Molecular interactions underlying the phase separation of HP1α: role of phosphorylation, ligand and nucleic acid binding.

Heterochromatin protein 1α (HP1α) is a crucial element of chromatin organization. It has been proposed that HP1α functions through liquid-liquid phase separation (LLPS), which allows it to compact chromatin into transcriptionally repressed heterochromatin regions. In vitro, HP1α can undergo phase separation upon phosphorylation of its N-terminus extension (NTE) and/or through interactions with DNA and chromatin. Here, we combine computational and experimental approaches to elucidate the molecular interactions that drive these processes. In phosphorylation-driven LLPS, HP1α can exchange intradimer hinge-NTE interactions with interdimer contacts, which also leads to a structural change from a compacted to an extended HP1α dimer conformation. This process can be enhanced by the presence of positively charged HP1α peptide ligands and disrupted by the addition of negatively charged or neutral peptides. In DNA-driven LLPS, both positively and negatively charged peptide ligands can perturb phase separation. Our findings demonstrate the importance of electrostatic interactions in HP1α LLPS where binding partners can modulate the overall charge of the droplets and screen or enhance hinge region interactions through specific and non-specific effects. Our study illuminates the complex molecular framework that can fine-tune the properties of HP1α and that can contribute to heterochromatin regulation and function.

Determining interchromophore effects for energy transport in molecular networks using machine-learning algorithms.

Nature uses chromophore networks, with highly optimized structural and energetic characteristics, to perform important chemical functions. Due to its modularity, predictable aggregation characteristics, and established synthetic protocols, structural DNA nanotechnology is a promising medium for arranging chromophore networks with analogous structural and energetic controls. However, this high level of control creates a greater need to know how to optimize the systems precisely. This study uses the system's modularity to produce variations of a coupled 14-Site chromophore network. It uses machine-learning algorithms and spectroscopy measurements to reveal the energy-transport roles of these Sites, paying particular attention to the cooperative and inhibitive effects they impose on each other for transport across the network. The physical significance of these patterns is contextualized, using molecular dynamics simulations and energy-transport modeling. This analysis yields insights about how energy transfers across the Donor-Relay and Relay-Acceptor interfaces, as well as the energy-transport pathways through the homogeneous Relay segment. Overall, this report establishes an approach that uses machine-learning methods to understand, in fine detail, the role that each Site plays in an optoelectronic molecular network.

TDP-43 α-helical structure tunes liquid-liquid phase separation and function.

Liquid-liquid phase separation (LLPS) is involved in the formation of membraneless organelles (MLOs) associated with RNA processing. The RNA-binding protein TDP-43 is present in several MLOs, undergoes LLPS, and has been linked to the pathogenesis of amyotrophic lateral sclerosis (ALS). While some ALS-associated mutations in TDP-43 disrupt self-interaction and function, here we show that designed single mutations can enhance TDP-43 assembly and function via modulating helical structure. Using molecular simulation and NMR spectroscopy, we observe large structural changes upon dimerization of TDP-43. Two conserved glycine residues (G335 and G338) are potent inhibitors of helical extension and helix-helix interaction, which are removed in part by variants at these positions, including the ALS-associated G335D. Substitution to helix-enhancing alanine at either of these positions dramatically enhances phase separation in vitro and decreases fluidity of phase-separated TDP-43 reporter compartments in cells. Furthermore, G335A increases TDP-43 splicing function in a minigene assay. Therefore, the TDP-43 helical region serves as a short but uniquely tunable module where application of biophysical principles can precisely control assembly and function in cellular and synthetic biology applications of LLPS.

Developing Bonded Potentials for a Coarse-Grained Model of Intrinsically Disordered Proteins.

Recent advances in residue-level coarse-grained (CG) computational models have enabled molecular-level insights into biological condensates of intrinsically disordered proteins (IDPs), shedding light on the sequence determinants of their phase separation. The existing CG models that treat protein chains as flexible molecules connected via harmonic bonds cannot populate common secondary-structure elements. Here, we present a CG dihedral angle potential between four neighboring beads centered at Cα atoms to faithfully capture the transient helical structures of IDPs. In order to parameterize and validate our new model, we propose Cα-based helix assignment rules based on dihedral angles that succeed in reproducing the atomistic helicity results of a polyalanine peptide and folded proteins. We then introduce sequence-dependent dihedral angle potential parameters (εd) and use experimentally available helical propensities of naturally occurring 20 amino acids to find their optimal values. The single-chain helical propensities from the CG simulations for commonly studied prion-like IDPs are in excellent agreement with the NMR-based α-helix fraction, demonstrating that the new HPS-SS model can accurately produce structural features of IDPs. Furthermore, this model can be easily implemented for large-scale assembly simulations due to its simplicity.

Sequence dependent phase separation of protein-polynucleotide mixtures elucidated using molecular simulations.

Ribonucleoprotein (RNP) granules are membraneless organelles (MLOs), which majorly consist of RNA and RNA-binding proteins and are formed via liquid-liquid phase separation (LLPS). Experimental studies investigating the drivers of LLPS have shown that intrinsically disordered proteins (IDPs) and nucleic acids like RNA and other polynucleotides play a key role in modulating protein phase separation. There is currently a dearth of modelling techniques which allow one to delve deeper into how polynucleotides play the role of a modulator/promoter of LLPS in cells using computational methods. Here, we present a coarse-grained polynucleotide model developed to fill this gap, which together with our recently developed HPS model for protein LLPS, allows us to capture the factors driving protein-polynucleotide phase separation. We explore the capabilities of the modelling framework with the LAF-1 RGG system which has been well studied in experiments and also with the HPS model previously. Further taking advantage of the fact that the HPS model maintains sequence specificity we explore the role of charge patterning on controlling polynucleotide incorporation into condensates. With increased charge patterning we observe formation of structured or patterned condensates which suggests the possible roles of polynucleotides in not only shifting the phase boundaries but also introducing microscopic organization in MLOs.

Strategies for Controlling the Spatial Orientation of Single Molecules Tethered on DNA Origami Templates Physisorbed on Glass Substrates: Intercalation and Stretching.

Nanoarchitectural control of matter is crucial for next-generation technologies. DNA origami templates are harnessed to accurately position single molecules; however, direct single molecule evidence is lacking regarding how well DNA origami can control the orientation of such molecules in three-dimensional space, as well as the factors affecting control. Here, we present two strategies for controlling the polar (θ) and in-plane azimuthal (ϕ) angular orientations of cyanine Cy5 single molecules tethered on rationally-designed DNA origami templates that are physically adsorbed (physisorbed) on glass substrates. By using dipolar imaging to evaluate Cy5's orientation and super-resolution microscopy, the absolute spatial orientation of Cy5 is calculated relative to the DNA template. The sequence-dependent partial intercalation of Cy5 is discovered and supported theoretically using density functional theory and molecular dynamics simulations, and it is harnessed as our first strategy to achieve θ control for a full revolution with dispersion as small as ±4.5°. In our second strategy, ϕ control is achieved by mechanically stretching the Cy5 from its two tethers, being the dispersion ±10.3° for full stretching. These results can in principle be applied to any single molecule, expanding in this way the capabilities of DNA as a functional templating material for single-molecule orientation control. The experimental and modeling insights provided herein will help engineer similar self-assembling molecular systems based on polymers, such as RNA and proteins.

Data-Driven and Multiscale Modeling of DNA-Templated Dye Aggregates.

Dye aggregates are of interest for excitonic applications, including biomedical imaging, organic photovoltaics, and quantum information systems. Dyes with large transition dipole moments (µ) are necessary to optimize coupling within dye aggregates. Extinction coefficients (ε) can be used to determine the µ of dyes, and so dyes with a large ε (>150,000 M−1cm−1) should be engineered or identified. However, dye properties leading to a large ε are not fully understood, and low-throughput methods of dye screening, such as experimental measurements or density functional theory (DFT) calculations, can be time-consuming. In order to screen large datasets of molecules for desirable properties (i.e., large ε and µ), a computational workflow was established using machine learning (ML), DFT, time-dependent (TD-) DFT, and molecular dynamics (MD). ML models were developed through training and validation on a dataset of 8802 dyes using structural features. A Classifier was developed with an accuracy of 97% and a Regressor was constructed with an R2 of above 0.9, comparing between experiment and ML prediction. Using the Regressor, the ε values of over 18,000 dyes were predicted. The top 100 dyes were further screened using DFT and TD-DFT to identify 15 dyes with a µ relative to a reference dye, pentamethine indocyanine dye Cy5. Two benchmark MD simulations were performed on Cy5 and Cy5.5 dimers, and it was found that MD could accurately capture experimental results. The results of this study exhibit that our computational workflow for identifying dyes with a large µ for excitonic applications is effective and can be used as a tool to develop new dyes for excitonic applications.

A predictive coarse-grained model for position-specific effects of post-translational modifications.

Biomolecules undergo liquid-liquid phase separation (LLPS), resulting in the formation of multicomponent protein-RNA membraneless organelles in cells. However, the physiological and pathological role of post-translational modifications (PTMs) on the biophysics of phase behavior is only beginning to be probed. To study the effect of PTMs on LLPS in silico, we extend our transferable coarse-grained model of intrinsically disordered proteins to include phosphorylated and acetylated amino acids. Using the parameters for modified amino acids available for fixed-charge atomistic force fields, we parameterize the size and atomistic hydropathy of the coarse-grained-modified amino acid beads and, hence, the interactions between the modified and natural amino acids. We then elucidate how the number and position of phosphorylated and acetylated residues alter the protein's single-chain compactness and its propensity to phase separate. We show that both the number and the position of phosphorylated threonines/serines or acetylated lysines can serve as a molecular on/off switch for phase separation in the well-studied disordered regions of Fused in Sarcoma (FUS) and DDX3X, respectively. We also compare modified residues to their commonly used PTM mimics for their impact on chain properties. Importantly, we show that the model can predict and capture experimentally measured differences in the phase behavior for position-specific modifications, showing that the position of modifications can dictate phase separation. In sum, this model will be useful for studying LLPS of post-translationally modified intrinsically disordered proteins and predicting how modifications control phase behavior with position-specific resolution.

Understanding Disorder, Vibronic Structure, and Delocalization in Electronically Coupled Dimers on DNA Duplexes.

Structural DNA nanotechnology is a promising approach to create chromophore networks with modular structures and Hamiltonians to control the material's functions. The functional behaviors of these systems depend on the interactions of the chromophores' vibronic states, as well as interactions with their environment. To optimize their functions, it is necessary to characterize the chromophore network's structural and energetic properties, including the electronic delocalization in some cases. In this study, parameters of interest are deduced in DNA-scaffolded Cyanine 3 and Cyanine 5 dimers. The methods include steady-state optical measurements, physical modeling, and a genetic algorithm approach. The parameters include the chromophore network's vibronic Hamiltonian, molecular positions, transition dipole orientations, and environmentally induced energy broadening. Additionally, the study uses temperature-dependent optical measurements to characterize the spectral broadening further. These combined results reveal the quantum mechanical delocalization, which is important for functions like coherent energy transport and quantum information applications.

Relation between single-molecule properties and phase behavior of intrinsically disordered proteins.

Proteins that undergo liquid-liquid phase separation (LLPS) have been shown to play a critical role in many physiological functions through formation of condensed liquid-like assemblies that function as membraneless organelles within biological systems. To understand how different proteins may contribute differently to these assemblies and their functions, it is important to understand the molecular driving forces of phase separation and characterize their phase boundaries and material properties. Experimental studies have shown that intrinsically disordered regions of these proteins are a major driving force, as many of them undergo LLPS in isolation. Previous work on polymer solution phase behavior suggests a potential correspondence between intramolecular and intermolecular interactions that can be leveraged to discover relationships between single-molecule properties and phase boundaries. Here, we take advantage of a recently developed coarse-grained framework to calculate the θ temperature [Formula: see text], the Boyle temperature [Formula: see text], and the critical temperature [Formula: see text] for 20 diverse protein sequences, and we show that these three properties are highly correlated. We also highlight that these correlations are not specific to our model or simulation methodology by comparing between different pairwise potentials and with data from other work. We, therefore, suggest that smaller simulations or experiments to determine [Formula: see text] or [Formula: see text] can provide useful insights into the corresponding phase behavior.

Sequence determinants of protein phase behavior from a coarse-grained model.

Membraneless organelles important to intracellular compartmentalization have recently been shown to comprise assemblies of proteins which undergo liquid-liquid phase separation (LLPS). However, many proteins involved in this phase separation are at least partially disordered. The molecular mechanism and the sequence determinants of this process are challenging to determine experimentally owing to the disordered nature of the assemblies, motivating the use of theoretical and simulation methods. This work advances a computational framework for conducting simulations of LLPS with residue-level detail, and allows for the determination of phase diagrams and coexistence densities of proteins in the two phases. The model includes a short-range contact potential as well as a simplified treatment of electrostatic energy. Interaction parameters are optimized against experimentally determined radius of gyration data for multiple unfolded or intrinsically disordered proteins (IDPs). These models are applied to two systems which undergo LLPS: the low complexity domain of the RNA-binding protein FUS and the DEAD-box helicase protein LAF-1. We develop a novel simulation method to determine thermodynamic phase diagrams as a function of the total protein concentration and temperature. We show that the model is capable of capturing qualitative changes in the phase diagram due to phosphomimetic mutations of FUS and to the presence or absence of the large folded domain in LAF-1. We also explore the effects of chain-length, or multivalency, on the phase diagram, and obtain results consistent with Flory-Huggins theory for polymers. Most importantly, the methodology presented here is flexible so that it can be easily extended to other pair potentials, be used with other enhanced sampling methods, and may incorporate additional features for biological systems of interest.

Protein Composition Determines the Effect of Crowding on the Properties of Disordered Proteins.

Unlike dilute experimental conditions under which biological molecules are typically characterized, the cell interior is crowded by macromolecules, which affects both the thermodynamics and kinetics of in vivo processes. Although the excluded-volume effects of macromolecular crowding are expected to cause compaction of unfolded and disordered proteins, the extent of this effect is uncertain. We use a coarse-grained model to represent proteins with varying sequence content and directly observe changes in chain dimensions in the presence of purely repulsive spherical crowders. We find that the extent of crowding-induced compaction is dependent not only on crowder size and concentration, but also on the properties of the protein itself. In fact, we observe a nonmonotonic trend between the dimensions of the polypeptide chain in bulk and the degree of compaction: the most extended chains experience up to 24% compaction, the most compact chains show virtually no change, and intermediate chains compress by up to 40% in size at a 40% crowder volume fraction. Free-volume theory combined with an impenetrable ellipsoidal representation of the chains predicts the crowding effects only for collapsed protein chains. An additional scaling factor, which can be easily computed from protein-crowder potential of mean force, corrects for the penetrability of extended chains and is sufficient to capture the observed nonmonotonic trend in compaction.

Coarse-Grained Models to Study Protein-DNA Interactions and Liquid-Liquid Phase Separation.

Recent advances in coarse-grained (CG) computational models for DNA have enabled molecular-level insights into the behavior of DNA in complex multiscale systems. However, most existing CG DNA models are not compatible with CG protein models, limiting their applications for emerging topics such as protein-nucleic acid assemblies. Here, we present a new computationally efficient CG DNA model. We first use experimental data to establish the model's ability to predict various aspects of DNA behavior, including melting thermodynamics and relevant local structural properties such as the major and minor grooves. We then employ an all-atom hydropathy scale to define nonbonded interactions between protein and DNA sites, to make our DNA model compatible with an existing CG protein model (HPS-Urry), which is extensively used to study protein phase separation, and show that our new model reasonably reproduces the experimental binding affinity for a prototypical protein-DNA system. To further demonstrate the capabilities of this new model, we simulate a full nucleosome with and without histone tails, on a microsecond time scale, generating conformational ensembles and provide molecular insights into the role of histone tails in influencing the liquid-liquid phase separation (LLPS) of HP1α proteins. We find that histone tails interact favorably with DNA, influencing the conformational ensemble of the DNA and antagonizing the contacts between HP1α and DNA, thus affecting the ability of DNA to promote LLPS of HP1α. These findings shed light on the complex molecular framework that fine-tunes the phase transition properties of heterochromatin proteins and contributes to heterochromatin regulation and function. Overall, the CG DNA model presented here is suitable to facilitate micrometer-scale studies with sub-nm resolution in many biological and engineering applications and can be used to investigate protein-DNA complexes, such as nucleosomes, or LLPS of proteins with DNA, enabling a mechanistic understanding of how molecular information may be propagated at the genome level.

A complex network of interdomain interactions underlies the conformational ensemble of monomeric TDP-43 and modulates its phase behavior.

TAR DNA-binding protein 43 (TDP-43) is a multidomain protein involved in the regulation of RNA metabolism, and its aggregates have been observed in neurodegenerative diseases, including amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD). Numerous studies indicate TDP-43 can undergo liquid-liquid phase separation (LLPS) in vitro and is a component of biological condensates. Homo-oligomerization via the folded N-terminal domain (aa:1-77) and the conserved helical region (aa:319-341) of the disordered, C-terminal domain is found to be an important driver of TDP-43 phase separation. However, a comprehensive molecular view of TDP-43 phase separation, particularly regarding the nature of heterodomain interactions, is lacking due to the challenges associated with its stability and purification. Here, we utilize all-atom and coarse-grained (CG) molecular dynamics (MD) simulations to uncover the network of interdomain interactions implicated in TDP-43 phase separation. All-atom simulations uncovered the presence of transient, interdomain interactions involving flexible linkers, RNA-recognition motif (RRM) domains and a charged segment of disordered C-terminal domain (CTD). CG simulations indicate these inter-domain interactions which affect the conformational landscape of TDP-43 in the dilute phase are also prevalent in the condensed phase. Finally, sequence and surface charge distribution analysis coupled with all-atom simulations (at high salt) confirmed that the transient interdomain contacts are predominantly electrostatic in nature. Overall, our findings from multiscale simulations lead to a greater appreciation of the complex interaction network underlying the structural landscape and phase separation of TDP-43.

Sequence-Dependent Conformational Transitions of Disordered Proteins During Condensation.

Intrinsically disordered proteins (IDPs) can form biomolecular condensates through phase separation. It is recognized that the conformation of IDPs in the dense and dilute phases as well as at the interfaces of condensates can critically impact the resulting properties associated with their functionality. However, a comprehensive understanding of the conformational transitions of IDPs during condensation remains elusive. In this study, we employ a coarse-grained polyampholyte model, comprising an equal number of oppositely charged residues-glutamic acid and lysine-whereby conformations and phase behavior can be readily tuned by altering the protein sequence. By manipulating the sequence patterns from perfectly alternating to block-like, we obtain chains with ideal-like conformations to semi-compact structures in the dilute phase, while in the dense phase, the chain conformation is approximately that of an ideal chain, irrespective of the protein sequence. By performing simulations at different concentrations, we find that the chains assemble from the dilute phase through small oligomeric clusters to the dense phase, accompanied by a gradual swelling of the individual chains. We further demonstrate that these findings are applicable to several naturally occurring proteins involved in the formation of biological condensates. Concurrently, we delve deeper into the chain conformations within the condensate, revealing that chains at the interface show a strong sequence dependence, but remain more collapsed than those in the bulk-like dense phase. This study addresses critical gaps in our knowledge of IDP conformations within condensates as a function of protein sequence.

Interplay between charge distribution and DNA in shaping HP1 paralog phase separation and localization.

The heterochromatin protein 1 (HP1) family is a crucial component of heterochromatin with diverse functions in gene regulation, cell cycle control, and cell differentiation. In humans, there are three paralogs, HP1α, HP1ß, and HP1γ, which exhibit remarkable similarities in their domain architecture and sequence properties. Nevertheless, these paralogs display distinct behaviors in liquid-liquid phase separation (LLPS), a process linked to heterochromatin formation. Here, we employ a coarse-grained simulation framework to uncover the sequence features responsible for the observed differences in LLPS. We highlight the significance of the net charge and charge patterning along the sequence in governing paralog LLPS propensities. We also show that both highly conserved folded and less-conserved disordered domains contribute to the observed differences. Furthermore, we explore the potential co-localization of different HP1 paralogs in multicomponent assemblies and the impact of DNA on this process. Importantly, our study reveals that DNA can significantly reshape the stability of a minimal condensate formed by HP1 paralogs due to competitive interactions of HP1α with HP1ß and HP1γ versus DNA. In conclusion, our work highlights the physicochemical nature of interactions that govern the distinct phase-separation behaviors of HP1 paralogs and provides a molecular framework for understanding their role in chromatin organization.

Sequence-Dependent Material Properties of Biomolecular Codensates and their Relation to Dilute Phase Conformations.

Material properties of phase-separated biomolecular assemblies, enriched with disordered proteins, dictate their ability to participate in many cellular functions. Despite the significant effort dedicated to understanding how the sequence of the disordered protein drives its phase separation to form condensates, little is known about the sequence determinants of condensate material properties. Here, we computationally decipher these relationships for charged disordered proteins using model sequences comprised of glutamic acid and lysine residues as well as naturally occurring sequences of LAF1's RGG domain and DDX4's N-terminal domain. We do so by delineating how the arrangement of oppositely charged residues within these sequences influences the dynamical, rheological, and interfacial properties of the condensed phase through equilibrium and non-equilibrium molecular simulations using the hydropathy scale and Martini models. Our computations yield material properties that are quantitatively comparable with experimentally characterized condensate systems. Interestingly, we find that the material properties of both the model and natural proteins respond similarly to the segregation of charges, despite their very different sequence compositions. Condensates of the highly charge-segregated sequences exhibit slower dynamics than the uniformly charge-patterned sequences, because of their comparatively long-lived molecular contacts between oppositely charged residues. Surprisingly, the molecular interactions within the condensate are highly similar to those within a single-chain for all sequences. Consequently, the condensate material properties of charged disordered proteins are strongly correlated with their dense phase contact dynamics and their single-chain structural properties. Our findings demonstrate the potential to harness the sequence characteristics of disordered proteins for predicting and engineering the material properties of functional condensates, with insights from the dilute phase properties.

Uncovering the molecular interactions underlying MBD2 and MBD3 phase separation.

Chromatin organization controls DNA's accessibility to regulatory factors to influence gene expression. Heterochromatin, or transcriptionally silent chromatin enriched in methylated DNA and methylated histone tails, self-assembles through multivalent interactions with its associated proteins into a condensed, but dynamic state. Liquid-liquid phase separation (LLPS) of key heterochromatin regulators, such as heterochromatin protein 1 (HP1), plays an essential role in heterochromatin assembly and function. Methyl-CpG-binding protein 2 (MeCP2), the most studied member of the methyl-CpG-binding domain (MBD) family of proteins, has been recently shown to undergo LLPS in the absence and presence of methylated DNA. These studies provide a new mechanistic framework for understanding the role of methylated DNA and its readers in heterochromatin formation. However, the details of the molecular interactions by which other MBD family members undergo LLPS to mediate genome organization and transcriptional regulation are not fully understood. Here, we focus on two MBD proteins, MBD2 and MBD3, that have distinct but interdependent roles in gene regulation. Using an integrated computational and experimental approach, we uncover the homotypic and heterotypic interactions governing MBD2 and MBD3 phase separation and DNA's influence on this process. We show that despite sharing the highest sequence identity and structural homology among all the MBD protein family members, MBD2 and MBD3 exhibit differing residue patterns resulting in distinct phase separation mechanisms. Understanding the molecular underpinnings of MBD protein condensation offers insights into the higher-order, LLPS-mediated organization of heterochromatin.

Sequence-dependent material properties of biomolecular condensates and their relation to dilute phase conformations.

Material properties of phase-separated biomolecular condensates, enriched with disordered proteins, dictate many cellular functions. Contrary to the progress made in understanding the sequence-dependent phase separation of proteins, little is known about the sequence determinants of condensate material properties. Using the hydropathy scale and Martini models, we computationally decipher these relationships for charge-rich disordered protein condensates. Our computations yield dynamical, rheological, and interfacial properties of condensates that are quantitatively comparable with experimentally characterized condensates. Interestingly, we find that the material properties of model and natural proteins respond similarly to charge segregation, despite different sequence compositions. Molecular interactions within the condensates closely resemble those within the single-chain ensembles. Consequently, the material properties strongly correlate with molecular contact dynamics and single-chain structural properties. We demonstrate the potential to harness the sequence characteristics of disordered proteins for predicting and engineering the material properties of functional condensates, with insights from the dilute phase properties.

Proton-pumping mechanism of cytochrome c oxidase: a kinetic master-equation approach.

Cytochrome c oxidase is an efficient energy transducer that reduces oxygen to water and converts the released chemical energy into an electrochemical membrane potential. As a true proton pump, cytochrome c oxidase translocates protons across the membrane against this potential. Based on a wealth of experiments and calculations, an increasingly detailed picture of the reaction intermediates in the redox cycle has emerged. However, the fundamental mechanism of proton pumping coupled to redox chemistry remains largely unresolved. Here we examine and extend a kinetic master-equation approach to gain insight into redox-coupled proton pumping in cytochrome c oxidase. Basic principles of the cytochrome c oxidase proton pump emerge from an analysis of the simplest kinetic models that retain essential elements of the experimentally determined structure, energetics, and kinetics, and that satisfy fundamental physical principles. The master-equation models allow us to address the question of how pumping can be achieved in a system in which all reaction steps are reversible. Whereas proton pumping does not require the direct modulation of microscopic reaction barriers, such kinetic gating greatly increases the pumping efficiency. Further efficiency gains can be achieved by partially decoupling the proton uptake pathway from the active-site region. Such a mechanism is consistent with the proposed Glu valve, in which the side chain of a key glutamic acid shuttles between the D channel and the active-site region. We also show that the models predict only small proton leaks even in the absence of turnover. The design principles identified here for cytochrome c oxidase provide a blueprint for novel biology-inspired fuel cells, and the master-equation formulation should prove useful also for other molecular machines. .