Brownian motion of the ends of oligopeptide chains in solution as estimated by energy transfer between the chain ends
Authors: Haas Elisha , Katchalski‐Katzir Ephraim , Steinberg Izchak Z. 
Published: December 2004

The kinetics of the fluorescence decay of the energy donor in a homologous series of oligopeptides each containing at its ends a donor and an acceptor of electronic excitation energy was investigated in solvent mixtures of different viscosities. The repeating unit in the peptides was N5‐(2‐hydroxyethyl)‐L‐glutamine and the chromophores used as donor and acceptor were naphthalene and dansyl, respectively. The number of units in the peptides studied varied from four to nine. The solvents used were mixtures of glycerol and trifluoroethanol in various proportions. The decay rate of the donor fluorescence increases when the solvent viscosity decreases. This behavior is due to the disturbance of the equilibrium end‐to‐end distribution of distance of the excited molecules by the energy transfer process, which is more favorable foe short than for long distances. The subsequent rearrangement towards the equilibrium distribution by diffusion of the molecular ends relative to one another enhances the efficiency of the energy transfer. Assuming a modified Fick equation to describe this diffusion motion, the fluorescence decay data were analyzed in terms of a diffusion coefficient describing the Brownian motion of the molecular ends. The diffusion coefficients thus evaluated increase systematically upon decreasing the solvent viscosity. For example, for the oligopeptides studied it changes from unmeasurably small values in glycerol solution to values varying between 10−8 to 10−7 cm2/sec at room temperature in a glycerol trifluoroethanol solvent mixture of viscosity of 8 centipoise. The values obtained for the diffusion coefficient are smaller by about an order of magnitude than the values expected for the diffusion coefficients of the free chromophores in solvents of comparable viscosity. It is thus concluded that the backbone of the polymeric chains possesses appreciable internal friction which exerts resistance to the Brownian motion of the polymer chains. The diffusion coefficient of the end‐to‐end motion is systematically smaller for the shorter than for the longer chains. For example, at room temperature in a solvent mixture of 8 centipoise it is 3×10−8, 5×10−8, 7.6×10−8, and 8.5×10−8 cm2/sec for oligomers containing four, five, eight, and nine N5‐(2‐hydroxylethyl)‐L‐glutamine repeating units, respectively. The internal friction thus impedes the motion of the molecular ends more effectively in the shorter chains than in the longer ones.

Analysis of the energy‐transfer experiments in solvents spanning a wide range of viscosities shows that the orientational factor appearing in Förster's equation for energy transfer does not interfere perceptibly with the evaluation of the end‐to‐end distances from the fluorescence decay data when naphthalene and dansyl serve as donor and acceptor, respectively. This is due to the fact that both the donor emission and acceptor absorption in the range of spectral overlap are characterized by more than one transition dipole moment, as is evident from the corresponding polarization data.