Development Of A Quantum-Mechanical Analysis Of Stark Effects Of Porphyrins Employed As Sensors Of Internal Electric Fields In Biological Systems

Chromophores in biological systems, such as heme, are exposed to strong electric fields that are generated by charge distributions of the biosystems themselves. These “internal electric fields” may be of magnitude of several MV/cm, and, thus, may contribute to functional properties of a system. The ability to measure such fields would help to elucidate the importance of “electrostatic structure” to a biosystemu0027s function. Our approach of measuring internal electric fields relies on changes to electronic transition energies of a chromophore when exposed to an electric field, i.e., the “Stark effect”. Analyzing the Stark shifts allows for extraction of magnitude and orientation the internal electric field. Classically, the Stark shift is analyzed with a series of terms that are linear, quadratic, etc., in the electric field, which requires knowledge of the polarizability tensors for both ground and excited states to extract the internal electric field. Usually the analysis is restricted to term linear in the external electric field, which for randomly oriented chromophores leads to a systematic error. We pose a quantum-mechanical alternative to the classical analysis based on infinite-order perturbation theory that overcomes the neglect of non-linear terms. The challenge with the quantum-mechanical analysis then becomes that, theoretically, it may require the description of an infinite number of electronic transitions to account for the Stark shift. Here, we present a method for determining the number and identity of electronic transitions that are required for quantum-mechanical Stark analysis, essentially opening a practical path to using this more exact analytical option. As demonstration, we apply this new protocol to a porphyrin sensor used to measure the internal electric field of myoglobin and show the accessibility of the method with reasonable computational resources.