We present a theory for polyelectrolyte gels that allow the effective charge of the polymer backbone to self-regulate. Using a variational approach, we obtain an expression for the free energy of gels that accounts for the gel elasticity, free energy of mixing, counterion adsorption, local dielectric constant, electrostatic interaction among polymer segments, electrolyte ion correlations, and self-consistent charge regularization on the polymer strands. This free energy is then minimized to predict the behavior of the system as characterized by the gel volume fraction as a function of external variables such as temperature and salt concentration. We present results for the volume transition of polyelectrolyte gels in salt-free solvents, solvents with monovalent salts, and solvents with divalent salts. The results of our theoretical analysis capture the essential features of existing experimental results and also provide predictions for further experimentation. Our analysis highlights the importance of the selfregularization of the effective charge for the volume transition of gels in particular, and for charged polymer systems in general. Our analysis also enables us to identify the dominant free energy contributions for charged polymer networks and provides a framework for further investigation of specific experimental systems.

We propose a general theory of crystallization of one component from an unstable mixture of two components by addressing the coupling between the spinodal decomposition associated with concentration fluctuations in the mixture and the nucleation kinetics for the crystallization. We propose that the domains created spontaneously by spinodal decomposition then present interfaces on which heterogeneous nucleation of the crystallizable component takes place with a much reduced nucleation barrier. Combining the theories of heterogeneous nucleation and spinodal decomposition kinetics, we present an analytic calculation of the nucleation rate as a function of the allowed duration of spinodal decomposition as well as the spinodal quench depth. In the present theory, shorter time evolution of spinodal decomposition or, equivalently, larger propensity of heterogeneous nucleation, results in faster crystallization. This is in contrast to the expectation of faster nucleation in more pure phases at later stages of spinodal decomposition. The analytic formula is found to correspond well with the recent experimental results on polymer mixtures for the late stage of spinodal decomposition kinetics. More detailed experiments are required to verify our prediction for the nucleation rate for early times and for different quench depths.

Recent experiments have demonstrated that dynein motors exhibit catch bonding behavior, in which the unbinding rate of a single dynein decreases with increasing force, for a certain range of force. Motivated by these experiments, we study the effect of catch bonding on unidirectional transport properties of cellular cargo carried by multiple dynein motors. We introduce a threshold force bond deformation (TFBD) model, consistent with the experiments, wherein catch bonding sets in beyond a critical applied load force. We find catch bonding can result in dramatic changes in the transport properties, which are in sharp contrast to kinesin-driven unidirectional transport, where catch bonding is absent. We predict that under certain conditions, the average velocity of the cellular cargo can actually increase as applied load is increased. We characterize the transport properties in terms of a velocity profile plot in the parameter space of the catch bond strength and the stall force of the motor. This plot yields predictions that may be experimentally accessed by suitable modifications of motor transport and binding properties.

Intracellular bidirectional transport of cargo on microtubule filaments is achieved by the collective action of oppositely directed dynein and kinesin motors. Experiments have found that in certain cases, inhibiting the activity of one type of motor results in an overall decline in the motility of the cellular cargo in both directions. This counterintuitive observation, referred to as the paradox of codependence, is inconsistent with the existing paradigm of a mechanistic tug of war between oppositely directed motors. Unlike kinesin motors, dynein motors exhibit catch bonding, wherein the unbinding rates of these motors decrease with increasing force on them. Incorporating this catch-bonding behavior of dyneins in a theoretical model, we show that the functional divergence of the two motor species manifests itself as an internal regulatory mechanism, and leads to codependent-transport behavior in biologically relevant regimes. Using analytical methods and stochastic simulations, we analyze the processivity characteristics and probability distribution of run times and pause times of transported cellular cargoes. We show that catch bonding can drastically alter the transport characteristics and also provide a plausible resolution of the paradox of codependence.

We propose a simple model for chromatin organization based on the interaction of the chromatin fibres with Lamin proteins along the nuclear membrane. Lamin proteins are known to be a major factor that influences chromatin organization, and hence gene expression in the cells. Our polymer model explains the formation of lamin associated domains, and for heteropolymers with sequence control, can reproduce observed length distributions of LADs. In particular, lamin mediated interaction can enhance the formation of chromosome territories as well as the organization of chromatin into tightly packed heterochromatin and the loosely-packed gene-rich euchromatin regions..

An exact treatment of the Anderson -Hasegawa two -site model, incorporating the presence of superexchange and polarons, is used to compute the heat capacity. The calculated results point to the dominance of the lattice contribution, especially in the ferromagnetic regime. This behavior is in qualitative agreement with experimental findings. 1 The Anderson-Hasegawa (AH) model [1] is a two-site realization of the basic idea of double -exchange (DE) proposed by Zener [2] almost fifty years ago. In the DE scenario a localized spin is visualized to be strongly 'Hund's rule' coupled to an itinerant spin at the same site governed by strength J H , whereas the itinerant spin can tunnel from site to site accompanied by a 'hopping integral' t. Because of large J H the itinerant spin is polarized along the localized spin, and as it hops to a neighboring site, it carries with it the memory of its spin polarization, thereby polarizing the neighboring local spin as well. Thus transport is correlated with spin ordering of localized moments, leading to concomitant metal-insulator transition and magnetic ordering.

The epigenetic pathway of a cell as it differentiates from a stem cell state to a mature lineage-committed one has been historically understood in terms of Waddington's landscape, consisting of hills and valleys. The smooth top and valley-strewn bottom of the hill represent their undifferentiated and differentiated states, respectively. Although mathematical ideas rooted in nonlinear dynamics and bifurcation theory have been used to quantify this picture, the importance of time delays arising from multistep chemical reactions or cellular shape transformations have been ignored so far. We argue that this feature is crucial in understanding cell differentiation and explore the role of time delay in a model of a single-gene regulatory circuit. We show that the interplay of time-dependent drive and delay introduces a new regime where the system shows sustained oscillations between the two admissible steady states. We interpret these results in the light of recent perplexing experiments on inducing the pluripotent state in mouse somatic cells. We also comment on how such an oscillatory state can provide a framework for understanding more general feedback circuits in cell development.

Waddington’s epigenetic landscape provides a phenomenological understanding of the cell differentiation pathways from the pluripotent to mature lineage-committed cell lines. In light of recent successes in the reverse programming process there has been significant interest in quantifying the underlying landscape picture through the mathematics of gene regulatory networks. We investigate the role of time delays arising from multi-step chemical reactions and epigenetic rearrangement on the cell differentiation landscape for a realistic two-gene regulatory network, consisting of self-promoting and mutually inhibiting genes. Our work provides the first theoretical basis of the transdifferentiation process in the presence of delays, where one differentiated cell type can transition to another directly without passing through the undifferentiated state. Additionally, the interplay of time-delayed feedback and a time dependent chemical drive leads to long-lived oscillatory states in appropriate parameter regimes. This work emphasizes the important role played by time-delayed feedback loops in gene regulatory circuits and provides a framework for the characterization of epigenetic landscapes.