Elucidating interprotein energy transfer dynamics within the antenna network from purple bacteria.

In photosynthesis, absorbed light energy transfers through a network of antenna proteins with near-unity quantum efficiency to reach the reaction center, which initiates the downstream biochemical reactions. While the energy transfer dynamics within individual antenna proteins have been extensively studied over the past decades, the dynamics between the proteins are poorly understood due to the heterogeneous organization of the network. Previously reported timescales averaged over such heterogeneity, obscuring individual interprotein energy transfer steps. Here, we isolated and interrogated interprotein energy transfer by embedding two variants of the primary antenna protein from purple bacteria, light-harvesting complex 2 (LH2), together into a near-native membrane disc, known as a nanodisc. We integrated ultrafast transient absorption spectroscopy, quantum dynamics simulations, and cryogenic electron microscopy to determine interprotein energy transfer timescales. By varying the diameter of the nanodiscs, we replicated a range of distances between the proteins. The closest distance possible between neighboring LH2, which is the most common in native membranes, is 25 Šand resulted in a timescale of 5.7 ps. Larger distances of 28 to 31 Šresulted in timescales of 10 to 14 ps. Corresponding simulations showed that the fast energy transfer steps between closely spaced LH2 increase transport distances by ∼15%. Overall, our results introduce a framework for well-controlled studies of interprotein energy transfer dynamics and suggest that protein pairs serve as the primary pathway for the efficient transport of solar energy.

Polariton Localization and Dispersion Properties of Disordered Quantum Emitters in Multimode Microcavities.

Experiments have demonstrated that the strong light-matter coupling in polaritonic microcavities significantly enhances transport. Motivated by these experiments, we have solved the disordered multimode Tavis-Cummings model in the thermodynamic limit and used this solution to analyze its dispersion and localization properties. The solution implies that wave-vector-resolved spectroscopic quantities can be described by single-mode models, but spatially resolved quantities require the multimode solution. Nondiagonal elements of the Green's function decay exponentially with distance, which defines the coherence length. The coherent length is strongly correlated with the photon weight and exhibits inverse scaling with respect to the Rabi frequency and an unusual dependence on disorder. For energies away from the average molecular energy E_{M} and above the confinement energy E_{C}, the coherence length rapidly diverges such that it exceeds the photon resonance wavelength λ_{0}. The rapid divergence allows us to differentiate the localized and delocalized regimes and identify the transition from diffusive to ballistic transport.

Superradiance and Exciton Delocalization in Perovskite Quantum Dot Superlattices.

Achieving superradiance in solids is challenging due to fast dephasing processes from inherent disorder and thermal fluctuations. Perovskite quantum dots (QDs) are an exciting class of exciton emitters with large oscillator strength and high quantum efficiency, making them promising for solid-state superradiance. However, a thorough understanding of the competition between coherence and dephasing from phonon scattering and energetic disorder is currently unavailable. Here, we present an investigation of exciton coherence in perovskite QD solids using temperature-dependent photoluminescence line width and lifetime measurements. Our results demonstrate that excitons are coherently delocalized over 3 QDs at 11 K in superlattices leading to superradiant emission. Scattering from optical phonons leads to the loss of coherence and exciton localization to a single QD at temperatures above 100 K. At low temperatures, static disorder and defects limit exciton coherence. These results highlight the promise and challenge in achieving coherence in perovskite QD solids.

ℏ2 expansion of the transmission probability through a barrier.

Ninety years ago, Wigner derived the leading order expansion term in ℏ2 for the tunneling rate through a symmetric barrier. His derivation included two contributions: one came from the parabolic barrier, but a second term involved the fourth-order derivative of the potential at the barrier top. He left us with a challenge, which is answered in this paper, to derive the same but for an asymmetric barrier. A crucial element of the derivation is obtaining the ℏ2 expansion term for the projection operator, which appears in the flux-side expression for the rate. It is also reassuring that an analytical calculation of semiclassical transition state theory (TST) reproduces the anharmonic corrections to the leading order of ℏ2. The efficacy of the resulting expression is demonstrated for an Eckart barrier, leading to the conclusion that especially when considering heavy atom tunneling, one should use the expansion derived in this paper, rather than the parabolic barrier approximation. The rate expression derived here reveals how the classical TST limit is approached as a function of ℏ and, thus, provides critical insights to understand the validity of popular approximate theories, such as the classical Wigner, centroid molecular dynamics, and ring polymer molecular dynamics methods.

Dynamical Symmetries and Symmetry-Protected Selection Rules in Periodically Driven Quantum Systems.

In recent experiments, the light-matter interaction has reached the ultrastrong coupling limit, which can give rise to dynamical generalizations of spatial symmetries in periodically driven systems. Here, we present a unified framework of dynamical-symmetry-protected selection rules based on Floquet response theory. Within this framework, we study rotational, parity, particle-hole, chiral, and time-reversal symmetries and the resulting selection rules in spectroscopy, including symmetry-protected dark states (spDS), symmetry-protected dark bands, and symmetry-induced transparency. Specifically, dynamical rotational and parity symmetries establish spDS and symmetry-protected dark band conditions. A particle-hole symmetry introduces spDSs for symmetry-related Floquet states and also a symmetry-induced transparency at quasienergy crossings. Chiral symmetry and time-reversal symmetry alone do not imply spDS conditions but can be combined to define a particle-hole symmetry. These symmetry conditions arise from destructive interference due to the synchronization of symmetric quantum systems with the periodic driving. Our predictions reveal new physical phenomena when a quantum system reaches the strong light-matter coupling regime, which is important for superconducting qubits, atoms and molecules in optical or plasmonic field cavities, and optomechanical systems.

Universal Scalings in Two-Dimensional Anisotropic Dipolar Excitonic Systems.

Low-dimensional excitonic materials have inspired much interest owing to their novel physical and technological prospects. In particular, those with strong in-plane anisotropy are among the most intriguing but short of general analyses. We establish the universal functional form of the anisotropic dispersion in the small k limit for 2D dipolar excitonic systems. While the energy is linearly dispersed in the direction parallel to the dipole in plane, the perpendicular direction is dispersionless up to linear order, which can be explained by the quantum interference effect of the interaction among the constituents of 1D subsystems. The anisotropic dispersion results in a E^{∼0.5} scaling of the system density of states and predicts unique spectroscopic signatures including: (1) disorder-induced absorption linewidth, W(σ)∼σ^{2.8}, with σ the disorder strength, (2) temperature dependent absorption linewidth, W(T)∼T^{s+1.5}, with s the exponent of the environment spectral density, and (3) the out-of-plane angular θ dependence of the peak splittings in absorption spectra, ΔE(θ)∝sin^{2}θ. These predictions are confirmed quantitatively with numerical simulations of molecular thin films and tubules.

Temperature-Induced Catch-Slip to Slip Bond Transit in Plasmodium falciparum-Infected Erythrocytes.

Plasmodium falciparum malaria-infected red blood cells (IRBCs), or erythrocytes, avoid splenic clearance by adhering to host endothelium. Upregulation of endothelial receptors intercellular adhesion molecule-1 (ICAM-1) and cluster of differentiation 36 (CD36) are associated with severe disease pathology. Most in vitro studies of IRBCs interacting with these molecules were conducted at room temperature. However, as IRBCs are exposed to temperature variations between 37°C (body temperature) and 41°C (febrile temperature) in the host, it is important to understand IRBC-receptor interactions at these physiologically relevant temperatures. Here, we probe IRBC interactions against ICAM-1 and CD36 at 37 and 41°C. Single bond force-clamp spectroscopy is used to determine the bond dissociation rates and hence, unravel the nature of the IRBC-receptor interaction. The association rates are also extracted from a multiple bond flow assay using a cellular stochastic model. Surprisingly, IRBC-ICAM-1 bond transits from a catch-slip bond at 37°C toward a slip bond at 41°C. Moreover, binding affinities of both IRBC-ICAM-1 and IRBC-CD36 decrease as the temperature rises from 37 to 41°C. This study highlights the significance of examining receptor-ligand interactions at physiologically relevant temperatures and reveals biophysical insight into the temperature dependence of P. falciparum malaria cytoadherent bonds.

Discontinuities in Driven Spin-Boson Systems due to Coherent Destruction of Tunneling: Breakdown of the Floquet-Gibbs Distribution.

If an open quantum system is periodically driven with high frequency and the driving commutes with the system-bath coupling operator, it is known that the system approaches a Floquet-Gibbs state, a generalization of Gibbs states to periodically driven systems. Here, we investigate the stationary state of an ac-driven system when the driving and dissipation are noncommutative. Then, the resulting stationary state does not obey the Floquet-Gibbs distribution, and the system dynamics is determined by inelastic scattering processes of the driving field. Based on the Floquet-Redfield formalism, we show that the probability distribution can exhibit population inversion and discontinuities, i.e., jumps, for parameters at which coherent destruction of tunneling takes place. These discontinuities can be observed as intensity jumps in the emission into the bath.

Expression dynamics and physiologically relevant functional study of STEVOR in asexual stages of Plasmodium falciparum infection.

The extensive modification of Plasmodium falciparum-infected erythrocytes by variant surface antigens plays a major role in immune evasion and malaria-induced pathology. Here, using high-resolution microscopy, we visualize the spatio-temporal expression dynamics of STEVOR, an important variant surface antigens family, in a stage-dependent manner. We demonstrate that it is exported to the cell surface where protein molecules cluster and preferentially localize in proximity to knobs. Quantitative evidence from our force measurements and microfluidic assays reveal that STEVOR can effectively mediate the formation of stable, robust rosettes under static and physiologically relevant flow conditions. Our results extend previously published studies in P. falciparum and emphasize the role of STEVOR in rosetting, an important contributor to disease pathology.

A unified stochastic formulation of dissipative quantum dynamics. II. Beyond linear response of spin baths.

We use the "generalized hierarchical equation of motion" proposed in Paper I [C.-Y. Hsieh and J. Cao, J. Chem. Phys. 148, 014103 (2018)] to study decoherence in a system coupled to a spin bath. The present methodology allows a systematic incorporation of higher-order anharmonic effects of the bath in dynamical calculations. We investigate the leading order corrections to the linear response approximations for spin bath models. Two kinds of spin-based environments are considered: (1) a bath of spins discretized from a continuous spectral density and (2) a bath of localized nuclear or electron spins. The main difference resides with how the bath frequency and the system-bath coupling parameters are distributed in an environment. When discretized from a continuous spectral density, the system-bath coupling typically scales as ∼1/NB where NB is the number of bath spins. This scaling suppresses the non-Gaussian characteristics of the spin bath and justifies the linear response approximations in the thermodynamic limit. For the nuclear/electron spin bath models, system-bath couplings are directly deduced from spin-spin interactions and do not necessarily obey the 1/NB scaling. It is not always possible to justify the linear response approximations in this case. Furthermore, if the spin-spin Hamiltonian is highly symmetrical, there exist additional constraints that generate highly non-Markovian and persistent dynamics that is beyond the linear response treatments.

A unified stochastic formulation of dissipative quantum dynamics. I. Generalized hierarchical equations.

We extend a standard stochastic theory to study open quantum systems coupled to a generic quantum environment. We exemplify the general framework by studying a two-level quantum system coupled bilinearly to the three fundamental classes of non-interacting particles: bosons, fermions, and spins. In this unified stochastic approach, the generalized stochastic Liouville equation (SLE) formally captures the exact quantum dissipations when noise variables with appropriate statistics for different bath models are applied. Anharmonic effects of a non-Gaussian bath are precisely encoded in the bath multi-time correlation functions that noise variables have to satisfy. Starting from the SLE, we devise a family of generalized hierarchical equations by averaging out the noise variables and expand bath multi-time correlation functions in a complete basis of orthonormal functions. The general hierarchical equations constitute systems of linear equations that provide numerically exact simulations of quantum dynamics. For bosonic bath models, our general hierarchical equation of motion reduces exactly to an extended version of hierarchical equation of motion which allows efficient simulation for arbitrary spectral densities and temperature regimes. Similar efficiency and flexibility can be achieved for the fermionic bath models within our formalism. The spin bath models can be simulated with two complementary approaches in the present formalism. (I) They can be viewed as an example of non-Gaussian bath models and be directly handled with the general hierarchical equation approach given their multi-time correlation functions. (II) Alternatively, each bath spin can be first mapped onto a pair of fermions and be treated as fermionic environments within the present formalism.

Frequency-dependent current noise in quantum heat transfer: A unified polaron calculation.

To investigate frequency-dependent current noise (FDCN) in open quantum systems at steady states, we present a theory which combines Markovian quantum master equations with a finite time full counting statistics. Our formulation of the FDCN generalizes previous zero-frequency expressions and can be viewed as an application of MacDonald's formula for electron transport to heat transfer. As a demonstration, we consider the paradigmatic example of quantum heat transfer in the context of a non-equilibrium spin-boson model. We adopt a recently developed polaron-transformed Redfield equation which allows us to accurately investigate heat transfer with arbitrary system-reservoir coupling strength, arbitrary values of spin bias, and temperature differences. We observe a turn-over of FDCN in the intermediate coupling regimes, similar to the zero-frequency case. We find that the FDCN with varying coupling strengths or bias displays a universal Lorentzian-shape scaling form in the weak coupling regime, and a white noise spectrum emerges with zero bias in the strong coupling regime due to distinctive spin dynamics. We also find that the bias can suppress the FDCN in the strong coupling regime, in contrast to its zero-frequency counterpart which is insensitive to bias changes. Furthermore, we utilize the Saito-Utsumi relation as a benchmark to validate our theory and study the impact of temperature differences at finite frequencies. Together, our results provide detailed dissections of the finite time fluctuation of heat current in open quantum systems.

Construction of Multichromophoric Spectra from Monomer Data: Applications to Resonant Energy Transfer.

We develop a model that establishes a quantitative link between the physical properties of molecular aggregates and their constituent building blocks. The relation is built on the coherent potential approximation, calibrated against exact results, and proven reliable for a wide range of parameters. It provides a practical method to compute spectra and transfer rates in multichromophoric systems from experimentally accessible monomer data. Applications to Förster energy transfer reveal optimal transfer rates as functions of both the system-bath coupling and intra-aggregate coherence.

Evolution of the Single-Nanocrystal Photoluminescence Linewidth with Size and Shell: Implications for Exciton-Phonon Coupling and the Optimization of Spectral Linewidths.

The optimization of photoluminescence spectral linewidths in semiconductor nanocrystal preparations involves minimizing both the homogeneous and inhomogeneous contributions to the ensemble spectrum. Although the inhomogeneous contribution can be controlled by eliminating interparticle inhomogeneities, far less is known about how to synthetically control the homogeneous, or single-nanocrystal, spectral linewidth. Here, we use solution photon-correlation Fourier spectroscopy (S-PCFS) to measure how the sample-averaged single-nanocrystal emission linewidth of CdSe core and core/shell nanocrystals change with systematic changes in the size of the cores and the thickness and composition of the shells. We find that the single-nanocrystal linewidth at room temperature is heavily influenced by the nature of the CdSe surface and the epitaxial shell, which have a profound impact on the internal electric fields that affect exciton-phonon coupling. Our results explain the wide variations, both experimental and theoretical, in the magnitude and size dependence in previous reports on exciton-phonon coupling in CdSe nanocrystals. Moreover, our findings offer a general pathway for achieving the narrow spectral linewidths required for many applications of nanocrystals.

Quantum Diffusion on Molecular Tubes: Universal Scaling of the 1D to 2D Transition.

The transport properties of disordered systems are known to depend critically on dimensionality. We study the diffusion coefficient of a quantum particle confined to a lattice on the surface of a tube, where it scales between the 1D and 2D limits. It is found that the scaling relation is universal and independent of the temperature, disorder, and noise parameters, and the essential order parameter is the ratio between the localization length in 2D and the circumference of the tube. Phenomenological and quantitative expressions for transport properties as functions of disorder and noise are obtained and applied to real systems: In the natural chlorosomes found in light-harvesting bacteria the exciton transfer dynamics is predicted to be in the 2D limit, whereas a family of synthetic molecular aggregates is found to be in the homogeneous limit and is independent of dimensionality.

Transitions in genetic toggle switches driven by dynamic disorder in rate coefficients.

In biochemical systems, intrinsic noise may drive the system switch from one stable state to another. We investigate how kinetic switching between stable states in a bistable network is influenced by dynamic disorder, i.e., fluctuations in the rate coefficients. Using the geometric minimum action method, we first investigate the optimal transition paths and the corresponding minimum actions based on a genetic toggle switch model in which reaction coefficients draw from a discrete probability distribution. For the continuous probability distribution of the rate coefficient, we then consider two models of dynamic disorder in which reaction coefficients undergo different stochastic processes with the same stationary distribution. In one, the kinetic parameters follow a discrete Markov process and in the other they follow continuous Langevin dynamics. We find that regulation of the parameters modulating the dynamic disorder, as has been demonstrated to occur through allosteric control in bistable networks in the immune system, can be crucial in shaping the statistics of optimal transition paths, transition probabilities, and the stationary probability distribution of the network.

How two-dimensional brick layer J-aggregates differ from linear ones: Excitonic properties and line broadening mechanisms.

We study the excitonic coupling and homogeneous spectral line width of brick layer J-aggregate films. We begin by analysing the structural information revealed by the two-exciton states probed in two-dimensional spectra. Our first main result is that the relation between the excitonic couplings and the spectral shift in a two-dimensional structure is different (larger shift for the same nearest neighbour coupling) from that in a one-dimensional structure, which leads to an estimation of dipolar coupling in two-dimensional lattices. We next investigate the mechanisms of homogeneous broadening--population relaxation and pure dephasing--and evaluate their relative importance in linear and two-dimensional aggregates. Our second main result is that pure dephasing dominates the line width in two-dimensional systems up to a crossover temperature, which explains the linear temperature dependence of the homogeneous line width. This is directly related to the decreased density of states at the band edge when compared with linear aggregates, thus reducing the contribution of population relaxation to dephasing. Pump-probe experiments are suggested to directly measure the lifetime of the bright state and can therefore support the proposed model.

Optimal fold symmetry of LH2 rings on a photosynthetic membrane.

An intriguing observation of photosynthetic light-harvesting systems is the N-fold symmetry of light-harvesting complex 2 (LH2) of purple bacteria. We calculate the optimal rotational configuration of N-fold rings on a hexagonal lattice and establish two related mechanisms for the promotion of maximum excitation energy transfer (EET). (i) For certain fold numbers, there exist optimal basis cells with rotational symmetry, extendable to the entire lattice for the global optimization of the EET network. (ii) The type of basis cell can reduce or remove the frustration of EET rates across the photosynthetic network. We find that the existence of a basis cell and its type are directly related to the number of matching points S between the fold symmetry and the hexagonal lattice. The two complementary mechanisms provide selection criteria for the fold number and identify groups of consecutive numbers. Remarkably, one such group consists of the naturally occurring 8-, 9-, and 10-fold rings. By considering the inter-ring distance and EET rate, we demonstrate that this group can achieve minimal rotational sensitivity in addition to an optimal packing density, achieving robust and efficient EET. This corroborates our findings i and ii and, through their direct relation to S, suggests the design principle of matching the internal symmetry with the lattice order.

Large Area Directed Self-Assembly of Sub-10 nm Particles with Single Particle Positioning Resolution.

Directed self-assembly of nanoparticles (DSA-n) holds great potential for device miniaturization in providing patterning resolution and throughput that exceed existing lithographic capabilities. Although nanoparticles excel at assembling into regular close-packed arrays, actual devices on the other hand are often laid out in sparse and complex configurations. Hence, the deterministic positioning of single or few particles at specific positions with low defect density is imperative. Here, we report an approach of DSA-n that satisfies these requirements with less than 1% defect density over micrometer-scale areas and at technologically relevant sub-10 nm dimensions. This technique involves a simple and robust process where a solvent film containing sub-10 nm gold nanoparticles climbs against gravity to coat a prepatterned template. Particles are placed individually into nanoscale cavities, or between nanoposts arranged in varying degrees of geometric complexity. Brownian dynamics simulations suggest a mechanism in which the particles are pushed into the template by a nanomeniscus at the drying front. This process enables particle-based self-assembly to access the sub-10 nm dimension, and for device fabrication to benefit from the wealth of chemically synthesized nanoparticles with unique material properties.

Stiffening of Red Blood Cells Induced by Cytoskeleton Disorders: A Joint Theory-Experiment Study.

The functions and elasticities of the cell are largely related to the structures of the cytoskeletons underlying the lipid bilayer. Among various cell types, the red blood cell (RBC) possesses a relatively simple cytoskeletal structure. Underneath the membrane, the RBC cytoskeleton takes the form of a two-dimensional triangular network, consisting of nodes of actins (and other proteins) and edges of spectrins. Recent experiments focusing on the malaria-infected RBCs (iRBCs) show that there is a correlation between the elongation of spectrins in the cytoskeletal network and the stiffening of the iRBCs. Here we rationalize the correlation between these two observations by combining the wormlike chain model for single spectrins and the effective medium theory for the network elasticity. We specifically focus on how the disorders in the cytoskeletal network affect its macroscopic elasticity. Analytical and numerical solutions from our model reveal that the stiffness of the membrane increases with increasing end-to-end distances of spectrins, but has a nonmonotonic dependence on the variance of the end-to-end distance distributions. These predictions are verified quantitatively by our atomic force microscopy and micropipette aspiration measurements of iRBCs. The model may, from a molecular level, provide guidelines for future identification of new treatment methods for RBC-related diseases, such as malaria infection.