Time resolution in cryo-EM using a PDMS-based microfluidic chip assembly and its application to the study of HflX-mediated ribosome recycling.

The rapid kinetics of biological processes and associated short-lived conformational changes pose a significant challenge in attempts to structurally visualize biomolecules during a reaction in real time. Conventionally, on-pathway intermediates have been trapped using chemical modifications or reduced temperature, giving limited insights. Here, we introduce a time-resolved cryo-EM method using a reusable PDMS-based microfluidic chip assembly with high reactant mixing efficiency. Coating of PDMS walls with SiO2 virtually eliminates non-specific sample adsorption and ensures maintenance of the stoichiometry of the reaction, rendering it highly reproducible. In an operating range from 10 to 1,000 ms, the device allows us to follow in vitro reactions of biological molecules at resolution levels in the range of 3 Å. By employing this method, we show the mechanism of progressive HflX-mediated splitting of the 70S E. coli ribosome in the presence of the GTP via capture of three high-resolution reaction intermediates within 140 ms.

High-Spatial-Resolution Multi-Omics Sequencing via Deterministic Barcoding in Tissue.

We present deterministic barcoding in tissue for spatial omics sequencing (DBiT-seq) for co-mapping of mRNAs and proteins in a formaldehyde-fixed tissue slide via next-generation sequencing (NGS). Parallel microfluidic channels were used to deliver DNA barcodes to the surface of a tissue slide, and crossflow of two sets of barcodes, A1-50 and B1-50, followed by ligation in situ, yielded a 2D mosaic of tissue pixels, each containing a unique full barcode AB. Application to mouse embryos revealed major tissue types in early organogenesis as well as fine features like microvasculature in a brain and pigmented epithelium in an eye field. Gene expression profiles in 10-µm pixels conformed into the clusters of single-cell transcriptomes, allowing for rapid identification of cell types and spatial distributions. DBiT-seq can be adopted by researchers with no experience in microfluidics and may find applications in a range of fields including developmental biology, cancer biology, neuroscience, and clinical pathology.

Modulation of Phase Shift between Wnt and Notch Signaling Oscillations Controls Mesoderm Segmentation.

How signaling dynamics encode information is a central question in biology. During vertebrate development, dynamic Notch signaling oscillations control segmentation of the presomitic mesoderm (PSM). In mouse embryos, this molecular clock comprises signaling oscillations of several pathways, i.e., Notch, Wnt, and FGF signaling. Here, we directly address the role of the relative timing between Wnt and Notch signaling oscillations during PSM patterning. To this end, we developed a new experimental strategy using microfluidics-based entrainment that enables specific control of the rhythm of segmentation clock oscillations. Using this approach, we find that Wnt and Notch signaling are coupled at the level of their oscillation dynamics. Furthermore, we provide functional evidence that the oscillation phase shift between Wnt and Notch signaling is critical for PSM segmentation. Our work hence reveals that dynamic signaling, i.e., the relative timing between oscillatory signals, encodes essential information during multicellular development.

Conceptual and Experimental Tools to Understand Spatial Effects and Transport Phenomena in Nonlinear Biochemical Networks Illustrated with Patchy Switching.

Many biochemical systems are spatially heterogeneous and exhibit nonlinear behaviors, such as state switching in response to small changes in the local concentration of diffusible molecules. Systems as varied as blood clotting, intracellular calcium signaling, and tissue inflammation are all heavily influenced by the balance of rates of reaction and mass transport phenomena including flow and diffusion. Transport of signaling molecules is also affected by geometry and chemoselective confinement via matrix binding. In this review, we use a phenomenon referred to as patchy switching to illustrate the interplay of nonlinearities, transport phenomena, and spatial effects. Patchy switching describes a change in the state of a network when the local concentration of a diffusible molecule surpasses a critical threshold. Using patchy switching as an example, we describe conceptual tools from nonlinear dynamics and chemical engineering that make testable predictions and provide a unifying description of the myriad possible experimental observations. We describe experimental microfluidic and biochemical tools emerging to test conceptual predictions by controlling transport phenomena and spatial distribution of diffusible signals, and we highlight the unmet need for in vivo tools.

A patterned human neural tube model using microfluidic gradients.

The human nervous system is a highly complex but organized organ. The foundation of its complexity and organization is laid down during regional patterning of the neural tube, the embryonic precursor to the human nervous system. Historically, studies of neural tube patterning have relied on animal models to uncover underlying principles. Recently, models of neurodevelopment based on human pluripotent stem cells, including neural organoids1-5 and bioengineered neural tube development models6-10, have emerged. However, such models fail to recapitulate neural patterning along both rostral-caudal and dorsal-ventral axes in a three-dimensional tubular geometry, a hallmark of neural tube development. Here we report a human pluripotent stem cell-based, microfluidic neural tube-like structure, the development of which recapitulates several crucial aspects of neural patterning in brain and spinal cord regions and along rostral-caudal and dorsal-ventral axes. This structure was utilized for studying neuronal lineage development, which revealed pre-patterning of axial identities of neural crest progenitors and functional roles of neuromesodermal progenitors and the caudal gene CDX2 in spinal cord and trunk neural crest development. We further developed dorsal-ventral patterned microfluidic forebrain-like structures with spatially segregated dorsal and ventral regions and layered apicobasal cellular organizations that mimic development of the human forebrain pallium and subpallium, respectively. Together, these microfluidics-based neurodevelopment models provide three-dimensional lumenal tissue architectures with in vivo-like spatiotemporal cell differentiation and organization, which will facilitate the study of human neurodevelopment and disease.

Identification of astrocyte regulators by nucleic acid cytometry.

Multiple sclerosis is a chronic inflammatory disease of the central nervous system1. Astrocytes are heterogeneous glial cells that are resident in the central nervous system and participate in the pathogenesis of multiple sclerosis and its model experimental autoimmune encephalomyelitis2,3. However, few unique surface markers are available for the isolation of astrocyte subsets, preventing their analysis and the identification of candidate therapeutic targets; these limitations are further amplified by the rarity of pathogenic astrocytes. Here, to address these challenges, we developed focused interrogation of cells by nucleic acid detection and sequencing (FIND-seq), a high-throughput microfluidic cytometry method that combines encapsulation of cells in droplets, PCR-based detection of target nucleic acids and droplet sorting to enable in-depth transcriptomic analyses of cells of interest at single-cell resolution. We applied FIND-seq to study the regulation of astrocytes characterized by the splicing-driven activation of the transcription factor XBP1, which promotes disease pathology in multiple sclerosis and experimental autoimmune encephalomyelitis4. Using FIND-seq in combination with conditional-knockout mice, in vivo CRISPR-Cas9-driven genetic perturbation studies and bulk and single-cell RNA sequencing analyses of samples from mouse experimental autoimmune encephalomyelitis and humans with multiple sclerosis, we identified a new role for the nuclear receptor NR3C2 and its corepressor NCOR2 in limiting XBP1-driven pathogenic astrocyte responses. In summary, we used FIND-seq to identify a therapeutically targetable mechanism that limits XBP1-driven pathogenic astrocyte responses. FIND-seq enables the investigation of previously inaccessible cells, including rare cell subsets defined by unique gene expression signatures or other nucleic acid markers.

HIV silencing and cell survival signatures in infected T cell reservoirs.

Rare CD4 T cells that contain HIV under antiretroviral therapy represent an important barrier to HIV cure1-3, but the infeasibility of isolating and characterizing these cells in their natural state has led to uncertainty about whether they possess distinctive attributes that HIV cure-directed therapies might exploit. Here we address this challenge using a microfluidic technology that isolates the transcriptomes of HIV-infected cells based solely on the detection of HIV DNA. HIV-DNA+ memory CD4 T cells in the blood from people receiving antiretroviral therapy showed inhibition of six transcriptomic pathways, including death receptor signalling, necroptosis signalling and antiproliferative Gα12/13 signalling. Moreover, two groups of genes identified by network co-expression analysis were significantly associated with HIV-DNA+ cells. These genes (n = 145) accounted for just 0.81% of the measured transcriptome and included negative regulators of HIV transcription that were higher in HIV-DNA+ cells, positive regulators of HIV transcription that were lower in HIV-DNA+ cells, and other genes involved in RNA processing, negative regulation of mRNA translation, and regulation of cell state and fate. These findings reveal that HIV-infected memory CD4 T cells under antiretroviral therapy are a distinctive population with host gene expression patterns that favour HIV silencing, cell survival and cell proliferation, with important implications for the development of HIV cure strategies.

Microfluidic chain reaction of structurally programmed capillary flow events.

Chain reactions, characterized by initiation, propagation and termination, are stochastic at microscopic scales and underlie vital chemical (for example, combustion engines), nuclear and biotechnological (for example, polymerase chain reaction) applications1-5. At macroscopic scales, chain reactions are deterministic and limited to applications for entertainment and art such as falling dominoes and Rube Goldberg machines. On the other hand, the microfluidic lab-on-a-chip (also called a micro-total analysis system)6,7 was visualized as an integrated chip, akin to microelectronic integrated circuits, yet in practice remains dependent on cumbersome peripherals, connections and a computer for automation8-11. Capillary microfluidics integrate energy supply and flow control onto a single chip by using capillary phenomena, but programmability remains rudimentary with at most a handful (eight) operations possible12-19. Here we introduce the microfluidic chain reaction (MCR) as the conditional, structurally programmed propagation of capillary flow events. Monolithic chips integrating a MCR are three-dimensionally printed, and powered by the free energy of a paper pump, autonomously execute liquid handling algorithms step-by-step. With MCR, we automated (1) the sequential release of 300 aliquots across chained, interconnected chips, (2) a protocol for severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) antibodies detection in saliva and (3) a thrombin generation assay by continuous subsampling and analysis of coagulation-activated plasma with parallel operations including timers, iterative cycles of synchronous flow and stop-flow operations. MCRs are untethered from and unencumbered by peripherals, encode programs structurally in situ and can form a frugal, versatile, bona fide lab-on-a-chip with wide-ranging applications in liquid handling and point-of-care diagnostics.

Low-cost, versatile, and highly reproducible microfabrication pipeline to generate 3D-printed customised cell culture devices with complex designs.

Cell culture devices, such as microwells and microfluidic chips, are designed to increase the complexity of cell-based models while retaining control over culture conditions and have become indispensable platforms for biological systems modelling. From microtopography, microwells, plating devices, and microfluidic systems to larger constructs such as live imaging chamber slides, a wide variety of culture devices with different geometries have become indispensable in biology laboratories. However, while their application in biological projects is increasing exponentially, due to a combination of the techniques, equipment and tools required for their manufacture, and the expertise necessary, biological and biomedical labs tend more often to rely on already made devices. Indeed, commercially developed devices are available for a variety of applications but are often costly and, importantly, lack the potential for customisation by each individual lab. The last point is quite crucial, as often experiments in wet labs are adapted to whichever design is already available rather than designing and fabricating custom systems that perfectly fit the biological question. This combination of factors still restricts widespread application of microfabricated custom devices in most biological wet labs. Capitalising on recent advances in bioengineering and microfabrication aimed at solving these issues, and taking advantage of low-cost, high-resolution desktop resin 3D printers combined with PDMS soft lithography, we have developed an optimised a low-cost and highly reproducible microfabrication pipeline. This is thought specifically for biomedical and biological wet labs with not prior experience in the field, which will enable them to generate a wide variety of customisable devices for cell culture and tissue engineering in an easy, fast reproducible way for a fraction of the cost of conventional microfabrication or commercial alternatives. This protocol is designed specifically to be a resource for biological labs with limited expertise in those techniques and enables the manufacture of complex devices across the µm to cm scale. We provide a ready-to-go pipeline for the efficient treatment of resin-based 3D-printed constructs for PDMS curing, using a combination of polymerisation steps, washes, and surface treatments. Together with the extensive characterisation of the fabrication pipeline, we show the utilisation of this system to a variety of applications and use cases relevant to biological experiments, ranging from micro topographies for cell alignments to complex multipart hydrogel culturing systems. This methodology can be easily adopted by any wet lab, irrespective of prior expertise or resource availability and will enable the wide adoption of tailored microfabricated devices across many fields of biology.

Microfluidics: reframing biological enquiry.

The underlying physical properties of microfluidic tools have led to new biological insights through the development of microsystems that can manipulate, mimic and measure biology at a resolution that has not been possible with macroscale tools. Microsystems readily handle sub-microlitre volumes, precisely route predictable laminar fluid flows and match both perturbations and measurements to the length scales and timescales of biological systems. The advent of fabrication techniques that do not require highly specialized engineering facilities is fuelling the broad dissemination of microfluidic systems and their adaptation to specific biological questions. We describe how our understanding of molecular and cell biology is being and will continue to be advanced by precision microfluidic approaches and posit that microfluidic tools - in conjunction with advanced imaging, bioinformatics and molecular biology approaches - will transform biology into a precision science.

Cellular fluidics.

The natural world provides many examples of multiphase transport and reaction processes that have been optimized by evolution. These phenomena take place at multiple length and time scales and typically include gas-liquid-solid interfaces and capillary phenomena in porous media1,2. Many biological and living systems have evolved to optimize fluidic transport. However, living things are exceptionally complex and very difficult to replicate3-5, and human-made microfluidic devices (which are typically planar and enclosed) are highly limited for multiphase process engineering6-8. Here we introduce the concept of cellular fluidics: a platform of unit-cell-based, three-dimensional structures-enabled by emerging 3D printing methods9,10-for the deterministic control of multiphase flow, transport and reaction processes. We show that flow in these structures can be 'programmed' through architected design of cell type, size and relative density. We demonstrate gas-liquid transport processes such as transpiration and absorption, using evaporative cooling and CO2 capture as examples. We design and demonstrate preferential liquid and gas transport pathways in three-dimensional cellular fluidic devices with capillary-driven and actively pumped liquid flow, and present examples of selective metallization of pre-programmed patterns. Our results show that the design and fabrication of architected cellular materials, coupled with analytical and numerical predictions of steady-state and dynamic behaviour of multiphase interfaces, provide deterministic control of fluidic transport in three dimensions. Cellular fluidics may transform the design space for spatial and temporal control of multiphase transport and reaction processes.

Three-dimensional electronic microfliers inspired by wind-dispersed seeds.

Large, distributed collections of miniaturized, wireless electronic devices1,2 may form the basis of future systems for environmental monitoring3, population surveillance4, disease management5 and other applications that demand coverage over expansive spatial scales. Aerial schemes to distribute the components for such networks are required, and-inspired by wind-dispersed seeds6-we examined passive structures designed for controlled, unpowered flight across natural environments or city settings. Techniques in mechanically guided assembly of three-dimensional (3D) mesostructures7-9 provide access to miniature, 3D fliers optimized for such purposes, in processes that align with the most sophisticated production techniques for electronic, optoelectronic, microfluidic and microelectromechanical technologies. Here we demonstrate a range of 3D macro-, meso- and microscale fliers produced in this manner, including those that incorporate active electronic and colorimetric payloads. Analytical, computational and experimental studies of the aerodynamics of high-performance structures of this type establish a set of fundamental considerations in bio-inspired design, with a focus on 3D fliers that exhibit controlled rotational kinematics and low terminal velocities. An approach that represents these complex 3D structures as discrete numbers of blades captures the essential physics in simple, analytical scaling forms, validated by computational and experimental results. Battery-free, wireless devices and colorimetric sensors for environmental measurements provide simple examples of a wide spectrum of applications of these unusual concepts.

Viscoelastic control of spatiotemporal order in bacterial active matter.

Active matter consists of units that generate mechanical work by consuming energy1. Examples include living systems (such as assemblies of bacteria2-5 and biological tissues6,7), biopolymers driven by molecular motors8-11 and suspensions of synthetic self-propelled particles12-14. A central goal is to understand and control the self-organization of active assemblies in space and time. Most active systems exhibit either spatial order mediated by interactions that coordinate the spatial structure and the motion of active agents12,14,15 or the temporal synchronization of individual oscillatory dynamics2. The simultaneous control of spatial and temporal organization is more challenging and generally requires complex interactions, such as reaction-diffusion hierarchies16 or genetically engineered cellular circuits2. Here we report a simple technique to simultaneously control the spatial and temporal self-organization of bacterial active matter. We confine dense active suspensions of Escherichia coli cells and manipulate a single macroscopic parameter-namely, the viscoelasticity of the suspending fluid- through the addition of purified genomic DNA. This reveals self-driven spatial and temporal organization in the form of a millimetre-scale rotating vortex with periodically oscillating global chirality of tunable frequency, reminiscent of a torsional pendulum. By combining experiments with an active-matter model, we explain this behaviour in terms of the interplay between active forcing and viscoelastic stress relaxation. Our findings provide insight into the influence of bacterial motile behaviour in complex fluids, which may be of interest in health- and ecology-related research, and demonstrate experimentally that rheological properties can be harnessed to control active-matter flows17,18. We envisage that our millimetre-scale, tunable, self-oscillating bacterial vortex may be coupled to actuation systems to act a 'clock generator' capable of providing timing signals for rhythmic locomotion of soft robots and for programmed microfluidic pumping19, for example, by triggering the action of a shift register in soft-robotic logic devices20.

Mimicking angiogenic microenvironment of alveolar soft-part sarcoma in a microfluidic coculture vasculature chip.

Alveolar soft-part sarcoma (ASPS) is a slow-growing soft tissue sarcoma with high mortality rates that affects adolescents and young adults. ASPS resists conventional chemotherapy; thus, decades of research have elucidated pathogenic mechanisms driving the disease, particularly its angiogenic capacities. Integrated blood vessels that are rich in pericytes (PCs) and metastatic potential are distinctive of ASPS. To mimic ASPS angiogenic microenvironment, a microfluidic coculture vasculature chip has been developed as a three-dimensional (3D) spheroid composed of mouse ASPS, a layer of PCs, and endothelial cells (ECs). This ASPS-on-a-chip provided functional and morphological similarity as the in vivo mouse model to elucidate the cellular crosstalk within the tumor vasculature before metastasis. We successfully reproduce ASPS spheroid and leaky vessels representing the unique tumor vasculature to assess effective drug delivery into the core of a solid tumor. Furthermore, this ASPS angiogenesis model enabled us to investigate the role of proteins in the intracellular trafficking of bioactive signals from ASPS to PCs and ECs during angiogenesis, including Rab27a and Sytl2. The results can help to develop drugs targeting the crosstalk between ASPS and the adjacent cells in the tumoral microenvironment.

Genetic and phenotypic profiling of single living circulating tumor cells from patients with microfluidics.

Accurate prediction of the efficacy of immunotherapy for cancer patients through the characterization of both genetic and phenotypic heterogeneity in individual patient cells holds great promise in informing targeted treatments, and ultimately in improving care pathways and clinical outcomes. Here, we describe the nanoplatform for interrogating living cell host-gene and (micro-)environment (NICHE) relationships, that integrates micro- and nanofluidics to enable highly efficient capture of circulating tumor cells (CTCs) from blood samples. The platform uses a unique nanopore-enhanced electrodelivery system that efficiently and rapidly integrates stable multichannel fluorescence probes into living CTCs for in situ quantification of target gene expression, while on-chip coculturing of CTCs with immune cells allows for the real-time correlative quantification of their phenotypic heterogeneities in response to immune checkpoint inhibitors (ICI). The NICHE microfluidic device provides a unique ability to perform both gene expression and phenotypic analysis on the same single cells in situ, allowing us to generate a predictive index for screening patients who could benefit from ICI. This index, which simultaneously integrates the heterogeneity of single cellular responses for both gene expression and phenotype, was validated by clinically tracing 80 non-small cell lung cancer patients, demonstrating significantly higher AUC (area under the curve) (0.906) than current clinical reference for immunotherapy prediction.

Time-resolved cryo-EM using a combination of droplet microfluidics with on-demand jetting.

Single-particle cryogenic electron microscopy (cryo-EM) allows reconstruction of high-resolution structures of proteins in different conformations. Protein function often involves transient functional conformations, which can be resolved using time-resolved cryo-EM (trEM). In trEM, reactions are arrested after a defined delay time by rapid vitrification of protein solution on the EM grid. Despite the increasing interest in trEM among the cryo-EM community, making trEM samples with a time resolution below 100 ms remains challenging. Here we report the design and the realization of a time-resolved cryo-plunger that combines a droplet-based microfluidic mixer with a laser-induced generator of microjets that allows rapid reaction initiation and plunge-freezing of cryo-EM grids. Using this approach, a time resolution of 5 ms was achieved and the protein density map was reconstructed to a resolution of 2.1 Å. trEM experiments on GroEL:GroES chaperonin complex resolved the kinetics of the complex formation and visualized putative short-lived conformations of GroEL-ATP complex.

Migrating Myeloid Cells Sense Temporal Dynamics of Chemoattractant Concentrations.

Chemoattractant-mediated recruitment of hematopoietic cells to sites of pathogen growth or tissue damage is critical to host defense and organ homeostasis. Chemotaxis is typically considered to rely on spatial sensing, with cells following concentration gradients as long as these are present. Utilizing a microfluidic approach, we found that stable gradients of intermediate chemokines (CCL19 and CXCL12) failed to promote persistent directional migration of dendritic cells or neutrophils. Instead, rising chemokine concentrations were needed, implying that temporal sensing mechanisms controlled prolonged responses to these ligands. This behavior was found to depend on G-coupled receptor kinase-mediated negative regulation of receptor signaling and contrasted with responses to an end agonist chemoattractant (C5a), for which a stable gradient led to persistent migration. These findings identify temporal sensing as a key requirement for long-range myeloid cell migration to intermediate chemokines and provide insights into the mechanisms controlling immune cell motility in complex tissue environments.

Spin-enhanced nanodiamond biosensing for ultrasensitive diagnostics.

The quantum spin properties of nitrogen-vacancy defects in diamond enable diverse applications in quantum computing and communications1. However, fluorescent nanodiamonds also have attractive properties for in vitro biosensing, including brightness2, low cost3 and selective manipulation of their emission4. Nanoparticle-based biosensors are essential for the early detection of disease, but they often lack the required sensitivity. Here we investigate fluorescent nanodiamonds as an ultrasensitive label for in vitro diagnostics, using a microwave field to modulate emission intensity5 and frequency-domain analysis6 to separate the signal from background autofluorescence7, which typically limits sensitivity. Focusing on the widely used, low-cost lateral flow format as an exemplar, we achieve a detection limit of 8.2 × 10-19 molar for a biotin-avidin model, 105 times more sensitive than that obtained using gold nanoparticles. Single-copy detection of HIV-1 RNA can be achieved with the addition of a 10-minute isothermal amplification step, and is further demonstrated using a clinical plasma sample with an extraction step. This ultrasensitive quantum diagnostics platform is applicable to numerous diagnostic test formats and diseases, and has the potential to transform early diagnosis of disease for the benefit of patients and populations.

Rapid formation of bioaggregates and morphology transition to biofilm streamers induced by pore-throat flows.

Bioaggregates are condensed porous materials comprising microbes, organic and inorganic matters, and water. They are commonly found in natural and engineered porous media and often cause clogging. Despite their importance, the formation mechanism of bioaggregates in porous media systems is largely unknown. Through microfluidic experiments and direct numerical simulations of fluid flow, we show that the rapid bioaggregation is driven by the interplay of the viscoelastic nature of biomass and hydrodynamic conditions at pore throats. At an early stage, unique flow structures around a pore throat promote the biomass attachment at the throat. Then, the attached biomass fluidizes when the shear stress at the partially clogged pore throat reaches a critical value. After the fluidization, the biomass is displaced and accumulated in the expansion region of throats forming bioaggregates. We further find that such criticality in shear stress triggers morphological changes in bioaggregates from rounded- to streamer-like shapes. This knowledge was used to control the clogging of throats by tuning the flow conditions: When the shear stress at the throat exceeded the critical value, clogging was prevented. The bioaggregation process did not depend on the detailed pore-throat geometry, as we reproduced the same dynamics in various pore-throat geometries. This study demonstrates that pore-throat structures, which are ubiquitous in porous media systems, induce bioaggregation and can lead to abrupt disruptions in flow.

Impact of crowding on the diversity of expanding populations.

Crowding effects critically impact the self-organization of densely packed cellular assemblies, such as biofilms, solid tumors, and developing tissues. When cells grow and divide, they push each other apart, remodeling the structure and extent of the population's range. Recent work has shown that crowding has a strong impact on the strength of natural selection. However, the impact of crowding on neutral processes, which controls the fate of new variants as long as they are rare, remains unclear. Here, we quantify the genetic diversity of expanding microbial colonies and uncover signatures of crowding in the site frequency spectrum. By combining Luria-Delbrück fluctuation tests, lineage tracing in a novel microfluidic incubator, cell-based simulations, and theoretical modeling, we find that the majority of mutations arise behind the expanding frontier, giving rise to clones that are mechanically "pushed out" of the growing region by the proliferating cells in front. These excluded-volume interactions result in a clone-size distribution that solely depends on where the mutation first arose relative to the front and is characterized by a simple power law for low-frequency clones. Our model predicts that the distribution depends on a single parameter-the characteristic growth layer thickness-and hence allows estimation of the mutation rate in a variety of crowded cellular populations. Combined with previous studies on high-frequency mutations, our finding provides a unified picture of the genetic diversity in expanding populations over the whole frequency range and suggests a practical method to assess growth dynamics by sequencing populations across spatial scales.