11.2 Electronic structure and spectroscopy of biomolecules

Quantum mechanics unlocks the secrets of biomolecules' electronic structure. From wave functions to molecular orbitals, these principles explain how electrons behave in biological systems, shaping chemical bonds and interactions crucial for life.

Spectroscopic techniques like UV-Vis and fluorescence let us peek into this quantum world. By probing electronic transitions, we can unravel biomolecule structures, track conformational changes, and even design new tools for studying life's molecular machinery.

Electronic Structure of Biomolecules

Quantum Mechanical Principles Governing Electronic Structure

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• The electronic structure of biomolecules is governed by the principles of quantum mechanics, which describe the behavior of electrons in atoms and molecules
• The wave-particle duality of electrons is a fundamental concept in quantum mechanics, where electrons exhibit both wave-like (interference and diffraction) and particle-like (quantized energy and momentum) properties
• The Schrödinger equation is the fundamental equation of quantum mechanics that describes the behavior of electrons in atoms and molecules
  • The solutions to the Schrödinger equation for a given system are called wave functions, which provide information about the probability distribution of electrons in space
  • The square of the wave function gives the probability density of finding an electron at a particular point in space (e.g., the electron density around a molecule)

Electronic Configuration and Chemical Bonding

• The Pauli exclusion principle states that no two electrons in an atom or molecule can have the same set of four quantum numbers (principal, angular momentum, magnetic, and spin), which determines the electronic configuration of biomolecules
• The electronic structure of biomolecules is influenced by the presence of multiple atoms and the formation of chemical bonds, leading to the creation of molecular orbitals
  • Covalent bonds are formed by the sharing of electrons between atoms, resulting in the formation of bonding molecular orbitals (e.g., σ and π bonds)
  • Non-covalent interactions, such as hydrogen bonding and van der Waals forces, also play a crucial role in the structure and stability of biomolecules (e.g., the double helix structure of DNA)

Molecular Orbitals in Biomolecules

Formation and Properties of Molecular Orbitals

• Molecular orbitals are formed by the linear combination of atomic orbitals (LCAO) when atoms come together to form molecules
  • Bonding molecular orbitals are formed when atomic orbitals constructively interfere, resulting in increased electron density between the nuclei and a lower energy state (e.g., σ and π bonding orbitals)
  • Antibonding molecular orbitals are formed when atomic orbitals destructively interfere, resulting in decreased electron density between the nuclei and a higher energy state (e.g., σ* and π* antibonding orbitals)
• The energy and shape of molecular orbitals determine the electronic properties of biomolecules, such as their stability, reactivity, and spectroscopic behavior
• The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are particularly important in determining the chemical and spectroscopic properties of biomolecules
  • The HOMO-LUMO gap represents the energy required for electronic transitions, which can be probed by spectroscopic techniques (e.g., UV-Vis absorption spectroscopy)

Delocalization and Heteroatoms

• Molecular orbital theory can be used to explain the delocalization of electrons in conjugated systems, such as aromatic rings in nucleic acid bases (e.g., adenine and guanine) and amino acid side chains (e.g., phenylalanine and tryptophan), which contributes to their stability and spectroscopic properties
  • Delocalization of electrons leads to the formation of extended π systems, which lower the overall energy of the molecule and increase its stability (e.g., the resonance structures of benzene)
  • Conjugated systems often exhibit characteristic absorption and emission properties due to the presence of delocalized electronic transitions (e.g., the UV absorption of nucleic acids at 260 nm)
• The electronic structure of biomolecules can be influenced by the presence of heteroatoms, such as nitrogen and oxygen, which introduce additional molecular orbitals and alter the electronic properties of the molecule
  • Heteroatoms can participate in hydrogen bonding and other non-covalent interactions, which play a crucial role in the structure and function of biomolecules (e.g., the base pairing in DNA and RNA)
  • The presence of heteroatoms can also give rise to specific electronic transitions, such as n → π* transitions, which involve the excitation of non-bonding electrons to antibonding orbitals (e.g., the absorption of carbonyl groups in proteins)

Spectroscopic Techniques for Biomolecules

Absorption and Fluorescence Spectroscopy

• Electronic absorption spectroscopy (UV-Vis) is based on the absorption of photons by molecules, leading to the excitation of electrons from the ground state to higher energy states
  • The wavelength of absorbed light depends on the energy difference between the molecular orbitals involved in the electronic transition (e.g., π → π* and n → π* transitions)
  • The intensity of absorption is related to the probability of the electronic transition, which is governed by selection rules based on the symmetry of the molecular orbitals (e.g., the allowed and forbidden transitions in porphyrins)
• Fluorescence spectroscopy involves the emission of photons by molecules that have been excited to higher energy states by the absorption of light
  • The wavelength of emitted light is typically longer than the absorbed light due to the loss of energy through non-radiative processes, such as vibrational relaxation and internal conversion (Stokes shift)
  • The fluorescence quantum yield and lifetime are important parameters that provide information about the efficiency and dynamics of the emission process (e.g., the high quantum yield of fluorescent proteins like GFP)

Circular Dichroism and Raman Spectroscopy

• Circular dichroism (CD) spectroscopy measures the differential absorption of left and right circularly polarized light by chiral molecules
  • The CD signal arises from the interaction between the electric and magnetic transition dipole moments of the molecule, which are sensitive to the asymmetric environment of chiral centers (e.g., the α-helical and β-sheet structures of proteins)
  • CD spectroscopy can provide information about the secondary structure of proteins and the conformational changes induced by ligand binding or environmental factors (e.g., the folding and unfolding of proteins)
• Raman spectroscopy is based on the inelastic scattering of photons by molecules, which results in a change in the vibrational energy of the molecule
  • The Raman shift, which is the difference between the incident and scattered photon energies, provides information about the vibrational modes of the molecule, which are sensitive to its electronic structure and bonding (e.g., the characteristic Raman bands of nucleic acids and proteins)
  • Resonance Raman spectroscopy involves the use of excitation wavelengths that coincide with electronic transitions, leading to the selective enhancement of vibrational modes coupled to the electronic transition (e.g., the enhancement of heme vibrational modes in cytochrome c)

Electronic Spectra of Biomolecules

Interpretation of Absorption and Emission Spectra

• The electronic absorption spectrum of a biomolecule represents the wavelength-dependent absorption of light, which is determined by the energy differences between the molecular orbitals involved in the electronic transitions
  • The absorption bands in the spectrum correspond to specific electronic transitions, such as π → π* transitions in conjugated systems (e.g., the absorption of aromatic amino acids) or n → π* transitions in molecules containing heteroatoms with non-bonding electrons (e.g., the absorption of peptide bonds)
  • The position and intensity of the absorption bands can provide information about the electronic structure, conjugation length, and the presence of specific functional groups in the biomolecule (e.g., the red-shift of absorption bands in extended conjugated systems)
• The electronic emission spectrum of a biomolecule represents the wavelength-dependent emission of light following the excitation of the molecule to higher energy states
  • The emission spectrum is typically red-shifted relative to the absorption spectrum due to the energy loss through non-radiative processes, such as vibrational relaxation and solvent reorganization (Stokes shift)
  • The shape and intensity of the emission spectrum can provide information about the excited state dynamics, the presence of different emitting species, and the influence of the molecular environment on the emission process (e.g., the solvatochromic shift of fluorescent probes)

Applications and Computational Methods

• The electronic spectra of biomolecules can be sensitive to changes in their structure and environment, such as pH, polarity, and interactions with other molecules
  • Changes in the absorption or emission spectra can be used to monitor conformational changes (e.g., protein folding), ligand binding events (e.g., enzyme-substrate interactions), or the formation of molecular complexes (e.g., protein-protein interactions)
  • The spectroscopic properties of biomolecules can be exploited for various applications, such as the design of fluorescent probes (e.g., calcium indicators), the study of protein folding and dynamics (e.g., single-molecule FRET), and the development of biosensors (e.g., glucose sensors)
• The interpretation of electronic spectra often requires the use of computational methods, such as quantum chemical calculations and molecular dynamics simulations, to provide a detailed understanding of the electronic structure and the factors influencing the spectroscopic properties of biomolecules
  • These computational approaches can help to assign the observed spectroscopic features to specific electronic transitions, predict the effect of structural modifications on the spectra, and guide the rational design of biomolecules with desired spectroscopic properties (e.g., the development of novel fluorescent proteins)
  • Quantum chemical methods, such as density functional theory (DFT) and time-dependent DFT (TD-DFT), can be used to calculate the electronic structure and excitation energies of biomolecules, providing a theoretical framework for interpreting experimental spectra (e.g., the prediction of absorption and emission wavelengths)