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Intrinsically disordered regions (IDR) and short linear motifs (SLiMs) play pivotal roles in the intricate signaling networks governed by phosphatases and kinases. B56δ (encoded by PPP2R5D) is a regulatory subunit of protein phosphatase 2A (PP2A) with long IDRs that harbor a substrate-mimicking SLiM and multiple phosphorylation sites. De novo missense mutations in PPP2R5D cause intellectual disabilities (ID), macrocephaly, Parkinsonism, and a broad range of neurological symptoms. Our single-particle cryo-EM structures of the PP2A-B56δ holoenzyme reveal that the long, disordered arms at the B56δ termini fold against each other and the holoenzyme core. This architecture suppresses both the phosphatase active site and the substrate-binding protein groove, thereby stabilizing the enzyme in a closed latent form with dual autoinhibition. The resulting interface spans over 190 Šand harbors unfavorable contacts, activation phosphorylation sites, and nearly all residues with ID-associated mutations. Our studies suggest that this dynamic interface is coupled to an allosteric network responsive to phosphorylation and altered globally by mutations. Furthermore, we found that ID mutations increase the holoenzyme activity and perturb the phosphorylation rates, and the severe variants significantly increase the mitotic duration and error rates compared to the normal variant.
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Proteína Fosfatase 2 , Proteína Fosfatase 2/metabolismo , Jordânia , Fosforilação , Mutação , Holoenzimas/genética , Holoenzimas/metabolismoRESUMO
DksA and ppGpp are the central players in the stringent response and mediate a complete reprogramming of the transcriptome. A major component of the response is a reduction in ribosome synthesis, which is accomplished by the synergistic action of DksA and ppGpp bound to RNA polymerase (RNAP) inhibiting transcription of rRNAs. Here, we report the X-ray crystal structures of Escherichia coli RNAP in complex with DksA alone and with ppGpp. The structures show that DksA accesses the template strand at the active site and the downstream DNA binding site of RNAP simultaneously and reveal that binding of the allosteric effector ppGpp reshapes the RNAP-DksA complex. The structural data support a model for transcriptional inhibition in which ppGpp potentiates the destabilization of open complexes by DksA. This work establishes a structural basis for understanding the pleiotropic effects of DksA and ppGpp on transcriptional regulation in proteobacteria.
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Proteínas de Escherichia coli/química , Escherichia coli/química , Nucleotídeos de Guanina/química , Modelos Químicos , Modelos Moleculares , Regulação Alostérica , Domínio Catalítico , Cristalografia por Raios X , RNA Polimerases Dirigidas por DNA/química , RNA Polimerases Dirigidas por DNA/metabolismo , Escherichia coli/metabolismo , Proteínas de Escherichia coli/metabolismo , Nucleotídeos de Guanina/metabolismo , Transcriptoma/fisiologiaRESUMO
The ability to predict and understand complex molecular motions occurring over diverse timescales ranging from picoseconds to seconds and even hours in biological systems remains one of the largest challenges to chemical theory. Markov state models (MSMs), which provide a memoryless description of the transitions between different states of a biochemical system, have provided numerous important physically transparent insights into biological function. However, constructing these models often necessitates performing extremely long molecular simulations to converge the rates. Here, we show that by incorporating memory via the time-convolutionless generalized master equation (TCL-GME) one can build a theoretically transparent and physically intuitive memory-enriched model of biochemical processes with up to a three order of magnitude reduction in the simulation data required while also providing a higher temporal resolution. We derive the conditions under which the TCL-GME provides a more efficient means to capture slow dynamics than MSMs and rigorously prove when the two provide equally valid and efficient descriptions of the slow configurational dynamics. We further introduce a simple averaging procedure that enables our TCL-GME approach to quickly converge and accurately predict long-time dynamics even when parameterized with noisy reference data arising from short trajectories. We illustrate the advantages of the TCL-GME using alanine dipeptide, the human argonaute complex, and FiP35 WW domain.
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Dipeptídeos , Simulação de Dinâmica Molecular , Humanos , Cadeias de MarkovRESUMO
A family of six homologous subunits, Mcm2, -3, -4, -5, -6, and -7, each with its own unique features, forms the catalytic core of the eukaryotic replicative helicase. The necessity of six similar but non-identical subunits has been a mystery since its initial discovery. Recent cryo-EM structures of the Mcm2-7 (MCM) double hexamer, its precursors, and the origin recognition complex (ORC)-Cdc6-Cdt1-Mcm2-7 (OCCM) intermediate showed that each of these subunits plays a distinct role in orchestrating the assembly of the pre-replication complex (pre-RC) by ORC-Cdc6 and Cdt1.
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Replicação do DNA , Proteínas de Manutenção de Minicromossomo/metabolismo , Complexo de Reconhecimento de Origem/metabolismo , Animais , Domínio Catalítico , Proteínas de Ciclo Celular/metabolismo , Humanos , Proteínas de Manutenção de Minicromossomo/química , Proteínas de Manutenção de Minicromossomo/ultraestrutura , Modelos Moleculares , Complexos Multiproteicos , Proteínas Nucleares/metabolismo , Conformação de Ácido Nucleico , Complexo de Reconhecimento de Origem/química , Complexo de Reconhecimento de Origem/ultraestrutura , Ligação Proteica , Subunidades Proteicas , Relação Estrutura-AtividadeRESUMO
Here, we report the use of an amphiphilic Pt(II) complex, K[Pt{(O3SCH2CH2CH2)2bzimpy}Cl] (PtB), as a model to elucidate the key role of Pt···Pt interactions in directing self-assembly by combining temperature-dependent ultraviolet-visible (UV-Vis) spectroscopy, stopped-flow kinetic experiments, quantum mechanics (QM) calculations, and molecular dynamics (MD) simulations. Interestingly, we found that the self-assembly mechanism of PtB in aqueous solution follows a nucleation-free isodesmic model, as revealed by the temperature-dependent UV-Vis experiments. In contrast, a cooperative growth is found for the self-assembly of PtB in acetonewater (7:1, vol/vol) solution, which is further verified by the stopped-flow experiments, which clearly indicates the existence of a nucleation phase in the acetonewater (7:1, vol/vol) solution. To reveal the underlying reasons and driving forces for these self-assembly processes, we performed QM calculations and show that the Pt···Pt interactions arising from the interaction between the pz and dz2 orbitals play a crucial role in determining the formation of ordered self-assembled structures. In subsequent oligomer MD simulations, we demonstrate that this directional Pt···Pt interaction can indeed facilitate the formation of linear structures packed in a helix-like fashion. Our results suggest that the self-assembly of PtB in acetonewater (7:1, vol/vol) solution is predominantly driven by the directional noncovalent Pt···Pt interaction, leading to the cooperative growth and the formation of fibrous nanostructures. On the contrary, the self-assembly in aqueous solution forms spherical nanostructures of PtB, which is primarily due to the predominant contribution from the less directional hydrophobic interactions over the directional Pt···Pt and π−π interactions that result in an isodesmic growth.
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RNA polymerase II (Pol II) incorporates complementary ribonucleotides into the growing RNA chain one at a time via the nucleotide addition cycle. The nucleotide addition cycle, however, is prone to misincorporation of noncomplementary nucleotides. Thus, to ensure transcriptional fidelity, Pol II backtracks and then cleaves the misincorporated nucleotides. These two reverse reactions, nucleotide addition and cleavage, are catalyzed in the same active site of Pol II, which is different from DNA polymerases or other endonucleases. Recently, substantial progress has been made to understand how Pol II effectively performs its dual role in the same active site. Our review highlights these recent studies and provides an overall model of the catalytic mechanisms of Pol II. In particular, RNA extension follows the two-metal-ion mechanism, and several Pol II residues play important roles to facilitate the catalysis. In sharp contrast, the cleavage reaction is independent of any Pol II residues. Interestingly, Pol II relies on its residues to recognize the misincorporated nucleotides during the backtracking process, prior to cleavage. In this way, Pol II efficiently compartmentalizes its two distinct catalytic functions using the same active site. Lastly, we also discuss a new perspective on the potential third Mg2+ in the nucleotide addition and intrinsic cleavage reactions.
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Nucleotídeos , RNA Polimerase II , Catálise , Domínio Catalítico , Nucleotídeos/química , RNA , RNA Polimerase II/metabolismo , Magnésio/químicaRESUMO
Nontargeted lipidomics using liquid chromatography-tandem mass spectrometry can detect thousands of molecules in biological samples. However, the annotation of unknown oxidized lipids is limited to the structures present in libraries, restricting the analysis and interpretation of experimental data. Here, we describe Doxlipid, a computational tool for oxidized lipid annotation that predicts a dynamic MS/MS library for every experiment. Doxlipid integrates three key simulation algorithms to predict libraries and covers 32 subclasses of oxidized lipids from the three main classes. In the evaluation, Doxlipid achieves very high prediction and characterization performance and outperforms the current oxidized lipid annotation methods. Doxlipid, combined with a molecular network, further annotates unknown chemical analogs in the same reaction or pathway. We demonstrate the broad utility of Doxlipid by analyzing oxidized lipids in ferroptosis hepatocellular carcinoma, tissue samples, and other biological samples, substantially advancing the discovery of biological pathways at the trace oxidized lipid level.
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Lipídeos , Espectrometria de Massas em Tandem , Espectrometria de Massas em Tandem/métodos , Lipídeos/análise , Cromatografia Líquida/métodos , Algoritmos , Simulação por ComputadorRESUMO
Non-targeted analysis of high-resolution mass spectrometry (MS) can identify thousands of compounds, which also gives a huge challenge to their quantification. The aim of this study is to investigate the impact of mass spectrometry ionization efficiency on various compounds in food at different solvent ratios and to develop a predictive model for mass spectrometry ionization efficiency to enable non-targeted quantitative prediction of unknown compounds. This study covered 70 compounds in 14 different mobile phase ratio environments in positive ion mode to analyze the rules of the matrix effect. With the organic phase ratio from low to high, most compounds changed by 1.0 log units in log IE. The addition of formic acid enhanced the signal but also promoted the matrix effect, which often occurred in compounds with strong ionization capacity. It was speculated that the matrix effect was mainly in the form of competitive charge and charged droplet' gasification sites during MS detection. Subsequently, we present a log IE prediction method built using the COSMO-RS software and the artificial neural network (ANN) algorithm to address this difficulty and overcome the shortcomings of previous models, which always ignore the matrix effect. This model was developed following the principles of QSAR modeling recommended by the Organization for Economic Cooperation and Development (OECD). Furthermore, we validated this approach by predicting the log IE of 70 compounds, including those not involved in the log IE model development. The results presented demonstrate that the method we put forward has an excellent prediction accuracy for log IE (R2pred = 0.880), which means that it has the potential to predict the log IE of new compounds without authentic standards.
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This experiment prepared magnetic composite siderophores (DMPs) with strong magnetism, excellent adsorption capacity, and high specific surface area. Exploring the synergistic effect of magnetic nanoparticles and siderophores on Microcystis aeruginosa growth under iron-deficient condition, by utilizing the characteristics of the three-layer core-shell structure of DMPs. This study elucidated the potential mechanism by which DMPs promote the cyanobacterial growth through physiological indicators and transcriptome analysis. On the experiment's final day, cell density in DMPs treatment group at 2, 4, and 8 mg/L were 1.10, 1.14 and 1.16 times higher than those in the control group (Ct), respectively. Similarly, chlorophyll and photosynthetic efficiency results showed improved algae growth with increasing DMPs dosage. The microcystin content in DMPs experimental groups at low, medium, and high concentration were 0.91, 0.86, and 0.83 times that of Ct, indicating alleviation of iron deficiency stress. Additionally, based on extracellular polymers, intracellular and extracellular siderophores, and visualization techniques, DMPs nanoparticles captured free iron sources in the environment, promoting algae growth by entering algal cells and facilitating the uptake and utilization of free iron ions from the solution. During the experiment, the iron uptake and transport genes (feoA and feoB) were significantly upregulated, whereas the algal siderophore synthesis gene (pchF) and the TonB-dependent transport system gene (TonB_C) were significantly downregulated, suggesting heightened activity in intracellular iron uptake and transport. This indicates an abundance of intracellular iron, eliminating the need for secrete siderophores to overcome iron deficiency. Microcystis aeruginosa increased iron bioavailability by using iron transported through DMPs in the environment while internalizing these DMPs. This study explored the mechanism of this synergistic effect to boost algal growth, and provided new ideas for elucidating the mechanism of cyanobacterial bloom outbreaks as well as the innovative application of biotechnology.
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Desferroxamina , Microcystis , Microcystis/crescimento & desenvolvimento , Microcystis/efeitos dos fármacos , Desferroxamina/farmacologia , Sideróforos , Nanopartículas de Magnetita/química , Ferro/metabolismoRESUMO
Protein conformational changes play crucial roles in their biological functions. In recent years, the Markov State Model (MSM) constructed from extensive Molecular Dynamics (MD) simulations has emerged as a powerful tool for modeling complex protein conformational changes. In MSMs, dynamics are modeled as a sequence of Markovian transitions among metastable conformational states at discrete time intervals (called lag time). A major challenge for MSMs is that the lag time must be long enough to allow transitions among states to become memoryless (or Markovian). However, this lag time is constrained by the length of individual MD simulations available to track these transitions. To address this challenge, we have recently developed Generalized Master Equation (GME)-based approaches, encoding non-Markovian dynamics using a time-dependent memory kernel. In this Tutorial, we introduce the theory behind two recently developed GME-based non-Markovian dynamic models: the quasi-Markov State Model (qMSM) and the Integrative Generalized Master Equation (IGME). We subsequently outline the procedures for constructing these models and provide a step-by-step tutorial on applying qMSM and IGME to study two peptide systems: alanine dipeptide and villin headpiece. This Tutorial is available at https://github.com/xuhuihuang/GME_tutorials. The protocols detailed in this Tutorial aim to be accessible for non-experts interested in studying the biomolecular dynamics using these non-Markovian dynamic models.
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Simulação de Dinâmica Molecular , Proteínas , Cadeias de Markov , Proteínas/química , Peptídeos , DipeptídeosRESUMO
To initiate transcription, the holoenzyme (RNA polymerase [RNAP] in complex with σ factor) loads the promoter DNA via the flexible loading gate created by the clamp and ß-lobe, yet their roles in DNA loading have not been characterized. We used a quasi-Markov State Model (qMSM) built from extensive molecular dynamics simulations to elucidate the dynamics of Thermus aquaticus holoenzyme's gate opening. We showed that during gate opening, ß-lobe oscillates four orders of magnitude faster than the clamp, whose opening depends on the Switch 2's structure. Myxopyronin, an antibiotic that binds to Switch 2, was shown to undergo a conformational selection mechanism to inhibit clamp opening. Importantly, we reveal a critical but undiscovered role of ß-lobe, whose opening is sufficient for DNA loading even when the clamp is partially closed. These findings open the opportunity for the development of antibiotics targeting ß-lobe of RNAP. Finally, we have shown that our qMSMs, which encode non-Markovian dynamics based on the generalized master equation formalism, hold great potential to be widely applied to study biomolecular dynamics.
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Proteínas de Bactérias/metabolismo , RNA Polimerases Dirigidas por DNA/metabolismo , Simulação de Dinâmica Molecular , Thermus/enzimologia , Cadeias de MarkovRESUMO
Objective: This study aimed to investigate the clinical impact of goal-oriented, evidence-based nursing in preventing perioperative stress injuries. Methods: A total of 380 patients undergoing surgery were allocated into either the control or study group. The study group received goal-oriented, evidence-based nursing, while the control group received routine nursing care. Various perioperative indicators, including operating time, position change time, intraoperative bleeding, and length of hospitalization, were assessed and compared between the two groups. Additionally, the Mini-Nutritional Assessment (MNA) score, Munro score, incidence of stress injuries, and nursing satisfaction rate were compared. Patients with perioperative pressure sores (PS) were further evaluated using the Pressure Ulcer Healing Score (PUSH), Braden Stress Injury Scale (Braden), visual analogue scale of pain (VAS), and wound healing time. Results: The study group exhibited higher MNA levels during and after the operation, while Munro levels were lower compared to the control group (P < .05). The study group demonstrated a shorter length of stay and quicker body position changes than the control group. Incidence of pressure sores (PS) was lower in the study group, accompanied by higher nursing satisfaction. PS patients in the study group had lower VAS and PUSH scores, higher Braden scores, and shorter wound healing times than those in the control group. Conclusion: This study highlights the efficacy of goal-oriented, evidence-based nursing in reducing perioperative stress injuries, advocating its adoption for improved care and patient outcomes. However, the single-center design limits generalizability, necessitating further validation. Ultimately, this approach signifies a step forward in nursing practice, promising better patient recovery and satisfaction.
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Conformational changes underpin function and encode complex biomolecular mechanisms. Gaining atomic-level detail of how such changes occur has the potential to reveal these mechanisms and is of critical importance in identifying drug targets, facilitating rational drug design, and enabling bioengineering applications. While the past two decades have brought Markov state model techniques to the point where practitioners can regularly use them to glimpse the long-time dynamics of slow conformations in complex systems, many systems are still beyond their reach. In this Perspective, we discuss how including memory (i.e., non-Markovian effects) can reduce the computational cost to predict the long-time dynamics in these complex systems by orders of magnitude and with greater accuracy and resolution than state-of-the-art Markov state models. We illustrate how memory lies at the heart of successful and promising techniques, ranging from the Fokker-Planck and generalized Langevin equations to deep-learning recurrent neural networks and generalized master equations. We delineate how these techniques work, identify insights that they can offer in biomolecular systems, and discuss their advantages and disadvantages in practical settings. We show how generalized master equations can enable the investigation of, for example, the gate-opening process in RNA polymerase II and demonstrate how our recent advances tame the deleterious influence of statistical underconvergence of the molecular dynamics simulations used to parameterize these techniques. This represents a significant leap forward that will enable our memory-based techniques to interrogate systems that are currently beyond the reach of even the best Markov state models. We conclude by discussing some current challenges and future prospects for how exploiting memory will open the door to many exciting opportunities.
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Bioengenharia , Sistemas de Liberação de Medicamentos , Desenho de Fármacos , Coração , Simulação de Dinâmica MolecularRESUMO
Enzymes that degrade synthetic polymers have attracted intense interest for eco-friendly plastic recycling. However, because enzymes did not evolve for the cleavage of abiotic polymers, directed evolution strategies are needed to enhance activity for plastic degradation. Previous directed evolution efforts relied on polymer degradation assays that were limited to screening â¼104 mutants. Here, we report a high-throughput yeast surface display platform to rapidly evaluate >107 enzyme mutants for increased activity in cleaving synthetic polymers. In this platform, individual yeast cells display distinct mutants, and enzyme activity is detected by a change in fluorescence upon the cleavage of a synthetic probe resembling a polymer of interest. Highly active mutants are isolated by fluorescence activated cell sorting and identified through DNA sequencing. To demonstrate this platform, we performed directed evolution of a polyethylene terephthalate (PET)-depolymerizing enzyme, leaf and branch compost cutinase (LCC). We identified activity-boosting mutations that substantially increased the kinetics of degradation of solid PET films. Biochemical assays and molecular dynamics (MD) simulations of the most active variants suggest that the H218Y mutation improves the binding of the enzyme to PET. Overall, this evolution platform increases the screening throughput of polymer-degrading enzymes by 3 orders of magnitude and identifies mutations that enhance kinetics for depolymerizing solid substrates.
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Evolução Molecular Direcionada , Enzimas , Polímeros , Saccharomyces cerevisiae , Polietilenotereftalatos , Polímeros/metabolismo , Saccharomyces cerevisiae/genética , Saccharomyces cerevisiae/metabolismo , Enzimas/genética , Enzimas/metabolismoRESUMO
Integral equation theory (IET) provides an effective solvation model for chemical and biological systems that balances computational efficiency and accuracy. We present a new software package, the expanded package for IET-based solvation (EPISOL), that performs 3D-reference interaction site model (3D-RISM) calculations to obtain the solvation structure and free energies of solute molecules in different solvents. In EPISOL, we have implemented 22 different closures, multiple free energy functionals, and new variations of 3D-RISM theory, including the recent hydrophobicity-induced density inhomogeneity (HI) theory for hydrophobic solutes and ion-dipole correction (IDC) theory for negatively charged solutes. To speed up the convergence and enhance the stability of the self-consistent iterations, we have introduced several numerical schemes in EPISOL, including a newly developed dynamic mixing approach. We show that these schemes have significantly reduced the failure rate of 3D-RISM calculations compared to AMBER-RISM software. EPISOL consists of both a user-friendly graphic interface and a kernel library that allows users to call its routines and adapt them to other programs. EPISOL is compatible with the force-field and coordinate files from both AMBER and GROMACS simulation packages. Moreover, EPISOL is equipped with an internal memory control to efficiently manage the use of physical memory, making it suitable for performing calculations on large biomolecules. We demonstrate that EPISOL can efficiently and accurately calculate solvation density distributions around various solute molecules (including a protein chaperone consisting of 120,715 atoms) and obtain solvent free energy for a wide range of organic compounds. We expect that EPISOL can be widely applied as a solvation model for chemical and biological systems. EPISOL is available at https://github.com/EPISOLrelease/EPISOL.
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Software , Termodinâmica , Solventes/química , Soluções , Simulação por ComputadorRESUMO
The development of unnatural base pairs (UBPs) has greatly increased the information storage capacity of DNA, allowing for transcription of unnatural RNA by the heterologously expressed T7 RNA polymerase (RNAP) in Escherichia coli. However, little is known about how UBPs are transcribed by cellular RNA polymerases. Here, we investigated how synthetic unnatural nucleotides, NaM and TPT3, are recognized by eukaryotic RNA polymerase II (Pol II) and found that Pol II is able to selectively recognize UBPs with high fidelity when dTPT3 is in the template strand and rNaMTP acts as the nucleotide substrate. Our structural analysis and molecular dynamics simulation provide structural insights into transcriptional processing of UBPs in a stepwise manner. Intriguingly, we identified a novel 3'-RNA binding site after rNaM addition, termed the swing state. These results may pave the way for future studies in the design of transcription and translation strategies in higher organisms with expanded genetic codes.
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Eucariotos/enzimologia , RNA Polimerase II/genética , Transcrição Gênica/genética , Pareamento de Bases , Simulação de Dinâmica Molecular , RNA Polimerase II/química , RNA Polimerase II/metabolismoRESUMO
Seafood tends to be highly vulnerable to spoilage and deterioration due to biochemical reactions and microbial contaminations, which requires appropriate processing technologies to improve or maintain its quality. Flavor, as an indispensable aspect reflecting the quality profile of seafood and influencing the final choice of consumers, is closely related to the processing technologies adopted. This review gives updated information on traditional and emerging processing technologies used in seafood processing and their implications on flavor. Traditional processing technologies, especially thermal treatment, effectively deactivate microorganisms to enhance seafood safety and prolong its shelf life. Nonetheless, these methods come with limitations, including reduced processing efficiency, increased energy consumption, and alterations in flavor, color, and texture due to overheating. Emerging processing technologies like microwave heating, infrared heating, high pressure processing, cold plasma, pulsed electric field, and ultrasound show alternative effects to traditional technologies. In addition to deactivating microorganisms and extending shelf life, these technologies can also safeguard the sensory quality of seafood. This review discusses emerging processing technologies in seafood and covers their principles, applications, developments, advantages, and limitations. In addition, this review examines the potential synergies that can arise from combining certain processing technologies in seafood processing.
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De novo protein design holds promise for creating small stable proteins with shapes customized to bind therapeutic targets. We describe a massively parallel approach for designing, manufacturing and screening mini-protein binders, integrating large-scale computational design, oligonucleotide synthesis, yeast display screening and next-generation sequencing. We designed and tested 22,660 mini-proteins of 37-43 residues that target influenza haemagglutinin and botulinum neurotoxin B, along with 6,286 control sequences to probe contributions to folding and binding, and identified 2,618 high-affinity binders. Comparison of the binding and non-binding design sets, which are two orders of magnitude larger than any previously investigated, enabled the evaluation and improvement of the computational model. Biophysical characterization of a subset of the binder designs showed that they are extremely stable and, unlike antibodies, do not lose activity after exposure to high temperatures. The designs elicit little or no immune response and provide potent prophylactic and therapeutic protection against influenza, even after extensive repeated dosing.
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Desenho de Fármacos , Influenza Humana/tratamento farmacológico , Influenza Humana/prevenção & controle , Terapia de Alvo Molecular/métodos , Engenharia de Proteínas/métodos , Proteínas/química , Proteínas/uso terapêutico , Toxinas Botulínicas/classificação , Toxinas Botulínicas/metabolismo , Simulação por Computador , Glicoproteínas de Hemaglutininação de Vírus da Influenza/metabolismo , Temperatura Alta , Humanos , Influenza Humana/metabolismo , Simulação de Dinâmica Molecular , Ligação Proteica , Estabilidade Proteica , Proteínas/imunologia , Proteínas/metabolismo , TemperaturaRESUMO
The generalized master equation (GME) provides a powerful approach to study biomolecular dynamics via non-Markovian dynamic models built from molecular dynamics (MD) simulations. Previously, we have implemented the GME, namely the quasi Markov State Model (qMSM), where we explicitly calculate the memory kernel and propagate dynamics using a discretized GME. qMSM can be constructed with much shorter MD trajectories than the MSM. However, since qMSM needs to explicitly compute the time-dependent memory kernels, it is heavily affected by the numerical fluctuations of simulation data when applied to study biomolecular conformational changes. This can lead to numerical instability of predicted long-time dynamics, greatly limiting the applicability of qMSM in complicated biomolecules. We present a new method, the Integrative GME (IGME), in which we analytically solve the GME under the condition when the memory kernels have decayed to zero. Our IGME overcomes the challenges of the qMSM by using the time integrations of memory kernels, thereby avoiding the numerical instability caused by explicit computation of time-dependent memory kernels. Using our solutions of the GME, we have developed a new approach to compute long-time dynamics based on MD simulations in a numerically stable, accurate and efficient way. To demonstrate its effectiveness, we have applied the IGME in three biomolecules: the alanine dipeptide, FIP35 WW-domain, and Taq RNA polymerase. In each system, the IGME achieves significantly smaller fluctuations for both memory kernels and long-time dynamics compared to the qMSM. We anticipate that the IGME can be widely applied to investigate biomolecular conformational changes.
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Dipeptídeos , Simulação de Dinâmica Molecular , Dipeptídeos/químicaRESUMO
Uncovering slow collective variables (CVs) of self-assembly dynamics is important to elucidate its numerous kinetic assembly pathways and drive the design of novel structures for advanced materials through the bottom-up approach. However, identifying the CVs for self-assembly presents several challenges. First, self-assembly systems often consist of identical monomers, and the feature representations should be invariant to permutations and rotational symmetries. Physical coordinates, such as aggregate size, lack high-resolution detail, while common geometric coordinates like pairwise distances are hindered by the permutation and rotational symmetry challenges. Second, self-assembly is usually a downhill process, and the trajectories often suffer from insufficient sampling of backward transitions that correspond to the dissociation of self-assembled structures. Popular dimensionality reduction methods, such as time-structure independent component analysis, impose detailed balance constraints, potentially obscuring the true dynamics of self-assembly. In this work, we employ GraphVAMPnets, which combines graph neural networks with a variational approach for Markovian process (VAMP) theory to identify the slow CVs of the self-assembly processes. First, GraphVAMPnets bears the advantages of graph neural networks, in which the graph embeddings can represent self-assembly structures in high-resolution while being invariant to permutations and rotational symmetries. Second, it is built upon VAMP theory, which studies Markov processes without forcing detailed balance constraints, which addresses the out-of-equilibrium challenge in the self-assembly process. We demonstrate GraphVAMPnets for identifying slow CVs of self-assembly kinetics in two systems: the aggregation of two hydrophobic molecules and the self-assembly of patchy particles. We expect that our GraphVAMPnets can be widely applied to molecular self-assembly.