Sequence allignment The optimum cost of an alignment of the strings x1 x2 x3 x4

Question

Sequence allignment

The optimum cost of an alignment of the strings

x1 x2 x3 x4 ... x_m and y1 y2 y3 ... y_n

will always be greater than the optimum cost of an alignment of

   x2 x3 x4 ... x_m and y1 y2 y3 ... y_n

because any alignment of the first pair of strings necessarily contains an alignment of the second pair of strings.

This is NOT correct!

It is NOT true that any alignment of the first pair of strings necessarily contains an alignment of the second pair of strings: For example, let x = CT and let y = CG. It is NOT true that any alignment of these start with x1 = C against a gap, followed by an alignment of x2 against y1 y2 (i.e., an alignment of T against CG). Here is such an alignment:

A T
A G

This alignment has cost 1, whereas any alignment that starts with the first A in x against a gap necessarily will have cost at least 2 for that first gap, and optimally has cost 5:

A T -
- A G

Is it possible to have a situation in table "opt" where x_i is the same character as y_j and have

opt[ i ][ j ] = 2 + opt[ i+1][ j ] = 2 + opt[ i ][ j+1]    = 0 + opt[ i + 1][ j + 1]

(In other words, when creating the alignment, we could have come from ANY of the 3 neighboring squares below and to the right?

You need to compute the entire "opt" table, and see if there exists an i and a j such that x_i == y_j and when you are computing the value of opt[i][j], it is a 3-way tie between 2+opt[i + 1][j], 2+opt[i][j + 1], and opt[i+1][j+1].

Explanation / Answer

1 Induction of Fuzzy Rules by Means of Artificial Immune Systems 3 Fig. 1.1. Clonal selection principle in natural immune systems mediated immune responses, but will not be explicitly accounted for the de- velopment of our model. Lymphocytes, in addition to proliferating and/or dif- ferentiating into plasma cells, can differentiate into long-lived B memory cells. Memory cells circulate through the blood, lymph and tissues, and when exposed to a second antigenic stimulus commence to differentiate into large lymphocytes capable of producing high affinity antibodies, pre-selected for the specific antigen that had stimulated the primary response. Fig 1.1 depicts the clonal selection principle. The clonal selection and affinity maturation principles are used to explain how the immune system reacts to pathogens and how it improves its capability of recognizing and eliminating pathogens [14]. In a simple form, clonal selection states that when a pathogen invades the organism, a number of immune cells that recognize these pathogens will proliferate; some of them will become effector cells, while others will be maintained as memory cells. The effector cells secrete antibodies in large numbers, and the memory cells have long life spans so as to act faster and more effectively in future exposures to the same or a similar pathogen. During the cellular reproduction, the cells suffer somatic mutations with high rates and, together with a selective force, the higher affinity cells in relation to the invading pathogen differentiate into memory cells. This whole process of somatic mutation plus selection is known as affinity maturation. To a reader familiar with evolutionary biology, these two processes of clonal selection and affinity maturation are much akin to the (macro-)evolution of species. There 4 F. Menolascina et al. are a few basic differences however, between these immune processes and the evolution of species. Within the immune system, somatic cells reproduce in an asexual form (there is no crossover of genetic material during cell mitosis), the mutation suffered by an immune cell is proportional to its affinity with the selective pathogen (the higher the affinity, the smaller the mutation rate), and the number of progenies of each cell is also proportional to its affinity with the selective pathogen (the higher the affinity, the higher the number of progenies). Evolution in the immune system occurs within the organism and, thus it can be viewed as a micro-evolutionary process. As we know, in fact, immunology suggests that the natural Immune System (IS) has to assure recognition of each potentially dangerous molecule or substance, generically called antigen (Ag), by antibodies (Ab). The IS first recognizes an antigen as “dangerous” or external invaders and then adapts (by affinity maturation) its response to eliminate the threat. To detect an antigen, the IS activates a recognition process. In vertebrate organisms, this task is accomplished by the complex machinery made by cellular interactions and molecular productions. The main features of the clonal selection theory that will be explored in this chapter are [14]]: • Proliferation and differentiation on stimulation of cells with antigens; • Generation of new random genetic changes, subsequently expressed as diverse antibody patterns, by a form of accelerated somatic mutation (a process called affinity maturation); • Elimination of newly differentiated lymphocytes carrying low affinity antigenic receptors. To illustrate the adaptive immune learning mechanism, consider that an antigen Ag1 is introduced at time zero and it finds a few specific antibodies within the animal (see Fig. 1.2). After a lag phase, the antibody against antigen Ag1 appears and its concentration rises up to a certain level, and then starts to decline (primary response). When another antigen Ag2 is introduced, no antibody is present, showing the specificity of the antibody response [14]. On the other hand, Fig. 1.2. Immune response plotted as antibody concentration over time 1 Induction of Fuzzy Rules by Means of Artificial Immune Systems 5 Fig. 1.3. Antibody affinity as function of the specific antigen binding site one important characteristic of the immune memory is that it is associative: B cells adapted to a certain type of antigen Ag1 presents a faster and more efficient secondary response not only to Ag1, but also to any structurally related antigen Ag1 + Ag2. This phenomenon is called immunological cross-reaction, or cross-reactive response. This associative memory is contained in the process of vaccination and is called generalization capability, or simply generalization, in other artificial intelligence fields, like neural networks [14]. Receptor editing offers the ability to escape from local optima on an affin- ity landscape. Fig. 1.3 illustrates this idea by considering all possible antigen- binding sites depicted the x-axis, with the most similar ones adjacent to each other. The Ag-Ab affinity is shown on the y-axis. If we consider a particular antibody (Ab1 ) selected during a primary response, then point mutations allow the immune system to explore local areas around Ab1 by making small steps towards an antibody with higher affinity, leading to a local optimum (Ab1). Because mutations with lower affinity are lost, the antibodies can not go down the hill. Receptor editing allows an antibody to take large steps through the landscape, landing in a locale where the affinity might be lower (Ab2 ). However, occasionally the leap will lead to an antibody on the side of a hill where the climbing region is more promising (Ab3 ), reaching the global optimum. From this locale, point mutations can drive the antibody to the top of the hill (Ab3). In conclusion, point mutations are good for exploring local regions, while editing may rescue immune responses stuck on unsatisfactory local optima. Computational immunology is the research field that attempts to reproduce in silico the behavior of the natural IS. From this approach, the new field of Ar- tificial Immune Systems (AIS) attempts to use theories, principles, and concepts of modern immunology to design immunity-based system applications in science and engineering [14]. AIS are adaptive systems in which learning takes place using evolutionary mechanisms similar to biological evolution. These different research areas are tied together: the more we learn from in silico modeling of natural systems, the better we are able to exploit ideas for computer science and engineering applications.

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