Multidomain protein solves the folding problem by multifunnel combined landscape: theoretical investigation of a Y-family DNA polymerase

Three-metal ion mechanism of cross-linked and uncross-linked DNA polymerase β: A theoretical study

In our recent publication, we have proposed a revised base excision repair pathway in which DNA polymerase β (Polβ) catalyzes Schiff base formation prior to the gap-filling DNA synthesis followed by β-elimination. In addition, the polymerase activity of Polβ employs the "three-metal ion mechanism" instead of the long-standing "two-metal ion mechanism" to catalyze phosphodiester bond formation based on the fact derived from time-resolved x-ray crystallography that a third Mg2+ was captured in the polymerase active site after the chemical reaction was initiated. In this study, we develop the models of the uncross-linked and cross-linked Polβ complexes and investigate the "three-metal ion mechanism" vs the "two-metal ion mechanism" by using the quantum mechanics/molecular mechanics molecular dynamics simulations. Our results suggest that the presence of the third Mg2+ ion stabilizes the reaction-state structures, strengthens correct nucleotide binding, and accelerates phosphodiester bond formation. The improved understanding of Polβ's catalytic mechanism provides valuable insights into DNA replication and damage repair.

Unveiling Metastable Ensembles of GRB2 and the Relevance of Interdomain Communication during Folding

The folding process of multidomain proteins is a highly intricate phenomenon involving the assembly of distinct domains into a functional three-dimensional structure. During this process, each domain may fold independently while interacting with others. The folding of multidomain proteins can be influenced by various factors, including their composition, the structure of each domain, or the presence of disordered regions, as well as the surrounding environment. Misfolding of multidomain proteins can lead to the formation of nonfunctional structures associated with a range of diseases, including cancers or neurodegenerative disorders. Understanding this process is an important step for many biophysical analyses such as stability, interaction, malfunctioning, and rational drug design. One such multidomain protein is growth factor receptor-bound protein 2 (GRB2), an adaptor protein that is essential in regulating cell survival. GRB2 consists of one central Src homology 2 (SH2) domain flanked by two Src homology 3 (SH3) domains. The SH2 domain interacts with phosphotyrosine regions in other proteins, while the SH3 domains recognize proline-rich regions on protein partners during cell signaling. Here, we combined computational and experimental techniques to investigate the folding process of GRB2. Through computational simulations, we sampled the conformational space and mapped the mechanisms involved by the free energy profiles, which may indicate possible intermediate states. From the molecular dynamics trajectories, we used the energy landscape visualization method (ELViM), which allowed us to visualize a three-dimensional (3D) representation of the overall energy surface. We identified two possible parallel folding routes that cannot be seen in a one-dimensional analysis, with one occurring more frequently during folding. Supporting these results, we used differential scanning calorimetry (DSC) and fluorescence spectroscopy techniques to confirm these intermediate states in vitro. Finally, we analyzed the deletion of domains to compare our model outputs to previously published results, supporting the presence of interdomain modulation. Overall, our study highlights the significance of interdomain communication within the GRB2 protein and its impact on the formation, stability, and structural plasticity of the protein, which are crucial for its interaction with other proteins in key signaling pathways.

Protein folding in vitro and in the cell: From a solitary journey to a team effort

Correct protein folding is essential for the health and function of living organisms. Yet, it is not well understood how unfolded proteins reach their native state and avoid aggregation, especially within the cellular milieu. Some proteins, especially small, single-domain and apparent two-state folders, successfully attain their native state upon dilution from denaturant. Yet, many more proteins undergo misfolding and aggregation during this process, in a concentration-dependent fashion. Once formed, native and aggregated states are often kinetically trapped relative to each other. Hence, the early stages of protein life are absolutely critical for proper kinetic channeling to the folded state and for long-term solubility and function. This review summarizes current knowledge on protein folding/aggregation mechanisms in buffered solution and within the bacterial cell, highlighting early stages. Remarkably, teamwork between nascent chain, ribosome, trigger factor and Hsp70 molecular chaperones enables all proteins to overcome aggregation propensities and reach a long-lived bioactive state.

Perspectives on the landscape and flux theory for describing emergent behaviors of the biological systems

We give a review on the landscape theory of the equilibrium biological systems and landscape-flux theory of the nonequilibrium biological systems as the global driving force. The emergences of the behaviors, the associated thermodynamics in terms of the entropy and free energy and dynamics in terms of the rate and paths have been quantitatively demonstrated. The hierarchical organization structures have been discussed. The biological applications ranging from protein folding, biomolecular recognition, specificity, biomolecular evolution and design for equilibrium systems as well as cell cycle, differentiation and development, cancer, neural networks and brain function, and evolution for nonequilibrium systems, cross-scale studies of genome structural dynamics and experimental quantifications/verifications of the landscape and flux are illustrated. Together, this gives an overall global physical and quantitative picture in terms of the landscape and flux for the behaviors, dynamics and functions of biological systems.

Investigating the Conformational Dynamics of a Y-Family DNA Polymerase during Its Folding and Binding to DNA and a Nucleotide

During DNA polymerization, the Y-family DNA polymerases are capable of bypassing various DNA damage, which can stall the replication fork progression. It has been well acknowledged that the structures of the Y-family DNA polymerases have been naturally evolved to undertake this vital task. However, the mechanisms of how these proteins utilize their unique structural and conformational dynamical features to perform the translesion DNA synthesis are less understood. Here, we developed structure-based models to study the precatalytic DNA polymerization process, including DNA and nucleotide binding to DPO4, a paradigmatic Y-family polymerase from Sulfolobus solfataricus. We studied the interplay between the folding and the conformational dynamics of DPO4 and found that DPO4 undergoes first unraveling (unfolding) and then folding for accomplishing the functional "open-to-closed" conformational transition. DNA binding dynamically modulates the conformational equilibrium in DPO4 during the stepwise binding through different types of interactions, leading to different conformational distributions of DPO4 at different DNA binding stages. We observed that nucleotide binding induces modulation of a few contacts surrounding the active site of the DPO4-DNA complex associated with a high free energy barrier. Our simulation results resonate with the experimental evidence that the conformational change at the active site led by nucleotide is the rate-limiting step of nucleotide incorporation. In combination with localized frustration analyses, we underlined the importance of DPO4 conformational dynamics and fluctuations in facilitating DNA and nucleotide binding. Our findings offer mechanistic insights into the processes of DPO4 conformational dynamics associated with the substrate binding and contribute to the understanding of the "structure-dynamics-function" relationship in the Y-family DNA polymerases.

Physics of biomolecular recognition and conformational dynamics

Biomolecular recognition usually leads to the formation of binding complexes, often accompanied by large-scale conformational changes. This process is fundamental to biological functions at the molecular and cellular levels. Uncovering the physical mechanisms of biomolecular recognition and quantifying the key biomolecular interactions are vital to understand these functions. The recently developed energy landscape theory has been successful in quantifying recognition processes and revealing the underlying mechanisms. Recent studies have shown that in addition to affinity, specificity is also crucial for biomolecular recognition. The proposed physical concept of intrinsic specificity based on the underlying energy landscape theory provides a practical way to quantify the specificity. Optimization of affinity and specificity can be adopted as a principle to guide the evolution and design of molecular recognition. This approach can also be used in practice for drug discovery using multidimensional screening to identify lead compounds. The energy landscape topography of molecular recognition is important for revealing the underlying flexible binding or binding-folding mechanisms. In this review, we first introduce the energy landscape theory for molecular recognition and then address four critical issues related to biomolecular recognition and conformational dynamics: (1) specificity quantification of molecular recognition; (2) evolution and design in molecular recognition; (3) flexible molecular recognition; (4) chromosome structural dynamics. The results described here and the discussions of the insights gained from the energy landscape topography can provide valuable guidance for further computational and experimental investigations of biomolecular recognition and conformational dynamics.

Effects of electrostatic interactions on global folding and local conformational dynamics of a multidomain Y-family DNA polymerase

The Y-family DNA polymerases specialize in translesion DNA synthesis, which is essential for replicating damaged DNA. The Y-family polymerases, which are made up of four stable domains, exhibit extensive distributions of charged residues, and are responsible for the tight formation of the protein-DNA complex. However, it is still unclear how the electrostatic interactions influence the conformational dynamics of the polymerases. Here, we focus on the case of a prototype Y-family DNA polymerase, Dpo4. Using coarse-grained models including a salt-dependent electrostatic potential, we investigate the effects of the electrostatic interactions on the folding process of Dpo4. Our simulations show that strong electrostatic interactions result in a three-state folding of Dpo4, consistent with the experimental observations. This folding process exhibits low cooperativity led by low salt concentration, where the individual domains fold one by one through one single pathway. Since the refined folding order of domains in multidomain proteins can shrink the configurational space, we suggest that the electrostatic interactions facilitate the Dpo4 folding. In addition, we study the local conformational dynamics of Dpo4 in terms of fluctuation and frustration analyses. We show that the electrostatic interactions can exaggerate the local conformational properties, which are in favor of the large-scale conformational transition of Dpo4 during the functional DNA binding. Our results underline the importance of electrostatic interactions in the conformational dynamics of Dpo4 at both the global and local scale, providing useful guidance in protein engineering at the multidomain level.

Investigating the trade-off between folding and function in a multidomain Y-family DNA polymerase

The way in which multidomain proteins fold has been a puzzling question for decades. Until now, the mechanisms and functions of domain interactions involved in multidomain protein folding have been obscure. Here, we develop structure-based models to investigate the folding and DNA-binding processes of the multidomain Y-family DNA polymerase IV (DPO4). We uncover shifts in the folding mechanism among ordered domain-wise folding, backtracking folding, and cooperative folding, modulated by interdomain interactions. These lead to ‘U-shaped’ DPO4 folding kinetics. We characterize the effects of interdomain flexibility on the promotion of DPO4–DNA (un)binding, which probably contributes to the ability of DPO4 to bypass DNA lesions, which is a known biological role of Y-family polymerases. We suggest that the native topology of DPO4 leads to a trade-off between fast, stable folding and tight functional DNA binding. Our approach provides an effective way to quantitatively correlate the roles of protein interactions in conformational dynamics at the multidomain level.

Binding-Induced Conformational Changes Involved in Sliding Clamp PCNA and DNA Polymerase DPO4

Cooperation between DNA polymerases and DNA sliding clamp proteins is essential for DNA replication and repair. However, it is still challenging to clarify the binding mechanism and the movements of Y-family DNA polymerase IV (DPO4) on the proliferating cell nuclear antigen (PCNA) ring. Here we develop the simulation models of DPO4–PCNA123 and DPO4–PCNA12 complexes and uncover the underlying dynamics of DPO4 during binding and the binding order of the DPO4 domains. Two important intermediate states are found on the free energy surface before reaching the final bound state. Our results suggest that both PCNA3 and DPO4 can influence the PCNA12 planar conformation, whereas the impact of PCNA3 on PCNA12 is more significant than DPO4. These findings provide the crucial information of the conformational dynamics of DPO4 and PCNA, as well as the clue of the underlying mechanism of the cooperation between DPO4 and PCNA during DNA replication.

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The mechanism of DPO4 binding to PCNA ring and PCNA dimer is investigated

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Two important intermediate states are found before reaching the final bound state

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Both PCNA3 and DPO4 can influence the PCNA12 planar conformation

Confinement and Crowding Effects on Folding of a Multidomain Y-Family DNA Polymerase

Proteins in vivo endure highly various interactions from the luxuriant surrounding macromolecular cosolutes. Confinement and macromolecular crowding are the two major effects that should be considered while comparing the results of protein dynamics from in vitro to in vivo. However, efforts have been largely focused on single domain protein folding up to now, and the quantifications of the in vivo effects in terms of confinements and crowders on modulating the structure and dynamics as well as the physical understanding of the underlying mechanisms on multidomain protein folding are still challenging. Here we developed a topology-based model to investigate folding of a multidomain Y-family DNA polymerase (DPO4) within spherical confined space and in the presence of repulsive and attractive crowders. We uncovered that the entropic component of the thermodynamic driving force led by confinements and repulsive crowders increases the stability of folded states relative to the folding intermediates and unfolded states, while the enthalpic component of the thermodynamic driving force led by attractive crowders gives rise to the opposite effects with less stability. We found that the shapes of DPO4 conformations influenced by the confinements and the crowders are quite different even when only the entropic component of the thermodynamic driving force is considered. We uncovered that under all in vivo conditions, the folding cooperativity of DPO4 decreases compared to that in bulk. We showed that the loss of folding cooperativity can promote the sequential domain-wise folding, which was widely found in cotranslational multidomain protein folding, and effectively prohibit the backtracking led by topological frustrations during multidomain protein folding processes.

Multiscale landscape of molecular mechanism of SIRT1 activation by STACs

Sirtuins are a family of highly conserved NAD-dependent deacetylase that are involved in multiple biological processes in both prokaryotes and eukaryotes. Many sirtuin-activating compounds (STACs) have been reported for SIRT1, which is the best-characterized sirtuin. However, the molecular mechanism of SIRT1 activation by STACs remains controversial. Here, we developed a multiscale simulation model to explore this mechanism. By quantifying the free energy landscape for the closed conformation of a SIRT1-FdL peptide-resveratrol complex, we found a positive correlation between the barrier height of the active free energy basin and the experimentally determined fluctuations in the rate of SIRT1 deacetylation by resveratrol. In addition, by monitoring dynamics, we found that the open conformation of a SIRT1-p53-STAC-1 complex had a faster rate of conformational change than the closed structure. We also determined the structural properties of each thermodynamic or dynamic state and found that two potential activating factors, the stability of FdL peptide (the p53 peptide substrate including an AMC fluorophore group) binding and the stability of the SIRT1 conformation, were weakly correlated under certain conditions. These results address the controversial question of whether the AMC fluorophore group and native hydrophobic residues have similar roles in the SIRT1 activation process. Finally, we captured the global landscape of the transition, including less stable and more stable states, and proposed a global physical landscape for the mechanism of SIRT1 activation by STACs.

Successes and challenges in simulating the folding of large proteins

Computational simulations of protein folding can be used to interpret experimental folding results, to design new folding experiments, and to test the effects of mutations and small molecules on folding. However, whereas major experimental and computational progress has been made in understanding how small proteins fold, research on larger, multidomain proteins, which comprise the majority of proteins, is less advanced. Specifically, large proteins often fold via long-lived partially folded intermediates, whose structures, potentially toxic oligomerization, and interactions with cellular chaperones remain poorly understood. Molecular dynamics based folding simulations that rely on knowledge of the native structure can provide critical, detailed information on folding free energy landscapes, intermediates, and pathways. Further, increases in computational power and methodological advances have made folding simulations of large proteins practical and valuable. Here, using serpins that inhibit proteases as an example, we review native-centric methods for simulating the folding of large proteins. These synergistic approaches range from Gō and related structure-based models that can predict the effects of the native structure on folding to all-atom-based methods that include side-chain chemistry and can predict how disease-associated mutations may impact folding. The application of these computational approaches to serpins and other large proteins highlights the successes and limitations of current computational methods and underscores how computational results can be used to inform experiments. These powerful simulation approaches in combination with experiments can provide unique insights into how large proteins fold and misfold, expanding our ability to predict and manipulate protein folding.

Molecular dynamics simulation reveals how phosphorylation of tyrosine 26 of phosphoglycerate mutase 1 upregulates glycolysis and promotes tumor growth

Phosphoglycerate mutase 1 (PGAM1) catalyzes the eighth step of glycolysis and is often found upregulated in cancer cells. To test the hypothesis that the phosphorylation of tyrosine 26 residue of PGAM1 greatly enhances its activity, we performed both conventional and steered molecular dynamics simulations on the binding and unbinding of PGAM1 to its substrates, with tyrosine 26 either phosphorylated or not. We analyzed the simulated data in terms of structural stability, hydrogen bond formation, binding free energy, etc. We found that tyrosine 26 phosphorylation enhances the binding of PGAM1 to its substrates through generating electrostatic environment and structural features that are advantageous to the binding. Our results may provide valuable insights into computer-aided design of drugs that specifically target cancer cells with PGAM1 tyrosine 26 phosphorylated.

Molecular mechanism of multispecific recognition of Calmodulin through conformational changes

Calmodulin (CaM) is found to have the capability to bind multiple targets. Investigations on the association mechanism of CaM to its targets are crucial for understanding protein-protein binding and recognition. Here, we developed a structure-based model to explore the binding process between CaM and skMLCK binding peptide. We found the cooperation between nonnative electrostatic interaction and nonnative hydrophobic interaction plays an important role in nonspecific recognition between CaM and its target. We also found that the conserved hydrophobic anchors of skMLCK and binding patches of CaM are crucial for the transition from high affinity to high specificity. Furthermore, this association process involves simultaneously both local conformational change of CaM and global conformational changes of the skMLCK binding peptide. We found a landscape with a mixture of the atypical "induced fit," the atypical "conformational selection," and "simultaneously binding-folding," depending on the synchronization of folding and binding. Finally, we extend our discussions on multispecific binding between CaM and its targets. These association characteristics proposed for CaM and skMLCK can provide insights into multispecific binding of CaM.

Enzymatic Activity and Thermodynamic Stability of Biliverdin IXβ Reductase Are Maintained by an Active Site Serine

Biliverdin reductase IXβ (BLVRB) is a crucial enzyme in heme metabolism. Recent studies in humans have identified a loss-of-function mutation (Ser111Leu) that unmasks a fundamentally important role in hematopoiesis. We have undertaken experimental and thermodynamic modeling studies to provide further insight into the role of the cofactor in substrate accessibility and protein folding properties regulating BLVRB catalytic mechanisms. Site-directed mutagenesis with molecular dynamic (MD) simulations establish the critical role of NAD(P)H-dependent conformational changes on substrate accessibility by forming the "hydrophobic pocket", along with identification of a single key residue (Arg35) modulating NADPH/NADH selectivity. Loop80 and Loop120 block the hydrophobic substrate binding pocket in apo BLVRB (open), whereas movement of these structures after cofactor binding results in the "closed" (catalytically active) conformation. Both enzymatic activity and thermodynamic stability are affected by mutation(s) involving Ser111, which is located in the core of the BLVRB active site. This work 1) elucidates the crucial role of Ser111 in enzymatic catalysis and thermodynamic stability by active site hydrogen bond network; 2) defines a dynamic model for apo BLVRB extending beyond the crystal structure of the binary BLVRB/NADP⁺ complex; 3) provides a structural basis for the "encounter" and "equilibrium" states of the binary complex, which are regulated by NAD(P)H.

Effects of heme binding on myoglobin folding: Coarse grained molecular simulations

Many proteins contain cofactors, such as heme, ATP and metal ions. Binding of cofactors is not only essential for their biological functions, but also can reshape the intrinsic energy landscape of protein molecules and modulate the folding and stability. However, the molecular mechanism of cofactor coupled protein folding is not well understood. In this work, we study the cofactor coupled folding of myoglobin, which is a typical cofactor (heme) containing protein, by performing molecular dynamics simulations with a structure-based protein model developed based on the energy landscape theory. We showed that the heme binding increases the stability of the myoglobin. More importantly, the heme binding tends to increase the protein folding cooperativity, and switch the folding process from a “three-state” mechanism to a “two-state” mechanism. We also showed that the folding pathways of the myoglobin can be modulated by the heme binding. By performing comparative simulations, we revealed that the above effects of heme binding are resulted from the heme induced folding of F-helix, which is otherwise unstructured at apo state, and the heme mediated contacting interactions around the heme binding site. The simulation results are consistent with available experimental data, and provide insights into the molecular mechanism of the effects of cofactor binding on the protein folding and stability.

Single-molecule FRET reveals hidden complexity in a protein energy landscape

Here, using single-molecule FRET, we reveal previously hidden conformations of the ankyrin-repeat domain of AnkyrinR, a giant adaptor molecule that anchors integral membrane proteins to the spectrin-actin cytoskeleton through simultaneous binding of multiple partner proteins. We show that the ankyrin repeats switch between high-FRET and low-FRET states, controlled by an unstructured "safety pin" or "staple" from the adjacent domain of AnkyrinR. Opening of the safety pin leads to unravelling of the ankyrin repeat stack, a process that will dramatically affect the relative orientations of AnkyrinR binding partners and, hence, the anchoring of the spectrin-actin cytoskeleton to the membrane. Ankyrin repeats are one of the most ubiquitous molecular recognition platforms in nature, and it is therefore important to understand how their structures are adapted for function. Our results point to a striking mechanism by which the order-disorder transition and, thereby, the activity of repeat proteins can be regulated.

How Co-translational Folding of Multi-domain Protein Is Affected by Elongation Schedule: Molecular Simulations

Co-translational folding (CTF) facilitates correct folding in vivo, but its precise mechanism remains elusive. For the CTF of a three-domain protein SufI, it was reported that the translational attenuation is obligatory to acquire the functional state. Here, to gain structural insights on the underlying mechanisms, we performed comparative molecular simulations of SufI that mimic CTF as well as refolding schemes. A CTF scheme that relied on a codon-based prediction of translational rates exhibited folding probability markedly higher than that by the refolding scheme. When the CTF schedule is speeded up, the success rate dropped. These agree with experiments. Structural investigation clarified that misfolding of the middle domain was much more frequent in the refolding scheme than that in the codon-based CTF scheme. The middle domain is less stable and can fold via interactions with the folded N-terminal domain. Folding pathway networks showed the codon-based CTF gives narrower pathways to the native state than the refolding scheme.

Proteins are synthesized in vivo by ribosome from their N-termini. When N-terminal fragments of nascent proteins get out of the ribosome exit, they start folding, which is called co-translational folding. It has been suggested that well-scheduled co-translational folding schemes would facilitate correct acquisition of their native structures for some multi-domain proteins. In particular, an un-ambiguous experiment was recently reported for a model protein, SufI where pauses at certain positions in the translational elongation are obligatory for efficient folding. Here, for the first time to our knowledge, we performed molecular dynamics simulations of SufI with co-translational folding as well as re-folding schemes. We found a co-translational folding shceme with rare codon-based pauses indeed increased the success ratio of folding, which is consistent with recent experiments. On top, molecular simulations provided much of structural insights on the folding routes and misfolding in the case of re-folding scheme. This explains why pauses in the translational elongation rescue SufI from misfolding.

Nonspecific yet decisive: Ubiquitination can affect the native-state dynamics of the modified protein

Ubiquitination is one of the most common post-translational modifications of proteins, and mediates regulated protein degradation among other cellular processes. A fundamental question regarding the mechanism of protein ubiquitination is whether and how ubiquitin affects the biophysical nature of the modified protein. For some systems, it was shown that the position of ubiquitin within the attachment site is quite flexible and ubiquitin does not specifically interact with its substrate. Nevertheless, it was revealed that polyubiquitination can decrease the thermal stability of the modified protein in a site-specific manner because of alterations of the thermodynamic properties of the folded and unfolded states. In this study, we used detailed atomistic simulations to focus on the molecular effects of ubiquitination on the native structure of the modified protein. As a model, we used Ubc7, which is an E2 enzyme whose in vivo ubiquitination process is well characterized and known to lead to degradation. We found that, despite the lack of specific direct interactions between the ubiquitin moiety and Ubc7, ubiquitination decreases the conformational flexibility of certain regions of the substrate Ubc7 protein, which reduces its entropy and thus destabilizes it. The strongest destabilizing effect was observed for systems in which Lys48-linked tetra-ubiquitin was attached to sites used for in vivo degradation. These results reveal how changes in the configurational entropy of the folded state may modulate the stability of the protein's native state. Overall, our results imply that ubiquitination can modify the biophysical properties of the attached protein in the folded state and that, in some proteins, different ubiquitination sites will lead to different biophysical outcomes. We propose that this destabilizing effect of polyubiquitin on the substrate is linked to the functions carried out by the modification, and in particular, regulatory control of protein half-life through proteasomal degradation.

In the multi-domain protein adenylate kinase, domain insertion facilitates cooperative folding while accommodating function at domain interfaces

Having multiple domains in proteins can lead to partial folding and increased aggregation. Folding cooperativity, the all or nothing folding of a protein, can reduce this aggregation propensity. In agreement with bulk experiments, a coarse-grained structure-based model of the three-domain protein, E. coli Adenylate kinase (AKE), folds cooperatively. Domain interfaces have previously been implicated in the cooperative folding of multi-domain proteins. To understand their role in AKE folding, we computationally create mutants with deleted inter-domain interfaces and simulate their folding. We find that inter-domain interfaces play a minor role in the folding cooperativity of AKE. On further analysis, we find that unlike other multi-domain proteins whose folding has been studied, the domains of AKE are not singly-linked. Two of its domains have two linkers to the third one, i.e., they are inserted into the third one. We use circular permutation to modify AKE chain-connectivity and convert inserted-domains into singly-linked domains. We find that domain insertion in AKE achieves the following: (1) It facilitates folding cooperativity even when domains have different stabilities. Insertion constrains the N- and C-termini of inserted domains and stabilizes their folded states. Therefore, domains that perform conformational transitions can be smaller with fewer stabilizing interactions. (2) Inter-domain interactions are not needed to promote folding cooperativity and can be tuned for function. In AKE, these interactions help promote conformational dynamics limited catalysis. Finally, using structural bioinformatics, we suggest that domain insertion may also facilitate the cooperative folding of other multi-domain proteins.

Most individual protein domains fold in an all or nothing fashion. This cooperative folding is important because it reduces the existence of partially folded proteins which can stick to each other and create disease causing aggregates. However, numerous proteins have multiple domains, independent units of folding, stability and/or function. Several such proteins also fold cooperatively. It is thought that strong interactions between individual domains allow the folding to propagate from a nucleating domain to neighbouring ones and this enables cooperative folding in multi-domain proteins. Here, we computationally study the folding of the three-domain protein AKE and find instead that the topology of the protein, wherein the two less stable domains are inserted into the more stable one, promotes folding cooperativity. When the more stable domain is folded, the ends of the inserted domains are constrained and this allows them to fold easily. In such a protein topology, strong inter-domain interactions are not needed to promote folding cooperativity. Interface amino acids which would have been involved in ensuring that the domains fit together correctly can now be tuned for binding or catalysis or conformational transitions. Thus, inserted domains may be present in multi-domain proteins to promote both function and folding.

Folding pathway of a multidomain protein depends on its topology of domain connectivity

How do the folding mechanisms of multidomain proteins depend on protein topology? We addressed this question by developing an Ising-like structure-based model and applying it for the analysis of free-energy landscapes and folding kinetics of an example protein, Escherichia coli dihydrofolate reductase (DHFR). DHFR has two domains, one comprising discontinuous N- and C-terminal parts and the other comprising a continuous middle part of the chain. The simulated folding pathway of DHFR is a sequential process during which the continuous domain folds first, followed by the discontinuous domain, thereby avoiding the rapid decrease in conformation entropy caused by the association of the N- and C-terminal parts during the early phase of folding. Our simulated results consistently explain the observed experimental data on folding kinetics and predict an off-pathway structural fluctuation at equilibrium. For a circular permutant for which the topological complexity of wild-type DHFR is resolved, the balance between energy and entropy is modulated, resulting in the coexistence of the two folding pathways. This coexistence of pathways should account for the experimentally observed complex folding behavior of the circular permutant.

Dynamic conformational change regulates the protein-DNA recognition: an investigation on binding of a Y-family polymerase to its target DNA

Protein-DNA recognition is a central biological process that governs the life of cells. A protein will often undergo a conformational transition to form the functional complex with its target DNA. The protein conformational dynamics are expected to contribute to the stability and specificity of DNA recognition and therefore may control the functional activity of the protein-DNA complex. Understanding how the conformational dynamics influences the protein-DNA recognition is still challenging. Here, we developed a two-basin structure-based model to explore functional dynamics in Sulfolobus solfataricus DNA Y-family polymerase IV (DPO4) during its binding to DNA. With explicit consideration of non-specific and specific interactions between DPO4 and DNA, we found that DPO4-DNA recognition is comprised of first 3D diffusion, then a short-range adjustment sliding on DNA and finally specific binding. Interestingly, we found that DPO4 is under a conformational equilibrium between multiple states during the binding process and the distributions of the conformations vary at different binding stages. By modulating the strength of the electrostatic interactions, the flexibility of the linker, and the conformational dynamics in DPO4, we drew a clear picture on how DPO4 dynamically regulates the DNA recognition. We argue that the unique features of flexibility and conformational dynamics in DPO4-DNA recognition have direct implications for low-fidelity translesion DNA synthesis, most of which is found to be accomplished by the Y-family DNA polymerases. Our results help complete the description of the DNA synthesis process for the Y-family polymerases. Furthermore, the methods developed here can be widely applied for future investigations on how various proteins recognize and bind specific DNA substrates.

Protein-DNA recognition is crucial for many key biological processes in cells. Protein often undergoes large-scale conformational change during DNA recognition. However, the physical and global understanding of flexible protein-DNA binding is still challenging. Here, we developed a theoretical approach to investigate binding of a Y-family DNA polymerase to its target DNA during the DNA synthesis process. The results of electrostatic-controlled multi-step DNA binding process accompanied with multi-state conformational transition of protein occurring throughout are in remarkable agreement with experiments. During the process of protein-DNA recognition, the flexibility is found to facilitate both the conformational transition of protein (intra-chain dynamics) and DNA binding (inter-chain dynamics) simultaneously. Therefore, we provided a quantitative description of protein-DNA binding mechanism that flexibility or conformational change regulates DNA recognition dynamically, leading to high efficiency and specificity of function for protein-DNA recognition.

PolyUbiquitin chain linkage topology selects the functions from the underlying binding landscape

Ubiquitin (Ub) can generate versatile molecular signals and lead to different celluar fates. The functional poly-valence of Ub is believed to be resulted from its ability to form distinct polymerized chains with eight linkage types. To provide a full picture of ubiquitin code, we explore the binding landscape of two free Ub monomers and also the functional landscapes of of all eight linkage types by theoretical modeling. Remarkably, we found that most of the compact structures of covalently connected dimeric Ub chains (diUbs) pre-exist on the binding landscape. These compact functional states were subsequently validated by corresponding linkage models. This leads to the proposal that the folding architecture of Ub monomer has encoded all functional states into its binding landscape, which is further selected by different topologies of polymeric Ub chains. Moreover, our results revealed that covalent linkage leads to symmetry breaking of interfacial interactions. We further propose that topological constraint not only limits the conformational space for effective switching between functional states, but also selects the local interactions for realizing the corresponding biological function. Therefore, the topological constraint provides a way for breaking the binding symmetry and reaching the functional specificity. The simulation results also provide several predictions that qualitatively and quantitatively consistent with experiments. Importantly, the K48 linkage model successfully predicted intermediate states. The resulting multi-state energy landscape was further employed to reconcile the seemingly contradictory experimental data on the conformational equilibrium of K48-diUb. Our results further suggest that hydrophobic interactions are dominant in the functional landscapes of K6-, K11-, K33- and K48 diUbs, while electrostatic interactions play a more important role in the functional landscapes of K27, K29, K63 and linear linkages.

Order statistics inference for describing topological coupling and mechanical symmetry breaking in multidomain proteins

Cooperativity is a hallmark of proteins, many of which show a modular architecture comprising discrete structural domains. Detecting and describing dynamic couplings between structural regions is difficult in view of the many-body nature of protein-protein interactions. By utilizing the GPU-based computational acceleration, we carried out simulations of the protein forced unfolding for the dimer WW - WW of the all-β-sheet WW domains used as a model multidomain protein. We found that while the physically non-interacting identical protein domains (WW) show nearly symmetric mechanical properties at low tension, reflected, e.g., in the similarity of their distributions of unfolding times, these properties become distinctly different when tension is increased. Moreover, the uncorrelated unfolding transitions at a low pulling force become increasingly more correlated (dependent) at higher forces. Hence, the applied force not only breaks "the mechanical symmetry" but also couples the physically non-interacting protein domains forming a multi-domain protein. We call this effect "the topological coupling." We developed a new theory, inspired by order statistics, to characterize protein-protein interactions in multi-domain proteins. The method utilizes the squared-Gaussian model, but it can also be used in conjunction with other parametric models for the distribution of unfolding times. The formalism can be taken to the single-molecule experimental lab to probe mechanical cooperativity and domain communication in multi-domain proteins.

Free energy landscapes for initiation and branching of protein aggregation

Experiments on artificial multidomain protein constructs have probed the early stages of aggregation processes, but structural details of the species that initiate aggregation remain elusive. Using the associative-memory, water-mediated, structure and energy model known as AWSEM, a transferable coarse-grained protein model, we performed simulations of fused constructs composed of up to four copies of the Titin I27 domain or its mutant I27* (I59E). Free energy calculations enable us to quantify the conditions under which such multidomain constructs will spontaneously misfold. Consistent with experimental results, the dimer of I27 is found to be the smallest spontaneously misfolding construct. Our results show how structurally distinct misfolded states can be stabilized under different thermodynamic conditions, and this result provides a plausible link between the single-molecule misfolding experiments under native conditions and aggregation experiments under denaturing conditions. The conditions for spontaneous misfolding are determined by the interplay among temperature, effective local protein concentration, and the strength of the interdomain interactions. Above the folding temperature, fusing additional domains to the monomer destabilizes the native state, and the entropically stabilized amyloid-like state is favored. Because it is primarily energetically stabilized, the domain-swapped state is more likely to be important under native conditions. Both protofibril-like and branching structures are found in annealing simulations starting from extended structures, and these structures suggest a possible connection between the existence of multiple amyloidogenic segments in each domain and the formation of branched, amorphous aggregates as opposed to linear fibrillar structures.

Multiscaled exploration of coupled folding and binding of an intrinsically disordered molecular recognition element in measles virus nucleoprotein

Numerous relatively short regions within intrinsically disordered proteins (IDPs) serve as molecular recognition elements (MoREs). They fold into ordered structures upon binding to their partner molecules. Currently, there is still a lack of in-depth understanding of how coupled binding and folding occurs in MoREs. Here, we quantified the unbound ensembles of the α-MoRE within the intrinsically disordered C-terminal domain of the measles virus nucleoprotein. We developed a multiscaled approach by combining a physics-based and an atomic hybrid model to decipher the mechanism by which the α-MoRE interacts with the X domain of the measles virus phosphoprotein. Our multiscaled approach led to remarkable qualitative and quantitative agreements between the theoretical predictions and experimental results (e.g., chemical shifts). We found that the free α-MoRE rapidly interconverts between multiple discrete partially helical conformations and the unfolded state, in accordance with the experimental observations. We quantified the underlying global folding-binding landscape. This leads to a synergistic mechanism in which the recognition event proceeds via (minor) conformational selection, followed by (major) induced folding. We also provided evidence that the α-MoRE is a compact molten globule-like IDP and behaves as a downhill folder in the induced folding process. We further provided a theoretical explanation for the inherent connections between "downhill folding," "molten globule," and "intrinsic disorder" in IDP-related systems. Particularly, we proposed that binding and unbinding of IDPs proceed in a stepwise way through a "kinetic divide-and-conquer" strategy that confers them high specificity without high affinity.

Quantifying the topography of the intrinsic energy landscape of flexible biomolecular recognition

Biomolecular functions are determined by their interactions with other molecules. Biomolecular recognition is often flexible and associated with large conformational changes involving both binding and folding. However, the global and physical understanding for the process is still challenging. Here, we quantified the intrinsic energy landscapes of flexible biomolecular recognition in terms of binding-folding dynamics for 15 homodimers by exploring the underlying density of states, using a structure-based model both with and without considering energetic roughness. By quantifying three individual effective intrinsic energy landscapes (one for interfacial binding, two for monomeric folding), the association mechanisms for flexible recognition of 15 homodimers can be classified into two-state cooperative "coupled binding-folding" and three-state noncooperative "folding prior to binding" scenarios. We found that the association mechanism of flexible biomolecular recognition relies on the interplay between the underlying effective intrinsic binding and folding energy landscapes. By quantifying the whole global intrinsic binding-folding energy landscapes, we found strong correlations between the landscape topography measure Λ (dimensionless ratio of energy gap versus roughness modulated by the configurational entropy) and the ratio of the thermodynamic stable temperature versus trapping temperature, as well as between Λ and binding kinetics. Therefore, the global energy landscape topography determines the binding-folding thermodynamics and kinetics, crucial for the feasibility and efficiency of realizing biomolecular function. We also found "U-shape" temperature-dependent kinetic behavior and a dynamical cross-over temperature for dividing exponential and nonexponential kinetics for two-state homodimers. Our study provides a unique way to bridge the gap between theory and experiments.

Exploring the Dynamic Functional Landscape of Adenylate Kinase Modulated by Substrates

Adenylate kinase (ADK) has been explored widely, through both experimental and theoretical studies. However, still less is known about how the functional dynamics of ADK is modulated explicitly by its natural substrates. Here, we report a quantitative study of the dynamic energy landscape for ADK responding to the substrate binding by integrating both experimental investigations and theoretical modeling. We make theoretical predictions which are in remarkable agreement with the single molecule experiments on the substrate-bound complex. With our combined models of ADK in its apo form, in the presence of AMP or ATP, and in complex with both substrates, we specifically address the following key questions: (1) Are there intermediate state(s) during their catalytic cycle and if so how many? (2) How many pathways are there along the open-to-closed transitions and what are their corresponding weights? (3) How do substrates influence the pathway weights and the stability of the intermediates? (4) Which lid's motion is rate-limiting along the turnover cycle, the NMP or the LID domain? Our models predict two major parallel stepwise pathways and two on-pathway intermediates which are denoted as IN (NMP domain open while LID domain closed) and IL (LID domain open and NMP domain closed), respectively. Further investigation of temperature effects suggests that the IN pathway is dominant at room temperature, but the IL pathway is dominant at the optimal temperature. This leads us to propose that the IL pathway is more dominant by entropy and IN pathway by enthalpy. Remarkably, our results show that even with maximum concentrations of natural substrates, ADK still fluctuates between multiple functional states, reflecting an intrinsic capability of large-scale conformational fluctuations which may be essential to its biological function. The results based on the dual-ligands model provide the theoretical validation of random bisubstrate biproducts (Bi-Bi) mechanism for the enzymatic reaction of ADK. Additionally, the pathway flux analysis strongly suggests that the motion of the NMP domain is the rate-determining step for the conformational cycle (opening and closing).