Biochemistry on a leash: the roles of tether length and geometry in signal integration proteins

Optimizing Binding among Bimolecular Tethered Complexes

Tethered motion is ubiquitous in nature, offering controlled movement and spatial constraints to otherwise chaotic systems. The enhanced functionality and practical utility of tethers has been exploited in biotechnology, catalyzing the design of novel biosensors and molecular assembly techniques. While notable technological advances incorporating tethered motifs have been made, a theoretical gap persists within the paradigm, hindering a comprehensive understanding of tethered-based technologies. In this work, we focus on the characterization of the binding kinetics of two tethered molecules functionalized to a hard surface. Using a mean-field approximation, the binding time of such bimolecular system is determined analytically. Furthermore, estimates of the grafting site separation and polymer lengths which expedite binding are provided. These estimates, along with the analytical theories and frameworks established here, have the potential to improve efficacy in self-assembly methods in DNA nanotechnology and can be extended to more biologically specific endeavors including targeted drug-delivery and molecular sensing.

Myofilament-associated proteins with intrinsic disorder (MAPIDs) and their resolution by computational modeling

The cardiac sarcomere is a cellular structure in the heart that enables muscle cells to contract. Dozens of proteins belong to the cardiac sarcomere, which work in tandem to generate force and adapt to demands on cardiac output. Intriguingly, the majority of these proteins have significant intrinsic disorder that contributes to their functions, yet the biophysics of these intrinsically disordered regions (IDRs) have been characterized in limited detail. In this review, we first enumerate these myofilament-associated proteins with intrinsic disorder (MAPIDs) and recent biophysical studies to characterize their IDRs. We secondly summarize the biophysics governing IDR properties and the state-of-the-art in computational tools toward MAPID identification and characterization of their conformation ensembles. We conclude with an overview of future computational approaches toward broadening the understanding of intrinsic disorder in the cardiac sarcomere.

Interplay of Affinity and Surface Tethering in Protein Recognition

Surface-tethered ligand-receptor complexes are key components in biological signaling and adhesion. They also find increasing utility in single-molecule assays and biotechnological applications. Here, we study the real-time binding kinetics between various surface-immobilized peptide ligands and their unrestrained receptors. A long peptide tether increases the association of ligand-receptor complexes, experimentally proving the fly casting mechanism where the disorder accelerates protein recognition. On the other hand, a short peptide tether enhances the complex dissociation. Notably, the rate constants measured for the same receptor, but under different spatial constraints, are strongly correlated to one another. Furthermore, this correlation can be used to predict how surface tethering on a ligand-receptor complex alters its binding kinetics. Our results have immediate implications in the broad areas of biomolecular recognition, intrinsically disordered proteins, and biosensor technology.

Intrinsic disorder in protein kinase A anchoring proteins signaling complexes

Protein kinase A (PKA) is regulated by a diverse class of anchoring proteins known as AKAPs that target PKA to subsets of its activators and substrates. Recently, it was reported that PKA can remain bound to its regulatory subunit after activation in contrast to classical model of activation-by-dissociation. This implies that PKA remains bound to the AKAPs and its substrates, and thus suggest many phosphorylation reactions occur while PKA is physically connected to its substrate. Intra-complex reactions are sensitive to the architecture of the signaling complex, but generally concentration independent. We show that most AKAPs have long intrinsically disordered regions, and suggest that they represent an adaptation for intra-complex phosphorylation. Based on polymer models of the disordered proteins, we predict that the effective concentrations of tethered substrates range from the low millimolar range to tens of micromolar. Based on recent models for intra-complex enzyme reactions, we suggest that the structure of the AKAP signaling complex is likely to be source of allosteric regulation of PKA signaling.

Determination of the molecular reach of the protein tyrosine phosphatase SHP-1

Immune receptors signal by recruiting (or tethering) enzymes to their cytoplasmic tails to catalyze reactions on substrates within reach. This is the case for the phosphatase SHP-1, which, upon tethering to inhibitory receptors, dephosphorylates diverse substrates to control T cell activation. Precisely how tethering regulates SHP-1 activity is incompletely understood. Here, we measure binding, catalysis, and molecular reach for tethered SHP-1 reactions. We determine the molecular reach of SHP-1 to be 13.0 nm, which is longer than the estimate from the allosterically active structure (5.3 nm), suggesting that SHP-1 can achieve a longer reach by exploring multiple active conformations. Using modeling, we show that when uniformly distributed, receptor-SHP-1 complexes can only reach 15% of substrates, but this increases to 90% when they are coclustered. When within reach, we show that membrane recruitment increases the activity of SHP-1 by a 1000-fold increase in local concentration. The work highlights how molecular reach regulates the activity of membrane-recruited SHP-1 with insights applicable to other membrane-tethered reactions.

Intrinsic Disorder in the T Cell Receptor Creates Cooperativity and Controls ZAP70 Binding

Many immunoreceptors have cytoplasmic domains that are intrinsically disordered (i.e., have high configurational entropy), have multiple sites of posttranslational modification (e.g., tyrosine phosphorylation), and participate in nonlinear signaling pathways (e.g., exhibiting switch-like behavior). Several hypotheses to explain the origin of these nonlinearities fall under the broad hypothesis that modification at one site changes the immunoreceptor’s entropy, which in turn changes further modification dynamics. Here, we use coarse-grain simulation to study three scenarios, all related to the chains that constitute the T cell receptor (TCR). We find that first, if phosphorylation induces local changes in the flexibility of the TCR ζ-chain, this naturally leads to rate enhancements and cooperativity. Second, we find that TCR CD3ɛ can provide a switch by modulating its residence in the plasma membrane. By constraining our model to be consistent with the previous observation that both basic residues and phosphorylation control membrane residence, we find that there is only a moderate rate enhancement of 10% between first and subsequent phosphorylation events. Third, we find that volume constraints do not limit the number of ZAP70s that can bind the TCR but that entropic penalties lead to a 200-fold decrease in binding rate by the seventh ZAP70, potentially explaining the observation that each TCR has around six ZAP70 molecules bound after receptor triggering. In all three scenarios, our results demonstrate that phenomena that change an immunoreceptor chain’s entropy (stiffening, confinement to a membrane, and multiple simultaneous binding) can lead to nonlinearities (rate enhancement, switching, and negative cooperativity) in how the receptor participates in signaling. These polymer-entropy-driven nonlinearities may augment the nonlinearities that arise from, e.g., kinetic proofreading and cluster formation. They also suggest different design strategies for engineered receptors, e.g., whether or not to put signaling modules on one chain or multiple clustered chains.

Intrinsically disordered linkers control tethered kinases via effective concentration

Kinase specificity is crucial to the fidelity of signaling pathways, yet many pathways use the same kinases to achieve widely different effects. Specificity arises in part from the enzymatic domain but also from the physical tethering of kinases to their substrates. Such tethering can occur via protein interaction domains in the kinase or via anchoring and scaffolding proteins and can drastically increase the kinetics of phosphorylation. However, we do not know how such intracomplex reactions depend on the link between enzyme and substrate. Here we show that the kinetics of tethered kinases follow a Michaelis-Menten-like dependence on effective concentration. We find that phosphorylation kinetics scale with the length of the intrinsically disordered linkers that join the enzyme and substrate but that the scaling differs between substrates. Steady-state kinetics can only partially predict rates of tethered reactions as product release may obscure the rate of phosphotransfer. Our results suggest that changes in signaling complex architecture not only enhance the rates of phosphorylation reactions but may also alter the relative substrate usage. This suggests a mechanism for how scaffolding proteins can allosterically modify the output from a signaling pathway.

The Relationship between Effective Molarity and Affinity Governs Rate Enhancements in Tethered Kinase-Substrate Reactions

Scaffold proteins are thought to accelerate protein phosphorylation reactions by tethering kinases and substrates together, but there is little quantitative data on their functional effects. To assess the contribution of tethering to kinase reactivity, we compared intramolecular and intermolecular kinase reactions in a minimal model system. We found that tethering can enhance reaction rates in a flexible tethered kinase system and that the magnitude of the effect is sensitive to the structure of the tether. The largest effective molarity we obtained was ∼0.08 μM, which is much lower than the effects observed in small molecule model systems and other tethered protein reactions. We further demonstrated that the tethered intramolecular reaction only makes a significant contribution to the observed rates when the scaffolded complex assembles at concentrations below the effective molarity. These findings provide a quantitative framework that can be applied to understand endogenous protein scaffolds and engineer synthetic networks.

Proximity-induced caspase-9 activation on a DNA origami-based synthetic apoptosome

Living cells regulate key cellular processes by spatial organisation of catalytically active proteins in higher-order signalling complexes. These act as organising centres to facilitate proximity-induced activation and inhibition of multiple intrinsically weakly associating signalling components, which makes elucidation of the underlying protein-protein interactions challenging. Here we show that DNA origami nanostructures provide a programmable molecular platform for the systematic analysis of signalling proteins by engineering a synthetic DNA origami-based version of the apoptosome, a multi-protein complex that regulates apoptosis by co-localizing multiple caspase-9 monomers. Tethering of both wildtype and inactive caspase-9 variants to a DNA origami platform demonstrates that enzymatic activity is induced by proximity-driven dimerization with half-of-sites reactivity, and additionally, reveals a multivalent activity enhancement in oligomers of three and four enzymes. Our results offer fundamental insights in caspase-9 activity regulation and demonstrate that DNA origami-based protein assembly platforms have the potential to inform the function of other multi-enzyme complexes involved in inflammation, innate immunity and cell death.

The Influence of Molecular Reach and Diffusivity on the Efficacy of Membrane-Confined Reactions

Signaling by surface receptors often relies on tethered reactions whereby an enzyme bound to the cytoplasmic tail of a receptor catalyzes reactions on substrates within reach. The overall length and stiffness of the receptor tail, the enzyme, and the substrate determine a biophysical parameter termed the molecular reach of the reaction. This parameter determines the probability that the receptor-tethered enzyme will contact the substrate in the volume proximal to the membrane when separated by different distances within the membrane plane. In this work, we develop particle-based stochastic reaction-diffusion models to study the interplay between molecular reach and diffusion. We find that increasing the molecular reach can increase reaction efficacy for slowly diffusing receptors, whereas for rapidly diffusing receptors, increasing molecular reach reduces reaction efficacy. In contrast, if reactions are forced to take place within the two-dimensional plasma membrane instead of the three-dimensional volume proximal to it or if molecules diffuse in three dimensions, increasing molecular reach increases reaction efficacy for all diffusivities. We show results in the context of immune checkpoint receptors (PD-1 dephosphorylating CD28), a standard opposing kinase-phosphatase reaction, and a minimal two-particle model. The work highlights the importance of the three-dimensional nature of many two-dimensional membrane-confined interactions, illustrating a role for molecular reach in controlling biochemical reactions.

Calmodulin-Calcineurin Interaction beyond the Calmodulin-Binding Region Contributes to Calcineurin Activation

Calcineurin (CaN) is a calcium-dependent phosphatase involved in numerous signaling pathways. Its activation is in part driven by the binding of calmodulin (CaM) to a CaM recognition region (CaMBR) within CaN's regulatory domain (RD). However, secondary interactions between CaM and the CaN RD may be necessary to fully activate CaN. Specifically, it is established that the CaN RD folds upon CaM binding and a region C-terminal to CaMBR, the "distal helix", assumes an α-helix fold and contributes to activation [Dunlap, T. B., et al. (2013) Biochemistry 52, 8643-8651]. We hypothesized in that previous study that this distal helix can bind CaM in a region distinct from the canonical CaMBR. To test this hypothesis, we utilized molecular simulations, including replica-exchange molecular dynamics, protein-protein docking, and computational mutagenesis, to determine potential distal helix-binding sites on CaM's surface. We isolated a potential binding site on CaM (site D) that facilitates moderate-affinity interprotein interactions and predicted that mutation of site D residues K30 and G40 on CaM would weaken CaN distal helix binding. We experimentally confirmed that two variants (K30E and G40D) indicate weaker binding of a phosphate substrate p-nitrophenyl phosphate to the CaN catalytic site by a phosphatase assay. This weakened substrate affinity is consistent with competitive binding of the CaN autoinhibition domain to the catalytic site, which we suggest is due to the weakened distal helix-CaM interactions. This study therefore suggests a novel mechanism for CaM regulation of CaN that may extend to other CaM targets.

Combinatorial diversity of Syk recruitment driven by its multivalent engagement with FcεRIγ

Syk/Zap70 family kinases are essential for signaling via multichain immune-recognition receptors such as tetrameric (αβγ2) FcεRI. Syk activation is generally attributed to cis binding of its tandem SH2 domains to dual phosphotyrosines within FcεRIγ-ITAMs (immunoreceptor tyrosine-based activation motifs). However, the mechanistic details of Syk docking on γ homodimers are unresolved. Here, we estimate that multivalent interactions for WT Syk improve cis-oriented binding by three orders of magnitude. We applied molecular dynamics (MD), hybrid MD/worm-like chain polymer modeling, and live cell imaging to evaluate relative binding and signaling output for all possible cis and trans Syk-FcεRIγ configurations. Syk binding is likely modulated during signaling by autophosphorylation on Y130 in interdomain A, since a Y130E phosphomimetic form of Syk is predicted to lead to reduced helicity of interdomain A and alter Syk's bias for cis binding. Experiments in reconstituted γ-KO cells, whose γ subunits are linked by disulfide bonds, as well as in cells expressing monomeric ITAM or hemITAM γ-chimeras, support model predictions that short distances between γ ITAM pairs are required for trans docking. We propose that the full range of docking configurations improves signaling efficiency by expanding the combinatorial possibilities for Syk recruitment, particularly under conditions of incomplete ITAM phosphorylation.

The CaMKII inhibitor KN93-calmodulin interaction and implications for calmodulin tuning of NaV1.5 and RyR2 function

Here we report the structure of the widely utilized calmodulin (CaM)-dependent protein kinase II (CaMKII) inhibitor KN93 bound to the Ca²⁺-sensing protein CaM. KN93 is widely believed to inhibit CaMKII by binding to the kinase. The CaM-KN93 interaction is significant as it can interfere with the interaction between CaM and it's physiological targets, thereby raising the possibility of ascribing modified protein function to CaMKII phosphorylation while concealing a CaM-protein interaction. NMR spectroscopy, stopped-flow kinetic measurements, and x-ray crystallography were used to characterize the structure and biophysical properties of the CaM-KN93 interaction. We then investigated the functional properties of the cardiac Na⁺ channel (Na_V1.5) and ryanodine receptor (RyR2). We find that KN93 disrupts a high affinity CaM-Na_V1.5 interaction and alters channel function independent of CaMKII. Moreover, KN93 increases RyR2 Ca²⁺ release in cardiomyocytes independent of CaMKII. Therefore, when interpreting KN93 data, targets other than CaMKII need to be considered.

TnI Structural Interface with the N-Terminal Lobe of TnC as a Determinant of Cardiac Contractility

The heterotrimeric cardiac troponin complex is a key regulator of contraction and plays an essential role in conferring Ca²⁺ sensitivity to the sarcomere. During ischemic injury, rapidly accumulating protons acidify the myoplasm, resulting in markedly reduced Ca²⁺ sensitivity of the sarcomere. Unlike the adult heart, sarcomeric Ca²⁺ sensitivity in fetal cardiac tissue is comparatively pH insensitive. Replacement of the adult cardiac troponin I (cTnI) isoform with the fetal troponin I (ssTnI) isoform renders adult cardiac contractile machinery relatively insensitive to acidification. Alignment and functional studies have determined histidine 132 of ssTnI to be the predominant source of this pH insensitivity. Substitution of histidine at the cognate position 164 in cTnI confers the same pH insensitivity to adult cardiac myocytes. An alanine at position 164 of cTnI is conserved in all mammals, with the exception of the platypus, which expresses a proline. Prolines are biophysically unique because of their innate conformational rigidity and helix-disrupting function. To provide deeper structure-function insight into the role of the TnC-TnI interface in determining contractility, we employed a live-cell approach alongside molecular dynamics simulations to ascertain the chemo-mechanical implications of the disrupted helix 4 of cTnI where position 164 exists. This important motif belongs to the critical switch region of cTnI. Substitution of a proline at position 164 of cTnI in adult rat cardiac myocytes causes increased contractility independent of alterations in the Ca²⁺ transient. Free-energy perturbation calculations of cTnC-Ca²⁺ binding indicate no difference in cTnC-Ca²⁺ affinity. Rather, we propose the enhanced contractility is derived from new salt bridge interactions between cTnI helix 4 and cTnC helix A, which are critical in determining pH sensitivity and contractility. Molecular dynamics simulations demonstrate that cTnI A164P structurally phenocopies ssTnI under baseline but not acidotic conditions. These findings highlight the evolutionarily directed role of the TnI-cTnC interface in determining cardiac contractility.

Nature of the Pre-Chemistry Ensemble in Mitogen-Activated Protein Kinases

In spite of the availability of a significant amount of structural detail on docking interactions involving mitogen-activated protein kinases (MAPKs) and their substrates, the mechanism by which the disordered phospho-acceptor on the substrate transiently interacts with the kinase catalytic elements and is phosphorylated, often with high efficiency, remains poorly understood. Here, this dynamic interaction is analyzed in the context of available biophysical and biochemical data for ERK2, an archetypal MAPK. A hypothesis about the nature of the ternary complex involving a MAPK, its substrate, and ATP immediately prior to the chemical step (the pre-chemistry complex) is proposed. It is postulated that the solution ensemble (the pre-chemistry ensemble) representing the pre-chemistry complex comprises several conformations that are linked by dynamics on multiple timescales. These individual conformations possess different intrinsic abilities to proceed through the chemical step. The overall rate of chemistry is therefore related to the microscopic nature of the pre-chemistry ensemble, its constituent conformational microstates, and their intrinsic abilities to yield a phosphorylated product. While characterizing these microstates within the pre-chemistry ensemble in atomic or near-atomic detail is an extremely challenging proposition, recent developments in hybrid methodologies that employ computational approaches driven by experimental data appear to provide the most promising path forward toward achieving this goal.

Electrostatic control of calcineurin's intrinsically-disordered regulatory domain binding to calmodulin

Calcineurin (CaN) is a serine/threonine phosphatase that regulates a variety of physiological and pathophysiological processes in mammalian tissue. The calcineurin (CaN) regulatory domain (RD) is responsible for regulating the enzyme's phosphatase activity, and is believed to be highly-disordered when inhibiting CaN, but undergoes a disorder-to-order transition upon diffusion-limited binding with the regulatory protein calmodulin (CaM). The prevalence of polar and charged amino acids in the regulatory domain (RD) suggests electrostatic interactions are involved in mediating calmodulin (CaM) binding, yet the lack of atomistic-resolution data for the bound complex has stymied efforts to probe how the RD sequence controls its conformational ensemble and long-range attractions contribute to target protein binding. In the present study, we investigated via computational modeling the extent to which electrostatics and structural disorder facilitate CaM/CaN association kinetics. Specifically, we examined several RD constructs that contain the CaM binding region (CAMBR) to characterize the roles of electrostatics versus conformational diversity in controlling diffusion-limited association rates, via microsecond-scale molecular dynamics (MD) and Brownian dynamic (BD) simulations. Our results indicate that the RD amino acid composition and sequence length influence both the dynamic availability of conformations amenable to CaM binding, as well as long-range electrostatic interactions to steer association. These findings provide intriguing insight into the interplay between conformational diversity and electrostatically-driven protein-protein association involving CaN, which are likely to extend to wide-ranging diffusion-limited processes regulated by intrinsically-disordered proteins.

Quantifying the strength of quorum sensing crosstalk within microbial communities

In multispecies microbial communities, the exchange of signals such as acyl-homoserine lactones (AHL) enables communication within and between species of Gram-negative bacteria. This process, commonly known as quorum sensing, aids in the regulation of genes crucial for the survival of species within heterogeneous populations of microbes. Although signal exchange was studied extensively in well-mixed environments, less is known about the consequences of crosstalk in spatially distributed mixtures of species. Here, signaling dynamics were measured in a spatially distributed system containing multiple strains utilizing homologous signaling systems. Crosstalk between strains containing the lux, las and rhl AHL-receptor circuits was quantified. In a distributed population of microbes, the impact of community composition on spatio-temporal dynamics was characterized and compared to simulation results using a modified reaction-diffusion model. After introducing a single term to account for crosstalk between each pair of signals, the model was able to reproduce the activation patterns observed in experiments. We quantified the robustness of signal propagation in the presence of interacting signals, finding that signaling dynamics are largely robust to interference. The ability of several wild isolates to participate in AHL-mediated signaling was investigated, revealing distinct signatures of crosstalk for each species. Our results present a route to characterize crosstalk between species and predict systems-level signaling dynamics in multispecies communities.

Multisite Phosphorylation Modulates the T Cell Receptor ζ-Chain Potency but not the Switchlike Response

Multisite phosphorylation is ubiquitous in cellular signaling and is thought to provide signaling proteins with additional regulatory mechanisms. Indeed, mathematical models have revealed a large number of mechanisms by which multisite phosphorylation can produce switchlike responses. The T cell antigen receptor (TCR) is a multisubunit receptor on the surface of T cells that is a prototypical multisite substrate as it contains 20 sites that are distributed on 10 conserved immunoreceptor tyrosine-based activation motifs (ITAMs). The TCR ζ-chain is a homodimer subunit that contains six ITAMs (12 sites) and exhibits a number of properties that are predicted to be sufficient for a switchlike response. We have used cellular reconstitution to systematically study multisite phosphorylation of the TCR ζ-chain. We find that multisite phosphorylation proceeds by a nonsequential random mechanism, and find no evidence that multiple ITAMs modulate a switchlike response but do find that they alter receptor potency and maximum phosphorylation. Modulation of receptor potency can be explained by a reduction in molecular entropy of the disordered ζ-chain upon phosphorylation. We further find that the tyrosine kinase ZAP-70 increases receptor potency but does not modulate the switchlike response. In contrast to other multisite proteins, where phosphorylations act in strong concert to modulate protein function, we suggest that the multiple ITAMs on the TCR function mainly to amplify subsequent signaling.

Optimal Affinity Enhancement by a Conserved Flexible Linker Controls p53 Mimicry in MdmX

MdmX contains an intramolecular binding motif that mimics the binding of the p53 tumor suppressor. This intramolecular binding motif is connected to the p53 binding domain of MdmX by a conserved flexible linker that is 85 residues long. The sequence of this flexible linker has an identity of 51% based on multiple protein sequence alignments of 52 MdmX homologs. We used polymer statistics to estimate a global K_D value for p53 binding to MdmX in the presence of the flexible linker and the intramolecular binding motif by assuming the flexible linker behaves as a wormlike chain. The global K_D estimated from the wormlike chain modeling was nearly identical to the value measured using isothermal titration calorimetry. According to our calculations and measurements, the intramolecular binding motif reduces the apparent affinity of p53 for MdmX by a factor of 400. This study promotes a more quantitative understanding of the role that flexible linkers play in intramolecular binding and provides valuable information to further studies of cellular inhibition of the p53/MdmX interaction.

Biophysical assay for tethered signaling reactions reveals tether-controlled activity for the phosphatase SHP-1

Tethered enzymatic reactions are ubiquitous in signaling networks but are poorly understood. A previously unreported mathematical analysis is established for tethered signaling reactions in surface plasmon resonance (SPR). Applying the method to the phosphatase SHP-1 interacting with a phosphorylated tether corresponding to an immune receptor cytoplasmic tail provides five biophysical/biochemical constants from a single SPR experiment: two binding rates, two catalytic rates, and a reach parameter. Tether binding increases the activity of SHP-1 by 900-fold through a binding-induced allosteric activation (20-fold) and a more significant increase in local substrate concentration (45-fold). The reach parameter indicates that this local substrate concentration is exquisitely sensitive to receptor clustering. We further show that truncation of the tether leads not only to a lower reach but also to lower binding and catalysis. This work establishes a new framework for studying tethered signaling processes and highlights the tether as a control parameter in clustered receptor signaling.

Myofilament Calcium Sensitivity: Consequences of the Effective Concentration of Troponin I

Control of calcium binding to and dissociation from cardiac troponin C (TnC) is essential to healthy cardiac muscle contraction/relaxation. There are numerous aberrant post-translational modifications and mutations within a plethora of contractile, and even non-contractile, proteins that appear to imbalance this delicate relationship. The direction and extent of the resulting change in calcium sensitivity is thought to drive the heart toward one type of disease or another. There are a number of molecular mechanisms that may be responsible for the altered calcium binding properties of TnC, potentially the most significant being the ability of the regulatory domain of TnC to bind the switch peptide region of TnI. Considering TnI is essentially tethered to TnC and cannot diffuse away in the absence of calcium, we suggest that the apparent calcium binding properties of TnC are highly dependent upon an “effective concentration” of TnI available to bind TnC. Based on our previous work, TnI peptide binding studies and the calcium binding properties of chimeric TnC-TnI fusion constructs, and building upon the concept of effective concentration, we have developed a mathematical model that can simulate the steady-state and kinetic calcium binding properties of a wide assortment of disease-related and post-translational protein modifications in the isolated troponin complex and reconstituted thin filament. We predict that several TnI and TnT modifications do not alter any of the intrinsic calcium or TnI binding constants of TnC, but rather alter the ability of TnC to “find” TnI in the presence of calcium. These studies demonstrate the apparent consequences of the effective TnI concentration in modulating the calcium binding properties of TnC.

Computational simulation of formin-mediated actin polymerization predicts homologue-dependent mechanosensitivity

Many actin structures are nucleated and assembled by the barbed-end tracking polymerase formin family, including filopodia, focal adhesions, the cytokinetic ring and cell cortex. These structures respond to forces in distinct ways. Formins typically have profilin-actin binding sites embedded in highly flexible disordered FH1 domains, hypothesized to diffusively explore space to rapidly capture actin monomers for delivery to the barbed end. Recent experiments demonstrate that formin-mediated polymerization accelerates when under tension. The acceleration has been attributed to modifying the state of the FH2 domain of formin. Intriguingly, the same acceleration is reported when tension is applied to the FH1 domains, ostensibly pulling monomers away from the barbed end. Here we develop a mesoscale coarse-grain model of formin-mediated actin polymerization, including monomer capture and delivery by FH1, which sterically interacts with actin along its entire length. The binding of actin monomers to their specific sites on FH1 is entropically disfavored by the high disorder. We find that this penalty is attenuated when force is applied to the FH1 domain by revealing the binding site, increasing monomer capture efficiency. Overall polymerization rates can decrease or increase with increasing force, depending on the length of FH1 domain and location of binding site. Our results suggest that the widely varying FH1 lengths and binding site locations found in known formins could be used to differentially respond to force, depending on the actin structure being assembled. © 2016 Wiley Periodicals, Inc.

Interplay of Protein Binding Interactions, DNA Mechanics, and Entropy in DNA Looping Kinetics

DNA looping plays a key role in many fundamental biological processes, including gene regulation, recombination, and chromosomal organization. The looping of DNA is often mediated by proteins whose structural features and physical interactions can alter the length scale at which the looping occurs. Looping and unlooping processes are controlled by thermodynamic contributions associated with mechanical deformation of the DNA strand and entropy arising from thermal fluctuations of the conformation. To determine how these confounding effects influence DNA looping and unlooping kinetics, we present a theoretical model that incorporates the role of the protein interactions, DNA mechanics, and conformational entropy. We show that for shorter DNA strands the interaction distance affects the transition state, resulting in a complex relationship between the looped and unlooped state lifetimes and the physical properties of the looped DNA. We explore the range of behaviors that arise with varying interaction distance and DNA length. These results demonstrate how DNA deformation and entropy dictate the scaling of the looping and unlooping kinetics versus the J-factor, establishing the connection between kinetic and equilibrium behaviors. Our results show how the twist-and-bend elasticity of the DNA chain modulates the kinetics and how the influence of the interaction distance fades away at intermediate to longer chain lengths, in agreement with previous scaling predictions.

Modulation of DNA loop lifetimes by the free energy of loop formation

Storage and retrieval of the genetic information in cells is a dynamic process that requires the DNA to undergo dramatic structural rearrangements. DNA looping is a prominent example of such a structural rearrangement that is essential for transcriptional regulation in both prokaryotes and eukaryotes, and the speed of such regulations affects the fitness of individuals. Here, we examine the in vitro looping dynamics of the classic Lac repressor gene-regulatory motif. We show that both loop association and loop dissociation at the DNA-repressor junctions depend on the elastic deformation of the DNA and protein, and that both looping and unlooping rates approximately scale with the looping J factor, which reflects the system's deformation free energy. We explain this observation by transition state theory and model the DNA-protein complex as an effective worm-like chain with twist. We introduce a finite protein-DNA binding interaction length, in competition with the characteristic DNA deformation length scale, as the physical origin of the previously unidentified loop dissociation dynamics observed here, and discuss the robustness of this behavior to perturbations in several polymer parameters.

Structural insights into the lipoprotein outer membrane regulator of penicillin-binding protein 1B

In bacteria, the synthesis of the protective peptidoglycan sacculus is a dynamic process that is tightly regulated at multiple levels. Recently, the lipoprotein co-factor LpoB has been found essential for the in vivo function of the major peptidoglycan synthase PBP1b in Enterobacteriaceae. Here, we reveal the crystal structures of Salmonella enterica and Escherichia coli LpoB. The LpoB protein can be modeled as a ball and tether, consisting of a disordered N-terminal region followed by a compact globular C-terminal domain. Taken together, our structural data allow us to propose new insights into LpoB-mediated regulation of peptidoglycan synthesis.

Do GGA adaptors bind internal DXXLL motifs?

The GGA family of clathrin adaptor proteins mediates the intracellular trafficking of transmembrane proteins by interacting with DXXLL-type sorting signals on the latter. These signals were originally identified at the carboxy-termini of the transmembrane cargo proteins. Subsequent studies, however, showed that internal DXXLL sorting motifs occur within the N- or C-terminal cytoplasmic domains of cargo molecules. The GGAs themselves also contain internal DXXLL motifs that serve to auto-regulate GGA function. A recent study challenged the notion that internal DXXLL signals are competent for binding to GGAs. Since the question of whether GGA adaptors interact with internal DXXLL motifs is fundamental to the identification of bona fide GGA cargo, and to an accurate understanding of GGA regulation within cells, we have extended our previous findings. We now present additional evidence confirming that GGAs do interact with internal DXXLL motifs. We also summarize the recent reports from other laboratories documenting internal GGA binding motifs.

A novel dimerization interface of cyclic nucleotide binding domain, which is disrupted in presence of cAMP: implications for CNG channels gating

Cyclic nucleotide binding domain (CNBD) is a ubiquitous domain of effector proteins involved in signalling cascades of prokaryota and eukaryota. CNBD activation by cyclic nucleotide monophosphate (cNMP) is studied well in the case of several proteins. However, this knowledge is hardly applicable to cNMP-modulated cation channels. Despite the availability of CNBD crystal structures of bacterial cyclic nucleotide-gated (CNG) and mammalian hyperpolarization-activated cyclic nucleotide-modulated (HCN) channels in presence and absence of the cNMP, the full understanding of CNBD conformational changes during activation is lacking. Here, we describe a novel CNBD dimerization interface found in crystal structures of bacterial CNG channel MlotiK1 and mammalian cAMP-activated guanine nucleotide-exchange factor Epac2. Molecular dynamics simulations show that the found interface is stable on the studied timescale of 100 ns, in contrast to the dimerization interface, reported previously. Comparisons with cN-bound structures of CNBD show that the dimerization is incompatible with cAMP binding. Thus, the cAMP-dependent monomerization of CNBD may be an alternative mechanism of the cAMP sensing. Based on these findings, we propose a model of the bacterial CNG channel modulation by cAMP.

Quantifying intramolecular binding in multivalent interactions: a structure-based synergistic study on Grb2-Sos1 complex

Numerous signaling proteins use multivalent binding to increase the specificity and affinity of their interactions within the cell. Enhancement arises because the effective binding constant for multivalent binding is larger than the binding constants for each individual interaction. We seek to gain both qualitative and quantitative understanding of the multivalent interactions of an adaptor protein, growth factor receptor bound protein-2 (Grb2), containing two SH3 domains interacting with the nucleotide exchange factor son-of-sevenless 1 (Sos1) containing multiple polyproline motifs separated by flexible unstructured regions. Grb2 mediates the recruitment of Sos1 from the cytosol to the plasma membrane where it activates Ras by inducing the exchange of GDP for GTP. First, using a combination of evolutionary information and binding energy calculations, we predict an additional polyproline motif in Sos1 that binds to the SH3 domains of Grb2. This gives rise to a total of five polyproline motifs in Sos1 that are capable of binding to the two SH3 domains of Grb2. Then, using a hybrid method combining molecular dynamics simulations and polymer models, we estimate the enhancement in local concentration of a polyproline motif on Sos1 near an unbound SH3 domain of Grb2 when its other SH3 domain is bound to a different polyproline motif on Sos1. We show that the local concentration of the Sos1 motifs that a Grb2 SH3 domain experiences is approximately 1000 times greater than the cellular concentration of Sos1. Finally, we calculate the intramolecular equilibrium constants for the crosslinking of Grb2 on Sos1 and use thermodynamic modeling to calculate the stoichiometry. With these equilibrium constants, we are able to predict the distribution of complexes that form at physiological concentrations. We believe this is the first systematic analysis that combines sequence, structure, and thermodynamic analyses to determine the stoichiometry of the complexes that are dominant in the cellular environment.

Regulation of biochemical reaction rates by flexible tethers

We explore how ligand-receptor binding kinetics can be controlled by tethering the receptor to the end of a flexible polymer. The tether confines the diffusive motion of the receptor thus influencing the rate at which it captures ligands that are free in solution. We compute steady-state collision rates between ligand and receptor for this "tethered-capture" mechanism using a combination of analytic and numerical techniques. In doing so, we uncover a dimensionless control parameter, the "opacity," that determines under what conditions and to what extent a tether regulates the ligand-receptor collision rate. We compute the opacity for a number of different tethering scenarios that appear in biology and use these results to predict the affect of changing the length and flexibility of the tether on the rate at which ligands are captured from solution.

Thermodynamics of biological processes

There is a long and rich tradition of using ideas from both equilibrium thermodynamics and its microscopic partner theory of equilibrium statistical mechanics. In this chapter, we provide some background on the origins of the seemingly unreasonable effectiveness of ideas from both thermodynamics and statistical mechanics in biology. After making a description of these foundational issues, we turn to a series of case studies primarily focused on binding that are intended to illustrate the broad biological reach of equilibrium thinking in biology. These case studies include ligand-gated ion channels, thermodynamic models of transcription, and recent applications to the problem of bacterial chemotaxis. As part of the description of these case studies, we explore a number of different uses of the famed Monod-Wyman-Changeux (MWC) model as a generic tool for providing a mathematical characterization of two-state systems. These case studies should provide a template for tailoring equilibrium ideas to other problems of biological interest.