Pathological C-terminal phosphomimetic substitutions alter the mechanism of liquid-liquid phase separation of TDP-43 low complexity domain.

C-terminally phosphorylated TAR DNA-binding protein of 43 kDa (TDP-43) marks the proteinaceous inclusions that characterize a number of age-related neurodegenerative diseases, including amyotrophic lateral sclerosis, frontotemporal lobar degeneration and Alzheimer's disease. TDP-43 phosphorylation at S403/S404, and especially at S409/S410, is in fact accepted as a biomarker of proteinopathy. These residues are located within the low complexity domain (LCD), which also drives the protein's liquid-liquid phase separation (LLPS). The impact of phosphorylation at these LCD sites on phase separation of the protein is a topic of great interest, as these post-translational modifications and LLPS are both implicated in proteinopathies. Here, we employed a combination of experimental and simulation-based approaches to explore this question on a phosphomimetic model of the TDP-43 LCD. Our turbidity and fluorescence microscopy data show that Ser-to-Asp substitutions at residues S403, S404, S409 and S410 alter the LLPS behavior of TDP-43 LCD. In particular, in contrast to the unmodified protein, the phosphomimetic variants display a biphasic dependence on salt concentration. Through coarse-grained modeling, we find that this biphasic salt dependence is derived from an altered mechanism of phase separation, in which LLPS-driving short-range intermolecular hydrophobic interactions are modulated by long-range attractive electrostatic interactions. Overall, this in vitro and in silico study provides a physiochemical foundation for understanding the impact of pathologically-relevant C-terminal phosphorylation on the LLPS of the TDP-43 in a more complex cellular environment.

Bioenergetic costs and the evolution of noise regulation by microRNAs.

Noise control, together with other regulatory functions facilitated by microRNAs (miRNAs), is believed to have played important roles in the evolution of multicellular eukaryotic organisms. miRNAs can dampen protein fluctuations via enhanced degradation of messenger RNA (mRNA), but this requires compensation by increased mRNA transcription to maintain the same expression levels. The overall mechanism is metabolically expensive, leading to questions about how it might have evolved in the first place. We develop a stochastic model of miRNA noise regulation, coupled with a detailed analysis of the associated metabolic costs. Additionally, we calculate binding free energies for a range of miRNA seeds, the short sequences which govern target recognition. We argue that natural selection may have fine-tuned the Michaelis-Menten constant [Formula: see text] describing miRNA-mRNA affinity and show supporting evidence from analysis of experimental data. [Formula: see text] is constrained by seed length, and optimal noise control (minimum protein variance at a given energy cost) is achievable for seeds of 6 to 7 nucleotides in length, the most commonly observed types. Moreover, at optimality, the degree of noise reduction approaches the theoretical bound set by the Wiener-Kolmogorov linear filter. The results illustrate how selective pressure toward energy efficiency has potentially shaped a crucial regulatory pathway in eukaryotes.

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.

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. 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 accurately reflect the selection fo drug resistant genotypes. Furthermore, we find that the spatial structure of MSWs shapes the evolution of drug resistance in an agent-based model. Our work highlights the importance and utility of considering dose-dependent fitness seascapes in evolutionary medicine.

Fano resonant optical coatings platform for full gamut and high purity structural colors.

Structural coloring is a photostable and environmentally friendly coloring approach that harnesses optical interference and nanophotonic resonances to obtain colors with a range of applications including display technologies, colorful solar panels, steganography, décor, data storage, and anticounterfeiting measures. We show that optical coatings exhibiting the photonic Fano Resonance present an ideal platform for structural coloring; they provide full color access, high color purity, high brightness, controlled iridescence, and scalable manufacturing. We show that an additional oxide film deposited on Fano resonant optical coatings (FROCs) increases the color purity (up to 99%) and color gamut coverage range of FROCs to 61% of the CIE color space. For wide-area structural coloring applications, FROCs have a significant advantage over existing structural coloring schemes.

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.

Chirality in Light-Matter Interaction.

The scientific effort to control the interaction between light and matter has grown exponentially in the last 2 decades. This growth has been aided by the development of scientific and technological tools enabling the manipulation of light at deeply sub-wavelength scales, unlocking a large variety of novel phenomena spanning traditionally distant research areas. Here, the role of chirality in light-matter interactions is reviewed by providing a broad overview of its properties, materials, and applications. A perspective on future developments is highlighted, including the growing role of machine learning in designing advanced chiroptical materials to enhance and control light-matter interactions across several scales.

Cheater suppression and stochastic clearance through quorum sensing.

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

Cellular Signaling beyond the Wiener-Kolmogorov Limit.

Accurate propagation of signals through stochastic biochemical networks involves significant expenditure of cellular resources. The same is true for regulatory mechanisms that suppress fluctuations in biomolecular populations. Wiener-Kolmogorov (WK) optimal noise filter theory, originally developed for engineering problems, has recently emerged as a valuable tool to estimate the maximum performance achievable in such biological systems for a given metabolic cost. However, WK theory has one assumption that potentially limits its applicability: it relies on a linear, continuum description of the reaction dynamics. Despite this, up to now no explicit test of the theory in nonlinear signaling systems with discrete molecular populations has ever seen performance beyond the WK bound. Here we report the first direct evidence of the bound being broken. To accomplish this, we develop a theoretical framework for multilevel signaling cascades, including the possibility of feedback interactions between input and output. In the absence of feedback, we introduce an analytical approach that allows us to calculate exact moments of the stationary distribution for a nonlinear system. With feedback, we rely on numerical solutions of the system's master equation. The results show WK violations in two common network motifs: a two-level signaling cascade and a negative feedback loop. However, the magnitude of the violation is biologically negligible, particularly in the parameter regime where signaling is most effective. The results demonstrate that while WK theory does not provide strict bounds, its predictions for performance limits are excellent approximations, even for nonlinear systems.

Integrating deep learning with microfluidics for biophysical classification of sickle red blood cells adhered to laminin.

Sickle cell disease, a genetic disorder affecting a sizeable global demographic, manifests in sickle red blood cells (sRBCs) with altered shape and biomechanics. sRBCs show heightened adhesive interactions with inflamed endothelium, triggering painful vascular occlusion events. Numerous studies employ microfluidic-assay-based monitoring tools to quantify characteristics of adhered sRBCs from high resolution channel images. The current image analysis workflow relies on detailed morphological characterization and cell counting by a specially trained worker. This is time and labor intensive, and prone to user bias artifacts. Here we establish a morphology based classification scheme to identify two naturally arising sRBC subpopulations-deformable and non-deformable sRBCs-utilizing novel visual markers that link to underlying cell biomechanical properties and hold promise for clinically relevant insights. We then set up a standardized, reproducible, and fully automated image analysis workflow designed to carry out this classification. This relies on a two part deep neural network architecture that works in tandem for segmentation of channel images and classification of adhered cells into subtypes. Network training utilized an extensive data set of images generated by the SCD BioChip, a microfluidic assay which injects clinical whole blood samples into protein-functionalized microchannels, mimicking physiological conditions in the microvasculature. Here we carried out the assay with the sub-endothelial protein laminin. The machine learning approach segmented the resulting channel images with 99.1±0.3% mean IoU on the validation set across 5 k-folds, classified detected sRBCs with 96.0±0.3% mean accuracy on the validation set across 5 k-folds, and matched trained personnel in overall characterization of whole channel images with R2 = 0.992, 0.987 and 0.834 for total, deformable and non-deformable sRBC counts respectively. Average analysis time per channel image was also improved by two orders of magnitude (∼ 2 minutes vs ∼ 2-3 hours) over manual characterization. Finally, the network results show an order of magnitude less variance in counts on repeat trials than humans. This kind of standardization is a prerequisite for the viability of any diagnostic technology, making our system suitable for affordable and high throughput disease monitoring.

Point-of-care microchip electrophoresis for integrated anemia and hemoglobin variant testing.

Anemia affects over 25% of the world's population with the heaviest burden borne by women and children. Genetic hemoglobin (Hb) variants, such as sickle cell disease, are among the major causes of anemia. Anemia and Hb variant are pathologically interrelated and have an overlapping geographical distribution. We present the first point-of-care (POC) platform to perform both anemia detection and Hb variant identification, using a single paper-based electrophoresis test. Feasibility of this new integrated diagnostic approach is demonstrated via testing individuals with anemia and/or sickle cell disease. Hemoglobin level determination is performed by an artificial neural network (ANN) based machine learning algorithm, which achieves a mean absolute error of 0.55 g dL-1 and a bias of -0.10 g dL-1 against the gold standard (95% limits of agreement: 1.5 g dL-1) from Bland-Altman analysis on the test set. Resultant anemia detection is achieved with 100% sensitivity and 92.3% specificity. With the same tests, subjects with sickle cell disease were identified with 100% sensitivity and specificity. Overall, the presented platform enabled, for the first time, integrated anemia detection and hemoglobin variant identification using a single point-of-care test.

Fano-resonant ultrathin film optical coatings.

Optical coatings are integral components of virtually every optical instrument. However, despite being a century-old technology, there are only a handful of optical coating types. Here, we introduce a type of optical coatings that exhibit photonic Fano resonance, or a Fano-resonant optical coating (FROC). We expand the coupled mechanical oscillator description of Fano resonance to thin-film nanocavities. Using FROCs with thicknesses in the order of 300 nm, we experimentally obtained narrowband reflection akin to low-index-contrast dielectric Bragg mirrors and achieved control over the reflection iridescence. We observed that semi-transparent FROCs can transmit and reflect the same colour as a beam splitter filter, a property that cannot be realized through conventional optical coatings. Finally, FROCs can spectrally and spatially separate the thermal and photovoltaic bands of the solar spectrum, presenting a possible solution to the dispatchability problem in photovoltaics, that is, the inability to dispatch solar energy on demand. Our solar thermal device exhibited power generation of up to 50% and low photovoltaic cell temperatures (~30 °C), which could lead to a six-fold increase in the photovoltaic cell lifetime.

Low Force Unfolding of a Single-Domain Protein by Parallel Pathways.

Deviations from linearity in the dependence of the logarithm of protein unfolding rates, log ku(f), as a function of mechanical force, f, measurable in single molecule experiments, can arise for many reasons. In particular, upward curvature in log ku(f) as a function of f implies that the underlying energy landscape must be multidimensional with the possibility that unfolding ensues by parallel pathways. Here, simulations using the SOP-SC model of a wild type ß-sandwich protein and several mutants, with immunoglobulin folds, show upward curvature in the unfolding kinetics. There are substantial changes in the structures of the transition state ensembles as the force is increased, signaling a switch in the unfolding pathways. Our results, when combined with previous theoretical and experimental studies, show that parallel unfolding of structurally unrelated single domain proteins can be determined from the dependence of log ku(f) as a function of force (or log ku[C] where [C] is the denaturant concentration).

Myosin V executes steps of variable length via structurally constrained diffusion.

The molecular motor myosin V transports cargo by stepping on actin filaments, executing a random diffusive search for actin binding sites at each step. A recent experiment suggests that the joint between the myosin lever arms may not rotate freely, as assumed in earlier studies, but instead has a preferred angle giving rise to structurally constrained diffusion. We address this controversy through comprehensive analytical and numerical modeling of myosin V diffusion and stepping. When the joint is constrained, our model reproduces the experimentally observed diffusion, allowing us to estimate bounds on the constraint energy. We also test the consistency between the constrained diffusion model and previous measurements of step size distributions and the load dependence of various observable quantities. The theory lets us address the biological significance of the constrained joint and provides testable predictions of new myosin behaviors, including the stomp distribution and the run length under off-axis force.

Modeling the Growth of Organisms Validates a General Relation between Metabolic Costs and Natural Selection.

Metabolism and evolution are closely connected: if a mutation incurs extra energetic costs for an organism, there is a baseline selective disadvantage that may or may not be compensated for by other adaptive effects. A long-standing, but to date unproven, hypothesis is that this disadvantage is equal to the fractional cost relative to the total resting metabolic expenditure. We validate this result from physical principles through a general growth model and show it holds to excellent approximation for experimental parameters drawn from a wide range of species.

Generalized Brewster Angle Effect in Thin-Film Optical Absorbers and Its Application for Graphene Hydrogen Sensing.

The generalized Brewster angle (GBA) is the incidence angle at polarization by reflection for p- or s-polarized light. Realizing an s-polarization Brewster effect requires a material with magnetic response, which is challenging at optical frequencies since the magnetic response of materials at these frequencies is extremely weak. Here, we experimentally realize the GBA effect in the visible using a thin-film absorber system consisting of a dielectric film on an absorbing substrate. Polarization by reflection is realized for both p- and s-polarized light at different angles of incidence and multiple wavelengths. We provide a theoretical framework for the generalized Brewster effect in thin-film light absorbers. We demonstrate hydrogen gas sensing using a single-layer graphene film transferred on a thin-film absorber at the GBA with ∼1 fg/mm2 aerial mass sensitivity. The ultrahigh sensitivity stems from the strong phase sensitivity near the point of darkness, particularly at the GBA, and the strong light-matter interaction in planar nanocavities. These findings depart from the traditional domain of thin films as mere interference optical coatings and highlight its many potential applications including gas sensing and biosensing.

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.