Judith Herzfeld

Liquid-crystal phases of self-assembled molecular aggregates

A variety of molecules reversibly self-assemble in solution, forming non-covalently bonded molecular aggregates. In many cases these aggregates are asymmetric in shape and are observed to form liquid-crystal phases. The nature of and mechanisms for liquid-crystalline ordering in such self-assembled systems is the focus of this review.

Crowding-induced organization of cytoskeletal elements: I. Spontaneous demixing of cytosolic proteins and model filaments to form filament bundles

The theory for the effects of crowding on the behavior of reversibly self-assembling solutes is extended to mixtures containing nonassembling solutes. The theory predicts that excluded volume will cause dramatic demixing into domains of long, tightly packed, highly aligned fibers coexisting with an isotropic solution of unaggregated species. It suggests that the bundling of fibers in cells is entropically driven and that accessory binding proteins in the cytoplasm serve to modulate the process rather than create it.

CROWDING-INDUCED ORGANIZATION OF CYTOSKELETAL ELEMENTS. III: SPONTANEOUS BUNDLING AND SORTING OF SELF-ASSEMBLED FILAMENTS WITH DIFFERENT FLEXIBILITIES

The typical cell contains ca. 25 vol.-% protein, of which ca. 10% forms cytoskeletal filaments and ca. 90% is non-aggregating globular protein. It has previously been theoretically predicted that, under such highly crowded conditions, rigid filaments will coalesce into tight bundles coexisting with an isotropic solution of globular proteins. In the present work we show that such spontaneous bundling will occur even when filament flexibility is taken into account because the persistence length of the filaments is much longer than the diameter of the globular proteins. The theoretical results are consistent with experimentally observed bundling of F-actin (the most flexible of the three most common types of cytoskeletal filaments) in the presence of globular macromolecules.The main effect of increased filament flexibility on bundling is to cause somewhat looser packing. In mixtures of filaments, differences in flexibilities can lead to segregation. This segregation is accentuated when the stiffer filament is also wider. The results suggest that actin filaments and microtubules will spontaneously form segregated bundles in the presence of cellular concentrations of globular proteins. While cross-linking proteins may serve to stabilize these bundles, their more important function in bundling may be to fine tune the structure (e.g., polarity and registration of filaments).

Unexpected critical points in the nematic behavior of a reversibly polymerizing system

A variety of amphiphilic molecules reversibly aggregate to form rod‐like particles that spontaneously align at sufficiently high concentrations. A model combining a lattice description of excluded volume effects and a phenomenological description of aggregate assembly is used to calculate the phase behavior of such a system. An unexpectedly rich phase diagram is predicted with critical points dependent on end effects in the aggregates. When the aggregation is very weak, there is an apparent multicritical point in the isotropic–nematic transition. This situation applies to sickle cell hemoglobin and provides the first theoretical basis for the apparent critical point observed in that system. When aggregation is not quite so weak, a first‐order nematic–nematic transition is predicted, either in addition to or merged with, the isotropic–nematic transition. The denser nematic phase contains extremely long, closely packed rods, suggestive of the hexagonal phase formed by cylindrical surfactant micelles.

Liquid crystalline order in self‐assembling systems: Orientation dependence of the particle size distribution

Proteins and surfactants can associate reversibly into large asymmetric aggregates that can form liquid crystalline phases. A general theoretical treatment is given of such systems, allowing for spherical aggregates of arbitrary diameter and composition that can grow indefinitely in one direction to form rods, or in two directions to form disks. Assuming that interparticle interactions may be approximated by hard‐core repulsions, a fine‐mesh lattice model is used to derive the configurational free energy. Assuming further a simple phenomenological form for the intraparticle interactions, the equilibrium size and orientation distribution may be expressed in terms of a small number of parameters. The distribution function is a generalization of the well‐known most probable distribution for linear condensation polymers in ideal solutions. The generalization allows for the unequal growth of particles in different orientations under the influence of interparticle repulsions.

Theory of amphiphilic liquid crystals: multiple phase transitions in a model micellar system

A variety of amphiphilic molecules reversibly and spontaneously self‐assemble in aqueous solution forming a polydisperse population of asymmetric aggregates. In binary water/surfactant systems, aggregates may be either oblate or prolate and form corresponding orientationally ordered phases. Such binary systems are modeled using a lattice statistics calculation of the configurational entropy of a polydisperse collection of hard rods and plates, combined with a phenomenological description of aggregate assembly. Using parameter values relevant to micellar surfactant systems, a series of phase diagrams and associated particle size distributions have been computed. Depending upon the competition between rod and plate growth, the concentration dependent transition sequences I→A, I→P, and I→A→P (where I≡isotropic micellar, A≡axial nematic, and P≡planar nematic) are seen. The A→P transition occurs when rod and plate growth are equally favorable and is discussed in detail. Qualitative comparisons are drawn betwee...

Interpretation of the osmotic behavior of sickle cell hemoglobin solutions: different interactions among monomers and polymers.

It has long been known that a simple hard particle model quantitatively explains the osmotic properties of monomeric hemoglobin near its isoelectric point. However, we find that a hard particle model is not consistent with the osmotic properties of polymerized hemoglobin and that substantial soft repulsions are indicated. With allowance for different interactions among monomers and among polymers, a self-consistent quantitative fit to the experimental data is obtained. The results suggest that the decreasing solubility of deoxy sickle cell hemoglobin with increasing temperature from 20 to 37 degrees C is due to weaker repulsions between polymers at higher temperatures rather than stronger polymerization. The temperature dependence of these variables indicates that the aggregation of monomers is enthalpically and entropically driven (the latter effect being stronger), while the approach of polymers toward each other is enthalpically disfavored and entropically favored (with the former dominating). In both cases, the entropic contribution suggests that water is released.

Nematic behavior of reversibly polymerizing proteins

The nematic behavior exhibited by a variety of amphiphiles is driven by the coupling between the growth and alignment of elongated aggregates. We have previously studied these systems using a model derived from lattice combinatorics, with attendant restriction of particle orientations to the three mutually orthogonal lattice axes. In this work we present a generalization of the above model for rod‐like aggregates with a continuum of orientations. Overall, the calculated phase diagrams are similar to those obtained earlier for discrete orientations. This includes the second order isotropic‐to‐nematic transition in the weak aggregation regime. However, the nematic‐to‐nematic transition, obtained previously for intermediate aggregation strength, is not reproduced. We also consider the consequences of solvent filled spaces in the aggregates. Increasing the effective excluded volume of the solute by this mechanism causes the isotropic‐to‐nematic transition to shift to lower concentrations. This response of the...

Liquid Crystal Phases of Self-Assembled Amphiphilic Aggregates

Long-range order in solutions of reversibly self-assembling molecules results from interactions among the asymmetric aggregates. Even for electrically neutral species, repulsions between the aggregates become significant at high concentrations. At the very least, the excluded volume of asymmetric aggregates creates formidable packing constraints which are relieved by orientational and positional alignment. Aggregate growth thus promotes long-range order, and long-range order facilitates growth. Nematic phases occur if aggregate growth is strong enough to induce orientational ordering at concentrations lower than those that induce positional ordering. The symmetry of the positionally ordered phases reflects aggregate morphology: the polydispersity of aggregates that grow in one (two) dimension(s) to form rod-like (plate-like) particles suppresses the smectic (columnar) phase in favour of the columnar (smectic) phase. Because plate-like aggregates pack more easily than rod-like aggregates, increasing concentration induces a rearrangement from rod-like to plate-like aggregates, and a transition from columnar to smectic ordering, in solutions of molecules, such as surfactants, capable of forming both types of aggregates. In mixtures of aggregating and non-aggregating species, the difficulty of packing spherically shaped particles among elongated particles results in dramatic demixing such that a very concentrated solution of very large, highly aligned aggregates coexists with a relatively dilute solution depleted of the aggregating species.

Theory of Liquid Crystalline Phases in Amphiphilic Systems

Abstract A variety of amphiphilic molecules reversibly aggregate to form polydisperse asymmetric particles that spontaneously align at sufficiently high concentrations. Such system have been modeled using a lattice description of excluded volume effects and a phenomenological description of aggregate assembly. Our earlier calculations restricted to the formation of rod-like aggregates, have now been extended to include the formation of plate-like aggregates. Thus two types of aligned phases are possible: axial, in which the averagelength of particle edges parallel to the director is greater than perpendicular to the director, and planar, in which the opposite occurs. When rod and plate growth are equally favored the calculated phasediagram displays a sequence of first order transitions from isotropic to axial to planar phases. Additional sequences of phase transitions calculated from this model are reported.