A Neural Network Approach to the Rapid Computation of Rotational Correlation Times from Slow Motional ESR Spectra Gary V. Martinez and Glenn L. Millhauser 1 Department of Chemistry and Biochemistry, University of California, Santa Cruz, Santa Cruz, California 95064 Received August 18, 1997; revised April 7, 1998 We explore the use of feed forward artificial neural networks for determining rotational correlation times from slow motional ni- troxide electron spin resonance spectra. This approach is rapid and potentially eliminates the need for traditional iterative fitting procedures. Two networks are examined:the radial basis network and the multilayerperceptron. Although the radial basis network trains rapidly and performs well on simulated spectra, it is less satisfactory when applied to experimental spectra. In contrast, the multilayer perceptron trains slowly but is excellent at extracting correlation times from experimental spectra. In addition, the mul- tilayerperceptron operates well in the presence of noise as long as the signal-to-noise ratio is greater than approximately 200/1. These findings suggest neural networks offer a promising ap- proach for rapidly extracting correlation times without the need for iterative simulations. © 1998 Academic Press Key Words: neural networks; ESR; slow motional spectra; radial basis network; multilayer perceptron; rotational correlation time. INTRODUCTION Nitroxide spin labels, in conjunction with electron spin resonance (ESR), serve as probes for exploring dynamics in nucleic acids, peptides and proteins (1–3). The ESR lineshape is often used to determine the rotational correlation time ( R ) of the nitroxide, thereby revealing motion at the label site. When  R is less than approximately 1 ns, ESR spectra are character- ized by three motionally narrowed hyperfine lines, and straightforward lineshape measurement gives accurate values for the correlation time. However, when  R is between 1 ns and 100 ns—the so-called slow motional regime—lineshape anal- ysis is substantially more complicated (4). The correlation times of most macromolecules fall within this regime and consequently enormous effort has been directed toward ex- tracting dynamic information from slow motional spectra. Leading efforts in this field have come from Freed and co-workers (5) (see also Chapter 3 in Ref. 1). Throughout the 1970s and 1980s they developed and refined slow motional simulation techniques based on the stochastic Liouville equa- tion. Despite their great success, determining dynamic param- eters from slow motional spectra remains a challenge. The essential problem lies with the iterative approach one must employ when simulating spectra. Given an experimental spec- trum, one must first guess at a value for the correlation time (as well as other parameters, including motional anisotropy, local ordering, and sample heterogeneity) and then perform a sim- ulation. The result is compared to the experimental spectrum. If the agreement is not satisfactory, the input values are ad- justed and another simulation is performed. This process is repeated until good overlap between the experimental and simulated spectra is achieved. Recently, Budil et al. developed a nonlinear least squares approach to automate the procedure of fitting slow motional spectra (6). They applied a “model trust region” modification of the Levenberg–Marquardt algorithm and showed that com- plicated spectra could be successfully simulated using a com- puter workstation. Nevertheless, their method still relies on iteration. The difference in effort required for a noniterative approach, such as that used for analyzing fast motional spectra, and the iterative approach required for slow motional spectra is strik- ing. It would be quite helpful if a method could be developed that used a noniterative approach for analyzing slow motional spectra. Toward this goal we explore the use of artificial neural networks (7). Neural networks have emerged as remarkable tools for pattern recognition in scientific applications. They have been applied with good success to spectroscopic problems in nuclear magnetic resonance (8 –10), circular dichroism (11– 13), and infrared spectroscopy (14). Artificial neural networks were inspired by research into the interplay that takes place among networks of real biological neurons. In an artificial neural network, the synaptic connec- tions between neurons are represented by numerical weights, which measure the strength of a connection, and a transfer function that emulates the firing of the neuron. Training a network involves establishing a set of numerical weights that successfully connect a training input with a desired output. Once trained, an artificial neural network can be an effective tool for recognizing and extracting key features from previ- ously unseen input. In spectroscopic applications, neural networks have been 1 To whom correspondence should be addressed. Fax: (408) 459-2935. E-mail: glennm@hydrogen.ucsc.edu JOURNAL OF MAGNETIC RESONANCE 134, 124 –130 (1998) ARTICLE NO. MN981496 124 1090-7807/98 $25.00 Copyright © 1998 by Academic Press All rights of reproduction in any form reserved.