Theoretical analysis of degradation mechanisms in the formation of morphogen gradients

Fundamental biological processes of development of tissues and organs in multicellular organisms are governed by various signaling molecules, which are called morphogens. It is known that spatial and temporal variations in the concentration profiles of signaling molecules, which are frequently referred as morphogen gradients, lead to a cell differentiation via activating specific genes in a concentration-dependent manner. It is widely accepted that the establishment of the morphogen gradients involves multiple biochemical reactions and diffusion processes. One of the critical elements in the formation of morphogen gradients is a degradation of signaling molecules. We develop a new theoretical approach that provides a comprehensive description of the degradation mechanisms. It is based on the idea that the degradation works as an effective potential that drives the signaling molecules away from the source region. Utilizing the method of first-passage processes, the dynamics of the formation of morphogen gradients for various degradation mechanisms is explicitly evaluated. It is found that linear degradation processes lead to a dynamic behavior specified by times to form the morphogen gradients that depend linearly on the distance from the source. This is because the effective potential due to the degradation is quite strong. At the same time, nonlinear degradation mechanisms yield a quadratic scaling in the morphogen gradients formation times since the effective potentials are much weaker. Physical-chemical explanations of these phenomena are presented

Controlling the temperature sensitivity of DNA-mediated colloidal interactions through competing linkages

We propose a new strategy to improve the self-assembly properties of DNA-functionalised colloids. The problem that we address is that DNA-functionalised colloids typically crystallize in a narrow temperature window, if at all. The underlying reason is the extreme sensitivity of DNA-mediated interactions to temperature or other physical control parameters. We propose to widen the window for colloidal crystallization by exploiting the competition between DNA linkages with different nucleotide sequences, which results in a temperature-dependent switching of the dominant bond type. Following such a strategy, we can decrease the temperature dependence of DNA-mediated self assembly to make systems that can crystallize in a wider temperature window than is possible with existing systems of DNA functionalised colloids. We report Monte Carlo simulations that show that the proposed strategy can indeed work in practice for real systems and specific, designable DNA sequences. Depending on the length ratio of the different DNA constructs, we find that the bond switching is either energetically driven (equal length or `symmetric' DNA) or controlled by a combinatorial entropy gain (`asymmetric' DNA), which results from the large number of possible binding partners for each DNA strand. We provide specific suggestions for the DNA sequences with which these effects can be achieved experimentally

Liquid-vapor transition driven by bond disorder

We report grand-canonical Monte Carlo simulations of an equimolar mixture of hard colloids coated with long polymers that have a complementary functionalization. Such systems have the potential to function as self-healing materials. Under conditions where the complementary polymer ends are strongly associated, we observe a first-order vapor-liquid transition from a dilute gas of colloidal dimers to a dense, liquidlike phase. This transition is driven exclusively by the increase in entropy associated with bond disorder—an effect that was predicted theoretically by Zilman et al. [Phys. Rev. Lett. 91, 015901 (2003)]. Our simulations rationalize experimental observations by Schmatko et al. [Soft Matter 03 (2007) 703.

Lattice-based Monte Carlo method for telechelic chain molecules

We present a Monte Carlo (MC) scheme that makes it possible to perform efficient simulations of dense systems of self-avoiding polymers on a lattice.We show that the method is particularly useful to simulate dense systems of polymers with functionalized end groups. We compare the efficiency of the scheme with the configurational bias MC method and indicate the regime where the present approach is the method of choice