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Mathematics of DNA structure, function and interactions. Selected papers based on the presentations at the workshop, September 16–21, , Minneapolis. Mathematics of DNA Structure, Function and Interactions PDF · Mathematical Methods in Dna Topology: Applications to Chromosome Organization and. Mathematics of DNA Structure, Function and Interactions Digitally watermarked , DRM-free; Included format: PDF; ebooks can be used on all reading devices.

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C.J. Benham et al. (eds.), Mathematics of DNA Structure, Function and Interactions,. The IMA Volumes in Mathematics and its Applications Laura Finzi. Differences between positively and negatively supercoiled DNA that topoisomerases may distinguish. Read and learn for free about the following article: DNA structure and function. that are fine-tuned to interact with this molecular structure in specific ways.

If the structure is a deoxynucleoside, then C-2 bears two hydrogens. If it is a nucleoside, then C-2 bears one hydrogen and one hydroxide group, in which the hydroxide group faces south. Structural variations in DNA can occur if: 1.

There are different deoxyribose conformations 2. If there are rotations around the contiguous bonds in the phosphodeoxyribose backbone 3. The deoxy- prefix in Deoxyribonucleotides is the nomenclature used for DNA. The term ribonucleotides is employed when it is nomenclature for RNA, or in other words, C-2 on the sugar unit has an -OH group versus deoxy which C-2 has 2 hydrogens.

Symbols are used to simplify the names. The "A" in the front signifies that the base is Adenine and the "T" in the middle signifies tri-phosphates. AMP on the other hand, also has an adenine , but the M signifies that the sugar is bound to a single phosphate group.

In short, four nucleotide units of DNA are called deoxyadenylate, deoxyguanylate, deoxycitidylate, and thymidylate. Early foundation for DNA structures[ edit ] The primary structure of a nucleic acid is its covalent structure and nucleotide sequences.

One of most important parts of determining the structure of DNA comes from the work of Erwin Chargaff and his colleagues in the late s. They found that the four nucleotide bases of DNA of different organisms and that the amounts of certain bases are closely related.

The base composition of DNA generally varies from one species to another. DNA specimens isolated from different tissues of the same species have the same base composition. The base composition of DNA in a given species does not change over time, nutritional states, or environment.

Photographs produced by the X-ray crystallography method are not actually pictures of molecules, however the spots and smudges produced by X-rays that were diffracted deflected as they passed through crystallized DNA. Crystallographers use mathematical equations to translate such patterns of spots into information about the three-dimensional shape of DNA. Franklin and Wilkins found that DNA molecules are helical with two periodicities along their long axis, a primary one of 3.

Eventually, Watson and Crick formulated a DNA structure from the diffraction pattern of the x-ray photo and gave to incredible insight that is still accepted today. In this structure, they proposed that two helical DNA chains of opposite direction wound around the same axis to form a right handed double helix. The hydrophillic backbones form by phosphodiester bonds of alternating deoxyribose sugar and phosphate group that are faced outside of the helix, surrounded by aqueous environment.

The purine and pyrimidine bases of both strands are stacked inside the double helix and stabilized by Van Der Waals interactions.

Each adjacent base on one strand of the double-helix is 3. Nucleoside adenosin with beta glycosidic bond DNA strane Orientation[ edit ] DNA molecules are asymmetrical, such property is essential in the processes of DNA replication and transcription.

DNA as information: at the crossroads between biology, mathematics, physics and chemistry

A double-stranded DNA molecule consists of two complementary but disjoint strands that are intertwined into a helix formation through a network of H bonds. Although both the right-handed and left-handed helices are among the allowed conformations, right-handed helices are energetically more favorable due to less steric hindrance between the side chains and the backbone.

The direction of DNA is determined by the arrangement of the phosphate and deoxyribose sugar groups along the DNA backbone. One of the DNA ends terminates with the 3'-OH group, whereas the other one terminates with the 5'-phosphate group.

All sequences of DNA are usually written from 5' to 3' termini. In a double-helix formation, the complementary DNA strands are oriented in opposite directions.

DNA is a rather rigid molecule: at physiological conditions, DNA curves at the length scale of about 50 nm, which is 20 times the diameter of the double helix. More so, the alignment of the bases can indicate the global orientation of a DNA strand. Forces involved in DNA helices[ edit ] The DNA double helix is held together by two main forces: hydrogen bonds between complementary base pairs inside the helix and the Van der Waals base-stacking interaction.

It is important to note that three hydrogen bonds can form between G and C, but only two bonds can be found in A and T pairs. On the other hand, A-T pairs seem to destabilize the double helical structures.

Mathematics of DNA Structure, Function and Interactions

This conclusion was made possible by a known fact that in each species the G content is equal to that of C content and the T content is equal to that of A content. Below is the link to the demo of the Hydrogen bondings between base pairs: The three hydrogen bonds that constitute the linkage of Guanine G and Cytosine C consequently alters the thermal melting of DNA , which is dependent upon base compositions.

With varying base composition the melting point of such molecule will either increase or decrease. Denaturing and Annealing Ultraviolet UV light can detect whether bases are stacked or unstacked. This characteristic is known as the hypochromic effect, in which less color is emitted from the double helix of DNA molecules.

The Tm depends greatly on base composition. When heat is applied to a double-stranded DNA , each individual strand will eventually separate denature because hydrogen bonds are disrupted between base pairs.

Upon separation, the separated strands spontaneously reassociate to form the double helix again. This process is known as annealing. In biological systems, both denaturing and annealing can occur. Helicases use chemical energy from ATP to disrupt the structure of double-stranded nucleic acid molecules. The study of the ability of DNA to reanneal within the laboratory is important in discovering gene structure and expression.

A stem-loop is formed when complementary sequences, within the same strand, pair to form a double helix.

Mathematics of DNA Structure, Function and Interactions

Hydrogen bonds between base pairs within the same strand occur. Often, these structures include mismatched bases, resulting in destabilization of the local structure. Such action can be important in higher-order folding, like in tertiary structures. With the increase in light energy, its structure and therefore its function will still remain intact since there is low disturbance to its structure. The decreased absorbance observed with the DNA double helix with respect to the native and denatured forms is explained by the fact that the stacking of the nitrogenous bases that takes place with the double helix does not leave them as exposed to radiation and thus they are able to absorb less.

The aromaticity of the nitrogenous bases specifically in the purine and pyrimidine like ring structures accounts for the absorption peak being at nm. Hydrogen bonds, linkage between bases, although weak energy-wise, is able to stabilize the helix because of the large number present in DNA molecule.

Stacking interactions, or also known as Van der Waals interactions between bases are weak, but the large amounts of these interactions help to stabilize the overall structure of the helix.

Double helix is stabilized by hydrophobic effects by burying the bases in the interior of the helix increases its stability; having the hydrophobic bases clustered in the interior of the helix keeps it away from the surrounding water, whereas the more polar surfaces, hence hydrophilic heads are exposed and interaction with the exterior water Stacked base pairs also attract to one another through Van der Waals forces the energy associated with a single van der Waals interaction has small significant to the overall DNA structure however, the net effect summed over the numerous atom pairs, results in substantial stability.

Stacking also favors the conformations of rigid five-membered rings of the sugars of backbone.

Nitrogenous Bases[ edit ] Nitrogenous Bases are the foundational structure of DNA polymers, the structure of DNA polymers vary with the different attached nitrogenous bases. Nitrogenous Bases can tautomerize between keto and enol forms.

The keto tautomer is called a lactam and the enol tautomer is called lactim. The lactam predominates at pH 7. Keto-enol tautomerization is the interconversion of a keto and enol involving the movement of a proton and the shifting of bonding electrons, hence the isomerism qualifies as tautomerism. Keto-enol tautomerism is important in DNA structure because high phosphate-transfer potential of phosphenolpyruvate results in the phosphorylated compound to be trapped in the less stable enol form, whereas dephosphorylation results in the keto form.

Rare enol tautomers of bases guanine and thymine can lead to mutation because of the altered base-pairing properties. Base-stacking interactions[ edit ] The two strands of double-stranded DNA are held together by a number of weak interactions such as hydrogen bonds, stacking interactions, and hydrophobic effects.

Of these, the stacking interactions between base pairs are the most significant. The strength of base stacking interactions depends on the bases. It is strongest for stacks of G-C base pairs and weakest for stacks of A-T base pairs. The hydrophobic effect stacks the bases on top of one another. In addition, base stacking in DNA is favored by the conformations of the somewhat rigid five membered rings of the backbone phosphate-sugars.

The base-stacking interactions, which are largely nonspecific with respect to the identity of the stacked base, make the major contribution to the stability of the double helix.

A phosphodiester bond is the linkage formed between the 3' carbon atom and the 5' carbon of the sugar deoxyribose in DNA.

The emphasis is on the power of plasmids for studying DNA structure and function. The conditions that trigger the formation of alternative DNA structures such as left-handed Z-DNA, inter- and intra-molecular triplexes, triple-stranded DNA, and linked catenanes and hemicatenanes are explained.

The DNA dynamics and topological issues are detailed for stalled replication forks and for torsional and structural changes on DNA in front of and behind a transcription complex and a replisome.

The complex and interconnected roles of topoisomerases and abundant small nucleoid association proteins are explained. And methods are described for comparing in vivo and in vitro reactions to probe and understand the temporal pathways of DNA and chromosome chemistry that occur inside living cells.

DNA topology is a critical factor in essentially all in vivo chromosomal processes, including DNA replication, RNA transcription, homologous recombination, site-specific recombination, DNA repair, and integration of the abundant and mechanistically distinct forms of transposable elements.

Plasmids can be invaluable tools to define the dynamic mechanisms of proteins that shape DNA, organize chromosome structure, and channel chromosome movement inside living cells. The advantages of plasmids include their ease of isolation and the ability to quantitatively measure DNA knots, DNA catenation, hemicatenation between two DNA molecules, and positive or negative supercoils in purified DNA populations.

Under ideal conditions, in vitro and in vivo results can be compared to define the complex mechanism of enzymes that move along and change DNA chemistry in living cells. Many techniques that can be easily done with plasmids are not feasible for the massive chromosome that carries most of the genetic information in Escherichia coli or Salmonella typhimurium.DNA specimens isolated from different tissues of the same species have the same base composition.

About these proceedings

Supporting Information Table S1. Cozzarelli, a dynamic leader who fostered research and training at the interface between mathematics and molecular biology. The papers give and overview of state-of-the-art mathematical approaches to the understanding of DNA structure and function, and the interaction of DNA with proteins that mediate vital life processes. Considering that the exact value of parameters for parts is still a far off perspective, the automatic exploration of the design space presented here will provide useful guidance in construct design.

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