SnapShot: Influenza by the Numbers.

Influenza is one of the best-studied viruses of all time, and as such, it serves as a testbed to extend our biological knowledge to the nanoscale. Many of the key processes underlying influenza infection and our antibody response against the virus have been thoroughly investigated. This SnapShot describes these key numbers for prototypical lab-adapted strains of the human influenza A virus. To view this SnapShot, open or download the PDF.

How the avidity of polymerase binding to the -35/-10 promoter sites affects gene expression.

Although the key promoter elements necessary to drive transcription in Escherichia coli have long been understood, we still cannot predict the behavior of arbitrary novel promoters, hampering our ability to characterize the myriad sequenced regulatory architectures as well as to design new synthetic circuits. This work builds upon a beautiful recent experiment by Urtecho et al. [G. Urtecho, et al, Biochemistry, 68, 1539-1551 (2019)] who measured the gene expression of over 10,000 promoters spanning all possible combinations of a small set of regulatory elements. Using these data, we demonstrate that a central claim in energy matrix models of gene expression-that each promoter element contributes independently and additively to gene expression-contradicts experimental measurements. We propose that a key missing ingredient from such models is the avidity between the -35 and -10 RNA polymerase binding sites and develop what we call a multivalent model that incorporates this effect and can successfully characterize the full suite of gene expression data. We explore several applications of this framework, namely, how multivalent binding at the -35 and -10 sites can buffer RNA polymerase (RNAP) kinetics against mutations and how promoters that bind overly tightly to RNA polymerase can inhibit gene expression. The success of our approach suggests that avidity represents a key physical principle governing the interaction of RNA polymerase to its promoter.

Predictive shifts in free energy couple mutations to their phenotypic consequences.

Mutation is a critical mechanism by which evolution explores the functional landscape of proteins. Despite our ability to experimentally inflict mutations at will, it remains difficult to link sequence-level perturbations to systems-level responses. Here, we present a framework centered on measuring changes in the free energy of the system to link individual mutations in an allosteric transcriptional repressor to the parameters which govern its response. We find that the energetic effects of the mutations can be categorized into several classes which have characteristic curves as a function of the inducer concentration. We experimentally test these diagnostic predictions using the well-characterized LacI repressor of Escherichia coli, probing several mutations in the DNA binding and inducer binding domains. We find that the change in gene expression due to a point mutation can be captured by modifying only the model parameters that describe the respective domain of the wild-type protein. These parameters appear to be insulated, with mutations in the DNA binding domain altering only the DNA affinity and those in the inducer binding domain altering only the allosteric parameters. Changing these subsets of parameters tunes the free energy of the system in a way that is concordant with theoretical expectations. Finally, we show that the induction profiles and resulting free energies associated with pairwise double mutants can be predicted with quantitative accuracy given knowledge of the single mutants, providing an avenue for identifying and quantifying epistatic interactions.

When two are better than one: Modeling the mechanisms of antibody mixtures.

It is difficult to predict how antibodies will behave when mixed together, even after each has been independently characterized. Here, we present a statistical mechanical model for the activity of antibody mixtures that accounts for whether pairs of antibodies bind to distinct or overlapping epitopes. This model requires measuring n individual antibodies and their [Formula: see text] pairwise interactions to predict the 2n potential combinations. We apply this model to epidermal growth factor receptor (EGFR) antibodies and find that the activity of antibody mixtures can be predicted without positing synergy at the molecular level. In addition, we demonstrate how the model can be used in reverse, where straightforward experiments measuring the activity of antibody mixtures can be used to infer the molecular interactions between antibodies. Lastly, we generalize this model to analyze engineered multidomain antibodies, where components of different antibodies are tethered together to form novel amalgams, and characterize how well it predicts recently designed influenza antibodies.

Ultrapotent Broadly Neutralizing Human-llama Bispecific Antibodies against HIV-1.

Broadly neutralizing antibodies are proposed as therapeutic and prophylactic agents against HIV-1, but their potency and breadth are less than optimal. This study describes the immunization of a llama with the prefusion-stabilized HIV-1 envelope (Env) trimer, BG505 DS-SOSIP, and the identification and improvement of potent neutralizing nanobodies recognizing the CD4-binding site (CD4bs) of vulnerability. Two of the vaccine-elicited CD4bs-targeting nanobodies, G36 and R27, when engineered into a triple tandem format with llama IgG2a-hinge region and human IgG1-constant region (G36×3-IgG2a and R27×3-IgG2a), neutralized 96% of a multiclade 208-strain panel at geometric mean IC80s of 0.314 and 0.033 µg mL-1, respectively. Cryo-EM structures of these nanobodies in complex with Env trimer revealed the two nanobodies to neutralize HIV-1 by mimicking the recognition of the CD4 receptor. To enhance their neutralizing potency and breadth, nanobodies are linked to the light chain of the V2-apex-targeting broadly neutralizing antibody, CAP256V2LS. The resultant human-llama bispecific antibody CAP256L-R27×3LS exhibited ultrapotent neutralization and breadth exceeding other published HIV-1 broadly neutralizing antibodies, with pharmacokinetics determined in FcRn-Fc mice similar to the parent CAP256V2LS. Vaccine-elicited llama nanobodies, when combined with V2-apex broadly neutralizing antibodies, may therefore be able to fulfill anti-HIV-1 therapeutic and prophylactic clinical goals.

Using interpretable machine learning to extend heterogeneous antibody-virus datasets.

A central challenge in biology is to use existing measurements to predict the outcomes of future experiments. For the rapidly evolving influenza virus, variants examined in one study will often have little to no overlap with other studies, making it difficult to discern patterns or unify datasets. We develop a computational framework that predicts how an antibody or serum would inhibit any variant from any other study. We validate this method using hemagglutination inhibition data from seven studies and predict 2,000,000 new values ± uncertainties. Our analysis quantifies the transferability between vaccination and infection studies in humans and ferrets, shows that serum potency is negatively correlated with breadth, and provides a tool for pandemic preparedness. In essence, this approach enables a shift in perspective when analyzing data from "what you see is what you get" into "what anyone sees is what everyone gets."

Quantitatively Visualizing Bipartite Datasets.

As experiments continue to increase in size and scope, a fundamental challenge of subsequent analyses is to recast the wealth of information into an intuitive and readily interpretable form. Often, each measurement conveys only the relationship between a pair of entries, and it is difficult to integrate these local interactions across a dataset to form a cohesive global picture. The classic localization problem tackles this question, transforming local measurements into a global map that reveals the underlying structure of a system. Here, we examine the more challenging bipartite localization problem, where pairwise distances are available only for bipartite data comprising two classes of entries (such as antibody-virus interactions, drug-cell potency, or user-rating profiles). We modify previous algorithms to solve bipartite localization and examine how each method behaves in the presence of noise, outliers, and partially observed data. As a proof of concept, we apply these algorithms to antibody-virus neutralization measurements to create a basis set of antibody behaviors, formalize how potently inhibiting some viruses necessitates weakly inhibiting other viruses, and quantify how often combinations of antibodies exhibit degenerate behavior.

Harnessing low dimensionality to visualize the antibody-virus landscape for influenza.

Antibodies constitute a key line of defense against the diverse pathogens we encounter in our lives. Although the interactions between a single antibody and a single virus are routinely characterized in exquisite detail, the inherent tradeoffs between attributes such as potency and breadth remain unclear. Moreover, there is a wide gap between the discrete interactions of single antibodies and the collective behavior of antibody mixtures. Here we develop a form of antigenic cartography called a 'neutralization landscape' that visualizes and quantifies antibody-virus interactions for antibodies targeting the influenza hemagglutinin stem. This landscape transforms the potency-breadth tradeoff into a readily solvable geometry problem. With it, we decompose the collective neutralization from multiple antibodies to characterize the composition and functional properties of the stem antibodies within. Looking forward, this framework can leverage the serological assays routinely performed for influenza surveillance to analyze how an individual's antibody repertoire evolves after vaccination or infection.

Mapping the Antibody Repertoires in Ferrets with Repeated Influenza A/H3 Infections: Is Original Antigenic Sin Really "Sinful"?

The influenza-specific antibody repertoire is continuously reshaped by infection and vaccination. The host immune response to contemporary viruses can be redirected to preferentially boost antibodies specific for viruses encountered early in life, a phenomenon called original antigenic sin (OAS) that is suggested to be responsible for diminished vaccine effectiveness after repeated seasonal vaccination. Using a new computational tool called Neutralization Landscapes, we tracked the progression of hemagglutination inhibition antibodies within ferret antisera elicited by repeated influenza A/H3 infections and deciphered the influence of prior exposures on the de novo antibody response to evolved viruses. The results indicate that a broadly neutralizing antibody signature can nevertheless be induced by repeated exposures despite OAS induction. Our study offers a new way to visualize how immune history shapes individual antibodies within a repertoire, which may help to inform future universal influenza vaccine design.

Extrapolating missing antibody-virus measurements across serological studies.

The development of new vaccines, as well as our understanding of key processes that shape viral evolution and host antibody repertoires, relies on measuring multiple antibody responses against large panels of viruses. Given the enormous diversity of circulating virus strains and antibody responses, comprehensively testing all antibody-virus interactions is infeasible. Even within individual studies with limited panels, exhaustive testing is not always performed, and there is no common framework for combining information across studies with partially overlapping panels, especially when the assay type or host species differ. Prior studies have demonstrated that antibody-virus interactions can be characterized in a vastly simpler and lower dimensional space, suggesting that relatively few measurements could predict unmeasured antibody-virus interactions. Here, we apply matrix completion to several large-scale influenza and HIV-1 studies. We explore how prediction accuracy evolves as the number of measurements changes and approximates the number of additional measurements necessary in several highly incomplete datasets (suggesting ∼250,000 measurements could be saved). In addition, we show how the method can combine disparate datasets, even when the number of available measurements is below the theoretical limit that guarantees successful prediction. This approach can be readily generalized to other viruses or more broadly to other low-dimensional biological datasets.

Multiplexed characterization of rationally designed promoter architectures deconstructs combinatorial logic for IPTG-inducible systems.

A crucial step towards engineering biological systems is the ability to precisely tune the genetic response to environmental stimuli. In the case of Escherichia coli inducible promoters, our incomplete understanding of the relationship between sequence composition and gene expression hinders our ability to predictably control transcriptional responses. Here, we profile the expression dynamics of 8269 rationally designed, IPTG-inducible promoters that collectively explore the individual and combinatorial effects of RNA polymerase and LacI repressor binding site strengths. We then fit a statistical mechanics model to measured expression that accurately models gene expression and reveals properties of theoretically optimal inducible promoters. Furthermore, we characterize three alternative promoter architectures and show that repositioning binding sites within promoters influences the types of combinatorial effects observed between promoter elements. In total, this approach enables us to deconstruct relationships between inducible promoter elements and discover practical insights for engineering inducible promoters with desirable characteristics.

Combinatorial Control through Allostery.

Many instances of cellular signaling and transcriptional regulation involve switch-like molecular responses to the presence or absence of input ligands. To understand how these responses come about and how they can be harnessed, we develop a statistical mechanical model to characterize the types of Boolean logic that can arise from allosteric molecules following the Monod-Wyman-Changeux (MWC) model. Building upon previous work, we show how an allosteric molecule regulated by two inputs can elicit AND, OR, NAND, and NOR responses but is unable to realize XOR or XNOR gates. Next, we demonstrate the ability of an MWC molecule to perform ratiometric sensing-a response behavior where activity depends monotonically on the ratio of ligand concentrations. We then extend our analysis to more general schemes of combinatorial control involving either additional binding sites for the two ligands or an additional third ligand and show how these additions can cause a switch in the logic behavior of the molecule. Overall, our results demonstrate the wide variety of control schemes that biological systems can implement using simple mechanisms.

Harnessing Avidity: Quantifying the Entropic and Energetic Effects of Linker Length and Rigidity for Multivalent Binding of Antibodies to HIV-1.

IgG antibodies increase their apparent affinities by using both of their Fabs to simultaneously attach to antigens. HIV-1 foils this strategy by having few, and highly separated, Envelope (Env) spike targets for antibodies, forcing most IgGs to bind monovalently. Here, we develop a statistical mechanics model of synthetic diFabs joined by DNA linkers of different lengths and flexibilities. This framework enables us to translate the energetic and entropic effects of the linker into the neutralization potency of a diFab. We demonstrate that the strongest neutralization potencies are predicted to require a rigid linker that optimally spans the distance between two Fab binding sites on an Env trimer and that avidity can be further boosted by incorporating more Fabs into these constructs. These results inform the design of multivalent anti-HIV-1 therapeutics that utilize avidity effects to remain potent against HIV-1 in the face of the rapid mutation of Env spikes.

Theoretical analysis of inducer and operator binding for cyclic-AMP receptor protein mutants.

Allosteric transcription factors undergo binding events at inducer binding sites as well as at distinct DNA binding domains, and it is difficult to disentangle the structural and functional consequences of these two classes of interactions. We compare the ability of two statistical mechanical models-the Monod-Wyman-Changeux (MWC) and the Koshland-Némethy-Filmer (KNF) models of protein conformational change-to characterize the multi-step activation mechanism of the broadly acting cyclic-AMP receptor protein (CRP). We first consider the allosteric transition resulting from cyclic-AMP binding to CRP, then analyze how CRP binds to its operator, and finally investigate the ability of CRP to activate gene expression. We use these models to examine a beautiful recent experiment that created a single-chain version of the CRP homodimer, creating six mutants using all possible combinations of the wild type, D53H, and S62F subunits. We demonstrate that the MWC model can explain the behavior of all six mutants using a small, self-consistent set of parameters whose complexity scales with the number of subunits, providing a significant benefit over previous models. In comparison, the KNF model not only leads to a poorer characterization of the available data but also fails to generate parameter values in line with the available structural knowledge of CRP. In addition, we discuss how the conceptual framework developed here for CRP enables us to not merely analyze data retrospectively, but has the predictive power to determine how combinations of mutations will interact, how double mutants will behave, and how each construct would regulate gene expression.

Tuning Transcriptional Regulation through Signaling: A Predictive Theory of Allosteric Induction.

Allosteric regulation is found across all domains of life, yet we still lack simple, predictive theories that directly link the experimentally tunable parameters of a system to its input-output response. To that end, we present a general theory of allosteric transcriptional regulation using the Monod-Wyman-Changeux model. We rigorously test this model using the ubiquitous simple repression motif in bacteria by first predicting the behavior of strains that span a large range of repressor copy numbers and DNA binding strengths and then constructing and measuring their response. Our model not only accurately captures the induction profiles of these strains, but also enables us to derive analytic expressions for key properties such as the dynamic range and [EC50]. Finally, we derive an expression for the free energy of allosteric repressors that enables us to collapse our experimental data onto a single master curve that captures the diverse phenomenology of the induction profiles.

Monod-Wyman-Changeux Analysis of Ligand-Gated Ion Channel Mutants.

We present a framework for computing the gating properties of ligand-gated ion channel mutants using the Monod-Wyman-Changeux (MWC) model of allostery. We derive simple analytic formulas for key functional properties such as the leakiness, dynamic range, half-maximal effective concentration ([EC50]), and effective Hill coefficient, and explore the full spectrum of phenotypes that are accessible through mutations. Specifically, we consider mutations in the channel pore of nicotinic acetylcholine receptor (nAChR) and the ligand binding domain of a cyclic nucleotide-gated (CNG) ion channel, demonstrating how each mutation can be characterized as only affecting a subset of the biophysical parameters. In addition, we show how the unifying perspective offered by the MWC model allows us, perhaps surprisingly, to collapse the plethora of dose-response data from different classes of ion channels into a universal family of curves.

Statistical Mechanics of Allosteric Enzymes.

The concept of allostery in which macromolecules switch between two different conformations is a central theme in biological processes ranging from gene regulation to cell signaling to enzymology. Allosteric enzymes pervade metabolic processes, yet a simple and unified treatment of the effects of allostery in enzymes has been lacking. In this work, we take a step toward this goal by modeling allosteric enzymes and their interaction with two key molecular players-allosteric regulators and competitive inhibitors. We then apply this model to characterize existing data on enzyme activity, comment on how enzyme parameters (such as substrate binding affinity) can be experimentally tuned, and make novel predictions on how to control phenomena such as substrate inhibition.