Molecular dynamics simulations of nucleotide release from the circadian clock protein KaiC reveal atomic-resolution functional insights

Subunit shuffling dynamics in KaiC's central hub reveal the synchronization mechanism of the cyanobacterial circadian clock

Protein complexes are critical for cellular functions, and subunit exchange within these complexes is increasingly recognized as a key regulatory mechanism. In the cyanobacterial circadian clock, subunits shuffling of the core clock protein KaiC is thought to synchronize the clock, though the underlying mechanism remains unclear. We developed a chromatography-based method to monitor the shuffling dynamics of hexamerization domain of KaiC (KaiC-CI) and found that ATPase activity is essential for this process. By analyzing experiment data with quantitative models, we found that KaiC-CI hexamer stochastically disassembles into two oligomers for shuffling after hydrolysis. Further, by assuming a hidden conformation for post-hydrolysis hexamers, we established an ATPase activity-dependent model that quantitatively describes the shuffling dynamics of KaiC-CI hexamers, linking the shuffling rate to ATP hydrolysis and nucleotide exchange rates. Using this model, we estimated the shuffling dynamics of full-length KaiC with indirect experimental data. Our findings suggest that KaiC's phosphorylation states regulate nucleotide exchange rates in the CI domain, thereby modulating ATPase activity and influencing subunit shuffling. This study provides a mechanistic framework for understanding the role of ATPase activity in subunit exchange and its implications for circadian clock regulation.

A topological mechanism for robust and efficient global oscillations in biological networks

Long and stable timescales are often observed in complex biochemical networks, such as in emergent oscillations. How these robust dynamics persist remains unclear, given the many stochastic reactions and shorter time scales demonstrated by underlying components. We propose a topological model that produces long oscillations around the network boundary, reducing the system dynamics to a lower-dimensional current in a robust manner. Using this to model KaiC, which regulates the circadian rhythm in cyanobacteria, we compare the coherence of oscillations to that in other KaiC models. Our topological model localizes currents on the system edge, with an efficient regime of simultaneously increased precision and decreased cost. Further, we introduce a new predictor of coherence from the analysis of spectral gaps, and show that our model saturates a global thermodynamic bound. Our work presents a new mechanism and parsimonious description for robust emergent oscillations in complex biological networks.

Exploring Kinase Asp-Phe-Gly (DFG) Loop Conformational Stability with AlphaFold2-RAVE

Kinases compose one of the largest fractions of the human proteome, and their misfunction is implicated in many diseases, in particular, cancers. The ubiquitousness and structural similarities of kinases make specific and effective drug design difficult. In particular, conformational variability due to the evolutionarily conserved Asp-Phe-Gly (DFG) motif adopting in and out conformations and the relative stabilities thereof are key in structure-based drug design for ATP competitive drugs. These relative conformational stabilities are extremely sensitive to small changes in sequence and provide an important problem for sampling method development. Since the invention of AlphaFold2, the world of structure-based drug design has noticeably changed. In spite of it being limited to crystal-like structure prediction, several methods have also leveraged its underlying architecture to improve dynamics and enhanced sampling of conformational ensembles, including AlphaFold2-RAVE. Here, we extend AlphaFold2-RAVE and apply it to a set of kinases: the wild type DDR1 sequence and three mutants with single point mutations that are known to behave drastically differently. We show that AlphaFold2-RAVE is able to efficiently recover the changes in relative stability using transferable learned order parameters and potentials, thereby supplementing AlphaFold2 as a tool for exploration of Boltzmann-weighted protein conformations (Meller, A.; Bhakat, S.; Solieva, S.; Bowman, G. R. Accelerating Cryptic Pocket Discovery Using AlphaFold. J. Chem. Theory Comput. 2023, 19, 4355-4363).

The inner workings of an ancient biological clock

Circadian clocks evolved in diverse organisms as an adaptation to the daily swings in ambient light and temperature that derive from Earth's rotation. These timing systems, based on intracellular molecular oscillations, synchronize organisms' behavior and physiology with the 24-h environmental rhythm. The cyanobacterial clock serves as a special model for understanding circadian rhythms because it can be fully reconstituted in vitro. This review summarizes recent advances that leverage new biochemical, biophysical, and mathematical approaches to shed light on the molecular mechanisms of cyanobacterial Kai proteins that support the clock, and their homologues in other bacteria. Many questions remain in circadian biology, and the tools developed for the Kai system will bring us closer to the answers.

Determining subunit-subunit interaction from statistics of cryo-EM images: observation of nearest-neighbor coupling in a circadian clock protein complex

Biological processes are typically actuated by dynamic multi-subunit molecular complexes. However, interactions between subunits, which govern the functions of these complexes, are hard to measure directly. Here, we develop a general approach combining cryo-EM imaging technology and statistical modeling and apply it to study the hexameric clock protein KaiC in Cyanobacteria. By clustering millions of KaiC monomer images, we identify two major conformational states of KaiC monomers. We then classify the conformational states of (>160,000) KaiC hexamers by the thirteen distinct spatial arrangements of these two subunit states in the hexamer ring. We find that distributions of the thirteen hexamer conformational patterns for two KaiC phosphorylation mutants can be fitted quantitatively by an Ising model, which reveals a significant cooperativity between neighboring subunits with phosphorylation shifting the probability of subunit conformation. Our results show that a KaiC hexamer can respond in a switch-like manner to changes in its phosphorylation level.

Exploring kinase DFG loop conformational stability with AlphaFold2-RAVE

Kinases compose one of the largest fractions of the human proteome, and their misfunction is implicated in many diseases, in particular cancers. The ubiquitousness and structural similarities of kinases makes specific and effective drug design difficult. In particular, conformational variability due to the evolutionarily conserved DFG motif adopting in and out conformations and the relative stabilities thereof are key in structure-based drug design for ATP competitive drugs. These relative conformational stabilities are extremely sensitive to small changes in sequence, and provide an important problem for sampling method development. Since the invention of AlphaFold2, the world of structure-based drug design has noticably changed. In spite of it being limited to crystal-like structure prediction, several methods have also leveraged its underlying architecture to improve dynamics and enhanced sampling of conformational ensembles, including AlphaFold2-RAVE. Here, we extend AlphaFold2-RAVE and apply it to a set of kinases: the wild type DDR1 sequence and three mutants with single point mutations that are known to behave drastically differently. We show that AlphaFold2-RAVE is able to efficiently recover the changes in relative stability using transferable learnt order parameters and potentials, thereby supplementing AlphaFold2 as a tool for exploration of Boltzmann-weighted protein conformations.

Coupling of distant ATPase domains in the circadian clock protein KaiC

The AAA⁺ family member KaiC is the central pacemaker for circadian rhythms in the cyanobacterium Synechococcus elongatus. Composed of two hexameric rings of adenosine triphosphatase (ATPase) domains with tightly coupled activities, KaiC undergoes a cycle of autophosphorylation and autodephosphorylation on its C-terminal (CII) domain that restricts binding of clock proteins on its N-terminal (CI) domain to the evening. Here, we use cryogenic-electron microscopy to investigate how daytime and nighttime states of CII regulate KaiB binding on CI. We find that the CII hexamer is destabilized during the day but takes on a rigidified C₂-symmetric state at night, concomitant with ring-ring compression. Residues at the CI-CII interface are required for phospho-dependent KaiB association, coupling ATPase activity on CI to cooperative KaiB recruitment. Together, these studies clarify a key step in the regulation of cyanobacterial circadian rhythms by KaiC phosphorylation.

Spectres of Clock Evolution: Past, Present, and Yet to Come

Circadian clocks are phylogenetically widespread biological oscillators that allow organisms to entrain to environmental cycles and use their steady-state phase relationship to anticipate predictable daily phenomena – such as the light-dark transitions of a day – and prepare accordingly. Present from cyanobacteria to mammals, circadian clocks are evolutionarily ancient and are thought to increase the fitness of the organisms that possess them by allowing for better resource usage and/or proper internal temporal order. Here, we review literature with respect to the ecology and evolution of circadian clocks, with a special focus on cyanobacteria as model organisms. We first discuss what can be inferred about future clock evolution in response to climate change, based on data from latitudinal clines and domestication. We then address our current understanding of the role that circadian clocks might be contributing to the adaptive fitness of cyanobacteria at the present time. Lastly, we discuss what is currently known about the oldest known circadian clock, and the early Earth conditions that could have led to its evolution.

A Night-Time Edge Site Intermediate in the Cyanobacterial Circadian Clock Identified by EPR Spectroscopy

As the only circadian oscillator that can be reconstituted in vitro with its constituent proteins KaiA, KaiB, and KaiC using ATP as an energy source, the cyanobacterial circadian oscillator serves as a model system for detailed mechanistic studies of day-night transitions of circadian clocks in general. The day-to-night transition occurs when KaiB forms a night-time complex with KaiC to sequester KaiA, the latter of which interacts with KaiC during the day to promote KaiC autophosphorylation. However, how KaiB forms the complex with KaiC remains poorly understood, despite the available structures of KaiB bound to hexameric KaiC. It has been postulated that KaiB-KaiC binding is regulated by inter-KaiB cooperativity. Here, using spin labeling continuous-wave electron paramagnetic resonance spectroscopy, we identified and quantified two subpopulations of KaiC-bound KaiB, corresponding to the "bulk" and "edge" KaiBC sites in stoichiometric and substoichiometric KaiBiC6 complexes (i = 1-5). We provide kinetic evidence to support the intermediacy of the "edge" KaiBC sites as bridges and nucleation sites between free KaiB and the "bulk" KaiBC sites. Furthermore, we show that the relative abundance of "edge" and "bulk" sites is dependent on both KaiC phosphostate and KaiA, supporting the notion of phosphorylation-state controlled inter-KaiB cooperativity. Finally, we demonstrate that the interconversion between the two subpopulations of KaiC-bound KaiB is intimately linked to the KaiC phosphorylation cycle. These findings enrich our mechanistic understanding of the cyanobacterial clock and demonstrate the utility of EPR in elucidating circadian clock mechanisms.

Light exposure mediates circadian rhythms of rhizosphere microbial communities

Microbial community circadian rhythms have a broad influence on host health and even though light-induced environmental fluctuations could regulate microbial communities, the contribution of light to the circadian rhythms of rhizosphere microbial communities has received little attention. To address this gap, we monitored diel changes in the microbial communities in rice (Oryza sativa L.) rhizosphere soil under light-dark and constant dark regimes, identifying microbes with circadian rhythms caused by light exposure and microbial circadian clocks, respectively. While rhizosphere microbial communities displayed circadian rhythms under light-dark and constant dark regimes, taxa possessing circadian rhythms under the two conditions were dissimilar. Light exposure concealed microbial circadian clocks as a regulatory driver, leading to fewer ecological niches in light versus dark communities. These findings disentangle regulation mechanisms for circadian rhythms in the rice rhizosphere microbial communities and highlight the role of light-induced regulation of rhizosphere microbial communities.

Molecular dynamics free energy simulations of ATP:Mg2+ and ADP:Mg2+ using the polarizable force field AMOEBA

ATPases and GTPases are two important classes of protein that play critical roles in energy transduction, cellular signaling, gene regulation and catalysis. These proteins use cofactors such as nucleoside di and tri-phosphates (NTP, NDP) and can detect the difference between NDP and NTP which then induce different protein conformations. Mechanisms that drive proteins into the NTP or NDP conformation may depend on factors such as ligand structure and how Mg²⁺ coordinates with the ligand, amino acids in the pocket and water molecules. Here, we have used the advanced electrostatic and polarizable force field AMOEBA and molecular dynamics free energy simulations (MDFE) to examine the various binding mechanisms of ATP:Mg²⁺ and ADP:Mg²⁺.We compared the ATP:Mg²⁺ binding with previous studies using non-polarizable force fields and experimental data on the binding affinity. It was found that the total free energy of binding for ATP:Mg²⁺ (-7.00 ± 2.13 kcal/mol) is in good agreement with experimental values (-8.6 ± .2 kcal/mol)¹. In addition, parameters for relevant protonation states of ATP, ADP, GTP and GDP have been derived. These parameters will allow for researchers to investigate biochemical phenomena involving NTP's and NDP's with greater accuracy than previous studies involving non-polarizable force fields.

Monitoring Protein-Protein Interactions in the Cyanobacterial Circadian Clock in Real Time via Electron Paramagnetic Resonance Spectroscopy

The cyanobacterial circadian clock in Synechococcus elongatus consists of three proteins, KaiA, KaiB, and KaiC. KaiA and KaiB rhythmically interact with KaiC to generate stable oscillations of KaiC phosphorylation with a period of 24 h. The observation of stable circadian oscillations when the three clock proteins are reconstituted and combined in vitro makes it an ideal system for understanding its underlying molecular mechanisms and circadian clocks in general. These oscillations were historically monitored in vitro by gel electrophoresis of reaction mixtures based on the differing electrophoretic mobilities between various phosphostates of KaiC. As the KaiC phospho-distribution represents only one facet of the oscillations, orthogonal tools are necessary to explore other interactions to generate a full description of the system. However, previous biochemical assays are discontinuous or qualitative. To circumvent these limitations, we developed a spin-labeled KaiB mutant that can differentiate KaiC-bound KaiB from free KaiB using continuous-wave electron paramagnetic resonance spectroscopy that is minimally sensitive to KaiA. Similar to wild-type (WT-KaiB), this labeled mutant, in combination with KaiA, sustains robust circadian rhythms of KaiC phosphorylation. This labeled mutant is hence a functional surrogate of WT-KaiB and thus participates in and reports on autonomous macroscopic circadian rhythms generated by mixtures that include KaiA, KaiC, and ATP. Quantitative kinetics could be extracted with improved precision and time resolution. We describe design principles, data analysis, and limitations of this quantitative binding assay and discuss future research necessary to overcome these challenges.

Bayesian modeling reveals metabolite-dependent ultrasensitivity in the cyanobacterial circadian clock

Mathematical models can enable a predictive understanding of mechanism in cell biology by quantitatively describing complex networks of interactions, but such models are often poorly constrained by available data. Owing to its relative biochemical simplicity, the core circadian oscillator in Synechococcus elongatus has become a prototypical system for studying how collective dynamics emerge from molecular interactions. The oscillator consists of only three proteins, KaiA, KaiB, and KaiC, and near-24-h cycles of KaiC phosphorylation can be reconstituted in vitro. Here, we formulate a molecularly detailed but mechanistically naive model of the KaiA-KaiC subsystem and fit it directly to experimental data within a Bayesian parameter estimation framework. Analysis of the fits consistently reveals an ultrasensitive response for KaiC phosphorylation as a function of KaiA concentration, which we confirm experimentally. This ultrasensitivity primarily results from the differential affinity of KaiA for competing nucleotide-bound states of KaiC. We argue that the ultrasensitive stimulus-response relation likely plays an important role in metabolic compensation by suppressing premature phosphorylation at nighttime.

Myosin and Other Energy-Transducing ATPases: Structural Dynamics Studied by Electron Paramagnetic Resonance

The objective of this article was to document the energy-transducing and regulatory interactions in supramolecular complexes such as motor, pump, and clock ATPases. The dynamics and structural features were characterized by motion and distance measurements using spin-labeling electron paramagnetic resonance (EPR) spectroscopy. In particular, we focused on myosin ATPase with actin-troponin-tropomyosin, neural kinesin ATPase with microtubule, P-type ion-motive ATPase, and cyanobacterial clock ATPase. Finally, we have described the relationships or common principles among the molecular mechanisms of various energy-transducing systems and how the large-scale thermal structural transition of flexible elements from one state to the other precedes the subsequent irreversible chemical reactions.

ATP hydrolysis by KaiC promotes its KaiA binding in the cyanobacterial circadian clock system

ATP hydrolysis in the KaiC hexamer triggers the exposure of its C-terminal segments into the solvent so as to capture KaiA, providing mechanistic insights into the circadian periodicity regulation.

The cyanobacterial clock is controlled via the interplay among KaiA, KaiB, and KaiC, which generate a periodic oscillation of KaiC phosphorylation in the presence of ATP. KaiC forms a homohexamer harboring 12 ATP-binding sites and exerts ATPase activities associated with its autophosphorylation and dephosphorylation. The KaiC nucleotide state is a determining factor of the KaiB–KaiC interaction; however, its relationship with the KaiA–KaiC interaction has not yet been elucidated. With the attempt to address this, our native mass spectrometric analyses indicated that ATP hydrolysis in the KaiC hexamer promotes its interaction with KaiA. Furthermore, our nuclear magnetic resonance spectral data revealed that ATP hydrolysis is coupled with conformational changes in the flexible C-terminal segments of KaiC, which carry KaiA-binding sites. From these data, we conclude that ATP hydrolysis in KaiC is coupled with the exposure of its C-terminal KaiA-binding sites, resulting in its high affinity for KaiA. These findings provide mechanistic insights into the ATP-mediated circadian periodicity.

Effects of Stochastic Single-Molecule Reactions on Coherent Ensemble Oscillations in the KaiABC Circadian Clock

How do many constituent molecules in a biochemical system synchronize, giving rise to coherent system-level oscillations? One system that is particularly suitable for use in studying this problem is a mixture solution of three cyanobacterial proteins, KaiA, KaiB, and KaiC: the phosphorylation level of KaiC shows stable oscillations with a period of approximately 24 h when these three Kai proteins are incubated with ATP in vitro. Here, we analyze the mechanism behind synchronization in the KaiABC system theoretically by enhancing a model previously developed by the present author. Our simulation results suggest that positive feedback between stochastic ATP hydrolysis and the allosteric structural transitions in KaiC molecules drives oscillations of individual molecules and promotes synchronization of oscillations of many KaiC molecules. Our simulations also show that the ATPase activity of KaiC is correlated with the oscillation frequency of an ensemble of KaiC molecules. These results suggest that stochastic ATP hydrolysis in each KaiC molecule plays an important role in regulating the coherent system-level oscillations. This property is robust against changes in the binding and unbinding rate constants for KaiA to/from KaiC or KaiB, but the oscillations are sensitive to the rate constants of the KaiC phosphorylation and dephosphorylation reactions.