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Phage display libraries of differently sized bicyclic peptides

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Sequence motif

In biology, a sequence motif is a nucleotide or amino-acid sequence pattern that is widespread and usually assumed to be related to biological function of the macromolecule. For example, an N-glycosylation site motif can be defined as Asn, followed by anything but Pro, followed by either Ser or Thr, followed by anything but Pro residue. When a sequence motif appears in the exon of a gene, it may encode the "structural motif" of a protein; that is a stereotypical element of the overall structure of the protein.

Phage display

Phage display is a laboratory technique for the study of protein–protein, protein–peptide, and protein–DNA interactions that uses bacteriophages (viruses that infect bacteria) to connect proteins with the genetic information that encodes them. In this technique, a gene encoding a protein of interest is inserted into a phage coat protein gene, causing the phage to "display" the protein on its outside while containing the gene for the protein on its inside, resulting in a connection between genotype and phenotype.

Sequence alignment

In bioinformatics, a sequence alignment is a way of arranging the sequences of DNA, RNA, or protein to identify regions of similarity that may be a consequence of functional, structural, or evolutionary relationships between the sequences. Aligned sequences of nucleotide or amino acid residues are typically represented as rows within a matrix. Gaps are inserted between the residues so that identical or similar characters are aligned in successive columns.

Ring (mathematics)

In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist. In other words, a ring is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers. Ring elements may be numbers such as integers or complex numbers, but they may also be non-numerical objects such as polynomials, square matrices, functions, and power series.

Affinity maturation

In immunology, affinity maturation is the process by which TFH cell-activated B cells produce antibodies with increased affinity for antigen during the course of an immune response. With repeated exposures to the same antigen, a host will produce antibodies of successively greater affinities. A secondary response can elicit antibodies with several fold greater affinity than in a primary response. Affinity maturation primarily occurs on membrane immunoglobulin of germinal center B cells and as a direct result of somatic hypermutation (SHM) and selection by TFH cells.

Multiple sequence alignment

Multiple sequence alignment (MSA) may refer to the process or the result of sequence alignment of three or more biological sequences, generally protein, DNA, or RNA. In many cases, the input set of query sequences are assumed to have an evolutionary relationship by which they share a linkage and are descended from a common ancestor. From the resulting MSA, sequence homology can be inferred and phylogenetic analysis can be conducted to assess the sequences' shared evolutionary origins.

Algebraic variety

Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this concept in several different ways, while attempting to preserve the geometric intuition behind the original definition. Conventions regarding the definition of an algebraic variety differ slightly.

Abelian variety

In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions. Abelian varieties are at the same time among the most studied objects in algebraic geometry and indispensable tools for much research on other topics in algebraic geometry and number theory. An abelian variety can be defined by equations having coefficients in any field; the variety is then said to be defined over that field.

Nucleic acid sequence

A nucleic acid sequence is a succession of bases within the nucleotides forming alleles within a DNA (using GACT) or RNA (GACU) molecule. This succession is denoted by a series of a set of five different letters that indicate the order of the nucleotides. By convention, sequences are usually presented from the 5' end to the 3' end. For DNA, with its double helix, there are two possible directions for the notated sequence; of these two, the sense strand is used.

Projective variety

In algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective n-space over k that is the zero-locus of some finite family of homogeneous polynomials of n + 1 variables with coefficients in k, that generate a prime ideal, the defining ideal of the variety. Equivalently, an algebraic variety is projective if it can be embedded as a Zariski closed subvariety of .