Diverse mutant selection windows shape spatial heterogeneity in evolving populations.

Mutant selection windows (MSWs), the range of drug concentrations that select for drug-resistant mutants, have long been used as a model for predicting drug resistance and designing optimal dosing strategies in infectious disease. The canonical MSW model offers comparisons between two subtypes at a time: drug-sensitive and drug-resistant. In contrast, the fitness landscape model with N alleles, which maps genotype to fitness, allows comparisons between N genotypes simultaneously, but does not encode continuous drug response data. In clinical settings, there may be a wide range of drug concentrations selecting for a variety of genotypes in both cancer and infectious diseases. Therefore, there is a need for a more robust model of the pathogen response to therapy to predict resistance and design new therapeutic approaches. Fitness seascapes, which model genotype-by-environment interactions, permit multiple MSW comparisons simultaneously by encoding genotype-specific dose-response data. By comparing dose-response curves, one can visualize the range of drug concentrations where one genotype is selected over another. In this work, we show how N-allele fitness seascapes allow for N * 2N-1 unique MSW comparisons. In spatial drug diffusion models, we demonstrate how fitness seascapes reveal spatially heterogeneous MSWs, extending the MSW model to more fully reflect the selection of drug resistant genotypes. Furthermore, using synthetic data and empirical dose-response data in cancer, we find that the spatial structure of MSWs shapes the evolution of drug resistance in an agent-based model. By simulating a tumor treated with cyclic drug therapy, we find that mutant selection windows introduced by drug diffusion promote the proliferation of drug resistant cells. Our work highlights the importance and utility of considering dose-dependent fitness seascapes in evolutionary medicine.

Frequency-dependent ecological interactions increase the prevalence, and shape the distribution, of pre-existing drug resistance.

The evolution of resistance remains one of the primary challenges for modern medicine from infectious diseases to cancers. Many of these resistance-conferring mutations often carry a substantial fitness cost in the absence of treatment. As a result, we would expect these mutants to undergo purifying selection and be rapidly driven to extinction. Nevertheless, pre-existing resistance is frequently observed from drug-resistant malaria to targeted cancer therapies in non-small cell lung cancer (NSCLC) and melanoma. Solutions to this apparent paradox have taken several forms from spatial rescue to simple mutation supply arguments. Recently, in an evolved resistant NSCLC cell line, we found that frequency-dependent ecological interactions between ancestor and resistant mutant ameliorate the cost of resistance in the absence of treatment. Here, we hypothesize that frequency-dependent ecological interactions in general play a major role in the prevalence of pre-existing resistance. We combine numerical simulations with robust analytical approximations to provide a rigorous mathematical framework for studying the effects of frequency-dependent ecological interactions on the evolutionary dynamics of pre-existing resistance. First, we find that ecological interactions significantly expand the parameter regime under which we expect to observe pre-existing resistance. Next, even when positive ecological interactions between mutants and ancestors are rare, these resistant clones provide the primary mode of evolved resistance because even weak positive interaction leads to significantly longer extinction times. We then find that even in the case where mutation supply alone is sufficient to predict pre-existing resistance, frequency-dependent ecological forces still contribute a strong evolutionary pressure that selects for increasingly positive ecological effects (negative frequency-dependent selection). Finally, we genetically engineer several of the most common clinically observed resistance mechanisms to targeted therapies in NSCLC, a treatment notorious for pre-existing resistance. We find that each engineered mutant displays a positive ecological interaction with their ancestor. As a whole, these results suggest that frequency-dependent ecological effects can play a crucial role in shaping the evolutionary dynamics of pre-existing resistance.

Motion Blur Microscopy.

Imaging and characterizing the dynamics of cellular adhesion in blood samples is of fundamental importance in understanding biological function. In vitro microscopy methods are widely used for this task, but typically require diluting the blood with a buffer to allow for transmission of light. However whole blood provides crucial mechanical and chemical signaling cues that influence adhesion dynamics, which means that conventional approaches lack the full physiological complexity of living microvasculature. We propose to overcome this challenge by a new in vitro imaging method which we call motion blur microscopy (MBM). By decreasing the source light intensity and increasing the integration time during imaging, flowing cells are blurred, allowing us to identify adhered cells. Combined with an automated analysis using machine learning, we can for the first time reliably image cell interactions in microfluidic channels during whole blood flow. MBM provides a low cost, easy to implement alternative to intravital microscopy, the in vivo approach for studying how the whole blood environment shapes adhesion dynamics. We demonstrate the method's reproducibility and accuracy in two example systems where understanding cell interactions, adhesion, and motility is crucial-sickle red blood cells adhering to laminin, and CAR-T cells adhering to E-selectin. We illustrate the wide range of data types that can be extracted from this approach, including distributions of cell size and eccentricity, adhesion times, trajectories and velocities of adhered cells moving on a functionalized surface, as well as correlations among these different features at the single cell level. In all cases MBM allows for rapid collection and processing of large data sets, ranging from thousands to hundreds of thousands of individual adhesion events. The method is generalizable to study adhesion mechanisms in a variety of diseases, including cancer, blood disorders, thrombosis, inflammatory and autoimmune diseases, as well as providing rich datasets for theoretical modeling of adhesion dynamics.

Catch bonds in sickle cell disease: Shear-enhanced adhesion of red blood cells to laminin.

Could the phenomenon of catch bonding-force-strengthened cellular adhesion-play a role in sickle cell disease, where abnormal red blood cell (RBC) adhesion obstructs blood flow? Here, we investigate the dynamics of sickle RBCs adhering to a surface functionalized with the protein laminin (a component of the extracellular matrix around blood vessels) under physiologically relevant microscale flow. First, using total internal reflectance microscopy we characterize the spatial fluctuations of the RBC membrane above the laminin surface before detachment. The complex dynamics we observe suggest the possibility of catch bonding, where the mean detachment time of the cell from the surface initially increases to a maximum and then decreases as a function of shear force. We next conduct a series of shear-induced detachment experiments on blood samples from 25 sickle cell disease patients, quantifying the number and duration of adhered cells under both sudden force jumps and linear force ramps. The experiments reveal that a subset of patients does indeed exhibit catch bonding. By fitting the data to a theoretical model of the bond dynamics, we can extract the mean bond lifetime versus force for each patient. The results show a striking heterogeneity among patients, both in terms of the qualitative behavior (whether or not there is catch bonding) and in the magnitudes of the lifetimes. Patients with large bond lifetimes at physiological forces are more likely to have certain adverse clinical features, like a diagnosis of pulmonary arterial hypertension and intracardiac shunts. By introducing an in vitro platform for fully characterizing RBC-laminin adhesion dynamics, our approach could contribute to the development of patient-specific antiadhesive therapies for sickle cell disease. The experimental setup is also easily generalizable to studying adhesion dynamics in other cell types, for example, leukocytes or cancer cells, and can incorporate disease-relevant environmental conditions like oxygen deprivation.

Maintaining, masking, and mimicking selection: the interplay of cell-intrinsic and cell-extrinsic effects upon eco-evolutionary dynamics.

Evolution is a stochastic yet inevitable process that lies at the heart of biology yet in the multi-cellular environments within patients, ecological complexities arise via heterogeneity and microenvironments. The interplay of ecology and mutation is thus fundamental to predicting the evolution of complex diseases and engineering optimal treatment solutions. As experimental evidence of ecological interactions between disease agents continues to grow, so does the need for evolutionary theory and modeling that incorporates these interaction effects. Inspired by experimental cell biology, we transform the variables in the interaction payoff matrix to encode cell-cell interactions in our mathematical approach as growth-rate modifying, frequency-dependent interactions. In this way, we can show the extent to which the presence of these cell-extrinsic ecological interactions can modify the evolutionary trajectories that would be predicted from cell-intrinsic properties alone. To do this we form a Fokker-Planck equation for a genetic population undergoing diffusion, drift, and interactions and generate a novel, analytic solution for the stationary distribution. We use this solution to determine when these interactions can modify evolution in such ways as to maintain, mask, or mimic mono-culture fitness differences. This work has implications for the interpretation and understanding of experimental and patient evolution and is a result that may help to explain the abundance of apparently neutral evolution in cancer systems and heterogeneous populations in general. In addition, the derivation of an analytical result for stochastic, ecologically dependent evolution paves the way for treatment approaches requiring knowledge of a stationary solution for the development of control protocols.

The 2019 mathematical oncology roadmap.

Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic Science, there is no denying that mathematics continues to play an increasingly prominent role in cancer research. Mathematical Oncology-defined here simply as the use of mathematics in cancer research-complements and overlaps with a number of other fields that rely on mathematics as a core methodology. As a result, Mathematical Oncology has a broad scope, ranging from theoretical studies to clinical trials designed with mathematical models. This Roadmap differentiates Mathematical Oncology from related fields and demonstrates specific areas of focus within this unique field of research. The dominant theme of this Roadmap is the personalization of medicine through mathematics, modelling, and simulation. This is achieved through the use of patient-specific clinical data to: develop individualized screening strategies to detect cancer earlier; make predictions of response to therapy; design adaptive, patient-specific treatment plans to overcome therapy resistance; and establish domain-specific standards to share model predictions and to make models and simulations reproducible. The cover art for this Roadmap was chosen as an apt metaphor for the beautiful, strange, and evolving relationship between mathematics and cancer.

Unraveling the mechanism of the cadherin-catenin-actin catch bond.

The adherens junctions between epithelial cells involve a protein complex formed by E-cadherin, ß-catenin, α-catenin and F-actin. The stability of this complex was a puzzle for many years, since in vitro studies could reconstitute various stable subsets of the individual proteins, but never the entirety. The missing ingredient turned out to be mechanical tension: a recent experiment that applied physiological forces to the complex with an optical tweezer dramatically increased its lifetime, a phenomenon known as catch bonding. However, in the absence of a crystal structure for the full complex, the microscopic details of the catch bond mechanism remain mysterious. Building on structural clues that point to α-catenin as the force transducer, we present a quantitative theoretical model for how the catch bond arises, fully accounting for the experimental lifetime distributions. The underlying hypothesis is that force induces a rotational transition between two conformations of α-catenin, overcoming a significant energy barrier due to a network of salt bridges. This transition allosterically regulates the energies at the interface between α-catenin and F-actin. The model allows us to predict these energetic changes, as well as highlighting the importance of the salt bridge rotational barrier. By stabilizing one of the α-catenin states, this barrier could play a role in how the complex responds to additional in vivo binding partners like vinculin. Since significant conformational energy barriers are a common feature of other adhesion systems that exhibit catch bonds, our model can be adapted into a general theoretical framework for integrating structure and function in a variety of force-regulated protein complexes.

Design principles governing the motility of myosin V.

The molecular motor myosin V (MyoV) exhibits a wide repertoire of pathways during the stepping process, which is intimately connected to its biological function. The best understood of these is the hand-over-hand stepping by a swinging lever arm movement toward the plus end of actin filaments. Single-molecule experiments have also shown that the motor "foot stomps," with one hand detaching and rebinding to the same site, and back-steps under sufficient load. The complete taxonomy of MyoV's load-dependent stepping pathways, and the extent to which these are constrained by motor structure and mechanochemistry, are not understood. Using a polymer model, we develop an analytical theory to describe the minimal physical properties that govern motor dynamics. We solve the first-passage problem of the head reaching the target-binding site, investigating the competing effects of backward load, strain in the leading head biasing the diffusion in the direction of the target, and the possibility of preferential binding to the forward site due to the recovery stroke. The theory reproduces a variety of experimental data, including the power stroke and slow diffusive search regimes in the mean trajectory of the detached head, and the force dependence of the forward-to-backward step ratio, run length, and velocity. We derive a stall force formula, determined by lever arm compliance and chemical cycle rates. By exploring the MyoV design space, we predict that it is a robust motor whose dynamical behavior is not compromised by reasonable perturbations to the reaction cycle and changes in the architecture of the lever arm.