Comprehensive intuitionistic fuzzy network data envelopment analysis incorporating undesirable outputs and shared resources.

The economic growth rate is intricately linked to the efficiency and effectiveness of the banking industry. A widely applicable mathematical technique for such assessments is Data Envelopment Analysis (DEA), which evaluates the relative efficiency of Decision-Making Units (DMUs) by comparing their inputs and outputs. Traditional DEA treats DMUs as black boxes, neglecting internal processes that contribute to inefficiencies in individual DMUs. Additionally, it assumes precise values for inputs and outputs that do not apply to real-world problems. This study introduces a comprehensive network series of two-stage DEA, incorporating shared inputs and intermediate measures, undesirable outputs, external inputs and outputs, initial inputs, and terminal outputs. The network two-stage DEA is extended to intuitionistic fuzzy circumstances to address uncertainty. In this extension, a non-linear intuitionistic fuzzy number, namely a parabolic intuitionistic fuzzy number, represents higher-order imprecise datasets. An illustrative example validates the proposed methodology, and comparisons with existing methods are conducted. Moreover, the methodology is applied to assess the efficiency of Indian public sector banks, demonstrating its applicability and showcasing the efficacy of the procedures and algorithms used. Decision-makers can make better choices using optimal efficiency values to gain insights into inputs, intermediate measures, and outputs.•The research study focused on a network two-stage DEA model, incorporating undesirable outputs and shared resources in the presence of uncertainty.•The methodology involves solving the network two-stage DEA model using parabolic intuitionistic fuzzy numbers.•The experimental analysis involves assessing the efficiency of Indian public sector banks.

3site Multisubstrate-Bound State of Cytochrome P450cam.

We identified a multisubstrate-bound state, hereby referred as a 3site state, in cytochrome P450cam via integrating molecular dynamics simulation with nuclear magnetic resonance (NMR) pseudocontact shift measurements. The 3site state is a result of simultaneous binding of three camphor molecules in three locations around P450cam: (a) in a well-established "catalytic" site near heme, (b) in a kink-separated "waiting" site along channel-1, and (c) in a previously reported "allosteric" site at E, F, G, and H helical junctions. These three spatially distinct binding modes in the 3site state mutually communicate with each other via homotropic allostery and act cooperatively to render P450cam functional. The 3site state shows a significantly superior fit with NMR pseudo contact shift (PCS) data with a Q-score of 0.045 than previously known bound states and consists of D251 free of salt-bridges with K178 and R186, rendering the enzyme functionally primed. To date, none of the reported cocomplex of P450cam with its redox partner putidaredoxin (pdx) has been able to match solution NMR data and controversial pdx-induced opening of P450cam's channel-1 remains a matter of recurrent discourse. In this regard, inclusion of pdx to the 3site state is able to perfectly fit the NMR PCS measurement with a Q-score of 0.08 and disfavors the pdx-induced opening of channel-1, reconciling previously unexplained remarkably fast hydroxylation kinetics with a koff of 10.2 s-1. Together, our findings hint that previous experimental observations may have inadvertently captured the 3site state as an in vitro solution state, instead of the catalytic state alone, and provided a distinct departure from the conventional understanding of cytochrome P450.

Identifying Selectivity Filters in Protein Biosensor for Ligand Screening.

Specialized sensing mechanisms in bacteria enable the identification of cognate ligands with remarkable selectivity in highly xenobiotic-polluted environments where these ligands are utilized as energy sources. Here, via integrating all-atom computer simulation, biochemical assay, and isothermal titration calorimetry measurements, we determine the molecular basis of MopR, a phenol biosensor's complex selection process of ligand entry. Our results reveal a set of strategically placed selectivity filters along the ligand entry pathway of MopR. These filters act as checkpoints, screening diverse aromatic ligands at the protein surface based on their chemical features and sizes. Ligands meeting specific criteria are allowed to enter the sensing site in an orientation-dependent manner. Sequence and structural analyses demonstrate the conservation of this ligand entry mechanism across the sensor class, with individual amino acids along the selectivity filter path playing a critical role in ligand selection. Together, this investigation highlights the importance of interactions with the ligand entry pathway, in addition to interactions within the binding pocket, in achieving ligand selectivity in biological sensing. The findings enhance our understanding of ligand selectivity in bacterial phenol biosensors and provide insights for rational expansion of the biosensor repertoire, particularly for the biotechnologically relevant class of aromatic pollutants.

Resolving Protein Conformational Plasticity and Substrate Binding via Machine Learning.

A long-standing target in elucidating the biomolecular recognition process is the identification of binding-competent conformations of the receptor protein. However, protein conformational plasticity and the stochastic nature of the recognition processes often preclude the assignment of a specific protein conformation to an individual ligand-bound pose. Here, we demonstrate that a computational framework coined as RF-TICA-MD, which integrates an ensemble decision-tree-based Random Forest (RF) machine learning (ML) technique with an unsupervised dimension reduction approach time-structured independent component analysis (TICA), provides an efficient and unambiguous solution toward resolving protein conformational plasticity and the substrate binding process. In particular, we consider multimicrosecond-long molecular dynamics (MD) simulation trajectories of a ligand recognition process in solvent-inaccessible cavities of archetypal proteins T4 lysozyme and cytochrome P450cam. We show that in a scenario in which clear correspondence between protein conformation and binding-competent macrostates could not be obtained via an unsupervised dimension reduction approach, an a priori decision-tree-based supervised classification of the simulated recognition trajectories via RF would help characterize key amino acid residue pairs of the protein that are deemed sensitive for ligand binding. A subsequent unsupervised dimensional reduction of the selected residue pairs via TICA would then delineate a conformational landscape of protein which is able to demarcate ligand-bound poses from unbound ones. The proposed RF-TICA-MD approach is shown to be data agnostic and found to be robust when using other ML-based classification methods such as XGBoost. As a promising spinoff of the protocol, the framework is found to be capable of identifying distal protein locations which would be allosterically important for ligand binding and would characterize their roles in recognition pathways. A Python implementation of a proposed ML workflow is available in GitHub https://github.com/navjeet0211/rf-tica-md.

Long-time-step molecular dynamics can retard simulation of protein-ligand recognition process.

Molecular dynamics (MD) simulation of biologically relevant processes at realistic time scale and atomistic precision is generally limited by prohibitively large computational cost, due to its restriction of using an ultrashort integration time step (1-2 fs). A popular numerical recipe to reduce the associated computational burden is adopting schemes that would allow relatively longer-time-step for MD propagation. Here, we explore the perceived potential of one of the most frequently used long-time-step protocols, namely the hydrogen mass repartitioning (HMR) approach, in alleviating the computational overhead associated with simulation of the kinetic process of protein-ligand recognition events. By repartitioning the mass of heavier atoms to their linked hydrogen atoms, HMR leverages around twofold longer time step than regular simulation, holding promise of significant performance boost. However, our probe into direct simulation of the protein-ligand recognition event, one of the computationally most challenging processes, shows that long-time-step HMR MD simulations do not necessarily translate to a computationally affordable solution. Our investigations spanning cumulative 176 µs in three independent proteins (T4 lysozyme, sensor domain of MopR, and galectin-3) show that long-time-step HMR-based MD simulations can catch the ligand in its act of recognizing the native cavity. But, as a major caveat, the ligand is found to require significantly longer time to identify buried native protein cavity in an HMR MD simulation than regular simulation, thereby defeating the purpose of its usage for performance upgrade. A molecular analysis shows that the longer time required by a ligand to recognize the protein in HMR is rooted in faster diffusion of the ligand, which reduces the survival probability of decisive on-pathway metastable intermediates, thereby slowing down the eventual recognition process at the native cavity. Together, the investigation stresses careful assessment of pitfalls of long-time-step algorithms before attempting to utilize them for higher performance for biomolecular recognition simulations.

Phenol sensing in nature is modulated via a conformational switch governed by dynamic allostery.

The NtrC family of proteins senses external stimuli and accordingly stimulates stress and virulence pathways via activation of associated σ54-dependent RNA polymerases. However, the structural determinants that mediate this activation are not well understood. Here, we establish using computational, structural, biochemical, and biophysical studies that MopR, an NtrC protein, harbors a dynamic bidirectional electrostatic network that connects the phenol pocket to two distal regions, namely the "G-hinge" and the "allosteric linker." While the G-hinge influences the entry of phenol into the pocket, the allosteric linker passes the signal to the downstream ATPase domain. We show that phenol binding induces a rewiring of the electrostatic connections by eliciting dynamic allostery and demonstrates that perturbation of the core relay residues results in a complete loss of ATPase stimulation. Furthermore, we found a mutation of the G-hinge, ∼20 Å from the phenol pocket, promotes altered flexibility by shifting the pattern of conformational states accessed, leading to a protein with 7-fold enhanced phenol binding ability and enhanced transcriptional activation. Finally, we conducted a global analysis that illustrates that dynamic allostery-driven conserved community networks are universal and evolutionarily conserved across species. Taken together, these results provide insights into the mechanisms of dynamic allostery-mediated conformational changes in NtrC sensor proteins.