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Bacterial ice nucleating proteins (INPs) are exceptionally effective in promoting the kinetically hindered transition of water to ice. Their efficiency relies on the assembly of INPs into large functional aggregates, with the size of ice nucleation sites determining activity. Experimental freezing spectra have revealed two distinct, defined aggregate sizes, typically classified as class A and C ice nucleators (INs). Despite the importance of INPs and years of extensive research, the precise number of INPs forming the two aggregate classes, and their assembly mechanism have remained enigmatic. Here, we report that bacterial ice nucleation activity emerges from more than two prevailing aggregate species and identify the specific number of INPs responsible for distinct crystallization temperatures. We find that INP dimers constitute class C INs, tetramers class B INs, and hexamers and larger multimers are responsible for the most efficient class A activity. We propose a hierarchical assembly mechanism based on tyrosine interactions for dimers, and electrostatic interactions between INP dimers to produce larger aggregates. This assembly is membrane-assisted: Increasing the bacterial outer membrane fluidity decreases the population of the larger aggregates, while preserving the dimers. Inversely, Dulbecco’s Phosphate-Buffered Saline buffer increases the population of multimeric class A and B aggregates 200-fold and endows the bacteria with enhanced stability toward repeated freeze-thaw cycles. Our analysis suggests that the enhancement results from the better alignment of dimers in the negatively charged outer membrane, due to screening of their electrostatic repulsion. This demonstrates significant enhancement of the most potent bacterial INs. 

Theθ-temperature of linear, ring, and poly[n]catenane polymers as characterized by varying LJ cutoff,r_cvalues. Higherr_cvalues correspond to lowerθ-temperature. 

We present a generalization of the geometric phase to pure and thermal states in $$\mathcal{PT}$$-symmetric quantum mechanics (PTQM) based on the approach of the interferometric geometric phase (IGP). The formalism first introduces the parallel-transport conditions of quantum states and reveals two geometric phases, $$\theta^1$$ and $$\theta^2$$, for pure states in PTQM according to the states under parallel-transport. Due to the non-Hermitian Hamiltonian in PTQM, $$\theta^1$$ is complex and $$\theta^2$$ is its real part. The imaginary part of $$\theta^1$$ plays an important role when we generalize the IGP to thermal states in PTQM. The generalized IGP modifies the thermal distribution of a thermal state, thereby introducing effective temperatures. \textcolor{red}{At certain critical points, the generalized IGP may exhibit discrete jumps at finite temperatures, signaling a geometric phase transition. We illustrate the IGP of PTQM through two examples and compare their differences}. 

We first compare the geometric frameworks behind the Uhlmann andBerry phases in a fiber-bundle language and then evaluate the Uhlmannphases of bosonic and fermionic coherent states. The Uhlmann phases ofboth coherent states are shown to carry geometric information anddecrease smoothly with temperature. Importantly, the Uhlmann phasesapproach the corresponding Berry phases as temperature decreases.Together with previous examples in the literature, we propose acorrespondence between the Uhlmann and Berry phases in thezero-temperature limit as a general property except some special casesand present a conditional proof of the correspondence.