Lieberman-Aiden, E. et al. Comprehensive mapping of long-range interactions reveals folding principles of the human genome. Science 326, 289 (2009).
Google Scholar
Tang, F. et al. mRNA-seq whole-transcriptome analysis of a single cell. Nat. Methods 6, 377 (2009).
Google Scholar
Treutlein, B. et al. Reconstructing lineage hierarchies of the distal lung epithelium using single-cell RNA-seq. Nature 509, 371 (2014).
Google Scholar
Lubeck, E. & Cai, L. Single-cell systems biology by super-resolution imaging and combinatorial labeling. Nat. Methods 9, 743 (2012).
Google Scholar
Sureshchandra, S. et al. Deep profiling of human T cells defines compartmentalized clones and phenotypic trajectories across blood and tonsils. Immunity 58, 3130–3143.e8 (2025).
Google Scholar
Thompson, L. R. et al. A communal catalogue reveals Earth’s multiscale microbial diversity. Nature 551, 457 (2017).
Google Scholar
Sunagawa, S. et al. Tara Oceans: towards global ocean ecosystems biology. Nat. Rev. Microbiol. 18, 428 (2020).
Google Scholar
The Human Microbiome Project Consortium. Structure, function and diversity of the healthy human microbiome. Nature 486, 207 (2012).
Angelaki, D. et al. A brain-wide map of neural activity during complex behaviour. Nature 645, 177 (2025).
Google Scholar
McKenzie-Smith, G. C., Wolf, S. W., Ayroles, J. F. & Shaevitz, J. W. Capturing continuous, long timescale behavioral changes in Drosophila melanogaster postural data. PLoS Comput. Biol. 21, e1012753 (2025).
Google Scholar
Gutenkunst, R. N. et al. Universally sloppy parameter sensitivities in systems biology models. PLoS Comput. Biol. 3, e189 (2007).
Google Scholar
Transtrum, M. K., Machta, B. B. & Sethna, J. P. Geometry of nonlinear least squares with applications to sloppy models and optimization. Phys. Rev. E 83, 036701 (2011).
Transtrum, M. K. & Qiu, P. Model reduction by manifold boundaries. Phys. Rev. Lett. 113, 098701 (2014).
Google Scholar
Scott, M. et al. Interdependence of cell growth and gene expression: origins and consequences. Science 330, 1099 (2010).
Google Scholar
Scott, M. & Hwa, T. Shaping bacterial gene expression by physiological and proteome allocation constraints. Nat. Rev. Microbiol. 21, 327 (2023).
Google Scholar
Corson, F. & Siggia, E. D. Gene-free methodology for cell fate dynamics during development. eLife 6, e30743 (2017).
Google Scholar
Rand, D. A., Raju, A., Sáez, M., Corson, F. & Siggia, E. D. Geometry of gene regulatory dynamics. Proc. Natl. Acad. Sci. USA 118, e2109729118 (2021).
Google Scholar
Petti, S., Reddy, G. & Desai, M. M. Inferring sparse structure in genotype–phenotype maps. Genetics 225, iyad127 (2023).
Google Scholar
Johnson, M. S., Reddy, G. & Desai, M. M. Epistasis and evolution: recent advances and an outlook for prediction. BMC Biol. 21, 120 (2023).
Google Scholar
Van Den Brink, S. C. et al. Single-cell and spatial transcriptomics reveal somitogenesis in gastruloids. Nature 582, 405 (2020).
Google Scholar
Pyo, A. G. et al. Data-driven discovery of biophysical T cell receptor cospecificity rules. PRX Life 3, 033005 (2025).
Meshulam, L. & Bialek, W. Statistical mechanics for networks of real neurons. Rev. Mod. Phys. 97, 045002 (2025).
Zhong, L. et al. Unsupervised pretraining in biological neural networks. Nature 644, 741–748 (2025).
Google Scholar
Floyd, C., Dinner, A. R., Murugan, A. & Vaikuntanathan, S. Limits on the computational expressivity of non-equilibrium biophysical processes. Nat. Commun. 16, 7184 (2025).
Google Scholar
Chari, T. & Pachter, L. The specious art of single-cell genomics. PLoS Comput. Biol. 19, e1011288 (2023).
Google Scholar
Grobecker, P., Sakoparnig, T. & van Nimwegen, E. Identifying cell states in single-cell RNA-seq data at statistically maximal resolution. PLoS Comput. Biol. 20, e1012224 (2024).
Google Scholar
Furlong, E. E. & Levine, M. Developmental enhancers and chromosome topology. Science 361, 1341 (2018).
Google Scholar
Bintu, L. et al. Transcriptional regulation by the numbers: applications. Curr. Opin. Genet. Dev. 15, 125 (2005).
Google Scholar
Scholes, C., DePace, A. H. & Sánchez, Á. Combinatorial gene regulation through kinetic control of the transcription cycle. Cell Syst. 4, 97 (2017).
Google Scholar
Tkacik, G., Callan Jr, C. G. & Bialek, W. Information flow and optimization in transcriptional regulation. Proc. Natl. Acad. Sci. USA 105, 12265 (2008).
Google Scholar
Bauer, M., Petkova, M., Gregor, T., Wieschaus, E. F. & Bialek, W. Trading bits in the readout from a genetic network. Proc. Natl. Acad. Sci. USA 118, e2109011118 (2021).
Google Scholar
Tkačik, G. & ten Wolde, P. R. Information processing in biochemical networks. Annu. Rev. Biophys. 54, 249 (2025).
Google Scholar
Sokolowski, T. R., Gregor, T., Bialek, W. & Tkačik, G. Deriving a genetic regulatory network from an optimization principle. Proc. Natl. Acad. Sci. USA 122, e2402925121 (2025).
Google Scholar
Mijatović, T. et al. Weak transcription factor clustering at binding sites can facilitate information transfer from molecular signals. PRX Life 4, 013003 (2026).
Bialek, W. Biophysics: Searching for Principles (Princeton University Press, 2012).
Bialek, W., van Steveninck, R. R. D. R. & Tishby, N. Efficient coding in sensory systems. In Proc. IEEE International Symposium on Information Theory 659–663 (IEEE, 2016).
Laughlin, S. A simple coding procedure enhances a neuron’s information capacity. Z. Naturforsch. C 36, 910 (1981).
Google Scholar
Bauer, M. et al. Optimization and variability can coexist. Preprint at https://arXiv.org/abs/2505.23398 (2025).
Witteveen, O. et al. Optimizing information transmission in the canonical Wnt pathway. Phys. Rev. Res. 8, 01329 (2026).
Selimkhanov, J. et al. Accurate information transmission through dynamic biochemical signaling networks. Science 346, 1370 (2014).
Google Scholar
Ahamed, T., Costa, A. C. & Stephens, G. J. Capturing the continuous complexity of behaviour in Caenorhabditis elegans. Nat. Phys. 17, 275 (2021).
Google Scholar
Moor, A.-L. & Zechner, C. Dynamic information transfer in stochastic biochemical networks. Phys. Rev. Res. 5, 013032 (2023).
Google Scholar
Reinhardt, M., Tkačik, G. & ten Wolde, P. R. Path weight sampling: Exact Monte Carlo computation of the mutual information between stochastic trajectories. Phys. Rev. X 13, 041017 (2023).
Google Scholar
Reinhardt, M. et al. Mutual information rate–linear noise approximation and exact computation. Preprint at https://arXiv.org/abs/2508.21220 (2025).
Raju, A. & Siggia, E. D. A geometrical perspective on development. Dev. Growth Differ. 65, 245 (2023).
Google Scholar
Gilpin, W. Generative learning for nonlinear dynamics. Nat. Rev. Phys. 6, 194 (2024).
Yadav, M., Koch, D. & Koseska, A. Homeorhetic regulation of cellular phenotype. Preprint at bioRxiv https://doi.org/10.1101/2025.06.06.658216 (2025).
Nguyen, A. & Reddy, G. Differential learning kinetics govern the transition from memorization to generalization during in-context learning. International Conference for Learning Representations. (2025).
Zentner, A. et al. Information processing driven by multicomponent surface condensates. Preprint at https://arXiv.org/abs/2509.08100 (2025).
Rukhlenko, O. S. et al. Control of cell state transitions. Nature 609, 975 (2022).
Google Scholar
Zhou, P., Wang, S., Li, T. & Nie, Q. Dissecting transition cells from single-cell transcriptome data through multiscale stochastic dynamics. Nat. Commun. 12, 5609 (2021).
Google Scholar
Xing, J. & Kim, K. S. Application of the projection operator formalism to non-Hamiltonian dynamics. J. Chem. Phys. 134, 044132 (2011).
Google Scholar
Chen, Y. et al. GraphVelo allows for accurate inference of multimodal velocities and molecular mechanisms for single cells. Nat. Commun. 16, 7831 (2025).
Google Scholar
Wang, W., Ni, K., Poe, D. & Xing, J. Transiently increased coordination in gene regulation during cell phenotypic transitions. PRX Life 2, 043009 (2024).
Google Scholar
Hari, K. et al. Low dimensionality of phenotypic space as an emergent property of coordinated teams in biological regulatory networks. iScience 28, 111730 (2025).
Google Scholar
Qiu, X. et al. Mapping transcriptomic vector fields of single cells. Cell 185, 690 (2022).
Google Scholar
Islam, S. & Bhattacharya, S. Dynamical systems theory as an organizing principle for single-cell biology. npj Syst. Biol. Appl. 11, 85 (2025).
Google Scholar
Samal, A. & Jain, S. The regulatory network of E. coli as a Boolean dynamical system exhibits both homeostasis and flexibility of response. BMC Syst. Biol. 2, 21 (2008).
Google Scholar
Pandey, P. P., Singh, H. & Jain, S. Exponential trajectories, cell size fluctuations, and the adder property in bacteria follow from simple chemical dynamics and division control. Phys. Rev. E 101, 062406 (2020).
Google Scholar
Freedman, S. L., Xu, B., Goyal, S. & Mani, M. A dynamical systems treatment of transcriptomic trajectories in hematopoiesis. Development 150, dev201280 (2023).
Google Scholar
Farrell, S., Mani, M. & Goyal, S. Inferring single-cell transcriptomic dynamics with structured latent gene expression dynamics. Cell Rep. Methods 3, 100479 (2023).
Shakiba, N. et al. Cell competition during reprogramming gives rise to dominant clones. Science 364, eaan0925 (2019).
Google Scholar
Ryu, H. et al. Frequency modulation of ERK activation dynamics rewires cell fate. Mol. Syst. Biol. 11, 838 (2015).
Google Scholar
Rosen, S. et al. Anti-resonance in developmental signaling regulates cell fate decisions. eLife 14, RP107794 (2026).
Google Scholar
Kloeden, P. E. & Rasmussen, M. Nonautonomous Dynamical Systems Vol. 176 (American Mathematical Society, 2011).
Nandan, A., Das, A., Lott, R. & Koseska, A. Cells use molecular working memory to navigate in changing chemoattractant fields. eLife 11, e76825 (2022).
Google Scholar
Sáez, M. et al. Statistically derived geometrical landscapes capture principles of decision-making dynamics during cell fate transitions. Cell Syst. 13, 12 (2022).
Google Scholar
Raju, A. & Siggia, E. D. A geometrical model of cell fate specification in the mouse blastocyst. Development 151, dev202467 (2024).
Google Scholar
Bengio, Y., Courville, A. & Vincent, P. Representation learning: a review and new perspectives. IEEE Trans. Pattern Anal. Mach. Intell. 35, 1798 (2013).
Google Scholar
Kingma, D. P. & Welling, M. Auto-encoding variational Bayes. In Proc. International Conference on Learning Representations (ICLR, 2014).
Goodfellow, I. J. et al. Generative adversarial networks. In Proc. Advances in Neural Information Processing Systems 2672–268 (NeurIPS, 2014).
Lopez, R. et al. Deep generative modeling for single-cell transcriptomics. Nat. Methods 15, 1053 (2018).
Google Scholar
Marouf, M. et al. Realistic in silico generation and augmentation of single-cell RNA-seq data using generative adversarial networks. Nat. Commun. 11, 166 (2020).
Google Scholar
Nikhat, A. et al. Transcriptional noise sets fundamental limits to decoding circadian clock phase from single-cell RNA snapshots. https://doi.org/10.1016/j.isci.2026.115394 (iScience, 2026).
Wigner, E. P. On the statistical distribution of the widths and spacings of nuclear resonance levels. Math. Proc. Camb. Phil. Soc. 47, 790–798 (1951).
Google Scholar
Dyson, F. J. Statistical theory of the energy levels of complex systems. I. J. Math. Phys. 3, 140 (1962).
Google Scholar
May, R. M. Will a large complex system be stable? Nature 238, 413 (1972).
Google Scholar
Nemenman, I. & Mehta, P. Randomness with constraints: constructing minimal models for high-dimensional biology. Preprint at https://arXiv.org/abs/2509.03765 (2025).
Cui, W., Marsland III, R. & Mehta, P. Les Houches lectures on community ecology: From niche theory to statistical mechanics. Preprint at https://arXiv.org/abs/2403.05497 (2024).
Bunin, G. Ecological communities with Lotka–Volterra dynamics. Phys. Rev. E 95, 042414 (2017).
Google Scholar
Feng, Z., Blumenthal, E., Mehta, P. & Goyal, A. A theory of ecological invasions and its implications for eco-evolutionary dynamics. Proc. Natl. Acad. Sci. USA 122, e250585012 (2025).
Desponds, J., Mora, T. & Walczak, A. M. Fluctuating fitness shapes the clone-size distribution of immune repertoires. Proc. Natl. Acad. Sci. USA 113, 274 (2016).
Google Scholar
Gaimann, M. U., Nguyen, M., Desponds, J. & Mayer, A. Early life imprints the hierarchy of T cell clone sizes. eLife 9, e61639 (2020).
Google Scholar
Stephens, G. J., Johnson-Kerner, B., Bialek, W. & Ryu, W. S. Dimensionality and dynamics in the behavior of C. elegans. PLoS Comput. Biol. 4, e1000028 (2008).
Google Scholar
Brown, A. E. X. et al. A dictionary of behavioral motifs reveals clusters of genes affecting Caenorhabditis elegans locomotion. Proc. Natl. Acad. Sci. USA 110, 791 (2013).
Google Scholar
Brandstäter, A. et al. Low-dimensional chaos in a hydrodynamic system. Phys. Rev. Lett. 51, 1442 (1983).
Bialek, W. & Shaevitz, J. W. Long timescales, individual differences, and scale invariance in animal behavior. Phys. Rev. Lett. 132, 048401 (2024).
Google Scholar
Costa, A. C., Sridhar, G., Wyart, C. & Vergassola, M. Fluctuating landscapes and heavy tails in animal behavior. PRX Life 2, 023001 (2024).
Perich, M. G., Narain, D. & Gallego, J. A. A neural manifold view of the brain. Nat. Neurosci. 28, 1582–1597 (2025).
Google Scholar
Manley, J. et al. Simultaneous, cortex-wide dynamics of up to 1 million neurons reveal unbounded scaling of dimensionality with neuron number. Neuron 112, 1694 (2024).
Google Scholar
Fontenele, A. J. et al. Low-dimensional criticality embedded in high-dimensional awake brain dynamics. Sci. Adv. 10, eadj9303 (2024).
Google Scholar
