The role of negative regulators in coordination of the Myxococcus xanthus developmental program

Myxococcus xanthus is a prokaryote that has a complex life cycle distinguished by multicellular behaviors and cell differentiation. Upon starvation, Myxococcus xanthus cells enter a developmental program wherein cells have different developmental fates: the majority of cells undergo programmed cell death (PCD), and the remaining cells either migrate into fruiting bodies and then differentiate into spores or do not aggregate and remain as peripheral rods. This developmental program is controlled by a cascade of positive developmental regulators whose expression is subject to positive autoregulation. Several histidine kinase (HK) homologs (espA, espC, red and todK) have been described that are necessary for appropriate progression through the developmental program. Mutants in these genes aggregate and sporulate earlier than wild type, producing disorganized fruiting bodies and spores outside of the fruiting bodies. These observations suggest that these kinases act as negative regulators (NRs) to repress the developmental program, but it is not clear if they function in one or more signaling pathways, how they mediate repression of the developmental program, and what ultimate advantage they provide to the developmental program. Using genetic epistasis analysis, we demonstrate that these NRs are organized into three distinct signaling systems comprised of 1) EspA/EspC, 2) TodK and 3) Red. Consistently, analysis of the accumulation patterns of several developmental regulatory proteins in each NR mutant demonstrated three distinct patterns: 1) in espA and espC mutants most developmental regulators accumulate earlier than in wild type, but the ordered cascade of production is maintained, 2) in red mutants most developmental marker proteins are under accumulated and the ordered cascade of production is not maintained, 3) in todK mutants certain developmental marker proteins are produced earlier than in wild type and the ordered cascade of production is perturbed. Phenotypic analysis of single, double, triple and quadruple NR mutants demonstrated that there is a strong negative correlation between the rate of progression through the developmental program and coordinated fruiting body formation. Loss of coordinated fruiting body formation appeared to be the result of uncoordinated developmental subpopulations. To determine whether the perturbation in the ordered cascade of developmental regulators in the red and todK mutants was due to misregulation of the developmental subpopulations, we first set out to define the temporal proportion of the different cell subpopulations and then examined the accumulation of key developmental regulator proteins in the two developmental subpopulations. Our analyses indicate that the cell population doubles over the course of 24 hours followed by a sudden burst programmed cell death (PCD). The aggregating and non-aggregating subpopulations displayed distinct accumulation patterns of components involved in Type IV pilus-mediated motility, and spore structural proteins. Most key developmental regulator proteins were shown to first gradually accumulate in the non-aggregating cell fraction and then to rapidly accumulate in the aggregating cell fraction. Using a similar approach to analyze the red and todK NR mutants, we demonstrate that both mutants do not increase their population to the same extent as wild type, likely because PCD is induced earlier than wild type. Furthermore, in both mutants, developmental regulatory proteins are induced inappropriately rapidly in the non-aggregating cell fraction, and subsequently fail to accumulate appropriately in the aggregating cell fraction. Consequently, many cells are induced to sporulate before they have completed aggregation, and coordinated fruiting body formation is perturbed. These results strongly suggest that TodK and Red mediate the gradual accumulation of one or more developmental coordinators during the aggregation phase of the developmental program. These results suggest that coordination of developmental subpopulations requires negative regulatory signaling systems that quench the positive autoregulatory loops that ensure coupling of sporulation and aggregation

Coarsening Dynamics of an Antiferromagnetic XY model on the Kagome Lattice: Breakdown of the Critical Dynamic Scaling

We find a breakdown of the critical dynamic scaling in the coarsening dynamics of an antiferromagnetic {\em XY} model on the kagome lattice when the system is quenched from disordered states into the Kosterlitz-Thouless ({\em KT}) phases at low temperatures. There exist multiple growing length scales: the length scales of the average separation between fractional vortices are found to be {\em not} proportional to the length scales of the quasi-ordered domains. They are instead related through a nontrivial power-law relation. The length scale of the quasi-ordered domains (as determined from optimal collapse of the correlation functions for the order parameter $\exp[3 i \theta (r)]$) does not follow a simple power law growth but exhibits an anomalous growth with time-dependent effective growth exponent. The breakdown of the critical dynamic scaling is accompanied by unusual relaxation dynamics in the decay of fractional ($3\theta$) vortices, where the decay of the vortex numbers is characterized by an exponential function of logarithmic powers in time.Comment: 13 pages, 26 figure

Patterns of Striped order in the Classical Lattice Coulomb Gas

We obtain via Monte Carlo simulations the low temperature charge configurations in the lattice Coulomb gas on square lattices for charge filling ratio $f$ in the range $1/3 < f < 1/2$. We find a simple regularity in the low temperature charge configurations which consist of a suitable periodic combination of a few basic striped patterns characterized by the existence of partially filled diagonal channels. In general there exist two separate transitions where the lower temperature transition ($T_p$) corresponds to the freezing of charges within the partially filled channels. $T_p$ is found to be sensitively dependent on $f$ through the charge number density $\nu = p_{1}/q_{1}$ within the channels.Comment: 4 pages, 8 figure

An efficient numerical approach for solving two-point fractional order nonlinear boundary value problems with Robin boundary conditions

This article proposes new strategies for solving two-point Fractional order Nonlinear Boundary Value Problems (FNBVPs) with Robin Boundary Conditions (RBCs). In the new numerical schemes, a two-point FNBVP is transformed into a system of Fractional order Initial Value Problems (FIVPs) with unknown Initial Conditions (ICs). To approximate ICs in the system of FIVPs, we develop nonlinear shooting methods based on Newton&apos;s method and Halley&apos;s method using the RBC at the right end point. To deal with FIVPs in a system, we mainly employ High-order Predictor-Corrector Methods (HPCMs) with linear interpolation and quadratic interpolation (Nguyen and Jang in Fract. Calc. Appl. Anal. 20(2):447-476, 2017) into Volterra integral equations which are equivalent to FIVPs. The advantage of the proposed schemes with HPCMs is that even though they are designed for solving two-point FNBVPs, they can handle both linear and nonlinear two-point Fractional order Boundary Value Problems (FBVPs) with RBCs and have uniform convergence rates of HPCMs, O(h(2)) and O(h(3)) for shooting techniques with Newton&apos;s method and Halley&apos;s method, respectively. A variety of numerical examples are demonstrated to confirm the effectiveness and performance of the proposed schemes. Also we compare the accuracy and performance of our schemes with another method