Fangzhou Xiao

Summary: Biocircuit behavior is usually discovered by drawing uncertain kinetic parameters and simulating, but the scored phenotypes are functions of steady-state species, catalytic fluxes, dominance relations, and local response matrices. We introduce flux–species sampling (FSS), which samples that functional layer directly and algebraically inverts to parameters. This coordinate change turns regulatory modes into simple dominance chambers, gives every full-dimensional behavior-realizing regime positive measure, and can replace the sampling stage of existing pipelines without changing downstream stability or phenotype tests. A sequestration toy shows how a large species regime can collapse into a narrow parameter strip. In an enzymatic feedback motif, FSS rescues free- A * adaptation missed by parameter sampling and identifies the regime as non-Michaelian and complex-dominated. In MultiFate- N , FSS separates a sampling limitation from a structural limitation and rescues parameter sets realizing all 2 ^N states. Highlights: Flux–species sampling (FSS) draws the control/function layer where biocircuit behavior is read FSS boxes intersect every full-dimensional behavior-realizing regime with positive measure FSS is no slower than parameter-space sampling and is a hot fix for existing pipelines FSS rescues non-Michaelian free- A * adaptation missed by parameter sampling FSS rescues the all-2 ^N symmetric MultiFate regime missed by fixed parameter boxes eTOC blurb: This study reframes biocircuit exploration by sampling steady-state species and fluxes rather than raw parameters. The resulting flux–species coordinate exposes regulatory dominance regimes, rescues adaptation and multistability regimes missed by parameter sampling, and gives finite sampling nulls an explicit scope.

Bacteria regulate homeostatic growth by adjusting proteome composition. In Escherichia coli , this coordination is mediated by guanosine tetraphosphate and pentaphosphate, collectively termed (p)ppGpp, which couple amino acid supply with ribsosome production. We identified a distinct architecture in Bacillus subtilis , in which guanosine triphosphate (GTP), not (p)ppGpp, controls proteome allocation. Translational inhibition resulted in GTP depletion and suppressed amino acid biosynthesis through feedback inhibition without altering ribosome abundance, establishing a regulated decoupling between total amino acid flux and proteome composition, with flux deviating from proteome-based predictions. By artificially adjusting GTP concentrations, we recoupled flux and proteome, restoring growth to maximal amounts. The regulated suboptimality enables a trade-off to balance growth and stress resilience. Similar GTP-based strategies were present in other Firmicute species, indicating possible evolutionary conservation. Proteome composition and metabolic flux have distinct regulatory layers in some bacteria.

Biocircuit functions are often valid only in specific parameter regimes, yet these regimes are rarely made explicit. We use a holistic analysis method based on regimes to derive validity conditions and introduce the Realizability Index ( R -index), quantifying the size of the valid regions in log-parameter space. The framework is applied to Michaelis-Menten kinetics, Hill functions, and enzymatic negative-feedback adaptation, showing how circuit structure and experimental control variables shape functional realizability. Our analysis shows the Hill function’s R -index goes to zero in sequential binding with increasing Hill coefficient. We also resolve an active debate about whether negative-feedback adaptation is realizable when competitive binding is taken into account, and demonstrates the superiority of the holistic R -index method over numerical parameter scans that lead to incorrect conclusions. R -index defines a validity-aware language for studying and designing functional biocircuits.

SUMMARY: Accurate signal processing is essential for proper cell functions, and can be achieved through kinetic proofreading, where an enzyme undergoes sequential state transitions and irreversible deactivation to enable high fidelity. However, synthetically constructing a biological proofreading system has been hindered by the difficulty in engineering single molecular state transitions. Here, we designed a protein circuit that combines diffusion and endocytosis to enable kinetic proofreading at the multimolecular level, without the conservation of total enzymes implicitly assumed in classic kinetic proofreading. Simulations revealed a previously overlooked yet experimentally crucial trade-off between circuit activity and fidelity, and theoretical analysis confirmed it to be fundamental in all kinetic proofreading systems. By integrating self-activation and mutual inhibition mechanisms, the circuit overcomes this activity-fidelity trade-off within biologically plausible parameter regimes. Our results extend proofreading schemes from single enzymes to a multimolecular context, and represent a practical and generalizable strategy for constructing high-fidelity synthetic biological circuits. HIGHLIGHTS: We design a multimolecular and multicellular proofreading circuit A previously overlooked yet practically relevant trade-off arises between circuit activity and fidelity The activity-fidelity trade-off is fundamental in all kinetic proofreading circuits Self-activation and mutual inhibition mechanisms collectively overcome the activity-fidelity trade-off

This paper focuses on rate-limited control of the generalized Ornstein-Uhlenbeck process where the control action can be either multiplicative or additive, and the noise variance can depend on the control action. We derive a lower bound on the data rate necessary to achieve the desired control cost. The lower bound is attained with equality if the control is performed via an additive white Gaussian channel. The system model approximates the dynamics of a discrete-state molecular birth-death process, and the result has direct implications on the control of a biomolecular system via chemical reactions, where the multiplicative control corresponds to the degradation rate, the additive control corresponds to the production rate, and the control objective is to decrease the fluctuations of the controlled molecular species around their desired concentration levels.

This paper focuses on rate-limited control of the generalized Ornstein-Uhlenbeck process where the control action can be either multiplicative or additive, and the noise variance can depend on the control action. We derive a lower bound on the data rate necessary to achieve the desired control cost. The lower bound is attained with equality if the control is performed via an additive white Gaussian channel. The system model approximates the dynamics of a discrete-state molecular birth-death process, and the result has direct implications on the control of a biomolecular system via chemical reactions, where the multiplicative control corresponds to the degradation rate, the additive control corresponds to the production rate, and the control objective is to decrease the fluctuations of the controlled molecular species around their desired concentration levels.

In a recent PNAS publication, Kirby and Zilman argued that when stochasticity is taken into account, having more steps in kinetic proofreading generally does not improve the discrimination of different receptor-binding ligands based on the counts of signaling molecules produced [1]. However, their conclusion is based on a major technical error that, once corrected, contradicts their main conclusion. Also, throughout their analysis, the authors made the implicit assumption that discrimination time is fixed. We argue below that, for a fuller understanding, kinetic proofreading for ligand discrimination should be studied in the context of speedaccuracy tradeoffs.

Balanced biosynthesis is the hallmark of bacterial cell physiology, where the concentrations of stable proteins remain steady. However, this poses a conceptual challenge to modeling the cell-cycle and cell-size controls in bacteria, as prevailing concentration-based eukaryote models are not directly applicable. In this study, we revisit and significantly extend the initiator-titration model, proposed thirty years ago, and explain how bacteria precisely and robustly control replication initiation based on the mechanism of protein copy-number sensing. Using a mean-field approach, we first derive an analytical expression of the cell size at initiation based on three biological mechanistic control parameters for an extended initiator-titration model. We also study the stability of our model analytically and show that initiation can become unstable in multifork replication conditions. Using simulations, we further show that the presence of the conversion between active and inactive initiator protein forms significantly represses initiation instability. Importantly, the two-step Poisson process set by the initiator titration step results in significantly improved initiation synchrony with CV ∼ 1 /N scaling rather than the standard scaling in the Poisson process, where N is the total number of initiators required for initiation. Our results answer two long-standing questions in replication initiation: (1) Why do bacteria produce almost two orders of magnitude more DnaA, the master initiator proteins, than required for initiation? (2) Why does DnaA exist in active (DnaA-ATP) and inactive (DnaA-ADP) forms if only the active form is competent for initiation? The mechanism presented in this work provides a satisfying general solution to how the cell can achieve precision control without sensing protein concentrations, with broad implications from evolution to the design of synthetic cells.