Energetic Coupling Research Articles

The genetic architecture of protein stability

There are more ways to synthesize a 100-amino acid (aa) protein (20100) than there are atoms in the universe. Only a very small fraction of such a vast sequence space can ever be experimentally or computationally surveyed. Deep neural networks are increasingly being used to navigate high-dimensional sequence spaces1. However, these models are extremely complicated. Here, by experimentally sampling from sequence spaces larger than 1010, we show that the genetic architecture of at least some proteins is remarkably simple, allowing accurate genetic prediction in high-dimensional sequence spaces with fully interpretable energy models. These models capture the nonlinear relationships between free energies and phenotypes but otherwise consist of additive free energy changes with a small contribution from pairwise energetic couplings. These energetic couplings are sparse and associated with structural contacts and backbone proximity. Our results indicate that protein genetics is actually both rather simple and intelligible.

Energetic portrait of the amyloid beta nucleation transition state.

Amyloid protein aggregates are pathological hallmarks of more than fifty human diseases including the most common neurodegenerative disorders. The atomic structures of amyloid fibrils have now been determined, but the process by which soluble proteins nucleate to form amyloids remains poorly characterised and difficult to study, even though this is the key step to understand to prevent the formation and spread of aggregates. Here we use massively parallel combinatorial mutagenesis, a kinetic selection assay, and machine learning to reveal the transition state of the nucleation reaction of amyloid beta, the protein that aggregates in Alzheimer's disease. By quantifying the nucleation of >140,000 proteins we infer the changes in activation energy for all 798 amino acid substitutions in amyloid beta and the energetic couplings between >600 pairs of mutations. This unprecedented dataset provides the first comprehensive view of the energy landscape and the first large-scale measurement of energetic couplings for a protein transition state. The energy landscape reveals that the amyloid beta nucleation transition state contains a short structured C-terminal hydrophobic core with a subset of interactions similar to mature fibrils. This study demonstrates the feasibility of using mutation-selection-sequencing experiments to study transition states and identifies the key molecular species that initiates amyloid beta aggregation and, potentially, Alzheimer's disease.

The effect of unliganded gating on agonist response in nicotinic receptors

Understanding the agonist concentration-response curve (CRC) is the cornerstone in pharmacology. While CRC parameters, agonist potency (EC50) and efficacy (maximum response, Imax) are well-studied, the role of unliganded gating (minimum response, Imin) on CRC is often overlooked. This study explores the effect of unliganded gating on agonist response in muscle-type acetylcholine (ACh) receptors, focusing on the underexplored role of Imin in modulating EC50 and Imax. Three Gain-of-Function (GOF) mutations that increase, and two Loss-of-Function (LOF) mutations that decrease the unliganded gating equilibrium constant (L0) were studied using automated patch-clamp electrophysiology. GOF mutations enhanced agonist potency, whereas LOF mutations reduced it. The calculated CRC aligned well with empirical results, indicating that agonist CRC can be estimated from knowledge of L0. Reduction in agonist efficacy due to LOF mutations was calculated and subsequently validated using single-channel patch-clamp electrophysiology, a factor often obscured in normalized CRC. The study also evaluated the combined impact of mutations (L0) on CRC, confirming the predictive model. Further, no significant energetic coupling between distant residues (>15 Å) was found, indicating that the mutations’ effects are localized and do not alter overall agonist affinity. These findings substantiate the role of unliganded gating in modulating agonist responses and establishes a predictive model for estimating CRC parameters from known changes in L0. The study highlights the importance of intrinsic activity in receptor theory.

Altered excitation energy transfer between phycobilisome and photosystems in the absence of ApcG, a small linker peptide, in Synechocystis sp. PCC 6803, a cyanobacterium

Phycobilisome (PBS) is a large pigment-protein complex in cyanobacteria and red algae responsible for capturing sunlight and transferring its energy to photosystems (PS). Spectroscopic and structural properties of various PBSs have been widely studied, however, the nature of so-called complex-complex interactions between PBS and PSs remains much less explored. In this work, we have investigated the function of a newly identified PBS linker protein, ApcG, some domain of which, together with a loop region (PB-loop in ApcE), is possibly located near the PBS-PS interface. Using Synechocystis sp. PCC 6803, we generated an ApcG deletion mutant and probed its deletion effect on the energetic coupling between PBS and photosystems. Steady-state and time-resolved spectroscopic characterization of the purified ΔApcG-PBS demonstrated that ApcG removal weakly affects the photophysical properties of PBS for which the spectroscopic properties of terminal energy emitters are comparable to those of PBS from wild-type strain. However, analysis of fluorescence decay imaging datasets reveals that ApcG deletion induces disruptions within the allophycocyanin (APC) core, resulting in the emergence (splitting) of two spectrally diverse subgroups with some short-lived APC. Profound spectroscopic changes of the whole ΔApcG mutant cell, however, emerge during state transition, a dynamic process of light scheme adaptation. The mutant cells in State I show a substantial increase in PBS-related fluorescence. On the other hand, global analysis of time-resolved fluorescence demonstrates that in general ApcG deletion does not alter or inhibit state transitions interpreted in terms of the changes of the PSII and PSI fluorescence emission intensity. The results revealed yet–to–be discovered mechanism of ApcG-docking induced excitation energy transfer regulation within PBS or to Photosystems.

Nonelectroactive clostridium obtains extracellular electron transfer-capability after forming chimera with Geobacter.

Extracellular electron transfer (EET) of microorganisms is a major driver of the microbial growth and metabolism, including reactions involved in the cycling of C, N, and Fe in anaerobic environments such as soils and sediments. Understanding the mechanisms of EET, as well as knowing which organisms are EET-capable (or can become so) is fundamental to electromicrobiology and geomicrobiology. In general, Gram-positive bacteria very seldomly perform EET due to their thick non-conductive cell wall. Here, we report that a Gram-positive Clostridium intestinale (C.i) attained EET-capability for ethanol metabolism only after forming chimera with electroactive Geobacter sulfurreducens (G.s). Mechanism analyses demonstrated that the EET was possible after the cell fusion of the two species was achieved. Under these conditions, the ethanol metabolism pathway of C.i was integrated by the EET pathway of G.s, by which achieved the oxidation of ethanol for the subsequent reduction of extracellular electron acceptors in the coculture. Our study displays a new approach to perform EET for Gram-positive bacteria via recruiting the EET pathway of an electroactive bacterium, which suggests a previously unanticipated prevalence of EET in the microbial world. These findings also provide new perspectives to understand the energetic coupling between bacterial species and the ecology of interspecies mutualisms.

A Na pump with reduced stoichiometry is up-regulated by brine shrimp in extreme salinities.

Brine shrimp (Artemia) are the only animals to thrive at sodium concentrations above 4 M. Salt excretion is powered by the Na+,K+-ATPase (NKA), a heterodimeric (αβ) pump that usually exports 3Na+ in exchange for 2 K+ per hydrolyzed ATP. Artemia express several NKA catalytic α-subunit subtypes. High-salinity adaptation increases abundance of α2KK, an isoform that contains two lysines (Lys308 and Lys758 in transmembrane segments TM4 and TM5, respectively) at positions where canonical NKAs have asparagines (Xenopus α1's Asn333 and Asn785). Using de novo transcriptome assembly and qPCR, we found that Artemia express two salinity-independent canonical α subunits (α1NN and α3NN), as well as two β variants, in addition to the salinity-controlled α2KK. These β subunits permitted heterologous expression of the α2KK pump and determination of its CryoEM structure in a closed, ion-free conformation, showing Lys758 residing within the ion-binding cavity. We used electrophysiology to characterize the function of α2KK pumps and compared it to that of Xenopus α1 (and its α2KK-mimicking single- and double-lysine substitutions). The double substitution N333K/N785K confers α2KK-like characteristics to Xenopus α1, and mutant cycle analysis reveals energetic coupling between these two residues, illustrating how α2KK's Lys308 helps to maintain high affinity for external K+ when Lys758 occupies an ion-binding site. By measuring uptake under voltage clamp of the K+-congener 86Rb+, we prove that double-lysine-substituted pumps transport 2Na+ and 1 K+ per catalytic cycle. Our results show how the two lysines contribute to generate a pump with reduced stoichiometry allowing Artemia to maintain steeper Na+ gradients in hypersaline environments.

Local glycolysis fuels actomyosin contraction during axonal retraction.

In response to repulsive cues, axonal growth cones can quickly retract. This requires the prompt activity of contractile actomyosin, which is formed by the non-muscle myosin II (NMII) bound to actin filaments. NMII is a molecular motor that provides the necessary mechanical force at the expense of ATP. Here, we report that this process is energetically coupled to glycolysis and is independent of cellular ATP levels. Induction of axonal retraction requires simultaneous generation of ATP by glycolysis, as shown by chemical inhibition and genetic knock-down of GAPDH. Co-immunoprecipitation and proximal-ligation assay showed that actomyosin associates with ATP-generating glycolytic enzymes and that this association is strongly enhanced during retraction. Using microfluidics, we confirmed that the energetic coupling between glycolysis and actomyosin necessary for axonal retraction is localized to the growth cone and near axonal shaft. These results indicate a tight coupling between on-demand energy production by glycolysis and energy consumption by actomyosin contraction suggesting a function of glycolysis in axonal guidance.

Molecular mechanism of GPCR spatial organization at the plasma membrane.

G-protein-coupled receptors (GPCRs) mediate many critical physiological processes. Their spatial organization in plasma membrane (PM) domains is believed to encode signaling specificity and efficiency. However, the existence of domains and, crucially, the mechanism of formation of such putative domains remain elusive. Here, live-cell imaging (corrected for topography-induced imaging artifacts) conclusively established the existence of PM domains for GPCRs. Paradoxically, energetic coupling to extremely shallow PM curvature (<1 µm-1) emerged as the dominant, necessary and sufficient molecular mechanism of GPCR spatiotemporal organization. Experiments with different GPCRs, H-Ras, Piezo1 and epidermal growth factor receptor, suggest that the mechanism is general, yet protein specific, and can be regulated by ligands. These findings delineate a new spatiomechanical molecular mechanism that can transduce to domain-based signaling any mechanical or chemical stimulus that affects the morphology of the PM and suggest innovative therapeutic strategies targeting cellular shape.

High-throughput thermal denaturation of tryptophanyl-tRNA synthetase combinatorial mutants reveals high-order energetic coupling determinants of conformational stability.

Landscape descriptions provide a framework for identifying functionally significant dynamic linkages in proteins but cannot supply details. Rate measurements of combinatorial mutations can implicate dynamic linkages in catalysis. A major difficulty is filtering dynamic linkages from the vastly more numerous static interactions that stabilize domain folding. The Geobacillus stearothermophilus (TrpRS) D1 switch is such a dynamic packing motif; it links domain movement to catalysis and specificity. We describe Thermofluor and far UV circular dichroism melting curves for all 16 D1 switch variants to determine their higher-order impact on unliganded TrpRS stability. A prominent transition at intermediate temperatures in TrpRS thermal denaturation is molten globule formation. Combinatorial analysis of thermal melting transcends the protein landscape in four significant respects: (i) bioinformatic methods identify dynamic linkages from coordinates of multiple conformational states. (ii) Relative mutant melting temperatures, δTM, are proportional to free energy changes. (iii) Structural analysis of thermal melting implicates unexpected coupling between the D1 switch packing and regions of high local frustration. Those segments develop molten globular characteristics at the point of greatest complementarity to the chemical transition state and are the first TrpRS structures to melt. (iv) Residue F37 stabilizes both native and molten globular states; its higher-order interactions modify the relative intrinsic impacts of mutations to other D1 switch residues from those estimated for single point mutants. The D1 switch is a central component of an escapement mechanism essential to free energy transduction. These conclusions begin to relate the escapement mechanism to differential TrpRS conformational stabilities.

Miles down for lunch: deep-sea in situ observations of Arctic finned octopods Cirroteuthis muelleri suggest pelagic-benthic feeding migration.

Deep-sea cephalopods are diverse, abundant, and poorly understood. The Cirrata are gelatinous finned octopods and among the deepest-living cephalopods ever recorded. Their natural feeding behaviour remains undocumented. During deep-sea surveys in the Arctic, we observed Cirroteuthis muelleri. Octopods were encountered with their web spread wide, motionless and drifting in the water column 500-2600 m from the seafloor. Individuals of C. muelleri were also repeatedly observed on the seafloor where they exhibited a repeated, behavioural sequence interpreted as feeding. The sequence (11-21 s) consisted of arm web spreading, enveloping and retreating. Prey capture happened during the enveloping phase and lasted 5-49 s. Numerous traces of feeding activity were also observed on the seafloor. The utilization of the water column for drifting and the deep seafloor for feeding is a novel migration behaviour for cephalopods, but known from gelatinous fishes and holothurians. By benthic feeding, the octopods benefit from the enhanced nutrient availability on the seafloor. Drifting in the water column may be an energetically efficient way of transportation while simultaneously avoiding seafloor-associated predators. In situ observations are indispensable to discover the behaviour of abundant megafauna, and the energetic coupling between the pelagic and benthic deep sea.

Energy and Information Fluxes at Upper Ocean Density Fronts

We present large eddy simulations of a midlatitude open ocean front using a modified state-of-the-art computational fluid dynamics code. We investigate the energy and information fluxes at the submesoscale/small-scale range in the absence of any atmospheric forcing. We find submesoscale conditions (Ro∼1, Ri∼1) near the surface within baroclinic structures, related to partially imbalanced frontogenetic activity. Near the surface, the simulations show a significant scale coupling on scales larger than ∼103 (m). This is manifested as a strong direct energy cascade and intense mutual communication between scales, where the latter is evaluated using an estimator based on Mutual Information Theory. At scales smaller than ∼103 (m), the results show near-zero energy flux; however, at this scale range, the estimator of mutual communication still shows values corresponding with a significant level of communication between them. This fact motivates investigation into the nature of the self-organized turbulent motion at this scale range with weak energetic coupling but where communication between scales is still significant and to inquire into the existence of synchronization or functional relationships between scales, with emphasis on the eventual underlying nonlocal processes.

Temperature-dependent properties of the antiferroelectric model PbZrO3 : An effective Hamiltonian study

A novel atomistic effective Hamiltonian scheme, incorporating an original and simple bilinear energetic coupling, is developed and used to investigate the temperature-dependent physical properties of the prototype antiferroelectric ${\mathrm{PbZrO}}_{3}$ (PZO) system. This scheme reproduces very well the known experimental hallmarks of the complex Pbam orthorhombic phase at low temperatures and the cubic paraelectric state of $\mathrm{Pm}\overline{3}\mathrm{m}$ symmetry at high temperatures. Unexpectedly, it further predicts a novel intermediate state also of Pbam symmetry, but in which antiphase oxygen octahedral tiltings have vanished with respect to the Pbam ground state. Interestingly, such a new state exhibits a large dielectric response and thermal expansion that remarkably agrees with previous experimental observations and the x-ray experiments we performed. We also conducted direct first-principles calculations at 0 K, which further support such a low-energy phase. Within this fresh framework, a reexamination of the properties of PZO is thus called for.

Negative cooperativity underlies dynamic assembly of the Par complex regulators Cdc42 and Par-3

The Par complex polarizes diverse animal cells through the concerted action of multiple regulators. Binding to the multi-PDZ domain containing protein Par-3 couples the complex to cortical flows that construct the Par membrane domain. Once localized properly, the complex is thought to transition from Par-3 to the Rho GTPase Cdc42 to activate the complex. While this transition is a critical step in Par-mediated polarity, little is known about how it occurs. Here, we used a biochemical reconstitution approach with purified, intact Par complex and qualitative binding assays and found that Par-3 and Cdc42 exhibit strong negative cooperativity for the Par complex. The energetic coupling arises from interactions between the second and third PDZ protein interaction domains of Par-3 and the aPKC Kinase-PBM (PDZ binding motif) that mediate the displacement of Cdc42 from the Par complex. Our results indicate that Par-3, Cdc42, Par-6, and aPKC are the minimal components that are sufficient for this transition to occur and that no external factors are required. Our findings provide the mechanistic framework for understanding a critical step in the regulation of Par complex polarization and activity.

Energetic and Kinetic Coupling between the Intercalated Atom and Intrinsic S Vacancy in the MoS2 Bilayer

Energetic and Kinetic Coupling between the Intercalated Atom and Intrinsic S Vacancy in the MoS₂ Bilayer

Diversity of structural phases in AGeX3 halides

Utilizing first-principles and particle swarm optimization methods, we performed a systematic investigation of crystal structural stability and electrical properties of $A\mathrm{Ge}{X}_{3}$ compounds $(A=\mathrm{Li},\mathrm{Na},\mathrm{K},\mathrm{Rb},\mathrm{Cs};X=\mathrm{F},\mathrm{Cl},\mathrm{Br},\mathrm{I})$. Our work not only found the perovskite phases, but also discovered the post-perovskite, post-post-perovskite, and octahedra face-sharing structure phases, which are usually stable under high pressure, large strain, or exist in the inorganic--organic compound. These diverse structural phases provide abundant and promising properties. One striking phase is the $P{2}_{1}{2}_{1}{2}_{1}$ perovskite in ${\mathrm{KGeCl}}_{3}$ and ${\mathrm{KGeBr}}_{3}$, which possesses intrinsic small polar vortices and antivortices that may lead to a gyrotropic phase transition. The ferroelectric phase of $R3c$ $(\mathrm{LiGe}{X}_{3}, \mathrm{NaGe}{X}_{3})$, $R3m$ $(\mathrm{CsGe}{X}_{3})$ and $Pna{2}_{1}$ $(\mathrm{KGe}{X}_{3}, \mathrm{RbGe}{X}_{3})$ were also found. The new $Pna{2}_{1}$ phase possesses both proper and hybrid improper polarization, and the latter is evidenced by two original energetic couplings: one coupling polarization with the antipolar distortion from Ge atoms and antipolar distortion from $A$-site atoms, and another coupling polarization with out-of-phase halide octahedral tilting, in-phase halide octahedral tilting, and antipolar distortion from Ge atoms. The diverse structural phases and electrical properties make Ge-based halide a promising ${ABX}_{3}$ structure family in ferroics and piezoelectrics.

Empirical Low-Dimensional Dynamics of Atmospheric Stable Boundary Layer Temperature Inversions

Abstract The atmospheric stable boundary layer (SBL) is observed to display multiple regimes of stratification, flow, and turbulence. Transitions between weakly stable regimes of sustained turbulence and very stable regimes of weak turbulence are observed to occur abruptly. The understanding and predictability of turbulent recovery remains limited, reducing the accuracy of numerical weather prediction and climate projections. Idealized SBL models have related regimes to dynamically stable equilibria. Under conditions of weak energetic surface coupling, two stable branches separated by an unstable branch are predicted by these models. Such bifurcation structures are associated with rapid transitions. This work investigates the extent to which observed temperature inversion variability can be described by an empirical one-dimensional stochastic differential equation (SDE). The drift and diffusion coefficients of the SDE of observed inversion strength are approximated from statistics of their averaged time tendencies, conditioned on wind speed. Functional forms of the state dependence of these coefficients are estimated using Gaussian process regression. Probabilistic estimates of the system’s deterministic equilibria are found and used to create empirical bifurcation diagrams of inversion strength as a function of wind speed. These data-driven bifurcation structures are first obtained from idealized model simulations, then repeated for observations from several meteorological towers. It is found that the effective low-dimensional dynamics of observed temperature inversions is similar to that of the idealized model. Evidence of multiple equilibria and hysteresis is found at a single site, Dome C, Antarctica, but is not robust to variations in the analysis. Evidence of state-dependent noise consistent with intermittent turbulence under very stably stratified conditions is presented.

Dynamics and growth rate implications of ribosomes and mRNAs interaction in E. coli

Understanding how cells grow and adapt under various nutrient conditions is pivotal in the study of biological stoichiometry. Recent studies provide empirical evidence that cells use multiple strategies to maintain an optimal protein production rate under different nutrient conditions. Mathematical models can provide a solid theoretical foundation that can explain experimental observations and generate testable hypotheses to further our understanding of the growth process. In this study, we generalize a modeling framework that centers on the translation process and study its asymptotic behaviors to validate algebraic manipulations involving the steady states. Using experimental results on the growth of E. coli under C-, N-, and P-limited environments, we simulate the expected quantitative measurements to show the feasibility of using the model to explain empirical evidence. Our results support the findings that cells employ multiple strategies to maintain a similar protein production rate across different nutrient limitations. Moreover, we find that the previous study underestimates the significance of certain biological rates, such as the binding rate of ribosomes to mRNA and the transition rate between different ribosomal stages. Furthermore, our simulation shows that the strategies used by cells under C- and P-limitations result in a faster overall growth dynamics than under N-limitation. In conclusion, the general modeling framework provides a valuable platform to study cell growth under different nutrient supply conditions, which also allows straightforward extensions to the coupling of transcription, translation, and energetics to deepen our understanding of the growth process.

Cascaded adaptive integral backstepping sliding mode and super-twisting controller for twin rotor system using bond graph model

This work presents a bond graph (BG) model and a robust cascaded controller for a twin-rotor system (TRS). The BG model accounts for all the energetic and dynamical couplings. An adaptive integral backstepping sliding mode (AIBSM) controller is used in the outer loop to control the slow yaw and pitch dynamics of the mechanical sub-system whereas a higher-order sliding mode (HOSM) observer-based super-twisting algorithm (STA) controller is used in the inner loop to control the fast electromechanical actuator dynamics. The gain of the discontinuous control term of the integral backstepping sliding mode (IBSM) controller is adjusted by using an adaptive switching gain law, where the adaptive gain decreases or increases as the system state variables move closer to or away from a sliding surface; thereby reducing chatter and discontinuities near the sliding manifold, and ensuring a nearly smooth reference signal to the inner-loop controller. The unavailable states are estimated by using an unscented Kalman filter. All the used controllers are shown to be Lyapunov stable. The performance of the developed controller is validated through simulation and experiment, and it is further compared with other existing robust controllers. The proposed controller is robust against un-modeled dynamics and external disturbances, and it performs better, in terms of trajectory tracking error and disturbance rejection, than presently existing controllers for the TRS.

P2X2 receptor subunit interfaces are missense variant hotspots, where mutations tend to increase apparent ATP affinity.

Background and PurposeP2X receptors are trimeric ligand‐gated ion channels that open a cation‐selective pore in response to ATP binding to their large extracellular domain. The seven known P2X subtypes can assemble as homotrimeric or heterotrimeric complexes and contribute to numerous physiological functions, including nociception, inflammation and hearing. The overall structure of P2X receptors is well established, but little is known about the range and prevalence of human genetic variations and the functional implications of specific domains.Experimental ApproachHere, we examine the impact of P2X2 receptor inter‐subunit interface missense variants identified in the human population or by structural predictions. We test both single and double mutants through electrophysiological and biochemical approaches.Key ResultsWe demonstrate that predicted extracellular domain inter‐subunit interfaces display a higher‐than‐expected density of missense variations and that the majority of mutations that disrupt putative inter‐subunit interactions result in channels with higher apparent ATP affinity. Lastly, we show that double mutants at the subunit interface show significant energetic coupling, especially if located in close proximity.Conclusion and ImplicationsWe provide the first structural mapping of the mutational distribution across the human population in a ligand‐gated ion channel and show that the density of missense mutations is constrained between protein domains, indicating evolutionary selection at the domain level. Our data may indicate that, unlike other ligand‐gated ion channels, P2X2 receptors have evolved an intrinsically high threshold for activation, possibly to allow for additional modulation or as a cellular protection mechanism against overstimulation.

The regulating effect of growth plasticity on the dynamics of structured populations

Plasticity is the extent to which life history processes such as growth and reproduction depend on the environment. Plasticity in individual growth varies widely between taxa. Nonetheless, little is known about the effect of plasticity in individual growth on the ecological dynamics of populations. In this article, we analyse a physiologically structured population model of a consumer population in which the individual growth rate can be varied between entirely plastic to entirely non-plastic. We derive this population level model from a dynamic energy budget model to ensure an accurate energetic coupling between ingestion, somatic maintenance, growth and reproduction within an individual. We show that the consumer population is either limited by adult fecundity or juvenile survival up to maturation, depending on the level of growth plasticity and the non-plastic individual growth rate. Under these two regimes, we also find two different types of population cycles which again arise due to fluctuation in, respectively, juvenile growth rate or adult fecundity. In the end, our model not only provides insight into the effects of growth plasticity on population dynamics, but also provides a link between the dynamics found in age- and size-structured models.