Kinetic Proofreading Research Articles

Trade-offs and thermodynamics of energy-relay proofreading.

Biological processes that are able to discriminate between different molecules consume energy and dissipate heat, using a mechanism known as proofreading. In this work, we thoroughly analyse the thermodynamic properties of one of the most important proofreading mechanisms, namely Hopfield's energy-relay proofreading. We discover several trade-off relations and scaling laws between several kinetic and thermodynamic observables. These trade-off relations are obtained both analytically and numerically through Pareto optimal fronts. We show that the scheme is able to operate in three distinct regimes: an energy-relay regime, a mixed relay-Michaelis-Menten (MM) regime and a Michaelis-Menten regime, depending on the kinetic and energetic parameters that tune transitions between states. The mixed regime features a dynamical phase transition in the error-entropy production Pareto trade-off, while the pure energy-relay regime contains a region where this type of proofreading energetically outperforms standard kinetic proofreading.

Crossing the Halfway Point: Aptamer-Based, Highly Multiplexed Assay for the Assessment of the Proteome.

Measuring responses in the proteome to various perturbations improves our understanding of biological systems. The value of information gained from such studies is directly proportional to the number of proteins measured. To overcome technical challenges associated with highly multiplexed measurements, we developed an affinity reagent-based method that uses aptamers with protein-like side chains along with an assay that takes advantage of their unique properties. As hybrid affinity reagents, modified aptamers are fully comparable to antibodies in terms of binding characteristics toward proteins, including epitope size, shape complementarity, affinity and specificity. Our assay combines these intrinsic binding properties with serial kinetic proofreading steps to allow highly effective partitioning of stable specific complexes from unstable nonspecific complexes. The use of these orthogonal methods to enhance specificity effectively overcomes the severe limitation to multiplexing inherent to the use of sandwich-based methods. Our assay currently measures half of the unique proteins encoded in the human genome with femtomolar sensitivity, broad dynamic range and exceptionally high reproducibility. Using machine learning to identify patterns of change, we have developed tests based on measurement of multiple proteins predictive of current health states and future disease risk to guide a holistic approach to precision medicine.

REAL-TIME VISUALIZATION OF SPLICEOSOME ASSEMBLY REVEALS BASIC PRINCIPLES OF SPLICE SITE SELECTION.

We apply a kinetic proofreading model to elucidate how transient U2AF binding leads to high fidelity splice site selection.

Kinetic Proofreading Can Enhance Specificity in a Nonenzymatic DNA Strand Displacement Network.

Kinetic proofreading is used throughout natural systems to enhance the specificity of molecular recognition. At its most basic level, kinetic proofreading uses a supply of chemical fuel to drive a recognition interaction out of equilibrium, allowing a single free-energy difference between correct and incorrect targets to be exploited two or more times. Despite its importance in biology, there has been little effort to incorporate kinetic proofreading into synthetic systems in which molecular recognition is important, such as nucleic acid nanotechnology. In this article, we introduce a DNA strand displacement-based kinetic proofreading motif, showing that the consumption of a DNA-based fuel can be used to enhance molecular recognition during a templated dimerization reaction. We then show that kinetic proofreading can enhance the specificity with which a probe discriminates single nucleotide mutations, both in terms of the initial rate with which the probe reacts and the long-time behavior.

Thermodynamic Bounds on Symmetry Breaking in Linear and Catalytic Biochemical Systems.

Living systems are maintained out of equilibrium by external driving forces. At stationarity, they exhibit emergent selection phenomena that break equilibrium symmetries and originate from the expansion of the accessible chemical space due to nonequilibrium conditions. Here, we use the matrix-tree theorem to derive upper and lower thermodynamic bounds on these symmetry-breaking features in linear and catalytic biochemical systems. Our bounds are independent of the kinetics and hold for both closed and open reaction networks. We also extend our results to master equations in the chemical space. Using our framework, we recover the thermodynamic constraints in kinetic proofreading. Finally, we show that the contrast of reaction-diffusion patterns can be bounded only by the nonequilibrium driving force. Our results provide a general framework for understanding the role of nonequilibrium conditions in shaping the steady-state properties of biochemical systems.

Reversible Kinetics in Multi-nucleotide Addition Catalyzed by S. cerevisiae RNA polymerase II Reveal Slow Pyrophosphate Release

Eukaryotes express at least three nuclear DNA dependent RNA polymerases (Pols). Pols I, II, and III synthesize ribosomal (r) RNA, messenger (m) RNA, and transfer (t) RNA, respectively. Pol I and Pol III have intrinsic nuclease activity conferred by the A12.2 and C11 subunits, respectively. In contrast, Pol II requires the transcription factor (TF) IIS to confer robust nuclease activity. We recently reported that in the absence of the A12.2 subunit Pol I reverses bond formation by pyrophosphorolysis in the absence of added PPi, indicating slow PPi release. Thus, we hypothesized that Pol II, naturally lacking TFIIS, would reverse bond formation through pyrophosphorolysis. Here we report the results of transient-state kinetic experiments to examine the addition of nine nucleotides to a growing RNA chain catalyzed by Pol II. Our results indicate that Pol II reverses bond formation by pyrophosphorolysis in the absence of added PPi. We propose that, in the absence of endonuclease activity, this bond reversal may represent kinetic proofreading. Thus, given the hypothesis that Pol I evolved from Pol II through the incorporation of general transcription factors, pyrophosphorolysis may represent a more ancient form of proofreading that has been evolutionarily replaced with nuclease activity.

Universal thermodynamic bounds on the Fano factor of discriminatory networks with unidirectional transitions

We derive a universal lower bound on the Fano factors of general biochemical discriminatory networks involving irreversible catalysis steps, based on the thermodynamic uncertainty relation, and compare it to a numerically exact Pareto optimal front. This bound is completely general, involving only the reversible entropy production per product formed and the error fraction of the system. We then show that by judiciously choosing which transitions to include in the reversible entropy production, one can derive a family of bounds that can be fine-tuned to include physical observables at hand. Lastly, we test our bound by considering three discriminatory schemes: a multi-stage Michaelis-Menten network, a Michaelis-Menten network with correlations between subsequent products, and a multi-stage kinetic proofreading network, where for the latter application the bound is altered to include the hydrolytic cost of the proofreading steps. We find that our bound is remarkably tight.

Quantitative Analysis of Therapeutic Antibody Interactions with Fcγ Receptors Using High-Speed Atomic Force Microscopy.

This study employed high-speed atomic force microscopy to quantitatively analyze the interactions between therapeutic antibodies and Fcγ receptors (FcγRs). Antibodies are essential components of the immune system and are integral to biopharmaceuticals. The focus of this study was on immunoglobulin G molecules, which are crucial for antigen binding via the Fab segments and cytotoxic functions through their Fc portions. We conducted real-time, label-free observations of the interactions of rituximab and mogamulizumab with the recombinant FcγRIIIa and FcγRIIa. The dwell times of FcγR binding were measured at the single-molecule level, which revealed an extended interaction duration of mogamulizumab with FcγRIIIa compared with that of rituximab. This is linked to enhanced antibody-dependent cellular cytotoxicity that is attributed to the absence of the core fucosylation of Fc-linked N-glycan. This study also emphasizes the crucial role of the Fab segments in the interaction with FcγRIIa as well as that with FcγRIIIa. This approach provided quantitative insight into therapeutic antibody interactions and exemplified kinetic proofreading, where cellular discrimination relies on ligand residence times. Observing the dwell times of antibodies on the effector molecules has emerged as a robust indicator of therapeutic antibody efficacy. Ultimately, these findings pave the way for the development of refined therapeutic antibodies with tailored interactions with specific FcγRs. This research contributes to the advancement of biopharmaceutical antibody design and optimizing antibody-based treatments for enhanced efficacy and precision.

Mathematical models of TCR initial triggering.

T cell receptors (TCRs) play crucial roles in regulating T cell response by rapidly and accurately recognizing foreign and non-self antigens. The process involves multiple molecules and regulatory mechanisms, forming a complex network to achieve effective antigen recognition. Mathematical modeling techniques can help unravel the intricate network of TCR signaling and identify key regulators that govern it. In this review, we introduce and briefly discuss relevant mathematical models of TCR initial triggering, with a focus on kinetic proofreading (KPR) models with different modified structures. We compare the topology structures, biological hypotheses, parameter choices, and simulation performance of each model, and summarize the advantages and limitations of them. Further studies on TCR modeling design, aiming for an optimized balance of specificity and sensitivity, are expected to contribute to the development of new therapeutic strategies.

Modulation of antigen discrimination by duration of immune contacts in a kinetic proofreading model of T cell activation with extreme statistics.

T cells form transient cell-to-cell contacts with antigen presenting cells (APCs) to facilitate surface interrogation by membrane bound T cell receptors (TCRs). Upon recognition of molecular signatures (antigen) of pathogen, T cells may initiate an adaptive immune response. The duration of the T cell/APC contact is observed to vary widely, yet it is unclear what constructive role, if any, such variations might play in immune signaling. Modeling efforts describing antigen discrimination often focus on steady-state approximations and do not account for the transient nature of cellular contacts. Within the framework of a kinetic proofreading (KP) mechanism, we develop a stochastic First Receptor Activation Model (FRAM) describing the likelihood that a productive immune signal is produced before the expiry of the contact. Through the use of extreme statistics, we characterize the probability that the first TCR triggering is induced by a rare agonist antigen and not by that of an abundant self-antigen. We show that defining positive immune outcomes as resilience to extreme statistics and sensitivity to rare events mitigates classic tradeoffs associated with KP. By choosing a sufficient number of KP steps, our model is able to yield single agonist sensitivity whilst remaining non-reactive to large populations of self antigen, even when self and agonist antigen are similar in dissociation rate to the TCR but differ largely in expression. Additionally, our model achieves high levels of accuracy even when agonist positive APCs encounters are rare. Finally, we discuss potential biological costs associated with high classification accuracy, particularly in challenging T cell environments.

Quantitative modeling of EGF receptor ligand discrimination via internalization proofreading.

The epidermal growth factor receptor (EGFR) is a central regulator of cell physiology that is stimulated by multiple distinct ligands. Although ligands bind to EGFR while the receptor is exposed on the plasma membrane, EGFR incorporation into endosomes following receptor internalization is an important aspect of EGFR signaling, with EGFR internalization behavior dependent upon the type of ligand bound. We develop quantitative modeling for EGFR recruitment to and internalization from clathrin domains, focusing on how internalization competes with ligand unbinding from EGFR. We develop two model versions: a kinetic model with EGFR behavior described as transitions between discrete states and a spatial model with EGFR diffusion to circular clathrin domains. We find that a combination of spatial and kinetic proofreading leads to enhanced EGFR internalization ratios in comparison to unbinding differences between ligand types. Various stages of the EGFR internalization process, including recruitment to and internalization from clathrin domains, modulate the internalization differences between receptors bound to different ligands. Our results indicate that following ligand binding, EGFR may encounter multiple clathrin domains before successful recruitment and internalization. The quantitative modeling we have developed describes competition between EGFR internalization and ligand unbinding and the resulting proofreading.

The importance of proteasome grip depends on substrate stability

The 26S proteasome is responsible for the unfolding and degradation of intracellular proteins in eukaryotes. A hexameric ring of ATPases (Rpt1-Rpt6) grabs onto substrates and unfolds them by pulling them through a central pore and translocating them into the 20S degradation chamber. A set of pore loops containing a so-called aromatic paddle motif in each Rpt subunit is believed to be important for the proteasome's ability to unfold and translocate substrates. Based on structural and mechanistic experiments, paddles from adjacent Rpt subunits, which are arrayed in a spiral staircase conformation, grip and pull on the substrate in a hand-over-hand type mechanism, disengaging at the bottom of the staircase and re-engaging at the top. We tested the contribution of the aromatic paddles to unfolding substrates of differing stabilities by mutating the paddles singly or in combination. For an easy-to-unfold substrate (a circular permutant of green fluorescent protein; GFP), mutations had little effect on degradation rates. For a substrate with moderate stability (enhanced GFP), there were modest effects of individual mutations on GFP unfolding rates, and alternating aromatic paddle mutants had a larger detrimental effect on unfolding than sequential mutants. For a more stable substrate (superfolder GFP), unfolding is overall slower, and multiple simultaneous mutations essentially prevent unfolding. Our results highlight the context-dependent need for grip during unfolding, support the hand-over-hand model for substrate unfolding and translocation, and suggest that for hard-to-unfold substrates, it is important to have simultaneous strong contacts to the substrate for unfolding to occur. The results also suggest a kinetic proofreading model, where substrates that cannot be easily unfolded are instead clipped, removing the initiation region and preventing futile unfolding attempts.

A dynamic biomimetic model of the membrane-bound CD4-CD3-TCR complex during pMHC disengagement

The coordinated (dis)engagement of the membrane-bound T cell receptor (TCR)-CD3-CD4 complex from the peptide-major histocompatibility complex (pMHC) is fundamental to TCR signal transduction and T cell effector function. As such, an atomic-scale understanding would not only enhance our basic understanding of the adaptive immune response but would also accelerate the rational design of TCRs for immunotherapy. In this study, we explore the impact of the CD4 coreceptor on the TCR-pMHC (dis)engagement by constructing a molecular-level biomimetic model of the CD3-TCR-pMHC and CD4-CD3-TCR-pMHC complexes within a lipid bilayer. After allowing the system complexes to equilibrate (engage), we use steered molecular dynamics to dissociate (disengage) the pMHC. We find that 1) the CD4 confines the pMHC closer to the T cell by 1.8 nm at equilibrium; 2) CD4 confinement shifts the TCR along the MHC binding groove engaging a different set of amino acids and enhancing the TCR-pMHC bond lifetime; 3) the CD4 translocates under load increasing the interaction strength between the CD4-pMHC, CD4-TCR, and CD4-CD3; and 4) upon dissociation, the CD3-TCR complex undergoes structural oscillation and increased energetic fluctuation between the CD3-TCR and CD3-lipids. These atomic-level simulations provide mechanistic insight on how the CD4 coreceptor impacts TCR-pMHC (dis)engagement. More specifically, our results provide further support (enhanced bond lifetime) for a force-dependent kinetic proofreading model and identify an alternate set of amino acids in the TCR that dominate the TCR-pMHC interaction and could thus impact the design of TCRs for immunotherapy.

Proofreading does not result in more reliable ligand discrimination in receptor signaling due to its inherent stochasticity

Kinetic proofreading (KPR) has been used as a paradigmatic explanation for the high specificity of ligand discrimination by cellular receptors. KPR enhances the difference in the mean receptor occupancy between different ligands compared to a nonproofread receptor, thus potentially enabling better discrimination. On the other hand, proofreading also attenuates the signal and introduces additional stochastic receptor transitions relative to a nonproofreading receptor. This increases the relative magnitude of noise in the downstream signal, which can interfere with reliable ligand discrimination. To understand the effect of noise on ligand discrimination beyond the comparison of the mean signals, we formulate the task of ligand discrimination as a problem of statistical estimation of the receptor affinity of ligands based on the molecular signaling output. Our analysis reveals that proofreading typically worsens ligand resolution compared to a nonproofread receptor. Furthermore, the resolution decreases further with more proofreading steps under most commonly biologically considered conditions. This contrasts with the usual notion that KPR universally improves ligand discrimination with additional proofreading steps. Our results are consistent across a variety of different proofreading schemes and metrics of performance, suggesting that they are inherent to the KPR mechanism itself rather than any particular model of molecular noise. Based on our results, we suggest alternative roles for KPR schemes such as multiplexing and combinatorial encoding in multi-ligand/multi-output pathways.

TCR/Chimeric Antigen Receptor (CAR) Cross-Antagonism to Fine-Tune CAR-T cell Immunotherapy

Abstract Chimeric antigen receptor (CAR) T cells, are created by extracting T cells from a cancer patient, engineering them to express a CAR targeting a tumor specific molecule, then reintroducing them back into the patient. A patient’s T cells contain their own endogenous T cell receptors (TCRs) however, which could potentially interact with the exogenous CAR inserted into the cell. In this study, we examine how TCR and CAR signals interact upon CAR-T activation. We show that weak TCR stimulation can reduce (antagonize) or increase overall CAR-T response, both in vitro and in vivo, across multiple tumor models, in both mouse and human T cells. We further show that the behavior of these TCR/CAR interactions can be manipulated by changing various characteristics of the TCR, CAR, and associated ligands. While this behavior is complex, we show that it can be described by a single mathematical model based on the adaptive kinetic proofreading scheme of ligand discrimination. We conclude by presenting potential applications for cancer immunotherapy. Intramural Research Program of the National Cancer Institute

Pareto optimal fronts of kinetic proofreading

Biological processes such as DNA replication, RNA transcription, and protein translation operate with remarkable speed and accuracy in selecting the right substrate from pools of chemically identical molecules. This result is obtained by non-equilibrium reactions that dissipate chemical energy. It is widely recognized that there must be a trade-off between speed, error, and dissipation characterizing these systems. In this paper, we quantify this trade-off using tools from mathematical optimization theory. We characterize the Pareto optimal front for a generalized version of Hopfield’s kinetic proofreading model, which is a paradigmatic example of biological error correction. We find that models with more proofreading steps are characterized by better trade-offs. Furthermore, we numerically study scaling relations between speed, accuracy, and dissipation on the Pareto front.

A single-amino acid substitution in the adaptor LAT accelerates TCR proofreading kinetics and alters T-cell selection, maintenance and function

Mature T cells must discriminate between brief interactions with self-peptides and prolonged binding to agonists. The kinetic proofreading model posits that certain T-cell antigen receptor signaling nodes serve as molecular timers to facilitate such discrimination. However, the physiological significance of this regulatory mechanism and the pathological consequences of disrupting it are unknown. Here we report that accelerating the normally slow phosphorylation of the linker for activation of T cells (LAT) residue Y136 by introducing an adjacent Gly135Asp alteration (LATG135D) disrupts ligand discrimination in vivo. The enhanced self-reactivity of LATG135D T cells triggers excessive thymic negative selection and promotes T-cell anergy. During Listeria infection, LATG135D T cells expand more than wild-type counterparts in response to very weak stimuli but display an imbalance between effector and memory responses. Moreover, despite their enhanced engagement of central and peripheral tolerance mechanisms, mice bearing LATG135D show features associated with autoimmunity and immunopathology. Our data reveal the importance of kinetic proofreading in balancing tolerance and immunity.

Graphical characterizations of robust stability in biological interaction networks

Previous studies have inferred robust stability of reaction networks by utilizing linear programs or iterative algorithms. Such algorithms become tedious or computationally infeasible for large networks. In addition, they operate like black boxes without offering intuition for the structures that are necessary to maintain stability. In this work, we provide several graphical criteria for constructing robust stability certificates, checking robust non-degeneracy, verifying persistence, and establishing global stability. By characterizing a set of stability-preserving graph modifications that includes the enzymatic modification motif, we show that the stability of arbitrarily large nonlinear networks can be examined by simple visual inspection. We show applications of this technique to ubiquitous motifs in systems biology such as post-translational modification (PTM) cycles, the ribosome flow model (RFM), T-cell kinetic proofreading, and others. The results of this paper are dedicated in honor of Eduardo D. Sontag’s seventieth birthday and his pioneering work in nonlinear dynamical systems and mathematical systems biology.

Avoidance of error catastrophe via proofreading innate to template-directed polymerization

An important issue for the origins of life is ensuring the accurate maintenance of information in replicating polymers in the face of inevitable errors. Here, we investigated how this maintenance depends on reaction kinetics by incorporating the elementary steps of polymerization into the population dynamics of polymers. We found that template-directed polymerization entails an inherent error-correction mechanism akin to kinetic proofreading, potentially generating the tolerance of long polymers to an error catastrophe at the cost of a slow polymerization process. As this mechanism does not require enzymes, it is likely to operate under broad prebiotic conditions.

A universal method for analyzing copolymer growth.

Polymers consisting of more than one type of monomer, known as copolymers, are vital to both living and synthetic systems. Copolymerization has been studied theoretically in a number of contexts, often by considering a Markov process in which monomers are added or removed from the growing tip of a long copolymer. To date, the analysis of the most general models of this class has necessitated simulation. We present a general method for analyzing such processes without resorting to simulation. Our method can be applied to models with an arbitrary network of sub-steps prior to addition or removal of a monomer, including non-equilibrium kinetic proofreading cycles. Moreover, the approach allows for a dependency of addition and removal reactions on the neighboring site in the copolymer and thermodynamically self-consistent models in which all steps are assumed to be microscopically reversible. Using our approach, thermodynamic quantities such as chemical work; kinetic quantities such as time taken to grow; and statistical quantities such as the distribution of monomer types in the growing copolymer can be directly derived either analytically or numerically from the model definition.