Tuning EPR spectral parameters with a genetic algorithm

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Abstract

We present an evolutionary computation approach to parameter tuning in electron paramagnetic resonance (EPR) spectroscopy which is a nondestructive technique suitable for inspection of complex biological systems. Characterization of such a system is much more reliable when spectral features are extracted from a biophysical model of the system. This involves optimization of the model parameters so that the spectrum generated by the model matches the experimental EPR spectrum. Various optimization methods have been applied to this task in the past, but nowadays stochastic algorithms are used more and more often. As many single-point algorithms require time-consuming preparation of promising starting points to produce reasonable results, we have addressed the problem with population-based search strategy. We have implemented a genetic algorithm for EPR spectral parameter optimization and tested it on synthetic spectra obtained in cell membrane inspection. Preliminary numerical experiments show the new approach is beneficial in that it produces satisfactory results and reduces the time a spectroscopist spends for navigating the optimization process.

Introduction

To inspect complex biological systems and acquire relevant information about their structure and dynamics in a nondestructive way, spectroscopic techniques are widely used. Among them is electron paramagnetic resonance (EPR) spectroscopy which exploits the physical phenomenon of absorption of microwave radiation by paramagnetic molecules or ions exposed to an external magnetic field. In combination with labeling based on nitroxide spin probes, EPR spectroscopy is especially suitable for studying cell membranes [6], [13]. It can detect alterations caused by biologically active substances and indicating pathological conditions, such as acute phase, cancer, etc. In the past, interpretation of EPR spectra was performed manually by measuring spectral peak characteristics and analyzing their relationships. However, the recorded EPR spectra provide much more reliable and biologically meaningful information when characterized through computer-aided spectrum simulation. This requires a biophysical model capable of reproducing EPR spectra, and an optimization procedure to find appropriate values of the model parameters.

Exploration of complex geometry of tissues or cell suspensions reveals a number of domains which reflect the heterogeneity of biological membranes [7]. A spectrum simulation model that, under certain preconditions, satisfactorily describes the EPR spectra recorded in such systems is the so-called motional-restricted fast-motion approximation [14]. The parameters used for spectrum simulation in this model provide data about ordering, dynamics and the polarity at various locations in different membrane domains. Furthermore, the approach seems to be a good compromise between the exact theoretical consideration, empirical knowledge and computational requirements in order to perform characterization of an experimental EPR spectrum in a reasonable period of time.

To characterize an experimental spectrum via computer simulation, parameters of the involved biophysical model have to be tuned to fit the simulated spectrum with the recorded EPR spectrum. Since the number of model parameters is usually high and nonlinear relations are involved, the problem is computationally demanding. It has been addressed by various optimization techniques, including both deterministic (grid search, Levenberg–Marquardt, simplex, etc.) and stochastic (Monte Carlo, simulated annealing) algorithms. Budil et al. [2], for example, applied a modified Levenberg–Marquardt algorithm to characterize slow-motion EPR spectra, and Feyer et al. [3] used the simplex algorithm in fitting high-resolution EPR spectra. To overcome weaknesses of local optimization, Puma et al. [12] applied the Monte Carlo approach which proved more robust. Štrancar et al. [14] estimated parameter values in characterization of biological membranes with downhill simplex and simulated annealing algorithms. These studies and other reports on optimization of EPR spectral parameters show that deterministic methods, which require less computational efforts but tend to converge to a local optimum, are very sensitive to initial points of exploration. Only with good starting parameter values the optimization procedure may be expected to produce a reasonable result. Stochastic algorithms are computationally more demanding, but were found more robust with respect to the starting point. However, single-point stochastic algorithms may still have difficulties with hard problems involving numerous parameters which are, in addition, partially correlated, as it is the case in EPR spectroscopy of membranes.

In either case, the burden of providing promising starting parameter settings falls to a spectroscopist who then also needs to navigate the search from various starting points in an iterative manner, employing empirical knowledge and results of previous iterations. As the approach may be very time-consuming, an automated optimization procedure for this problem is highly desired. It would allow the spectroscopist to focus on experiments and extract more information about the inspected biological system. In our view, evolutionary algorithms [1], which, unlike the single-point stochastic methods, perform population-based search and are known as robust and efficient global optimizers, are promising candidates for automating EPR spectral parameter optimization. To test this idea, we integrated a genetic algorithm [4] with the spectrum simulation model and carried out an experimental verification on synthetic EPR spectra consisting of various numbers of domains. Initial results are promising both in view of accuracy and reduction of the time spent on parameter tuning by a spectroscopist.

The paper is further organized as follows. Section 2 reviews the EPR spectrum simulation model used and spectral parameters tuned in this study. Section 3 describes the genetic algorithm integrated with the model and applied in spectrum fitting. Numerical experiments and results are presented in Section 4. The paper concludes with a summary of the investigation and issues for further work.

Section snippets

The spectrum simulation model and its parameters

To simulate EPR spectra, the restricted fast-motion approximation procedure was used which is discussed in detail in [14]. Here, it is briefly reviewed with an emphasis on the role of the involved spectral parameters.

Dealing with spin-labeled cell suspension or tissue we encounter superimposed EPR spectra consisting of several spectral components, also called domains. They arise from various compartments (solution, membrane domains, outer and inner layers of the membrane, aggregates, etc.) with

A genetic algorithm for tuning EPR spectral parameters

Genetic algorithms can be viewed as computer simulations of evolutionary phenomena known from biological systems, such as genetic recombination and survival of the fittest population members. Genetic algorithms apply these concepts as search heuristics to efficiently explore large solution spaces. Population-based search and robustness make genetic algorithms powerful problem-solving techniques applicable to a broad spectrum of tasks, including numerical optimization [9].

In this study, a

Numerical experiments and results

The aim of preliminary numerical experiments was to compare the performance of genetic optimization with that of parameter optimization techniques previously applied in EPR spectroscopy of biological membranes [14]. These include downhill simplex [10] and simulated annealing using the Metropolis criterion for accepting new parameter settings [8].

The experiments were performed on synthetic spectra artificially contaminated with noise to represent “experimental” spectra. The noise level was 5% of

Conclusions

A genetic algorithm was integrated with an EPR spectrum simulation model to perform parameter optimization which is an important step of characterization of complex biological systems with EPR spectroscopy. The approach was evaluated on synthetic spectra and its results were compared to that of human-navigated single-point search techniques. The hybrid method consisting of genetic search and additional local optimization of solutions produced superior results and its effectiveness was clearly

Acknowledgements

The work reported in this paper was supported by the Slovenian Ministry of Education, Science and Sport. This is an extended version of the paper presented at the Parallel Problem Solving from Nature (PPSN VI) Conference in Paris, France, 2000, and published in the Springer-Verlag series Lecture Notes in Computer Science. The authors wish to express their gratitude to Matjaž Kovač for implementing the genetic algorithm in the spectrum simulation and optimization environment, to Milan Schara and

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