Introduction to Biophysics Lecture 7 Brownian motion Diffusion

Charge – Dipole Interaction (fixed geometry): When r >> a Dipole moment Rotation weakens interaction Here and further on  =4  0  How rotation of molecules affect this interaction?

Dispersion forces (London fource) The charge distribution of a molecule fluctuates rapidly with time. At any instant there will be a transient dipole moment. Since the attractive configurations have a lower potential energy than the repulsive configurations, they will have larger weights in a Boltzmann average, leading to a net attraction. There are many theoretical approaches to the calculation of this interaction energy, all of which are quite complicated. where  1 and  2 denote the polarizabilities of the two interacting molecules, I 1 and I 2 denote their ionization energies, and n denotes the refractive index of the medium. The fluctuations in the electronic structure responsible for transient dipole moments are much faster than molecular rotations in a liquid. In water media dispersion force between molecules is much stronger than interactions involving rotating permanent dipoles. Two rotating permanent dipoles

DNA can be damaged by mutagens, which change the DNA sequence. Oxidizing agents, alkylating agents High-energy electromagnetic radiation: UV, X-ray For example, UV light can damage DNA by producing thymine dimers oxidants such as free radicals or hydrogen peroxide produce base modifications and double- strand breaks. The most dangerous are double-strand breaks, as these are difficult to repair. Many mutagens fit into the space between two adjacent base pairs - aromatic and planar molecules. This inhibits both transcription and DNA replication, causing toxicity and mutations. As a result, DNA intercalators are often carcinogens. Nevertheless, due to their ability to inhibit DNA transcription and replication, these toxins are also used in chemotherapy to inhibit rapidly-growing cancer cells. DNA damage

Heavy exposure of your skin to UV light causes many such thymine crosslinks to form in the DNA. Fortunately, we have repair enzymes that can remove the thymine crosslinks and restore the DNA in your skin cells back to the correct sequence. When you get a sunburn, it is because you have caused more thymine crosslinks than can be repaired, so the cells generally just die. This results in the pain and dead skin you get with sunburns.

See page in Nelson For calculations of viscous drag Question: How two DNA strands separate for replication if they are wound around each other?

DNA Replication DNA replication. The double helix is unwound by a helicase. Topoisomerase removes the excess of twisting generated by helicase. Next, one DNA polymerase produces the leading strand copy. Another DNA polymerase binds to the lagging strand. This enzyme makes discontinuous segments before DNA ligase joins them together.

Repeat Central Dogma of Molecular Biology with movie Finish calculations for viscous drag on DNA

Diffusion is the dominant form of material transport on sub-micrometer scales.

Brownian motion Botanist Robert Brown, 1828 Pollen grains 1  m in diameter can be observed in visible microscope (the wavelength of visible light is about 1/2  m.) Concerns: How collisions with very small molecules (nm size) can move “huge” pollen grain? Displacements seen in microscope are huge in comparison with size of molecules. Collisions rates of water molecules are about per seconds (10 3 m/sec – speed of molecule nm – distance between collision). Our eyes can resolve events at rates no faster than 30 s -1. How we can see displacements?

The mathematics of random walks is an appropriate language to describe diffusion

Calculating probabilities 2 steps walk, probability of coming back to starting point P 0 = 2/2 2 =0.5 4 steps walk P 0 =6/2 4 =0.375 How to do calculation for large number (10000 steps)? M 0 – number of different outcomes that land us at the starting point. Should have equal number of heads and tails (5000). Describe them as list containing 5000 different integers (n 1, …, n 5000 ); n 1 = any number between 1 and 10000, n 2 any of the 9999 remaining choices, and so on. We have a total of 10000x9999x…x5001 lists = 10000!/5000! But any two lists differing by exchange (or permutation) of the n i ’s are not really different, so we must divide our answer by total number of possible permutations, which is 5000x4999x…x1. M 0 = 10000!/(5000!x5000!) M 0 /M= 10000!/(5000!x5000!x )  (about 1%) Stirling’s formula: ln M!  MlnM – M +1/2(ln(2  M))

Reading Nelson Chapter 4 Check T2: Nelson problem 4.2, page 153.