Nonlinear protein structures

Basic data obtained from NMR studies consist of distance and torsion angle restraints. Once resonances have been assigned, nuclear Overhauser effect (NOE) contacts are selected and their intensities are used to calculate interproton distances. Information on torsion angles are based on the measurement of coupling constants and analysis of proton chemical shifts. Together, this information is used to formulate a nonlinear optimization problem, the solution of which should provide the correct protein structure. Typically, a hybrid energy function of the following form is employed ... 

Volkov, S.N. Conformational transitions and the mechanism of transmission of long-range effects in DNA. Preprint ITP-88-12E, Kiev (1988) 22 Krumhansl, J.A., Alexander, D.M. Nonlinear dynamics and conformational exitations in biomolecular materials. In Structure and dynamics nucleic acids and proteins. (Clementi, E., Sarma, R.H., eds) Adenine Press, New York (1983) 61-80... 

Another recent trend is to show the importance of hydrophobic profiles rather than molecular hydrophobicity. Giuliani et al. (2002) suggested nonlinear signal analysis methods in the elucidation of protein sequence-structure relationships. The major algorithm used for analyzing hydrophobicity sequences or profiles was recurrence quantification analysis (RQA), in which a recurrence plot depicted a single trajectory as a two-dimensional representation of experimental time-series data. Examples of the global properties used in this... 

Giuliani, A., Benigni, R., Zbilut, J.P., Webber, C.L. Jr, Sirabella, P and Colosimo, A. 2002. Nonlinear signal analysis methods in the elucidation of protein sequence-structure relationships. Chem. Rev. 102 1471-1492. 

We are beginning to develop a detailed understanding of these methods (18,21,30,33,34,37-40,42,44,47-49), many of which are described in this book. We have recently demonstrated a series of novel nonlinear all-IR spectroscopic techniques (IR-pump-IR-probe, IR-three-pulse photon echoes, IR-dynamic hole burning, IR-2D spectroscopy), all of them utilizing intense femtosecond IR pulses, with the intention to develop new multidimensional spectroscopic tools to study the structure and the dynamics of proteins (30,31,41,42,50-53). We shall summarize in this contribution our work, its underlying principles, and its applications. 

We have presented two types of nonlinear IR spectroscopic techniques sensitive to the structure and dynamics of peptides and proteins. While the 2D-IR spectra described in this section have been interpreted in terms of the static structure of the peptide, the first approach (i.e., the stimulated photon echo experiments of test molecules bound to enzymes) is less direct in that it measures the influence of the fluctuating surroundings (i.e., the peptide) on the vibrational frequency of a test molecule, rather than the fluctuations of the peptide backbone itself. Ultimately, one would like to combine both concepts and measure spectral diffusion processes of the amide I band directly. Since it is the geometry of the peptide groups with respect to each other that is responsible for the formation of the amide I excitation band, its spectral diffusion is directly related to structural fluctuations of the peptide backbone itself. A first step to measuring the structural dynamics of the peptide backbone is to measure stimulated photon echoes experiments on the amide I band (51). 

We shall conclude this chapter with a few speculative remarks on possible future developments of nonlinear IR spectroscopy on peptides and proteins. Up to now, we have demonstrated a detailed relationship between the known structure of a few model peptides and the excitonic system of coupled amide I vibrations and have proven the correctness of the excitonic coupling model (at least in principle). We have demonstrated two realizations of 2D-IR spectroscopy a frequency domain (incoherent) technique (Section IV.C) and a form of semi-impulsive method (Section IV.E), which from the experimental viewpoint is extremely simple. Other 2D methods, proposed recently by Mukamel and coworkers (47), would not pose any additional experimental difficulty. In the case of NMR, time domain Fourier transform (FT) methods have proven to be more sensitive by far as a result of the multiplex advantage, which compensates for the small population differences of spin transitions at room temperature. It was recently demonstrated that FT methods are just as advantageous in the infrared regime, although one has to measure electric fields rather than intensities, which cannot be done directly by an electric field detector but requires heterodyned echoes or spectral interferometry (146). Future work will have to explore which experimental technique is most powerful and reliable. 

Multidimentional nonlinear infrared spectroscopy is used for identification of dynamic structures in liquids and conformational dynamics of molecules, peptides and, in principle, small proteins in solution (Asplund et al., 2000 and references herein). This spectroscopy incorporates the ability to control the responses of particular vibrational transitions depending on their couplings to one another. Two and three-pulse IR photon echo techniques were used to eliminate the inhomogeneous broadening in the IR spectrum. In the third-order IR echo methods, three phase-locked IR pulses with wave vectors kb k2, and k3 are focused on the sample at time intervals. The IR photon echo eventually emitted and the complex 2D IR spectrum is obtained with the use of Fourier transformation. The method was applied to the examination of vibrational properties of N-methyl acetamid and a dipeptide, acyl-proline-NH2.in D20. The 2D IR spectrum showed peaks at 1,610 and 1, 670 cm 1, the two frequencies ofthe acyl-proline dipeptide. Geometry and time-ordering of the incoming pulse sequence in fifth-order 2D spectroscopy is shown in Fig. 1.3. 

For transporters, relatively low protein expression level and limited transport capacity makes for nonlinear, enzyme-like transport kinetics that is, the transport rate saturates with increasing substrate concentration. This phenomenon is the basis for the competitive interactions generally found for chemicals that are handled by one or more common transporters this is usually manifest as inhibition of the transport of one chemical by a structural analog. The extent to which these competitive interactions are important depends on the concentrations of the chemicals involved, their relative affinities for the common transporter, and their phar-macological/toxicological profiles (effects, effective concentrations, therapeutic index). Competition for transport is discussed below in the context of drug-drug interactions. 

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