemical information of a molecule is programmatically retrieved from reliable repositories (RLooM, Protein data bank etc.)of biochemical structures and a Nano-manipulator schema is obtained from the D-H representation of the molecular chain under consideration. The molecule is enclosed in a suitable bounding box, and using approximate cell decomposition in conjunction with bonding information, a volumetric steric clash description of the chain is proposed which serves as a model for infringement function estimation and subsequent structural prediction for proteins and nucleic acids. From the robotic representation, the variable kinematic description due to rotating atoms is always at hand to generate the new corresponding infringement description within the bounding cuboid. Volumes of appropriately indexed cells give a reasonably accurate estimate of infringement in a particular configuration and the estimates are found to be comparable to experimental results. The proposed rendering have been extensively compared with a number of professional software renderings from NMR and crystallographic data.

Structural modelling of RNAs have received relatively less attention compared to protein modelling, owing partly due to the involved, long and highly orientable loop structures. RNA loop structures determined by experimental methods are often found wanting due to chemical interactions of the detection method with the structures and for this reason alone, a computational analogue of an RNA loop structure is important to devise. In this work RNA loop modelling problem is presented as an energy minimization problem subject to kinematic and volumetric constraints of the loop. The kinematic constraints are generated from redundancy characterization of RNA loops like in case of a robotic manipulator. The loop energy is estimated from established force fields (like CHARMM etc.)with necessary approximations and the resulting potential optimization problem is solved by simulated annealing methods to obtain stable loop configurations free from loop-loop infringement and loop-anchor infringement. The algorithm is applied, with a fixed and geometric cooling schedule, on several RNA loops of varying number of residues and the resulting structures are accepted as valid configurations if certain statistical criteria are met related to the position error in loop-anchor atom coordinates. For small to moderate loop size, provides results that are comparable to the structures stored in established repositories (Protein data bank, RLooM etc.). Native and optimized structures of some such loops are presented as a proof of concept for the methodology discussed.

In this article, a method has been established for optimizing multivariate nonlinear discontinuous cost functions having multiple simple kinks in their domains of definition, by applying simple non-parametric inverse trigonometric functions and combinations thereof as smoothing agents. The original function is locally replaced by these smoothing agents at the points of jump discontinuity, while retaining the global structure of the original objective function. The non-parametric smoothing function is exact and devoid of complicated special functions or integral approximations and, hence, the resulting optimization algorithm is relatively simpler and faster. The absence of the parameter ensures little ill-conditioning effects in subsequent calculations. Relevant properties of the smoothing function are developed analytically and the shape of the resulting modified objective functions are illustrated with appropriate numerical simulations. Conjugate gradient and Broyden family of methods (DFP/BFGS) were employed to minimize the modified functions; although Levenberg Marquardt and gradient descent methods were also used occasionally to confirm the universal applicability of the proposed method. Over fifty problems were successfully minimized (maximized) and results for some of them are tabulated before the concluding remarks of the article. Constrained optimization of discontinuous functions with such smoothing agents is an active research within the working group.

Nucleic acid structures, like DNA and RNA, primarily involve hydrogen bonded, base-paired stretches interspersed with loops of various geometric shapes. Theoretical modelling and simulation of these loop structures have been an analytical challenge (with the exception of proteins) and most methods used are based on heuristics. The objectives of this research are to model loops in nucleic acid structures by developing an algorithm using the inverse kinematics for hyper-redundant manipulators and develop a database of theoretical analogue for corresponding experimental models in Protein Data Bank (PDB). First, a volumetric representation of the loops in nucleic acids is sought from a hyper-redundant manipulator schema with torsion angles as joint variables. Based on it, steric clashes, as a function of loop configuration, in side chains are predicted, acknowledging that a stable configuration should have minimal infringement. It is further shown that loop modelling is essentially a process of constrained energy optimization for redundant structures which, at its background, requires kinematic approximation of the loop and estimation of infringement. Simulated theoretical prediction of structure, of some such loops in specific RNA molecules and non-Watson-Crick duplex or quadruplex (along with statistical parameters), illustrate the validity of this approach to modelling. Predicted structures (with multiple possibilities) are considered for selection only if certain statistical criteria (indicating proximity) are satisfied when compared to their experimental counterparts.

This paper addresses the problem of designing an efficient implementation of a basic atomic read-write data structure over an asynchronous message-passing system. In particular, we consider time-efficient implementations of this abstraction in the case of a single writer, multiple readers (also called a SWMR atomic register) and S servers: the writer, the readers, and t out of the S servers may fail by crashing. Previous implementations tolerate the failure of any minority of servers (i.e., t < S/2) and require one communication round-trip for every write, and two round-trips for every read.We investigate the possibility of fast implementations, namely, implementations that complete both reads and writes in one round-trip. We show that, interestingly, the existence of a fast implementation depends on the maximum number of readers considered. More precisely, we show that a fast implementation is possible if and only if the number of readers is less that S t-2. We also show that a fast implementation is impossible in a multiple writers setting when t ≥ 1.Our results draw sharp lines between the time-complexity of regular and atomic register implementations, as well as between single-writer and multi-writer implementations. The results lead also to revisit, in a message-passing context, the folklore theorem that "atomic reads must write".