Statistical mechanics of complex systems and glass transition

We are interested in a number of problems related to the statistics and dynamics of complex systems ranging from molecular liquids to assemblies of biomolecules. Common to these systems is a complex energy landscape, with a high density of local minima. Complex relaxation patterns and uncommon activated kinetics follow from system’s exploration of the energy landscape by thermal agitation. Many of such problems cannot be described by canonical ensembles and the statistics of non-equilibrium ensembles is required. The related problems are ergodicity breaking and theoretical formalisms to describe the nonergodic activated kinetics.

Publications:

• "Protein electron transfer: is biology (thermo)dynamic", D. V. Matyushov, "Topical review" J. Phys.: Condens. Matter (preprint)
• "Nonergodic activated kinetics in polar media", D. V. Matyushov, J. Chem. Phys. 130, 164522 (2009)
• "Model energy landscapes of low-temperature fluids: Dipolar hard spheres", D. V. Matyushov, Phys. Rev. E 76, 011511 (2007)
• "Gaussian excitations model for glass-former dynamics and thermodynamics", D. V. Matyushov and C. A. Angell, J. Chem. Phys. 126, 094501 (2007) 

Dynamically Restricted Ensemble

Dielectrics

Dielectric spectroscopy probes dynamic response of the bulk polarization of the material to a uniform electric field. A recent interest, advanced by Prof. Ranko Richert at ASU, is to understand dynamics and statistics of nonlinear dielectric response, i.e., dielectric polarization proportional to at least the third power of the external electric field. This research is currently in an early stage, one recent publication is listed below.     

• "Nonlinear dielectric response of polar liquids", D. V. Matyushov, J. Chem. Phys. 142, 244502 (2015)

The theory of nonlinear response of bulk dielectrics was recently extended to protein solutions. Proteins show much enhanced nonlinear dielectric response relative to the surrounding electrolyte. The nonlinear dielectric response can be used to monitor protein conformations/unction.

• "Linear and Nonlinear Dielectric Response of Intrinsically Disordered Proteins" J. Phys. Chem. Lett. 2024, 15, 20, 5420–5427 

Solutions:

Absorption of radiation and dielectric spectroscopy of solutions helps in understanding the polarization of solution interfaces. Theory is required for interpreting the laboratory data. We work on theories of THz absorption  and dielectric spectroscopy of  solutions (also of proteins in water).

• "Depolarized light scattering and dielectric response of a peptide dissolved in water", D. R. Martin, D. Fioretto, and D. V. Matyushov, J. Chem. Phys. 140, 035101 (2014)
• "On the theory of dielectric spectroscopy of protein solutions", D. V. Matyushov, J. Phys.: Condens. matter 24, 325105 (2012)
• "Terahertz absorption of dilute aqueous solutions", M. Heyden, D. J. Tobias, D. V. Matyushov, J. Chem. Phys. 137, 235103 (2012)  

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Diffusion of a Brownian particle or a molecule in a liquid solvent is caused by unbalanced fluctuations of osmotic forces. When the diffusing particle carries a charge or a higher multipolar moment, this picture is amended by fluctuations of electrostatic forces inducing dielectric friction. Standard theories grossly overestimate the magnitude of dielectric friction for small dipolar solutes and larger colloidal particles, such as proteins. We study statistical and dynamical correlations between osmotic (van der Waals) and electrostatic forces in promoting molecular and colloidal diffusion.

Electron transfer

Electron transfer is the elementary process of under-barrier tunneling between two states of electron localization at the donor and acceptor molecules. This reaction is the basis of nearly all redox chemistry and is a fundamental step in the cross-membrane charge transport in biology. Formal theories are developed and large-scale computer simulations are performed to construct predictive theories of electron transfer applicable to interpreting experimental results.

Our research directions include:

• Fundamentals of electron transfer studied in model molecular systems
• Time-resolved linear and nonlinear (including 2D) spectroscopies 
• Electron transfer in complex media (protein, glasses, liquid crystals, etc.)

Publications:

• "Non-Gaussian lineshapes and dynamics of time-resolved linear and nonlinear (correlation) spectra", M. Dinpajooh and D. V. Matyushov, J. Phys. Chem. B 118, 7925 (2014)
• "Standard electrode potential, Tafel equation, and the solvation thermodynamics", D. V. Matyushov, J. Chem. Phys. 130, 234704 (2009) 
• "Energetics of electron transfer in soft condensed media", D. V. Matyushov, Acc. Chem. Res. 40, 294 (2007)  

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Energy production in biology

Simple physical mechanisms are behind the flow of energy in all forms of life. Energy comes to living systems through electrons occupying high energy states, either from food (respiratory chains) or from light (photosynthesis). Life's ability to transfer electrons over large distances with nearly zero loss of free energy is puzzling and has not been accomplished in synthetic systems. We study mechanisms of energetic efficiency in respiration energy chains and photosynthesis.

Publications:

• "Protein electron transfer: Dynamics and statistics", J. Chem. Phys. 139, 025102 (2013). 
•  "Microsecond dynamics of the protein and water affect electron transfer in a bacterial bc1 complex," Daniel R. Martin and Dmitry V. Matyushov, J. Chem. Phys. 142, 161101 (2015)
• "Protein-water electrostatics and principles of bioenergetics", D. N. LeBard and D. V. Matyushov, Phys. Chem. Chem. Phys. 12, 15335 (2010)

Electrowetting in Photosynthetic Electron Transfer

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Enzymes drain the chemical potentials from the surrounding medium to drive reactions. The relevant reduction of entropy is equivalent to creating the information content, with a strong analogy to the performance of a computational unit. To secure such information processing, the principle operation of a diode, allowing unidirectional electrical current, needs to be built into an electron transport enzyme. The bacterial reaction center is a central unit of the bacterial ‘‘computer’’. We find that water pumping in a protein cavity, following electron transfer, is the design principle behind the diode action.

Electrostatics of interfaces is fundamentally different from electrostatics of bulk materials. Electrostatic inhomogeneity extends deep into the bulk affecting charged and polar molecules in the interface. Observable properties such as absorption of radiation by solutions, optical spectroscopy of dyes, and dielectric spectroscopy of solutions connect the structure of the interface with observables measured in the laboratory. The extended nature of the aqueous interface is significant to cellular biology mostly operating in the interface.

Publications:

• "Electrophoretic Mobility of Nanoparticles in Water", J. Phys. Chem. B 2024, 128, 12, 2930–2938
• "Dielectric Susceptibility of Water in the Interface", J. Phys. Chem. B 2021, 125, 30, 8282–8293
• "Interfacial structural transition in hydration shells of a polarizable solute", M. Dinpajooh and D. V. Matyushov, Phys. Rev. Lett. 114, 207801 (2015)
• "Free energy of ion hydration: Interface susceptibility and scaling with the ion size", M. Dinpajooh and D. V. Matyushov, J. Chem. Phys. 143, 044511 (2015)
• "Electrostatics of liquid interfaces", D. V. Matyushov, J. Chem. Phys. 140, 224506 (2014) 

Interfacial Structural Transition in Hydration Shells of a Polarizable Solute

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Electrostatics of polar solvation is typically described by harmonic free energy functionals. Polarizability contributes a negative polarization term that can make the harmonic free energy negative. The harmonic truncation fails in this regime. Simulations of polarizable ideal dipoles in water show that water’s susceptibility passes through a maximum in the range of polarizabilities zeroing the harmonic term out.

The interface between a protein and hydration water is heterogeneous both dynamically and statistically. The structure of interface affects the electrostatics at protein's active site and rates of chemical reactions carried by enzymes. In our current projects we address the following questions: (i) Does the interfacial ``biological'' water produce electrostatic signatures specific to proteins? (ii) What is the spectrum of interfacial electrostatic fluctuations? (iii) How is protein-mediated chemistry affected by electrostatics?  

Publications:

• "Dipolar nanodomains in protein hydration shells", D. R. Martin and D. V. Matyushov, J. Phys. Chem. Lett. 6, 407 (2015)
• "Hydration shells of proteins probed by depolarized light scattering and dielectric spectroscopy: Orientational structure is significant, positional structure is not", J. Chem. Phys. 141, 22D501 (2014)
• "Solvated dissipative electro-elastic network model of hydrated proteins", D. R. Martin and D. V. Matyushov, J. Chem. Phys. 137, 165101 (2012)
• "Electrostatics of the protein-water interface and the dynamical transition in proteins", D. V. Matyushov and A. Y. Morozov, Phys. Rev. E 84, 011908 (2011)

Ordering of water in dipolar domains at the surface of lysozyme

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Nanodomains in the hydration shell of lysozyme extend 12−15 Å from the protein surface into the bulk. They are characterized by orientational order parameters of water in the interface. The formation of nano-domains is also reflected by the dipolar susceptibility of the hydration shells with phenomenology similar to that of relaxor ferroelectrics.