Phycobilisomes, the light-harvesting antennas of cyanobacteria, can adapt to a wide range of environments thanks to a composition and function response to stress conditions. We study how structural changes influence excitation transfer in these supercomplexes. Specifically, we show the influence of the rod length on the photon absorption and subsequent excitation transport to the core. Despite the fact that the efficiency of individual disks on the rod decreases with increasing rod length, we find an optimal length for which the average rod efficiency is maximal. Combining this study with experimental structural measurements, we propose models for the arrangement of the phycobiliproteins inside the thylakoid membranes, evaluate the importance of rod length, and predict the corresponding transport properties for different cyanobacterial species. This analysis, which links the functional and structural properties of full phycobilisome complexes, thus provides further rationales to help resolve their exact structure.

Recent ultrafast optical experiments show that excitons in large biological light-harvesting complexes are coupled to molecular vibration modes. These high-frequency vibrations will not only affect the optical response, but also drive the exciton transport. Here, using a model dimer system, the frequency of the underdamped vibration is shown to have a strong effect on the exciton dynamics such that quantum coherent oscillations in the system can be present even in the case of strong noise. Two mechanisms are identified to be responsible for the enhanced transport efficiency: critical damping due to the tunable effective strength of the coupling to the bath, and resonance coupling where the vibrational frequency coincides with the energy gap in the system. The interplay of these two mechanisms determines parameters responsible for the most efficient transport, and these optimal control parameters are comparable to those in realistic light-harvesting complexes. Interestingly, oscillations in the excitonic coherence at resonance are suppressed in comparison to the case of an off-resonant vibration.

We theoretically study the distance, chain length, and temperature dependence of the electronic couplings as well as the excitonic energy transfer rates between one-dimensional (1D) chromophore aggregates. In addition to the well-known geometry dependent factor that leads to the deviation from Förster’s classic RDA–6 scaling on the donor–acceptor separation, nonmonotonic dependence on aggregate size and the breakdown of far-field dipole selection rules are also investigated in detail and compared to prior calculations. Our analysis provides a simple, unifying framework to bridge the results of the ground state electronic couplings at low temperatures and those from the classical rate-summation at high temperatures. At low temperatures and in the near-field limit, the exciton transfer integral scales as RDA–1, in analogy to that of electric monopoles. For the case of aligned 1D J-aggregates, we predict a maximal excitonic energy transfer rate at temperatures on the order of the intra-aggregate coupling strength.

Mechanical characteristics of DNA in the sub-persistence-length (lP ≈ 150 base pairs) regime are vital to many of its biological functions but not well understood. Recent experimental studies in this regime have shown a dramatic departure from the traditional worm-like chain model, which is designed for long DNA chains and predicts a constant flexibility at all length scales. Here, we report an improved model with explicit considerations of a new length scale lD ≈ 10 base pairs, over which DNA local bend angles are correlated. In this correlated worm-like chain model, a finite length correction term is analytically derived, and DNA flexibility is found to be contour-length-dependent. While our model reduces to the traditional worm-like chain model at length scales much larger than lP, it predicts that DNA becomes much more flexible at shorter sizes, in good agreement with recent cyclization measurements of short DNA fragments around 100 base pairs.Keywords: coarse-grained model; correlated worm-like chain; DNA cyclization; DNA mechanics; single-molecule study;

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.

We report a study of DNA deformations using a coarse-grained mechanical model and quantitatively interpret the allosteric effects in protein–DNA binding affinity. A recent single-molecule study (Kim et al. Science 2013, 339, 816) showed that when a DNA molecule is deformed by specific binding of a protein, the binding affinity of a second protein separated from the first protein is altered. Experimental observations together with molecular dynamics simulations suggested that the origin of the DNA allostery is related to the observed deformation of DNA’s structure, in particular, the major groove width. To unveil and quantify the underlying mechanism for the observed major groove deformation behavior related to the DNA allostery, here we provide a simple but effective analytical model where DNA deformations upon protein binding are analyzed and spatial correlations of local deformations along the DNA are examined. The deformation of the DNA base orientations, which directly affect the major groove width, is found in both an analytical derivation and coarse-grained Monte Carlo simulations. This deformation oscillates with a period of 10 base pairs with an amplitude decaying exponentially from the binding site with a decay length lD ≈10 base pairs as a result of the balance between two competing terms in DNA base-stacking energy. This length scale is in agreement with that reported from the single-molecule experiment. Our model can be reduced to the worm-like chain form at length scales larger than lP but is able to explain DNA’s mechanical properties on shorter length scales, in particular, the DNA allostery of protein–DNA interactions.

We investigate the reaction event counting statistics (RECS) of an elementary biopolymer reaction in which the rate coefficient is dependent on states of the biopolymer and the surrounding environment and discover a universal kinetic phase transition in the RECS of the reaction system with dynamic heterogeneity. From an exact analysis for a general model of elementary biopolymer reactions, we find that the variance in the number of reaction events is dependent on the square of the mean number of the reaction events when the size of measurement time is small on the relaxation time scale of rate coefficient fluctuations, which does not conform to renewal statistics. On the other hand, when the size of the measurement time interval is much greater than the relaxation time of rate coefficient fluctuations, the variance becomes linearly proportional to the mean reaction number in accordance with renewal statistics. Gillespie’s stochastic simulation method is generalized for the reaction system with a rate coefficient fluctuation. The simulation results confirm the correctness of the analytic results for the time dependent mean and variance of the reaction event number distribution. On the basis of the obtained results, we propose a method of quantitative analysis for the reaction event counting statistics of reaction systems with rate coefficient fluctuations, which enables one to extract information about the magnitude and the relaxation times of the fluctuating reaction rate coefficient, without a bias that can be introduced by assuming a particular kinetic model of conformational dynamics and the conformation dependent reactivity. An exact relationship is established between a higher moment of the reaction event number distribution and the multitime correlation of the reaction rate for the reaction system with a nonequilibrium initial state distribution as well as for the system with the equilibrium initial state distribution.

Microarrays are widely used to investigate the blood stage of Plasmodium falciparum infection. Starting with synchronized cells, gene expression levels are continually measured over the 48-hour intra-erythrocytic cycle (IDC). However, the cell population gradually loses synchrony during the experiment. As a result, the microarray measurements are blurred. In this paper, we propose a generalized deconvolution approach to reconstruct the intrinsic expression pattern, and apply it to P. falciparum IDC microarray data.We develop a statistical model for the decay of synchrony among cells, and reconstruct the expression pattern through statistical inference. The proposed method can handle microarray measurements with noise and missing data. The original gene expression patterns become more apparent in the reconstructed profiles, making it easier to analyze and interpret the data. We hypothesize that reconstructed gene expression patterns represent better temporally resolved expression profiles that can be probabilistically modeled to match changes in expression level to IDC transitions. In particular, we identify transcriptionally regulated protein kinases putatively involved in regulating the P. falciparum IDC.By analyzing publicly available microarray data sets for the P. falciparum IDC, protein kinases are ranked in terms of their likelihood to be involved in regulating transitions between the ring, trophozoite and schizont developmental stages of the P. falciparum IDC. In our theoretical framework, a few protein kinases have high probability rankings, and could potentially be involved in regulating these developmental transitions.This study proposes a new methodology for extracting intrinsic expression patterns from microarray data. By applying this method to P. falciparum microarray data, several protein kinases are predicted to play a significant role in the P. falciparum IDC. Earlier experiments have indeed confirmed that several of these kinases are involved in this process. Overall, these results indicate that further functional analysis of these additional putative protein kinases may reveal new insights into how the P. falciparum IDC is regulated.

Many enzymatic reactions in biochemistry are far more complex than the celebrated Michaelis−Menten scheme, but the observed turnover rate often obeys the hyperbolic dependence on the substrate concentration, a relation established almost a century ago for the simple Michaelis−Menten mechanism. To resolve the longstanding puzzle, we apply the flux balance method to predict the functional form of the substrate dependence in the mean turnover time of complex enzymatic reactions and identify detailed balance (i.e., the lack of unbalanced conformtional current) as a sufficient condition for the Michaelis−Menten equation to describe the substrate concentration dependence of the turnover rate in an enzymatic network. This prediction can be verified in single-molecule event-averaged measurements using the recently proposed signatures of detailed balance violations. The finding helps analyze recent single-molecule studies of enzymatic networks and can be applied to other external variables, such as force-dependence and voltage-dependence.

The most recent crystal structure of the Fenna–Matthews–Olson (FMO) protein complex indicates the presence of an additional eighth chromophore, which has been proposed to serve as a link between the chlorosome and the remaining seven chromophores. Here, we investigate the implications of this scenario through numerical calculations with the generalized Bloch–Redfield (GBR) equation and the noninteracting blip approximation (NIBA). It is shown that the oscillations often observed in the population relaxation of sites 1 and 2 may be completely suppressed in the eight-site model due to the initial preparation. Second it is demonstrated that while the presence of the eighth chromophore does not cause a dramatic change in the energy-transfer efficiency, it does however lead to a dominant energy-transfer pathway that can be characterized by an effective three-site system. Finally, we confirm that the energy-transfer process in the eight-site complex remains efficient and robust through computations of the optimal values of the bath parameters.Keywords: energy transfer; exciton; Fenna−Matthews−Olson protein; light-harvesting; open quantum systems; photosynthesis;

Using a classical master equation that describes energy transfer over a given lattice, we explore how energy transfer efficiency along with the photon capturing ability depends on network connectivity, on transfer rates, and on volume fractions—the numbers and relative ratio of fluorescence chromophore components, e.g., donor (D), acceptor (A), and bridge (B) chromophores. For a one-dimensional AD array, the exact analytical expression (derived in Appendix A) for efficiency shows a steep increase with a D-to-A transfer rate when a spontaneous decay is sufficiently slow. This result implies that the introduction of B chromophores can be a useful method for improving efficiency for a two-component AD system with inefficient D-to-A transfer and slow spontaneous decay. Analysis of this one-dimensional system can be extended to higher-dimensional systems with chromophores arranged in structures such as a helical or stacked-disk rod, which models the self-assembling monomers of the tobacco mosaic virus coat protein. For the stacked-disk rod, we observe the following: (1) With spacings between sites fixed, a staggered conformation is more efficient than an eclipsed conformation. (2) For a given ratio of A and D chromophores, the uniform distribution of acceptors that minimizes the mean first passage time to acceptors is a key point to designing the optimal network for a donor−acceptor system with a relatively small D-to-A transfer rate. (3) For a three-component ABD system with a large B-to-A transfer rate, a key design strategy is to increase the number of the pathways in accordance with the directional energy flow from D to B to A chromophores. These conclusions are consistent with the experimental findings reported by Francis, Fleming, and their co-workers and suggest that synthetic architectures of self-assembling supermolecules and the distributions of AD or ABD chromophore components can be optimized for efficient light-harvesting energy transfer.

Cell adhesion plays a central role in multicellular organisms helping to maintain their integrity and homeostasis. This complex process involves many different types of adhesion proteins, and synergetic behavior of these proteins during cell adhesion is frequently observed in experiments. A well-known example is the cooperation of rolling and stationary adhesion proteins during the leukocytes extravasation. Despite the fact that such cooperation is vital for proper functioning of the immune system, its origin is not fully understood. In this study we constructed a simple analytic model of the interaction between a leukocyte and the blood vessel wall in shear flow. The model predicts existence of cell adhesion bistability, which results from a tug-of-war between two kinetic processes taking place in the cell-wall contact area—bond formation and rupture. Based on the model results, we suggest an interpretation of several cytoadhesion experiments and propose a simple explanation of the existing synergy between rolling and stationary adhesion proteins, which is vital for effective cell adherence to the blood vessel walls in living organisms.

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.