Understanding the structure and dynamics of proteins remains a critical challenge for understanding their physiological functions. The development of coherent non-linear spectroscopy over the past decades, such as two-dimensional infrared spectroscopy (2D-IR), has allowed for the study of the real-time dynamics of proteins from femtosecond to picosecond timescales . Hemoproteins are important in physiology because they are responsible for transport and storage of oxygen. Hemoprotein-CO complexes have been widely studied in the past, both experimentally and theoretically, in order to probe hemoprotein dynamics. In particular, it is known that carboxy-myoglobin (MbCO) exhibits complex dynamics with inter-conversion between different sub-states . Fewer spectroscopic studies have been performed to resolve the dynamics of the carboxy-hemoglobin (HbCO), which is known to have different dynamics than MbCO . Here, we present simulations of the ultrafast dynamics of HbCO in order to interpret recent high-resolution 2D-IR measurements . The simulations are based on a semi-classical model, which describes directly the fluctuations of the potential energy surface (PES) originating from the electrostatic environment and the heme group. The agreement between theory and experiment is achieved without using adjustable parameters and demonstrates the model contains the correct description for understanding the protein internal dynamics. Our simulations show the strong effect of the distal histidine through a hydrogen bond, which is responsible for the slow decay of the frequency-frequency correlation function. Some recent theoretical developments to extend coherent non-linear spectroscopy in order to probe non-equilibrium systems  will also be presented. The potential for this new technique to probe the vibrational decoherence of CO after photolysis will be discussed.
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