The aim of this review is to analyze the current state of knowledge concerning the blue copper protein plastocyanin (PC) focusing on its interactions with its reaction partners cytochromef and P700. Plastocyanin is a 10 kD blue copper protein which is located in the lumen of the thylakoid where it functions as a mobileelectron carrier shuttling electrons from cytochromef to P700 in Photosystem I. PC is a typical β-barrel protein containing a single copper center which is ligated to two histidines, a methionine and a cysteine in a distorted tetrahedral geometry. PC has two potential binding sites for reaction partners. Site 1 consists of the H87 ligand to the copper and Site 2 consists of Y83 which is surrounded by two clusters of negative charges which are highly conserved in higher plant PCs.The interaction of PC with cytochromef has been studied extensively. It is electrostatic in nature with negative charges on PC interacting with positive charges on cytochromef. Evidence from cross-linking, chemical modification, kinetics and site-directed mutagenesis studies implicate Site 2 as the binding site for Cytf. The interaction is thought to occur in two stages: an initial diffusional approach guided by electrostatic interactions, followed by more precise docking to form a final electron transfer complex.Due to the multisubunit nature of the Photosystem I complex, the evidence is not as clear for the binding site for P700. However, a small positively-charged subunit (Subunit III) of Photosystem I has been implicated in PC binding. Also, both chemical modification and site-directed mutagenesis experiments have suggested that PC interacts with P700 via Site 1.

The interaction of Chlamydomonas cytochrome f (cyt f) with either Chlamydomonas plastocyanin (PC) or Chlamydomonas cytochrome c(6) (cyt c(6)) was studied using Brownian dynamics simulations. The two electron acceptors (PC and cyt c(6)) were found to be essentially interchangeable despite a lack of sequence homology and different secondary structures (beta-sheet for PC and alpha-helix for cyt c(6)). Simulations using PC and cyt c(6) interacting with cyt f showed approximately equal numbers of successful complexes and calculated rates of electron transfer. Cyt f-PC and cyt f-cyt c(6) showed the same types of interactions. Hydrophobic residues surrounding the Y1 ligand to the heme on cyt f interacted with hydrophobic residues on PC (surrounding the H87 ligand to the Cu) or cyt c(6) (surrounding the heme). Both types of complexes were stabilized by electrostatic interactions between K65, K188, and K189 on cyt f and conserved anionic residues on PC (E43, D44, D53, and E85) or cyt c(6) (E2, E70, and E71). Mutations on cyt f had identical effects on its interaction with either PC or cyt c(6). K65A, K188A, and K189A showed the largest effects whereas residues such as K217A, R88A, and K110A, which are located far from the positive patch on cyt f, showed very little inhibition. The effect of mutations observed in Brownian dynamics simulations paralleled those observed in experiments.

Modeling complex systems and data using the language of graphs and networks has become an essential topic across a range of different disciplines. Arguably, this network-based perspective derives is success from the relative simplicity of graphs: A graph consists of nothing more than a set of vertices and a set of edges, describing relationships between pairs of such vertices. This simple combinatorial structure makes graphs interpretable and flexible modeling tools. The simplicity of graphs as system models, however, has been scrutinized in the literature recently. Specifically, it has been argued from a variety of different angles that there is a need for higher-order networks, which go beyond the paradigm of modeling pairwise relationships, as encapsulated by graphs. In this survey article we take stock of these recent developments. Our goals are to clarify (i) what higher-order networks are, (ii) why these are interesting objects of study, and (iii) how they can be used in applications.

The electrostatic properties of cytochrome f (cyt f), a member of the cytochrome b6f complex and reaction partner with plastocyanin (PC) in photosynthetic electron transport, are qualitatively studied with the goal of determining the mechanism of electron transfer between cyt f and PC. A crystal structure for cyt f was analyzed with the software package GRASP, revealing a large region of positive potential generated by a patch of positively charged residues (including K58, K65, K66, K122, K185, K187, and R209) and reinforced by the iron center of the heme. This positive field attracts the negative charges of the two acidic patches on the mobile electron carrier PC. Three docked complexes are obtained for the two proteins, based on electrostatic or hydrophobic interactions or both and on steric fits by manual docking methods. The first of these three complexes shows strong electrostatic interactions between K187 on cyt f and D44 on PC and between E59 on PC and K58 on cyt f. Two other manually docked complexes are proposed, implicating H87 on PC as the electron-accepting site from the iron center of cyt f through Y1. The second complex maintains the D44/K187 cross-link (but not the E59/K58 link) while increasing hydrophobic interactions between PC and cyt f. Hydrophobic interactions are increased still further in the third complex, whereas the link between K187 on cyt f and D44 on PC is broken. The proposed reaction mechanism, therefore, involves an initial electrostatic docking complex that gives rise to a nonpolar attraction between the regions surrounding H87 on PC and Y1 on cyt f, providing for an electron-transfer active complex.

The electrostatic interaction between plastocyanin (PC) and cytochrome f (cyt f), electron transfer partners in photosynthesis was studied using Brownian dynamics (BD) simulations. By using the software package MacroDox, which implements the BD algorithm of Northrup et al. (Northrup, S. H., J. O. Boles, and J. C. L. Reynolds. 1987. J. Phys. Chem. 91:5991-5998), we have modeled the interaction of the two proteins based on crystal structures of poplar PC and turnip cyt f at pH 7 and a variety of ionic strengths. We find that the electrostatic attraction between positively charged residues (K58, K65, K187, and R209, among others) on cyt f and negatively charged residues (E43, D44, E59, and E60, among others) on PC steers PC into a single dominant orientation with respect to cyt f, and furthermore, that the single dominant orientation that we observe is one that we had predicted in our previous work (Pearson, D. C., E. L. Gross, and E. S. David. 1996. Biophys. J. 71:64-76). This dominant orientation permits the formation of hydrophobic interactions, which are not implemented in the MacroDox algorithm. This proposed complex between PC and cyt f implicates H87, a copper ligand on PC, as the residue that accepts electrons from the heme on cyt f (and possibly through Y1 as we proposed previously). We argue for the existence of this single dominant complex on the basis of observations that the most favorable orientations of the interaction between PC and cyt f, as determined by grouping successful BD trajectories on the basis of closest contacts of charged residues, tend to overlap one another and have very close distances between the metal centers on the two proteins (copper on PC, iron on cyt f). We use this knowledge to develop a model for PC/cyt f interaction that places a reaction between the two proteins occurring when the copper-to-iron distance is between 16 and 17 A. This reaction distance gives a good estimate of the experimentally observed rate constant for PC-cyt f interaction. Analysis of BD results as a function of ionic strength predicts an interaction that happens less frequently and becomes less specific as ionic strength increases.

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This work addresses the problem of identifiability, that is, the question of whether parameters can be recovered from data, for linear compartment models. Using standard differential algebra techniques, the question of whether a given model is generically locally identifiable is equivalent to asking whether the Jacobian matrix of a certain coefficient map, arising from input-output equations, is generically full rank. We give a formula for these coefficient maps in terms of acyclic subgraphs of the model's underlying directed graph. As an application, we prove that two families of linear compartment models, cycle and mammillary (star) models with input and output in a single compartment, are identifiable, by determining the defining equation for the locus of non-identifiable parameter values. We also state a conjecture for the corresponding equation for a third family: catenary (path) models. These singular-locus equations, we show, give information on which submodels are identifiable. Finally, we introduce the identifiability degree, which is the number of parameter values that match generic input-output data. This degree was previously computed for mammillary and catenary models, and here we determine this degree for cycle models. Our work helps shed light on the question of which linear compartment models are identifiable.