Bilayer membranes composed of cholesterol and phospholipids exhibit diverse forms of nonideal mixing. In particular, many previous studies document macroscopic liquid-liquid phase separation as well ...as nanometer-scale heterogeneity in membranes of phosphatidylcholine (PC) lipids and cholesterol. Here, we present experimental measurements of cholesterol chemical potential (μc) in binary membranes containing dioleoyl PC (DOPC), 1-palmitoyl-2-oleoyl PC (POPC), or dipalmitoyl PC (DPPC), and in ternary membranes of DOPC and DPPC, referenced to crystalline cholesterol. μc is the thermodynamic quantity that dictates the availability of cholesterol to bind other factors, and notably must be equal between coexisting phases of a phase separated mixture. It is simply related to concentration under conditions of ideal mixing, but is far from ideal for the majority of lipid mixtures investigated here. Measurements of μc can vary with phospholipid composition by 1.5 kBT at constant cholesterol mole fraction implying a more than fivefold change in its availability for binding receptors and other reactions. Experimental measurements are fit to thermodynamic models including cholesterol-DPPC complexes or pairwise interactions between lipid species to provide intuition about the magnitude of interactions. These findings reinforce that μc depends on membrane composition overall, suggesting avenues for cells to alter the availability of cholesterol without varying cholesterol concentration.
Complex models in physics, biology, economics, and engineering are often
, meaning that the model parameters are not well determined by the model predictions for collective behavior. Many parameter ...combinations can vary over decades without significant changes in the predictions. This review uses information geometry to explore sloppiness and its deep relation to emergent theories. We introduce the
of predictions, whose coordinates are the model parameters. Its
structure explains why only a few parameter combinations matter for the behavior. We review recent rigorous results that connect the hierarchy of hyperribbon widths to approximation theory, and to the smoothness of model predictions under changes of the control variables. We discuss recent geodesic methods to find simpler models on nearby boundaries of the model manifold-emergent theories with fewer parameters that explain the behavior equally well. We discuss a Bayesian prior which optimizes the mutual information between model parameters and experimental data, naturally favoring points on the emergent boundary theories and thus simpler models. We introduce a 'projected maximum likelihood' prior that efficiently approximates this optimal prior, and contrast both to the poor behavior of the traditional Jeffreys prior. We discuss the way the renormalization group coarse-graining in statistical mechanics introduces a flow of the model manifold, and connect stiff and sloppy directions along the model manifold with relevant and irrelevant eigendirections of the renormalization group. Finally, we discuss recently developed 'intensive' embedding methods, allowing one to visualize the predictions of arbitrary probabilistic models as low-dimensional projections of an isometric embedding, and illustrate our method by generating the model manifold of the Ising model.
Diverse molecules induce general anesthesia with potency strongly correlated with both their hydrophobicity and their effects on certain ion channels. We recently observed that several n-alcohol ...anesthetics inhibit heterogeneity in plasma-membrane-derived vesicles by lowering the critical temperature (Tc) for phase separation. Here, we exploit conditions that stabilize membrane heterogeneity to further test the correlation between the anesthetic potency of n-alcohols and effects on Tc. First, we show that hexadecanol acts oppositely to n-alcohol anesthetics on membrane mixing and antagonizes ethanol-induced anesthesia in a tadpole behavioral assay. Second, we show that two previously described “intoxication reversers” raise Tc and counter ethanol’s effects in vesicles, mimicking the findings of previous electrophysiological and behavioral measurements. Third, we find that elevated hydrostatic pressure, long known to reverse anesthesia, also raises Tc in vesicles with a magnitude that counters the effect of butanol at relevant concentrations and pressures. Taken together, these results demonstrate that ΔTc predicts anesthetic potency for n-alcohols better than hydrophobicity in a range of contexts, supporting a mechanistic role for membrane heterogeneity in general anesthesia.
An analog communication channel typically achieves its full capacity when the distribution of inputs is discrete, composed of just
K
symbols, such as voltage levels or wavelengths. As the effective ...noise level goes to zero, for example by sending the same message multiple times, it is known that optimal codes become continuous. Here we derive a scaling law for the optimal number of symbols in this limit, finding a novel rational scaling exponent. The number of symbols in the optimal code grows as
log
K
∼
I
4
/
3
, where the channel capacity
I
increases with decreasing noise. The same scaling applies to other problems equivalent to maximizing channel capacity over a continuous distribution.
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