Project Summary: The structure, dynamics and function of a biomolecule play a key role in determining disease mechanisms, knowledge of which is essential for early diagnosis, drug development and effective treatment. Many biological studies focus on structure determination of biomolecules but the study of dynamics is vital to understand disease mechanisms, including their function and interaction with their environment. Compared to other biophysical methods, multi-frequency 2D Electron Spin Resonance (ESR) spectroscopy are powerful methods for studying structural dynamics of proteins at physiological temperatures for a wide range of time scales (sub-๐๐ to tens of ๐๐ ) and can provide a detailed description of motion that includes both dynamics as well as local structural ordering. Despite major advances, multi-frequency 2D-ESR lack sufficient sensitivity and resolution needed to study biological systems at ๐๐ timescales, because the signals are heavily dominated by noise with Signal-to-Noise Ratios (SNRs) of unity and so are hardly visible. To address this problem, the proposed research will develop computational methods based on wavelet transforms to remove noise for accurate signal recovery. The proposed research is aimed at developing multidimensional wavelet denoising for multi-frequency 2D-ESR signals at SNR ~ 1, extending the 1D wavelet denoising approach. Wavelet transforms provide a powerful approach to remove noise as they focus on separating noise from the signal, an active subject in the field of signal processing. The methods will include multi-dimensional representation of signals, development of new wavelets, enhancement in signal resolution in the wavelet domain, and development of noise thresholds based on well-defined statistical theorems, all of which will contribute to separate noise from signals. A new criterion will also be developed and adopted to quantify noise and uncertainty. The new denoising methods will be applied to reveal conformational dynamics of a well-characterized T4 Lysozyme protein and to understand lipid-transmembrane interactions ranging from ๐๐ to tens of ๐๐ time scales at physiological temperatures and concentrations for understanding signaling pathways related to diseases. This will lead to a detailed understanding of protein dynamics at the time scale of exchange between conformational substates and will create a platform for which motions of biological complexes can be studied, which currently remains elusive and are of key functional importance. Measurement of exchange rates under physiological conditions is a new experimental frontier and lifetimes in the range of ๐๐ are anticipated. It will also lay the foundation for using data processing methods to remove noise from experimental signals and permit their application during data acquisition for real-time processing. Data processing methods are inexpensive, easy-to-implement, and easily scalable to existing instruments.