{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T17:00:45Z","timestamp":1790787645579,"version":"4.1.0"},"reference-count":31,"publisher":"National Academy of Sciences","issue":"40","license":[{"start":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T00:00:00Z","timestamp":1790726400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2026,10,6]]},"abstract":"<jats:p>\n                    Droplet microfluidics enables compartmentalized single-cell analysis, but conventional single-nozzle systems cannot efficiently process millions of cells needed to identify rare populations. This bottleneck is particularly important in antibody discovery, which requires deep B cell sampling while preserving the native pairing of antibody heavy and light chains. Parallelization increases throughput, but cumulative pressure losses cause flow nonuniformity across large networks. Here, we establish an exact hydrodynamic model for ladder-geometry networks and demonstrate that the maximum flow deviation scales quadratically with the number of parallel units [\n                    <jats:italic toggle=\"yes\">O<\/jats:italic>\n                    (\n                    <jats:italic toggle=\"yes\">\n                      N\n                      <jats:sup>2<\/jats:sup>\n                    <\/jats:italic>\n                    )] rather than linearly [\n                    <jats:italic toggle=\"yes\">O<\/jats:italic>\n                    (\n                    <jats:italic toggle=\"yes\">N<\/jats:italic>\n                    )]. Computational fluid dynamics simulations for representative network geometries validate this scaling law. We extend it to hierarchical (\n                    <jats:italic toggle=\"yes\">A<\/jats:italic>\n                    \u00d7\n                    <jats:italic toggle=\"yes\">B<\/jats:italic>\n                    ) networks and implement the resulting rules in a computational tool for forward evaluation and inverse channel design. Guided by this framework, we develop 100- and 360-generator chips that increase droplet generation rates by up to 53.8-fold while maintaining stable dripping, low droplet-size variation (CV \u2264 13.8%), and low mean cell occupancy (\u03bb \u2264 0.02). Using a two-stage workflow, we construct natively paired antibody libraries from 1 million primary human B cells, achieving a 14-fold reduction in expensive reagent consumption relative to conventional methods. We further validate the encapsulation of 10 million cells within 40 min, increasing cell-processing and repertoire-sampling capacity by approximately one order of magnitude, crucial for the deep mining of immune repertoires. By overcoming fundamental scaling bottlenecks, this platform establishes a highly scalable, cost-efficient paradigm for massive-scale antibody library construction and broad microfluidic applications.\n                  <\/jats:p>","DOI":"10.1073\/pnas.2612455123","type":"journal-article","created":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T16:13:32Z","timestamp":1790784812000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":0,"title":["Scaling laws for massively parallel microfluidics enable rapid construction of ten-million-scale natively paired antibody libraries"],"prefix":"10.1073","volume":"123","author":[{"given":"Hongyu","family":"Chen","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/00mcjh785","id-type":"ROR","asserted-by":"publisher"}],"name":"State Key Laboratory of Vaccines for Infectious Diseases, Xiang An Biomedicine Laboratory, School of Public Health, Xiamen University","place":["Xiamen, 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M. Sidore F. Lan S. W. Lim A. R. Abate Enhanced sequencing coverage with digital droplet multiple displacement amplification. Nucleic Acids Res. 44 e66\u2013e66 (2016).","DOI":"10.1093\/nar\/gkv1493"},{"key":"e_1_3_4_15_2","doi-asserted-by":"publisher","DOI":"10.1021\/acs.analchem.8b01988"},{"key":"e_1_3_4_16_2","doi-asserted-by":"publisher","DOI":"10.1039\/c2lc21033a"},{"key":"e_1_3_4_17_2","doi-asserted-by":"publisher","DOI":"10.1039\/C5LC01025J"},{"key":"e_1_3_4_18_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2303567120"},{"key":"e_1_3_4_19_2","doi-asserted-by":"crossref","unstructured":"K. Adegoke R. Frontczak T. Goy Binomial fibonacci sums from chebyshev polynomials. J. Integer Seq. 26 Article 23.9.6 (2023).","DOI":"10.47443\/ejm.2023.055"},{"key":"e_1_3_4_20_2","volume-title":"Theoretical Microfluidics","author":"Bruus H.","year":"2008","unstructured":"H. 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