Cheater suppression and stochastic clearance through quorum sensing.

The evolutionary consequences of quorum sensing in regulating bacterial cooperation are not fully understood. In this study, we reveal unexpected effects of regulating public good production through quorum sensing on bacterial population dynamics, showing that quorum sensing can be a collectively harmful alternative to unregulated production. We analyze a birth-death model of bacterial population dynamics accounting for public good production and the presence of non-producing cheaters. Our model demonstrates that when demographic noise is a factor, the consequences of controlling public good production according to quorum sensing depend on the cost of public good production and the growth rate of populations in the absence of public goods. When public good production is inexpensive, quorum sensing is a destructive alternative to unconditional production, in terms of the mean population extinction time. When costs are higher, quorum sensing becomes a constructive strategy for the producing strain, both stabilizing cooperation and decreasing the risk of population extinction.

Modeling the Role of Immune Cell Conversion in the Tumor-Immune Microenvironment.

Tumors develop in a complex physical, biochemical, and cellular milieu, referred to as the tumor microenvironment. Of special interest is the set of immune cells that reciprocally interact with the tumor, the tumor-immune microenvironment (TIME). The diversity of cell types and cell-cell interactions in the TIME has led researchers to apply concepts from ecology to describe the dynamics. However, while tumor cells are known to induce immune cells to switch from anti-tumor to pro-tumor phenotypes, this type of ecological interaction has been largely overlooked. To address this gap in cancer modeling, we develop a minimal, ecological model of the TIME with immune cell conversion, to highlight this important interaction and explore its consequences. A key finding is that immune conversion increases the range of parameters supporting a co-existence phase in which the immune system and the tumor reach a stalemate. Our results suggest that further investigation of the consequences of immune cell conversion, using detailed, data-driven models, will be critical for greater understanding of TIME dynamics.

Structural Consequences of Multisite Phosphorylation in the BAK1 Kinase Domain.

Multisite phosphorylation is an important mechanism of post-translational control of protein kinases. The effects of combinations of possible phosphorylation states on protein kinase activity are difficult to study experimentally because of challenges in isolating a particular phosphorylation state; surprising little effort on this topic has been expended in computational studies. To understand the effects of multisite phosphorylation on the plant protein kinase brassinosteroid insensitive 1-associated kinase 1 (BAK1) conformational ensemble, we performed Gaussian accelerated molecular dynamics simulations on eight BAK1 mod-forms involving phosphorylation of the four activation-loop threonine residues and binding of ATP-Mg2+. We find that unphosphorylated BAK1 transitions into an inactive conformation with a "cracked" activation loop and with the αC helix swung away from the active site. T450 phosphorylation can prevent the activation loop from cracking and keep the αC helix in an active-like conformation, whereas phosphorylation of T455 only slightly stabilizes the activation loop. There is a general trend of reduced flexibility in interlobe motion with increased phosphorylation. Interestingly, the αC helix is destabilized when the activation loop is fully phosphorylated but is again stabilized with ATP-Mg2+ bound. Our results provide insight into the mechanism of phosphorylation-controlled BAK1 activation while at the same time represent the first, to our knowledge, comprehensive, comparative study of the effects of combinatorial phosphorylation states on protein kinase conformational dynamics.

Using molecular simulation to explore the nanoscale dynamics of the plant kinome.

Eukaryotic protein kinases (PKs) are a large family of proteins critical for cellular response to external signals, acting as molecular switches. PKs propagate biochemical signals by catalyzing phosphorylation of other proteins, including other PKs, which can undergo conformational changes upon phosphorylation and catalyze further phosphorylations. Although PKs have been studied thoroughly across the domains of life, the structures of these proteins are sparsely understood in numerous groups of organisms, including plants. In addition to efforts towards determining crystal structures of PKs, research on human PKs has incorporated molecular dynamics (MD) simulations to study the conformational dynamics underlying the switching of PK function. This approach of experimental structural biology coupled with computational biophysics has led to improved understanding of how PKs become catalytically active and why mutations cause pathological PK behavior, at spatial and temporal resolutions inaccessible to current experimental methods alone. In this review, we argue for the value of applying MD simulation to plant PKs. We review the basics of MD simulation methodology, the successes achieved through MD simulation in animal PKs, and current work on plant PKs using MD simulation. We conclude with a discussion of the future of MD simulations and plant PKs, arguing for the importance of molecular simulation in the future of plant PK research.

Molecular dynamics simulations reveal the conformational dynamics of Arabidopsis thaliana BRI1 and BAK1 receptor-like kinases.

The structural motifs responsible for activation and regulation of eukaryotic protein kinases in animals have been studied extensively in recent years, and a coherent picture of their activation mechanisms has begun to emerge. In contrast, non-animal eukaryotic protein kinases are not as well understood from a structural perspective, representing a large knowledge gap. To this end, we investigated the conformational dynamics of two key Arabidopsis thaliana receptor-like kinases, brassinosteroid-insensitive 1 (BRI1) and BRI1-associated kinase 1 (BAK1), through extensive molecular dynamics simulations of their fully phosphorylated kinase domains. Molecular dynamics simulations calculate the motion of each atom in a protein based on classical approximations of interatomic forces, giving researchers insight into protein function at unparalleled spatial and temporal resolutions. We found that in an otherwise "active" BAK1 the αC helix is highly disordered, a hallmark of deactivation, whereas the BRI1 αC helix is moderately disordered and displays swinging behavior similar to numerous animal kinases. An analysis of all known sequences in the A. thaliana kinome found that αC helix disorder may be a common feature of plant kinases.

Allosteric Control of a Plant Receptor Kinase through S-Glutathionylation.

Growing evidence supports the importance of protein S-glutathionylation as a regulatory post-translational modification with functional consequences for proteins. Discoveries of redox-state-dependent protein kinase S-glutathionylation have fueled discussion of redox-sensitive signaling. Following previously published experimental evidence for S-glutathionylation induced deactivation of the Arabidopsis thaliana kinase BRASSINOSTEROID INSENSITIVE 1-ASSOCIATED RECEPTOR-LIKE KINASE 1 (BAK1), we investigated the consequences of S-glutathionylation on the equilibrium conformational ensemble of BAK1 using all-atom molecular dynamics simulations. We found that glutathionylation of C408 allosterically destabilizes the active-like state of BAK1 and stabilizes an inactive conformation known to recur in protein kinases. Glutathionylation of C408 also has structural consequences throughout the BAK1 kinase domain, whereas glutathionylation of C353 in the N-lobe and C374 near the ATP-binding site have few notable effects on BAK1 compared with the unmodified protein. Our results suggest an allosteric mechanism for inhibition of BAK1 by C408 S-glutathionylation, and more generally, support the notion of protein kinase S-glutathionylation as a means of redox signaling in plant cells.

Minimal informational requirements for fitness.

The existing concept of the "fitness value of information" provides a theoretical upper bound on the fitness advantage of using information concerning a fluctuating environment. Using concepts from rate-distortion theory, we develop a theoretical framework to answer a different pair of questions: What is the minimal amount of information needed for a population to achieve a certain growth rate? What is the minimal amount of information gain needed for one subpopulation to achieve a certain average selection coefficient over another? We introduce a correspondence between fitness and distortion and solve for the rate-distortion functions of several systems using analytical and numerical methods. Because accurate information processing is energetically costly, our approach provides a theoretical basis for understanding evolutionary "design principles" underlying information-cost trade-offs.

Permissive and nonpermissive channel closings in CFTR revealed by a factor graph inference algorithm.

The closing of the gated ion channel in the cystic fibrosis transmembrane conductance regulator can be categorized as nonpermissive to reopening, which involves the unbinding of ADP or ATP, or permissive, which does not. Identifying the type of closing is of interest as interactions with nucleotides can be affected in mutants or by introducing agonists. However, all closings are electrically silent and difficult to differentiate. For single-channel patch-clamp traces, we show that the type of the closing can be accurately determined by an inference algorithm implemented on a factor graph, which we demonstrate using both simulated and lab-obtained patch-clamp traces.

Fitness value of information with delayed phenotype switching: Optimal performance with imperfect sensing.

The ability of organisms to accurately sense their environment and respond accordingly is critical for evolutionary success. However, exactly how the sensory ability influences fitness is a topic of active research, while the necessity of a time delay between when unreliable environmental cues are sensed and when organisms can mount a response has yet to be explored at any length. Accounting for this delay in phenotype response in models of population growth, we find that a critical error probability can exist under certain environmental conditions: An organism with a sensory system with any error probability less than the critical value can achieve the same long-term growth rate as an organism with a perfect sensing system. We also observe a tradeoff between the evolutionary value of sensory information and robustness to error, mediated by the rate at which the phenotype distribution relaxes to steady state. The existence of the critical error probability could have several important evolutionary consequences, primarily that sensory systems operating at the nonzero critical error probability may be evolutionarily optimal.

Molecular Mechanism of Brassinosteroid Perception by the Plant Growth Receptor BRI1.

Brassinosteroids (BRs) are essential phytohormones, which bind to the plant receptor, BRI1, to regulate various physiological processes. The molecular mechanism of the perception of BRs by the ectodomain of BRI1 remains not fully understood. It also remains elusive why a substantial difference in biological activity exists between the BRs. In this work, we study the binding mechanisms of the two most bioactive BRs, brassinolide (BLD) and castasterone (CAT), using molecular dynamics simulations. We report free-energy landscapes of the binding processes of both ligands, as well as detailed ligand binding pathways. Our results suggest that CAT has a lower binding affinity compared to BLD due to its inability to form hydrogen-bonding interactions with a tyrosine residue in the island domain of BRI1. We uncover a conserved nonproductive binding state for both BLD and CAT, which is more stable for CAT and may further contribute to the bioactivity difference. Finally, we validate past observations about the conformational restructuring and ordering of the island domain upon BLD binding. Overall, this study provides new insights into the fundamental mechanism of the perception of the two most bioactive BRs, which may create new avenues for genetic and agrochemical control of their signaling cascade.

Enhanced unbiased sampling of protein dynamics using evolutionary coupling information.

One of the major challenges in atomistic simulations of proteins is efficient sampling of pathways associated with rare conformational transitions. Recent developments in statistical methods for computation of direct evolutionary couplings between amino acids within and across polypeptide chains have allowed for inference of native residue contacts, informing accurate prediction of protein folds and multimeric structures. In this study, we assess the use of distances between evolutionarily coupled residues as natural choices for reaction coordinates which can be incorporated into Markov state model-based adaptive sampling schemes and potentially used to predict not only functional conformations but also pathways of conformational change, protein folding, and protein-protein association. We demonstrate the utility of evolutionary couplings in sampling and predicting activation pathways of the ß 2-adrenergic receptor (ß 2-AR), folding of the FiP35 WW domain, and dimerization of the E. coli molybdopterin synthase subunits. We find that the time required for ß 2-AR activation and folding of the WW domain are greatly diminished using evolutionary couplings-guided adaptive sampling. Additionally, we were able to identify putative molybdopterin synthase association pathways and near-crystal structure complexes from protein-protein association simulations.

Publisher Correction: Enhanced unbiased sampling of protein dynamics using evolutionary coupling information.

A correction to this article has been published and is linked from the HTML version of this paper. The error has been fixed in the paper.

Application of Hidden Markov Models in Biomolecular Simulations.

Hidden Markov models (HMMs) provide a framework to analyze large trajectories of biomolecular simulation datasets. HMMs decompose the conformational space of a biological molecule into finite number of states that interconvert among each other with certain rates. HMMs simplify long timescale trajectories for human comprehension, and allow comparison of simulations with experimental data. In this chapter, we provide an overview of building HMMs for analyzing bimolecular simulation datasets. We demonstrate the procedure for building a Hidden Markov model for Met-enkephalin peptide simulation dataset and compare the timescales of the process.