The Blueprint of Logical Decisions in a NF-κB Signaling System.

Nearly identical cells can exhibit substantially different responses to the same stimulus that causes phenotype diversity. Such interplay between phenotype diversity and the architecture of regulatory circuits is crucial since it determines the state of a biological cell. Here, we theoretically analyze how the circuit blueprints of NF-κB in cellular environments are formed and their role in determining the cells' metabolic state. The NF-κB is a collective name for a developmental conserved family of five different transcription factors that can form homodimers or heterodimers and often promote DNA looping to reprogram the inflammatory gene response. The NF-κB controls many biological functions, including cellular differentiation, proliferation, migration, and survival. Our model shows that nuclear localization of NF-κB differentially promotes logic operations such as AND, NAND, NOR, and OR in its regulatory network. Through the quantitative thermodynamic model of transcriptional regulation and systematic variation of promoter-enhancer interaction modes, we can account for the origin of various logic gates as formed in the NF-κB system. We further show that the interconversion or switching of logic gates yielded under systematic variations of the stimuli activity and DNA looping parameters. Such computation occurs in regulatory and signaling pathways in individual cells at a molecular scale, which one can exploit to design a biomolecular computer.

Can local heating and molecular crowders disintegrate amyloid aggregates?

The present study employs a blend of molecular dynamics simulations and a theoretical model to explore the potential disintegration mechanism of a matured Aß octamer, aiming to offer a strategy to combat Alzheimer's disease. We investigate local heating and crowding effects on Aß disintegration by selectively heating key Aß segments and varying the concentration of sodium dodecyl sulphate (SDS), respectively. Despite initiation of disruption, Aß aggregates resist complete disintegration during local heating due to rapid thermal energy distribution to the surrounding water. Conversely, although SDS molecules effectively inhibit Aß aggregation at higher concentration through micelle formation, they fail to completely disintegrate the aggregate due to the exceedingly high energy barrier. To address the sampling challenge posed by the formidable energy barrier, we have performed well-tempered metadynamics simulations. Simulations reveal a multi-step disintegration mechanism for the Aß octamer, suggesting a probable sequence: octamer → pentamer/hexamer ⇌ tetramer → monomer, with a rate-determining step constituting 45 kJ mol-1 barrier during the octamer to pentamer/hexamer transition. Additionally, we have proposed a novel two-state mean-field model based on Ising spins that offers an insight into the kinetics of the Aß growth process and external perturbation effects on disintegration. Thus, the current simulation study, coupled with the newly introduced mean-field model, offers an insight into the detailed mechanisms underlying the Aß aggregation process, guiding potential strategies for effective disintegration of Aß aggregates.

An Inherent Difference between Serine and Threonine Phosphorylation: Phosphothreonine Strongly Prefers a Highly Ordered, Compact, Cyclic Conformation.

Phosphorylation and dephosphorylation of proteins by kinases and phosphatases are central to cellular responses and function. The structural effects of serine and threonine phosphorylation were examined in peptides and in proteins, by circular dichroism, NMR spectroscopy, bioinformatics analysis of the PDB, small-molecule X-ray crystallography, and computational investigations. Phosphorylation of both serine and threonine residues induces substantial conformational restriction in their physiologically more important dianionic forms. Threonine exhibits a particularly strong disorder-to-order transition upon phosphorylation, with dianionic phosphothreonine preferentially adopting a cyclic conformation with restricted ϕ (ϕ ∼ -60°) stabilized by three noncovalent interactions: a strong intraresidue phosphate-amide hydrogen bond, an n → π* interaction between consecutive carbonyls, and an n → σ* interaction between the phosphate Oγ lone pair and the antibonding orbital of C-Hß that restricts the χ2 side-chain conformation. Proline is unique among the canonical amino acids for its covalent cyclization on the backbone. Phosphothreonine can mimic proline's backbone cyclization via noncovalent interactions. The preferred torsions of dianionic phosphothreonine are ϕ,ψ = polyproline II helix > α-helix (ϕ ∼ -60°); χ1 = g-; χ2 ∼ +115° (eclipsed C-H/O-P bonds). This structural signature is observed in diverse proteins, including in the activation loops of protein kinases and in protein-protein interactions. In total, these results suggest a structural basis for the differential use and evolution of threonine versus serine phosphorylation sites in proteins, with serine phosphorylation typically inducing smaller, rheostat-like changes, versus threonine phosphorylation promoting larger, step function-like switches, in proteins.

Theoretical investigation of functional responses of bio-molecular assembly networks.

Cooperative protein-protein and protein-DNA interactions form programmable complex assemblies, often performing non-linear gene regulatory operations involved in signal transductions and cell fate determination. The apparent structure of those complex assemblies is very similar, but their functional response strongly depends on the topology of the protein-DNA interaction networks. Here, we demonstrate how the coordinated self-assembly creates gene regulatory network motifs that corroborate the existence of a precise functional response at the molecular level using thermodynamic and dynamic analyses. Our theoretical and Monte Carlo simulations show that a complex network of interactions can form a decision-making loop, such as feedback and feed-forward circuits, only by a few molecular mechanisms. We characterize each possible network of interactions by systematic variations of free energy parameters associated with the binding among biomolecules and DNA looping. We also find that the higher-order networks exhibit alternative steady states from the stochastic dynamics of each network. We capture this signature by calculating stochastic potentials and attributing their multi-stability features. We validate our findings against the Gal promoter system in yeast cells. Overall, we show that the network topology is vital in phenotype diversity in regulatory circuits.

Identifying critical transitions in complex diseases.

Mortality and the burden of diseases worldwide continue to reach substantial numbers with societal development and urbanization. In the face of decline in human health, early detection of complex diseases is indispensable, albeit challenging. In this review, we document the research carried out thus far on the appearance of complex diseases marked by a critical transition or a sudden shift from a healthy state to a disease state. The theory of resilience and critical slowing down can provide practical tools to forecast the onset of various fatal and perpetuating diseases. However, critical transitions in diseases across diverse temporal and spatial scales may not always be preceded by critical slowing down. In this backdrop, an in-depth study of the underlying molecular mechanisms provides dynamic network biomarkers that can forecast potential critical transitions. We have put together the theory of complex diseases and resilience, and have discussed the need for advanced research in developing early warning signals in the field of medicine and health care. We conclude the review with a few open questions and prospects for research in this emerging field.

Combined electromechanically driven pulsating flow of nonlinear viscoelastic fluids in narrow confinements.

Controlled microscale transport is at the core of many scientific and technological advancements, including medical diagnostics, separation of biomolecules, etc., and often involves complex fluids. One of the challenges in this regard is to actuate flows at small scales in an energy efficient manner, given the strong viscous forces opposing fluid motion. We try to address this issue here by probing a combined time-periodic pressure and electrokinetically driven flow of a viscoelastic fluid obeying the simplified linear Phan-Thien-Tanner model, using numerical as well as asymptotic tools, in view of the fact that oscillatory fields are less energy intensive. We establish that the interplay between oscillatory electrical and mechanical forces can lead to complex temporal mass flow rate variations with short-term bursts and peaks in the flow rate. We further demonstrate that an oscillatory pressure gradient or an electric field, in tandem with another steady actuating force can indeed change the net throughput significantly-a paradigm that is not realized in Newtonian or other simpler polymeric liquids. Our results reveal that the extent of augmentation in the flow rate strongly depends on the frequency of the imposed actuating forces along with their waveforms. We also evaluate the streaming potential resulting from an oscillatory pressure-driven flow and illustrate that akin to the volume throughput, the streaming potential also shows complex temporal variations, while its time average gets augmented in the presence of a time-periodic pressure gradient in a nonlinear viscoelastic medium.

Effects of stochasticity and social norms on complex dynamics of fisheries.

Recreational fishing is a highly socioecological process. Although recreational fisheries are self-regulating and resilient, changing anthropogenic pressure drives these fisheries to overharvest and collapse. Here, we evaluate the effect of demographic and environmental stochasticity for a social-ecological two-species fish model. In the presence of noise, we find that an increase in harvesting rate drives a critical transition from high-yield-low-price fisheries to low-yield-high-price fisheries. To calculate stochastic trajectories for demographic noise, we derive the master equation corresponding to the model and perform a Monte Carlo simulation. Moreover, the analysis of the probabilistic potential and mean first-passage time reveals the resilience of alternative steady states. We also describe the efficacy of a few generic indicators in forecasting sudden transitions. Furthermore, we show that incorporating social norms on the model allows a moderate fish density to maintain despite higher harvesting rates. Overall, our study highlights the occurrence of critical transitions in a stochastic social-ecological model and suggests ways to mitigate them.

Anticipating the Novel Coronavirus Disease (COVID-19) Pandemic.

The COVID-19 outbreak was first declared an international public health, and it was later deemed a pandemic. In most countries, the COVID-19 incidence curve rises sharply over a short period of time, suggesting a transition from a disease-free (or low-burden disease) equilibrium state to a sustained infected (or high-burden disease) state. Such a transition is often known to exhibit characteristics of "critical slowing down." Critical slowing down can be, in general, successfully detected using many statistical measures, such as variance, lag-1 autocorrelation, density ratio, and skewness. Here, we report an empirical test of this phenomena on the COVID-19 datasets of nine countries, including India, China, and the United States. For most of the datasets, increases in variance and autocorrelation predict the onset of a critical transition. Our analysis suggests two key features in predicting the COVID-19 incidence curve for a specific country: (a) the timing of strict social distancing and/or lockdown interventions implemented and (b) the fraction of a nation's population being affected by COVID-19 at that time. Furthermore, using satellite data of nitrogen dioxide as an indicator of lockdown efficacy, we found that countries where lockdown was implemented early and firmly have been successful in reducing COVID-19 spread. These results are essential for designing effective strategies to control the spread/resurgence of infectious pandemics.

Anticipating critical transitions in epithelial-hybrid-mesenchymal cell-fate determination.

In the vicinity of a tipping point, critical transitions occur when small changes in an input condition cause sudden, large, and often irreversible changes in the state of a system. Many natural systems ranging from ecosystems to molecular biosystems are known to exhibit critical transitions in their response to stochastic perturbations. In diseases, an early prediction of upcoming critical transitions from a healthy to a disease state by using early-warning signals is of prime interest due to potential application in forecasting disease onset. Here, we analyze cell-fate transitions between different phenotypes (epithelial, hybrid-epithelial/mesenchymal [E/M], and mesenchymal states) that are implicated in cancer metastasis and chemoresistance. These transitions are mediated by a mutually inhibitory feedback loop-microRNA-200/ZEB-driven by the levels of transcription factor SNAIL. We find that the proximity to tipping points enabling these transitions among different phenotypes can be captured by critical slowing down-based early-warning signals, calculated from the trajectory of ZEB messenger RNA level. Further, the basin stability analysis reveals the unexpectedly large basin of attraction for a hybrid-E/M phenotype. Finally, we identified mechanisms that can potentially elude the transition to a hybrid-E/M phenotype. Overall, our results unravel the early-warning signals that can be used to anticipate upcoming epithelial-hybrid-mesenchymal transitions. With the emerging evidence about the hybrid-E/M phenotype being a key driver of metastasis, drug resistance, and tumor relapse, our results suggest ways to potentially evade these transitions, reducing the fitness of cancer cells and restricting tumor aggressiveness.

Size-Dependent Conformational Features of Aß17-42 Protofilaments from Molecular Simulation Studies.

Alzheimer's disease is caused due to aggregation of amyloid beta (Aß) peptide into soluble oligomers and insoluble fibrils in the brain. In this study, we have performed room temperature molecular dynamics simulations to probe the size-dependent conformational features and thermodynamic stabilities of five Aß17-42 protofilaments, namely, O5 (pentamer), O8 (octamer), O10 (decamer), O12 (dodecamer), and O14 (tetradecamer). Analysis of the free energy profiles of the aggregates showed that the higher order protofilaments (O10, O12, and O14) undergo conformational transitions between two minimum energy states separated by small energy barriers, while the smaller aggregates (O5 and O8) remain in single deep minima surrounded by high barriers. Importantly, it is demonstrated that O10 is the crossover point for which the twisting of the protofilament is maximum, beyond which the monomers tend to rearrange themselves in an intermediate state and eventually transform into more stable conformations. Our results suggest that the addition of monomers along the axis of an existing protofilament with a critical size (O10 according to the present study) proceeds via an intermediate step with relatively less stable twisted structure that allows the additional monomers to bind and form stable larger protofilaments with minor rearrangements among themselves. More importantly, it is demonstrated that a combination of twist angle and end-to-end distance can be used as a suitable reaction coordinate to describe the growth mechanism of Aß protofilaments in simulation studies.

Thermodynamics of complex structures formed between single-stranded DNA oligomers and the KH domains of the far upstream element binding protein.

The noncovalent interaction between protein and DNA is responsible for regulating the genetic activities in living organisms. The most critical issue in this problem is to understand the underlying driving force for the formation and stability of the complex. To address this issue, we have performed atomistic molecular dynamics simulations of two DNA binding K homology (KH) domains (KH3 and KH4) of the far upstream element binding protein (FBP) complexed with two single-stranded DNA (ss-DNA) oligomers in aqueous media. Attempts have been made to calculate the individual components of the net entropy change for the complexation process by adopting suitable statistical mechanical approaches. Our calculations reveal that translational, rotational, and configurational entropy changes of the protein and the DNA components have unfavourable contributions for this protein-DNA association process and such entropy lost is compensated by the entropy gained due to the release of hydration layer water molecules. The free energy change corresponding to the association process has also been calculated using the Free Energy Perturbation (FEP) method. The free energy gain associated with the KH4-DNA complex formation has been found to be noticeably higher than that involving the formation of the KH3-DNA complex.

Investigating Hydrophilic Pores in Model Lipid Bilayers Using Molecular Simulations: Correlating Bilayer Properties with Pore-Formation Thermodynamics.

Cell-penetrating and antimicrobial peptides show a remarkable ability to translocate across physiological membranes. Along with factors such as electric-potential-induced perturbations of membrane structure and surface tension effects, experiments invoke porelike membrane configurations during the solute transfer process into vesicles and cells. The initiation and formation of pores are associated with a nontrivial free-energy cost, thus necessitating a consideration of the factors associated with pore formation and the attendant free energies. Because of experimental and modeling challenges related to the long time scales of the translocation process, we use umbrella sampling molecular dynamics simulations with a lipid-density-based order parameter to investigate membrane-pore-formation free energy employing Martini coarse-grained models. We investigate structure and thermodynamic features of the pore in 18 lipids spanning a range of headgroups, charge states, acyl chain lengths, and saturation. We probe the dependence of pore-formation barriers on the area per lipid, lipid bilayer thickness, and membrane bending rigidities in three different lipid classes. The pore-formation free energy in pure bilayers and peptide translocating scenarios are significantly coupled with bilayer thickness. Thicker bilayers require more reversible work to create pores. The pore-formation free energy is higher in peptide-lipid systems than in peptide-free lipid systems due to penalties to maintain the solvation of charged hydrophilic solutes within the membrane environment.

In silico studies of the properties of water hydrating a small protein.

Atomistic molecular dynamics simulation of an aqueous solution of the small protein HP-36 has been carried out with explicit solvent at room temperature. Efforts have been made to explore the influence of the protein on the relative packing and ordering of water molecules around its secondary structures, namely, three α-helices. The calculations reveal that the inhomogeneous water ordering and density distributions around the helices are correlated with their relative hydrophobicity. Importantly, we have identified the existence of a narrow relatively dehydrated region containing randomly organized "quasi-free" water molecules beyond the first layer of "bound" waters at the protein surface. These water molecules with relatively weaker binding energies form the transition state separating the "bound" and "free" water molecules at the interface. Further, increased contribution of solid-like caging motions of water molecules around the protein is found to be responsible for reduced fluidity of the hydration layer. Interestingly, we notice that the hydration layer of helix-3 is more fluidic with relatively higher entropy as compared to the hydration layers of the other two helical segments. Such characteristics of helix-3 hydration layer correlate well with the activity of HP-36, as helix-3 contains the active site of the protein.

Reconciling structural and thermodynamic predictions using all-atom and coarse-grain force fields: the case of charged oligo-arginine translocation into DMPC bilayers.

Using the translocation of short, charged cationic oligo-arginine peptides (mono-, di-, and triarginine) from bulk aqueous solution into model DMPC bilayers, we explore the question of the similarity of thermodynamic and structural predictions obtained from molecular dynamics simulations using all-atom and Martini coarse-grain force fields. Specifically, we estimate potentials of mean force associated with translocation using standard all-atom (CHARMM36 lipid) and polarizable and nonpolarizable Martini force fields, as well as a series of modified Martini-based parameter sets. We find that we are able to reproduce qualitative features of potentials of mean force of single amino acid side chain analogues into model bilayers. In particular, modifications of peptide-water and peptide-membrane interactions allow prediction of free energy minima at the bilayer-water interface as obtained with all-atom force fields. In the case of oligo-arginine peptides, the modified parameter sets predict interfacial free energy minima as well as free energy barriers in almost quantitative agreement with all-atom force field based simulations. Interfacial free energy minima predicted by a modified coarse-grained parameter set are -2.51, -4.28, and -5.42 for mono-, di-, and triarginine; corresponding values from all-atom simulations are -0.83, -3.33, and -3.29, respectively, all in units of kcal/mol. We found that a stronger interaction between oligo-arginine and the membrane components and a weaker interaction between oligo-arginine and water are crucial for producing such minima in PMFs using the polarizable CG model. The difference between bulk aqueous and bilayer center states predicted by the modified coarse-grain force field are 11.71, 14.14, and 16.53 kcal/mol, and those by the all-atom model are 6.94, 8.64, and 12.80 kcal/mol; those are of almost the same order of magnitude. Our simulations also demonstrate a remarkable similarity in the structural aspects of the ensemble of configurations generated using the all-atom and coarse-grain force fields. Both resolutions show that oligo-arginine peptides adopt preferential orientations as they translocate into the bilayer. The guiding theme centers on charged groups maintaining coordination with polar and charged bilayer components as well as local water. We also observe similar behaviors related with membrane deformations.

Translocation thermodynamics of linear and cyclic nonaarginine into model DPPC bilayer via coarse-grained molecular dynamics simulation: implications of pore formation and nonadditivity.

Structural mechanisms and underlying thermodynamic determinants of efficient internalization of charged cationic peptides (cell-penetrating peptides, CPPs) such as TAT, polyarginine, and their variants, into cells, cellular constructs, and model membrane/lipid bilayers (large and giant unilamellar or multilamelar vesicles) continue to garner significant attention. Two widely held views on the translocation mechanism center on endocytotic and nonendocytotic (diffusive) processes. Espousing the view of a purely diffusive internalization process (supported by recent experimental evidence, [Säälik, P.; et al. J. Controlled Release 2011, 153, 117-125]), we consider the underlying free energetics of the translocation of a nonaarginine peptide (Arg9) into a model DPPC bilayer. In the case of the Arg9 cationic peptide, recent experiments indicate a higher internalization efficiency of the cyclic structure (cyclic Arg9) relative to the linear conformer. Furthermore, recent all-atom resolution molecular dynamics simulations of cyclic Arg9 [Huang, K.; et al. Biophys. J., 2013, 104, 412-420] suggested a critical stabilizing role of water- and lipid-constituted pores that form within the bilayer as the charged Arg9 translocates deep into the bilayer center. Herein, we use umbrella sampling molecular dynamics simulations with coarse-grained Martini lipids, polarizable coarse-grained water, and peptide to explore the dependence of translocation free energetics on peptide structure and conformation via calculation of potentials of mean force along preselected reaction paths allowing and preventing membrane deformations that lead to pore formation. Within the context of the coarse-grained force fields we employ, we observe significant barriers for Arg9 translocation from bulk aqueous solution to bilayer center. Moreover, we do not find free-energy minima in the headgroup-water interfacial region, as observed in simulations using all-atom force fields. The pore-forming paths systematically predict lower free-energy barriers (ca. 90 kJ/mol lower) than the non pore-forming paths, again consistent with all-atom force field simulations. The current force field suggests no preference for the more compact or covalently cyclic structures upon entering the bilayer. Decomposition of the PMF into the system's components indicates that the dominant stabilizing contribution along the pore-forming path originates from the membrane as both layers of it deformed due to the formation of pore. Furthermore, our analysis revealed that although there is significant entropic stabilization arising from the enhanced configurational entropy exposing more states as the peptide moves through the bilayer, the enthalpic loss (as predicted by the interactions of this coarse-grained model) far outweighs any former stabilization, thus leading to significant barrier to translocation. Finally, we observe reduction in the translocation free-energy barrier for a second Arg9 entering the bilayer in the presence of an initial peptide restrained at the center, again, in qualitative agreement with all-atom force fields.

Polar solvation dynamics of lysozyme from molecular dynamics studies.

The solvation dynamics of a protein are believed to be sensitive to its secondary structures. We have explored such sensitivity in this article by performing room temperature molecular dynamics simulation of an aqueous solution of lysozyme. Nonuniform long-time relaxation patterns of the solvation time correlation function for different segments of the protein have been observed. It is found that relatively slower long-time solvation components of the α-helices and ß-sheets of the protein are correlated with lower exposure of their polar probe residues to bulk solvent and hence stronger interactions with the dynamically restricted surface water molecules. These findings can be verified by appropriate experimental studies.

Local heterogeneous dynamics of water around lysozyme: a computer simulation study.

Water present near the surface of a protein exhibits dynamic properties different from that of water in the pure bulk state. In this work, we have carried out atomistic molecular dynamics simulation of an aqueous solution of hen egg-white lysozyme. Attempts have been made to explore the correlation between the local heterogeneous mobility of water around the protein segments and the rigidity of the hydration layers with the microscopic dynamics of hydrogen bonds formed by water molecules with the protein residues. The kinetics of breaking and reformation of hydrogen bonds involving the surface water molecules have been calculated. It is found that the reformations of broken hydrogen bonds are more frequent for the hydration layers of those segments of the protein that are more rigid. The calculation of the low-frequency vibrational modes of hydration layer water molecules reveals that the protein influences the transverse and longitudinal degrees of freedom of water around it in a differential manner. These findings can be verified by appropriate experimental studies.

Dynamic properties of water around a protein-DNA complex from molecular dynamics simulations.

Formation of protein-DNA complex is an important step in regulation of genes in living organisms. One important issue in this problem is the role played by water in mediating the protein-DNA interactions. In this work, we have carried out atomistic molecular dynamics simulations to explore the heterogeneous dynamics of water molecules present in different regions around a complex formed between the DNA binding domain of human TRF1 protein and a telomeric DNA. It is demonstrated that such heterogeneous water motions around the complex are correlated with the relaxation time scales of hydrogen bonds formed by those water molecules with the protein and DNA. The calculations reveal the existence of a fraction of extraordinarily restricted water molecules forming a highly rigid thin layer in between the binding motifs of the protein and DNA. It is further proved that higher rigidity of water layers around the complex originates from more frequent reformations of broken water-water hydrogen bonds. Importantly, it is found that the formation of the complex affects the transverse and longitudinal degrees of freedom of surrounding water molecules in a nonuniform manner.

Differential flexibility of the secondary structures of lysozyme and the structure and ordering of surrounding water molecules.

We have performed an atomistic molecular dynamics simulation of an aqueous solution of hen egg-white lysozyme at room temperature with explicit water molecules. Several analyses have been carried out to explore the differential flexibility of the secondary structural segments of the protein and the structure and ordering of water around them. It is found that the overall flexibility of the protein molecule is primarily controlled by few large-amplitude bistable motions exhibited by two coils; one connecting two α-helical segments in domain-1 and the other connecting a 3(10) helix and a ß-sheet in domain-2 of the protein. The heterogeneous structuring of water around the segments of the protein has been found to depend on the degree of exposure of the segments to water. The ordering of water molecules around the protein segments and their tagged potential energies have been found to be anticorrelated with each other. Some of these findings can be verified by suitable experimental studies.

Conformational fluctuations of a protein-DNA complex and the structure and ordering of water around it.

Protein-DNA binding is an important process responsible for the regulation of genetic activities in living organisms. The most crucial issue in this problem is how the protein recognizes the DNA and identifies its target base sequences. Water molecules present around the protein and DNA are also expected to play an important role in mediating the recognition process and controlling the structure of the complex. We have performed atomistic molecular dynamics simulations of an aqueous solution of the protein-DNA complex formed between the DNA binding domain of human TRF1 protein and a telomeric DNA. The conformational fluctuations of the protein and DNA and the microscopic structure and ordering of water around them in the complex have been explored. In agreement with experimental studies, the calculations reveal conformational immobilization of the terminal segments of the protein on complexation. Importantly, it is discovered that both structural adaptations of the protein and DNA, and the subsequent correlation between them to bind, contribute to the net entropy loss associated with the complex formation. Further, it is found that water molecules around the DNA are more structured with significantly higher density and ordering than that around the protein in the complex.