Positive feedback in biochemical networks can lead to a bifurcation in state space. Universality implies that if molecules are well mixed, this bifurcation should exhibit the critical scaling behavior of the Ising universality class in the mean-field limit. Making this statement quantitative requires the appropriate mapping between the biochemical parameters and the Ising parameters. Here we derive this mapping rigorously and uniquely for a broad class of stochastic birth-death models with feedback, and show that the expected static and dynamic critical exponents emerge. The generality of the mapping allows us to extract the order parameter, effective temperature, magnetic field,  and heat capacity from T cell flow cytometry data without needing to know the underlying molecular details. We find that T cells obey critical scaling relations and exhibit critical slowing down, and that the heat capacity determines molecule number from fluorescence data. We demonstrate that critical scaling holds even as our system is driven out of its steady state, via the Kibble-Zurek mechanism for driven critical systems. Our approach places a ubiquitous biological mechanism into a known class of physical systems and is immediately applicable to other biological data .
We make rigorous the notion of universality in well-mixed stochastic models of biochemical feedback, namely that they scale near their bifurcation point according to the exponents of the mean-field Ising universality class . In doing so, we derive a mapping of the biochemical parameters to an effective temperature, magnetic field, order parameter, and heat capacity . These effective thermodynamic quantities can be extracted from biological data without fitting or knowledge of the underlying molecular details. We demonstrate this procedure on fluorescence data from mouse T cells and interpret the findings. In the process, we discover an unanticipated result: the heat capacity allows inference of absolute molecule number from fluorescence intensity. We explain this result in terms of the underlying fluctuations and demonstrate the generality of our work .
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Positive feedback in biochemical networks can lead to a bifurcation in state space. Universality implies that if molecules are well mixed, this bifurcation should exhibit the critical scaling behavior of the
We make rigorous the notion of universality in well-mixed stochastic models of biochemical feedback, namely that they scale near their bifurcation point according to the exponents of the mean-field
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in the mean-field limit. Making this statement quantitative requires the appropriate mapping between the biochemical parameters and the Ising parameters. Here we derive this mapping rigorously and uniquely for a broad class of stochastic birth-death models with feedback, and show that the expected static and dynamic critical exponents emerge. The generality of the mapping allows us to extract the order parameter,
. In doing so, we derive a mapping of the biochemical parameters to an
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order parameter,
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from T cell flow cytometry data without needing to know
. These effective thermodynamic quantities can be extracted from biological data without fitting or knowledge of
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find that T cells obey critical scaling relations and exhibit critical slowing down, and that
demonstrate this procedure on fluorescence data from mouse T cells and interpret the findings. In the process, we discover an unanticipated result:
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determines
allows inference of absolute
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data. We demonstrate that critical scaling holds even as our system is driven out of its steady state, via the Kibble-Zurek mechanism for driven critical systems. Our approach places a ubiquitous biological mechanism into a known class of physical systems and is immediately applicable to other biological data
intensity. We explain this result in terms of the underlying fluctuations and demonstrate the generality of our work