Multicellular organisms contain a wide variety of highly specialized cell types. The consistency and robustness of developmental trajectories suggest that complex gene regulatory networks effectively act as low-dimensional cell fate landscapes. Prior work inspired by dynamical systems theory argues that cell fate transitions fall into universal decision-making classes, but the theory connecting these geometric landscapes to high-dimensional gene expression space is still in its infancy. Here, we introduce a phenomenological model that identifies experimental signatures of decision-making classes in single-cell RNA-sequencing time-series data. The model combines low-dimensional gradient-like dynamics with high-dimensional Hopfield networks to capture the interplay between cell fate, gene expression, and signaling. We apply the framework to experimental mouse data on maturing lung alveolar cells and lineage-traced hematopoietic differentiation and show that the measured cell fate dynamics are consistent with developmental landscapes containing intermediate progenitors and saddle points. We further show that the framework can be used to understand spatial patterning and cell fate organization, focusing on Notch signaling in lung airways. Together, these results provide evidence that collective transcriptomic dynamics carry signatures of landscape features associated with universal decision-making classes.
This work introduces a self-consistent training framework for learning residue–residue interaction parameters in matrix-based coarse-grained protein models. By combining direct coupling analysis with a physics-based design model, we construct a feedback loop in which the interaction matrix is iteratively updated from sequences generated by the model itself. We provide a mathematical foundation for this behavior by showing that, for a given iterative map satisfying explicit contact-locality and spectral assumptions, the training process is a contraction, guaranteeing convergence to a unique fixed point independent of the initial interaction matrix. This fixed-point property is general for coarse-grained models in which the residue-residue energy is represented by a distance-dependent term modulated by a type-dependent coupling matrix, while the learned interaction parameters remain specific to the underlying model physics. We then examine the empirical consequence of this framework in Caterpillar, a coarse-grained potential for folding and design. Independent training trajectories, defined by different target structures and stochastic sampling, converge to statistically equivalent interaction matrices. Each trajectory recovers the full interaction solution without requiring ensemble averaging, and the averaged trajectory reaches the same result. The resulting framework provides a link between sequence statistics and physically modeled interaction energies. Applied to protein design, it yields interaction matrices associated with improved structural fidelity and accurate contact prediction, while clarifying how learned sequence patterns relate to the interactions that stabilize protein structure.
Biomolecular condensates formed by liquid-liquid phase separation organize many cellular processes, yet it remains unclear how condensate localization is coupled to protein synthesis. In particular, proteins are often translated on polysomes, where multiple ribosomes on a single mRNA generate a bottlebrush-like assembly of nascent chains, raising the possibility that translation itself could be spatially coupled to condensates. Here we develop a theoretical framework for CoTranslational Condensation (CTC), in which nascent chains on a polysome for condensate proteins interact with their condensate and thus localize translation there. Using coarse-grained simulations, we show that protein domain architecture dictates the thermodynamics of CTC, consistent with a Langmuir adsorption model. Proteins with high-affinity regions exposed early on nascent chains display much stronger condensate association than architectures in which these regions appear only late in translation. A bioinformatic analysis of 7667 condensate-associated proteins further shows that sequence architectures compatible with strong CTC are common. At the dynamical level, combining simulations with reaction-diffusion modeling reveals that CTC is kinetically feasible within typical polysome lifetimes, either through densely packed polysomes nucleating new condensates or via diffusion to preexisting condensates. As an illustrative consequence, we show that CTC can reduce the accumulation of unmodified protein intermediates by localizing their synthesis with condensates, where modification can occur promptly. Together, our results establish physical principles for how translation can couple to phase separation and identify protein architectures and cellular regimes that favor CTC.
Bacteria regulate their motility through a variety of mechanisms, including quorum sensing and other density-dependent responses mediated by diffusible signals. While nonlinear density-dependent motility is well known in active-matter theory to generate nonequilibrium spatial patterns, its consequences for the coexistence of growing, interacting species remain less explored. Here we develop a minimal spatially structured model for two strongly competing species in which local demographic interactions are coupled to an escape response: Each species increases its motility nonlinearly (sigmoidal) with the local abundance of its competitor. We show that this sigmoidal motility regulation promotes optimal spatial self-organization and can sustain long term coexistence via segregation, even in parameter regimes that yield competitive exclusion in well-mixed Lotka-Volterra dynamics. On two-dimensional lattices, the interplay between demographic competition and density-dependent motility generates a range of emergent patterns, including regimes in which the weaker competitor counterintuitively has higher total abundance. Overall, our results identify nonlinear, competitor-induced motility as a fundamental mechanism capable of sustaining coexistence in competing microbial populations.
