Chromosome segregation by the Escherichia coli Min system.

The mechanisms underlying chromosome segregation in prokaryotes remain a subject of debate and no unifying view has yet emerged. Given that the initial disentanglement of duplicated chromosomes could be achieved by purely entropic forces, even the requirement of an active prokaryotic segregation machinery has been questioned. Using computer simulations, we show that entropic forces alone are not sufficient to achieve and maintain full separation of chromosomes. This is, however, possible by assuming repeated binding of chromosomes along a gradient of membrane-associated tethering sites toward the poles. We propose that, in Escherichia coli, such a gradient of membrane tethering sites may be provided by the oscillatory Min system, otherwise known for its role in selecting the cell division site. Consistent with this hypothesis, we demonstrate that MinD binds to DNA and tethers it to the membrane in an ATP-dependent manner. Taken together, our combined theoretical and experimental results suggest the existence of a novel mechanism of chromosome segregation based on the Min system, further highlighting the importance of active segregation of chromosomes in prokaryotic cell biology.

Variation in structure of a protein (H2AX) with knowledge-based interactions.

The structure of a protein (H2AX) as a function of temperature is examined by three knowledge-based phenomenological interactions, MJ (Miyazawa and Jernigan), BT (Betancourt and Thirumalai), and BFKV (Bastolla et al.) to identify similarities and differences in results. Data from the BT and BFKV residue-residue interactions verify finding with the MJ interaction, i.e., the radius of gyration (Rg ) of H2AX depends non-monotonically on temperature. The increase in Rg is followed by a decay on raising the temperature with a maximum at a characteristic value, Tc , which depends on the knowledge-based contact matrix, TcBFKV ≤ TcMJ ≤ TcBT . The range (ΔT) of non-monotonic thermal response and its decay pattern with the temperature are sensitive to interaction. A rather narrow temperature range of ΔTMJ ≈ 0.015-0.022 with the MJ interaction expands and shifts up to ΔTBT ≈ 0.018-0.30 at higher temperatures with the BT interaction and shifts down with the BFKV interaction to ΔTBFKV ≈ 0.011-0.018. The scaling of the structure factor with the wave vector reveals that the structure of the protein undergoes a transformation from a random coil at high temperature to a globular conformation at low temperatures.

The impact of entropy on the spatial organization of synaptonemal complexes within the cell nucleus.

We employ 4Pi-microscopy to study SC organization in mouse spermatocyte nuclei allowing for the three-dimensional reconstruction of the SC's backbone arrangement. Additionally, we model the SCs in the cell nucleus by confined, self-avoiding polymers, whose chain ends are attached to the envelope of the confining cavity and diffuse along it. This work helps to elucidate the role of entropy in shaping pachytene SC organization. The framework provided by the complex interplay between SC polymer rigidity, tethering and confinement is able to qualitatively explain features of SC organization, such as mean squared end-to-end distances, mean squared center-of-mass distances, or SC density distributions. However, it fails in correctly assessing SC entanglement within the nucleus. In fact, our analysis of the 4Pi-microscopy images reveals a higher ordering of SCs within the nuclear volume than what is expected by our numerical model. This suggests that while effects of entropy impact SC organization, the dedicated action of proteins or actin cables is required to fine-tune the spatial ordering of SCs within the cell nucleus.

Conformational temperature-dependent behavior of a histone H2AX: a coarse-grained Monte Carlo approach via knowledge-based interaction potentials.

Histone proteins are not only important due to their vital role in cellular processes such as DNA compaction, replication and repair but also show intriguing structural properties that might be exploited for bioengineering purposes such as the development of nano-materials. Based on their biological and technological implications, it is interesting to investigate the structural properties of proteins as a function of temperature. In this work, we study the spatial response dynamics of the histone H2AX, consisting of 143 residues, by a coarse-grained bond fluctuating model for a broad range of normalized temperatures. A knowledge-based interaction matrix is used as input for the residue-residue Lennard-Jones potential.We find a variety of equilibrium structures including global globular configurations at low normalized temperature (T* = 0.014), combination of segmental globules and elongated chains (T* = 0.016,0.017), predominantly elongated chains (T* = 0.019,0.020), as well as universal SAW conformations at high normalized temperature (T* ≥ 0.023). The radius of gyration of the protein exhibits a non-monotonic temperature dependence with a maximum at a characteristic temperature (T(c)* = 0.019) where a crossover occurs from a positive (stretching at T* ≤ T(c)*) to negative (contraction at T* ≥ T(c)*) thermal response on increasing T*.

A model for Escherichia coli chromosome packaging supports transcription factor-induced DNA domain formation.

What physical mechanism leads to organization of a highly condensed and confined circular chromosome? Computational modeling shows that confinement-induced organization is able to overcome the chromosome's propensity to mix by the formation of topological domains. The experimentally observed high precision of separate subcellular positioning of loci (located on different chromosomal domains) in Escherichia coli naturally emerges as a result of entropic demixing of such chromosomal loops. We propose one possible mechanism for organizing these domains: regulatory control defined by the underlying E. coli gene regulatory network requires the colocalization of transcription factor genes and target genes. Investigating this assumption, we find the DNA chain to self-organize into several topologically distinguishable domains where the interplay between the entropic repulsion of chromosomal loops and their compression due to the confining geometry induces an effective nucleoid filament-type of structure. Thus, we propose that the physical structure of the chromosome is a direct result of regulatory interactions. To reproduce the observed precise ordering of the chromosome, we estimate that the domain sizes are distributed between 10 and 700 kb, in agreement with the size of topological domains identified in the context of DNA supercoiling.

Looped star polymers show conformational transition from spherical to flat toroidal shapes.

Inspired by the topological organization of the circular Escherichia coli chromosome, which is compacted by separate domains, we study a polymer architecture consisting of a central ring to which either looped or linear side chains are grafted. A shape change from a spherical to a toroidal organization takes place as soon as the inner ring becomes large enough for the attached arms to fit within its circumference. Building up a torus, the system flattens, depending on the effective bending rigidity of the chain induced by entropic repulsion of the attached loops and, to a lesser extent, linear arms. Our results suggest that the natural formation of a toroidal structure with a decreased amount of writhe induced by a specific underlying topology could be one driving force, among others, that nature exploits to ensure proper packaging of the genetic material within a rod-shaped, bacterial envelope.

Temperature-dependent structural behavior of self-avoiding walks on three-dimensional Sierpinski sponges.

The statistics of self-avoiding random walks (SAWs), consisting of up to N=1280 steps, on deterministic fractal structures with infinite ramification, modeled by Sierpinski cubic lattices, in the presence of a finite temperature is investigated as a model for polymers absorbed on a disordered medium. Thereby, the three-dimensional Sierpinski sponge is defined by two types of sites with energy 0 and ϵ>0 , respectively, yielding a deterministic fractal energy landscape. The probability distribution function of the end-to-end distance of SAWs is obtained and its scaling behavior studied. In the limiting case of temperature T → ∞, the known behavior of SAWs on regular cubic lattices is recovered, while for T → 0 the resulting scaling exponents are confronted with previous calculations for much shorter linear chains based on the exact enumeration technique. For finite temperatures, the structural behavior of SAWs in three dimensions is compared to its two-dimensional counterpart and found to be intermediate between the two limiting cases (T → 0 and T → ∞, respectively), where the characteristic exponents, however, display a nontrivial dependence on temperature.

Mutation bias favors protein folding stability in the evolution of small populations.

Mutation bias in prokaryotes varies from extreme adenine and thymine (AT) in obligatory endosymbiotic or parasitic bacteria to extreme guanine and cytosine (GC), for instance in actinobacteria. GC mutation bias deeply influences the folding stability of proteins, making proteins on the average less hydrophobic and therefore less stable with respect to unfolding but also less susceptible to misfolding and aggregation. We study a model where proteins evolve subject to selection for folding stability under given mutation bias, population size, and neutrality. We find a non-neutral regime where, for any given population size, there is an optimal mutation bias that maximizes fitness. Interestingly, this optimal GC usage is small for small populations, large for intermediate populations and around 50% for large populations. This result is robust with respect to the definition of the fitness function and to the protein structures studied. Our model suggests that small populations evolving with small GC usage eventually accumulate a significant selective advantage over populations evolving without this bias. This provides a possible explanation to the observation that most species adopting obligatory intracellular lifestyles with a consequent reduction of effective population size shifted their mutation spectrum towards AT. The model also predicts that large GC usage is optimal for intermediate population size. To test these predictions we estimated the effective population sizes of bacterial species using the optimal codon usage coefficients computed by dos Reis et al. and the synonymous to non-synonymous substitution ratio computed by Daubin and Moran. We found that the population sizes estimated in these ways are significantly smaller for species with small and large GC usage compared to species with no bias, which supports our prediction.

Temperature-dependent structural behavior of self-avoiding walks on Sierpinski carpets.

We study the temperature-dependent structural behavior of self-avoiding walks (SAWs) on two-dimensional Sierpinski carpets as a simple model of polymers adsorbed on a disordered surface. Thereby, the Sierpinski carpet defines two types of sites with energy 0 and >0 , respectively, yielding a deterministic fractal energy landscape. In the limiting cases of temperature T-->0 and T-->infinity , the known behaviors of SAWs on Sierpinski carpets and on regular square lattices, respectively, are recovered. For finite temperatures, the structural behavior is found to be intermediate between the two limiting cases; the characteristic exponents, however, display a nontrivial dependence on temperature.