Generalisations of DNA Splicing Systems with One Palindromic Restriction Enzyme

In DNA splicing system, the potential effect of sets of restriction enzymes and a ligase that allow DNA molecules to be cleaved and re-associated to produce further molecules is modelled mathematically. This modelling is done in the framework of formal language theory, in which the nitrogen bases, nucleotides and restriction sites are modelled as alphabets, strings and rules respectively. The molecules resulting from a splicing system is depicted as the splicing language. In this research, the splicing language resulting from DNA splicing systems with one palindromic restriction enzyme for one and two (non-overlapping) cutting sites are generalised as regular expressions

Bio-Mathematical Concepts in DNA Splicing System

Splicing system is a formal characterization of the generative capacity of specified enzymatic activities operating on specified set of double-stranded DNA molecules

Sticker systems over monoids

Molecular computing has gained many interests among researchers since Head introduced the first theoretical model for DNA based computation using the splicing operation in 1987. Another model for DNA computing was proposed by using the sticker operation which Adlemanused in his successful experiment for the computation of Hamiltonian paths in a graph: a double stranded DNA sequence is composed by prolonging to the left and to the right a sequence of (single or double) symbols by using given single stranded strings or even more complex dominoes with sticky ends, gluing these ends together with the sticky ends of the current sequence according to a complementarity relation. According to this sticker operation, a language generative mechanism, called a sticker system, can be defined: a set of (incomplete) double-stranded sequences (axioms) and a set of pairs of single or double-stranded complementary sequences are given. The initial sequences are prolonged to the left and to the right by using sequences from the latter set, respectively. The iterations of these prolongations produce “computations” of possibly arbitrary length. These processes stop when a complete double stranded sequence is obtained. Sticker systems will generate only regular languages without restrictions. Additional restrictions can be imposed on the matching pairs of strands to obtain more powerful languages. Several types of sticker systems are shown to have the same power as regular grammars; one type is found to represent all linear languages whereas another one is proved to be able to represent any recursively enumerable language. The main aim of this research is to introduce and study sticker systems over monoids in which with each sticker operation, an element of a monoid is associated and a complete double stranded sequence is considered to be valid if the computation of the associated elements of the monoid produces the neutral element. Moreover, the sticker system over monoids is defined in this study

Computation of splicing languages from DNA splicing system with one palindromic restriction enzyme

In DNA splicing system, the potential effects of sets of restriction enzymes and a ligase that allow DNA molecules to be cleaved and reassociated to produce further molecules are studied. A splicing language depicts the molecules resulting from a splicing system. In this research, a C++ programming code for DNA splicing system with one palindromic restriction enzyme for one and two (non-overlapping) cutting sites is developed. A graphical user interface, GUI is then designed to allow the user to insert the initial DNA string and restriction enzymes to generate the splicing languages which are the result of the computation of the C++ programming. This interface displays the resulting splicing languages, which depict the results from in vitro experiments of the respective splicing system. The results from this research simplify the lenghty manual computation of the resulting splicing languages of DNA splicing systems with one palindromic restriction enzyme

DNA splicing systems with at most two cutting sites of a non-palindromic restriction enzyme

The modelling of splicing systems is simulated by the process of cleaving and recombining DNA molecules with the presence of a ligase and restriction enzymes which are biologically called as endodeoxyribonucleases. The molecules resulting from DNA splicing systems are known as splicing languages. Palindrome is a sequence of strings that reads the same forward and backward. In this research, the splicing languages resulting from DNA splicing systems with one non-palindromic restriction enzyme are determined using the notation from Head splicing system. The generalisations of splicing languages for DNA splicing systems involving a cutting site and two non-overlapping cutting sites of one non-palindromic restriction enzyme are presented in the first and second theorems, respectively, which are proved using direct and induction methods. The result from the first theorem shows a trivial string which is the initial DNA molecule; while the second theorem determines a splicing language consisting of a set of resulting DNA molecules from the respective DNA splicing system

Isomorphism and matrix representation of point groups

In chemistry, point group is a type of group used to describe the symmetry of molecules. It is a collection of symmetry elements controlled by a form or shape which all go through one point in space, which consists of all symmetry operations that are possible for every molecule. Next, a set of number or matrices which assigns to the elements of a group and represents the multiplication of the elements is said to constitute representation of a group. Here, each individual matrix is called a representative that corresponds to the symmetry operations of point groups, and the complete set of matrices is called a matrix representation of the group. This research was aimed to relate the symmetry in point groups with group theory in mathematics using the concept of isomorphism, where elements of point groups and groups were mapped such that the isomorphism properties were fulfilled. Then, matrix representations of point groups were found based on the multiplication table where symmetry operations were represented by matrices. From this research, point groups of order less than eight were shown to be isomorphic with groups in group theory. In addition, the matrix representation corresponding to the symmetry operations of these point groups wasis presented. This research would hence connect the field of mathematics and chemistry, where the relation between groups in group theory and point groups in chemistry were shown

Some properties of probabilistic semi-simple splicing systems

The concept of splicing system was first introduced by Head in 1987. This model has been introduced to investigate the recombinant behavior of DNA molecules. Over the years, various types of splicing languages have been defined and studied by different mathematicians. Splicing systems with finite sets of axioms only generate regular languages. Therefore, different restrictions have been considered to increase the computational power up to the recursively enumerable languages. In this research, a variant of splicing systems called probabilistic splicing systems has been used to define different types of splicing systems such as probabilistic simple splicing systems, probabilistic semi-simple splicing systems and probabilistic one-sided splicing systems. In probabilistic splicing systems, probabilities (real numbers in the range of 0 and 1) are associated with the axioms, and the probability p(z)of the string z generated from two strings x and y is calculated from the probability p(x)and p(y) according to the operation *(multiplication) defined on the probabilities, i.e., p(z) = p(x) * p(y)

The properties of probabilistic simple regular sticker system

A mathematical model for DNA computing using the recombination behavior of DNA molecules, known as a sticker system, has been introduced in 1998. In sticker system, the sticker operation is based on the Watson-Crick complementary feature of DNA molecules. The computation of sticker system starts from an incomplete double-stranded sequence. Then by iterative sticking operations, a complete double-stranded sequence is obtained. It is known that sticker systems with finite sets of axioms and sticker rule (including the simple regular sticker system) generate only regular languages. Hence, different types of restrictions have been considered to increase the computational power of the languages generated by the sticker systems. In this paper, we study the properties of probabilistic simple regular sticker systems. In this variant of sticker system, probabilities are associated with the axioms, and the probability of a generated string is computed by multiplying the probabilities of all occurrences of the initial strings. The language are selected according to some probabilistic requirements. We prove that the probabilistic enhancement increases the computational power of simple regular sticker systems

Probabilistic simple sticker systems

A model for DNA computing using the recombination behavior of DNA molecules, known as a sticker system, was introduced by by L. Kari, G. Paun, G. Rozenberg, A. Salomaa, and S. Yu in the paper entitled DNA computing, sticker systems and universality from the journal of Acta Informatica vol. 35, pp. 401-420 in the year 1998. A sticker system uses the Watson-Crick complementary feature of DNA molecules: starting from the incomplete double stranded sequences, and iteratively using sticking operations until a complete double stranded sequence is obtained. It is known that sticker systems with finite sets of axioms and sticker rules generate only regular languages. Hence, different types of restrictions have been considered to increase the computational power of sticker systems. Recently, a variant of restricted sticker systems, called probabilistic sticker systems, has been introduced [4]. In this variant, the probabilities are initially associated with the axioms, and the probability of a generated string is computed by multiplying the probabilities of all occurrences of the initial strings in the computation of the string. Strings for the language are selected according to some probabilistic requirements. In this paper, we study fundamental properties of probabilistic simple sticker systems. We prove that the probabilistic enhancement increases the computational power of simple sticker systems

A new variant of Petri net controlled grammars

A Petri net controlled grammar is a Petri net with respect to a context-free grammar where the successful derivations of the grammar can be simulated using the occurrence sequences of the net. In this paper, we introduce a new variant of Petri net controlled grammars, called a place-labeled Petri net controlled grammar, which is a context-free grammar equipped with a Petri net and a function which maps places of the net to productions of the grammar. The language consists of all terminal strings that can be obtained by parallelly applying multisets of the rules which are the images of the sets of the input places of transitions in a successful occurrence sequence of the Petri net. We study the effect of the different labeling strategies to the computational power and establish lower and upper bounds for the generative capacity of place- labeled Petri net controlled grammars