Tight coupling of cell width to nucleoid structure in Escherichia coli.

Cell dimensions of rod-shaped bacteria such as Escherichia coli are connected to mass growth and chromosome replication. During their interdivision cycle (τ min), cells enlarge by elongation only, but at faster growth in richer media, they are also wider. Changes in width W upon nutritional shift-up (shortening τ) occur during the division process. The elusive signal directing the mechanism for W determination is likely related to the tightly linked duplications of the nucleoid (DNA) and the sacculus (peptidoglycan), the only two structures (macromolecules) existing in a single copy that are coupled, temporally and spatially. Six known parameters related to the nucleoid structure and replication are reasonable candidates to convey such a signal, all simple functions of the key number of replication positions n(=C/τ), the ratio between the rates of growth (τ-1) and of replication (C-1). The current analysis of available literature-recorded data discovered that, of these, nucleoid complexity NC[=(2n-1)/(n×ln2)] is by far the most likely parameter affecting cell width W. The exceedingly high correlations found between these two seemingly unrelated measures (NC and W) indicate that coupling between them is of major importance to the species' survival. As an exciting corollary, to the best of our knowledge, a new, indirect approach to estimate DNA replication rate is revealed. Potential involvement of DNA topoisomerases in W determination is also proposed and discussed.

Causality analysis of leading singular value decomposition modes identifies rotor as the dominant driving normal mode in fibrillation.

Cardiac fibrillation is a major clinical and societal burden. Rotors may drive fibrillation in many cases, but their role and patterns are often masked by complex propagation. We used Singular Value Decomposition (SVD), which ranks patterns of activation hierarchically, together with Wiener-Granger causality analysis (WGCA), which analyses direction of information among observations, to investigate the role of rotors in cardiac fibrillation. We hypothesized that combining SVD analysis with WGCA should reveal whether rotor activity is the dominant driving force of fibrillation even in cases of high complexity. Optical mapping experiments were conducted in neonatal rat cardiomyocyte monolayers (diameter, 35 mm), which were genetically modified to overexpress the delayed rectifier K+ channel IKr only in one half of the monolayer. Such monolayers have been shown previously to sustain fast rotors confined to the IKr overexpressing half and driving fibrillatory-like activity in the other half. SVD analysis of the optical mapping movies revealed a hierarchical pattern in which the primary modes corresponded to rotor activity in the IKr overexpressing region and the secondary modes corresponded to fibrillatory activity elsewhere. We then applied WGCA to evaluate the directionality of influence between modes in the entire monolayer using clear and noisy movies of activity. We demonstrated that the rotor modes influence the secondary fibrillatory modes, but influence was detected also in the opposite direction. To more specifically delineate the role of the rotor in fibrillation, we decomposed separately the respective SVD modes of the rotor and fibrillatory domains. In this case, WGCA yielded more information from the rotor to the fibrillatory domains than in the opposite direction. In conclusion, SVD analysis reveals that rotors can be the dominant modes of an experimental model of fibrillation. Wiener-Granger causality on modes of the rotor domains confirms their preferential driving influence on fibrillatory modes.

Maximizing yields of virulent phage: the T4/Escherichia coli system as a test case.

A hybrid mathematical model was devised to obtain optimal values for bacterial doubling time and initial phage/bacteria multiplicity of infection for the purpose of reaching the highest possible phage titers in steady-state exponentially growing cultures. The computational model consists of an initial probabilistic stage, followed by a second one processed by a system of delayed differential equations. The model's approach can be used in any phage/bacteria system for which the relevant parameters have been measured. Results of a specific case, based on the detailed, known information about the interactions between virulent T4 phage and its host bacterium Escherichia coli, display a range of possible such values along a highlighted strip of parameter values in the relevant parameter plane. In addition, times to achieve these maxima and gains in phage concentrations are evaluated.

Bacteria and lytic phage coexistence in a chemostat with periodic nutrient supply.

The dynamics of bacteria and bacteriophage coexistence was examined in a chemostat in which the externally driven supply of nutrient for bacteria, and washout rate oscillates periodically. The proposed mathematical model for three interacting variables, bacteria, phage, and nutrient, consists of 3 differential equations with time delay, due to the phage latent period of lysing. The study was carried out in an interval of physical parameters where an equivalent model with constant supply of nutrient and washout rate is mathematically unstable, running in limit cycle regimes, with known self-frequencies. It addresses mainly the asymptotically persistent dynamics of the system.Bifurcation maps in terms of two externally controlled parameters, the amplitude and frequency of the controlled nutrient supply were constructed for various latent lysis periods, in order to determine the frequency entrainment, i.e., the resulting main operating frequency of the system, relative to the known external and self-frequencies. Also presented are bifurcation maps for the rich variety of dynamical types observed in the study. Bifurcation diagrams in terms of the lysing time delay were also included for completion.A new type of entrainment, combining in a simple way the external and self-periods (reciprocal frequencies), is shown to exist for a range of parameters.

Insights into the Dead Sea Transform Activity through the study of fracture-induced electromagnetic radiation (FEMR) signals before the Syrian-Turkey earthquake (Mw-6.3) on 20.2.2023.

Observations of fracture-induced electromagnetic radiation (FEMR) were conducted along the Dead Sea Transform (DST) from Sodom to Jericho, coinciding with a magnitude (Mw) 6.3 aftershock earthquake (EQ) in the Turkey-Syrian region on February 20, 2023. The FEMR parameters ("hits," Benioff strain release, frequency, rise-time, energy) and associated crack dimensions were analyzed, focusing on trends leading up to the EQ. This study investigated the Benioff Strain plot and other parameters in three consecutive earthquake nucleation stages leading to the catastrophe. The first stage showed increased FEMR hits and frequency, decreased rise time (T'), and crack dimensions. In the second stage, FEMR hits and crack width decreased while other parameters continued to rise, accumulating the second-highest energy, likely due to high-stress drop. The third stage exhibited steadily increasing FEMR hits and energy and a notable increase in crack dimensions, suggesting an imminent macro failure event. The cyclic trend in FEMR hits indicates alternating periods of high activity and silence, potentially linked to stress changes during crack propagation. Taken shortly before the earthquake, these measurements offer valuable insights into how FEMR parameters vary before seismic events, bridging the gap between lab-scale studies of rock collapses under stress and large-scale failure phenomena.

Kinetics of repeat propagation in the microgene polymerization reaction.

Repetitive DNA is a periodic copolymer with the intrinsic property of exponential propagation to longer repeats. Microgene polymerization reaction (MPR) is a model system in which a short nonrepetitive homo-duplex DNA evolves to multiple repetitive products during heat-cool cycles. The mechanism underlying this process involves staggered annealing of complementary DNA strands of variable lengths and polymerase-mediated filling-in of the generated overhangs. MPR is considered here as a process sharing common features with two polymerization types, chain-growth and step-growth, and significant distinctions from both types were highlighted. The involved reaction stages were formulated and a kinetic model was derived and tested experimentally. The model can quantitatively explain MPR propagation and be used as a good approximation for this phenomenon.

A combined astrocyte - G-lymphatic model of epilepsy initiation, maintenance and termination.

Although epilepsy afflicts numerous people worldwide, its dynamics are still controversial. Especially seizure termination is relatively unidentified. Here we suggest a coherent explanation to all stages of epilepsy, its genesis, seizure initiation and termination. We present biophysical features that could account for the phenomenon: all phases of epilepsy can be related to the brain's "waste disposal" systems. Although problems in the astrocytic system have already been suggested as a major player in this malfunction, the termination phase is not really understood. Here it is assumed to arise from a G-lymphatic clearance system. Our biophysical mechanism provides a coherent explanation of the phenomenon, offers support for the previously published mathematical model, and can shed light on the conflicting results encountered in norepinephrine measurements in epilepsy treatment.

Initiation of the microgene polymerization reaction with non-repetitive homo-duplexes.

Microgene Polymerization Reaction (MPR) is used as an experimental system to artificially simulate evolution of short, non-repetitive homo-duplex DNA into multiply-repetitive products that can code for functional proteins. Blunt-end ligation by DNA polymerase is crucial in expansion of homo-duplexes (HDs) into head-to-tail multiple repeats in MPR. The propagation mechanism is known, but formation of the initial doublet (ID) by juxtaposing two HDs and polymerization through the gap has been ambiguous. Initiation events with pairs of HDs using Real-Time PCR were more frequent at higher HD concentrations and slightly below the melting temperature. A process molecularity of about 3.1, calculated from the amplification efficiency and the difference in PCR cycles at which propagation was detected at varying HD concentrations, led to a simple mechanism for ID formation: the gap between two HDs is bridged by a third. Considering thermodynamic aspects of the presumed intermediate "nucleation complex" can predict relative propensity for the process with other HDs.

Thermodynamics of unstable DNA structures from the kinetics of the microgene PCR.

The microgene polymerization reaction (MPR) generates head-to-tail tandem repeats from homoduplexes (HDs). In MPR initiation, one HD putatively aligns two others in the proximity required to form a nucleation complex, thus allowing the DNA polymerase to skip the intertemplate gap and generate an initial doublet (ID) prone to repeat propagation. The current investigation refines this stage by additional thermodynamic considerations and elucidates the fundamental mechanism underlying propagation. Four different HD types were designed to extend the range of melting temperatures and to simultaneously modify the stabilities of their secondary structures. Following the propagation kinetics with these, using real-time PCR at different temperatures revealed a new stage in the MPR, amplification of an ID by an original HD, and enabled us to decipher the biphasic kinetics of the process. This amplification merges with the propagation stage if the lifetime of the staggered conformation of the ID is sufficiently long for DNA polymerase to fill in the overhangs. The observed increase with temperature of thermodynamically unfavorable conformations of singlet and doublet HDs that underlies, respectively, MPR initiation and propagation is well correlated with simulations by UNAFold.

Dynamical types of bacteria and bacteriophages interaction: shielding by debris.

The dynamics of the bacteria and bacteriophages interaction process was explored in depth, and laid on a firm basis through simulation and analysis. A modified Campbell model of phage-bacteria interaction was used to simulate three interacting species: bacteria, phages and bacterial debris, and their time behavior in terms of three parameters, in selected range values: the phages burst size (beta), the dissolution rate of the bacterial debris (q), and the lysing time delay (tau). Six types of dynamical behavior were identified, occupying various zones in the two-dimensional (2D) plane (q, beta) for several values of tau, allowing the determination of the region where shielding by bacterial debris is in effect. The problem of the occurrence of stability transitions between stable and unstable dynamical regimes was also addressed analytically, and compared with simulation results.

Does the eclipse limit bacterial nucleoid complexity and cell width?

Cell size of bacteria M is related to 3 temporal parameters: chromosome replication time C, period from replication-termination to subsequent division D, and doubling time τ. Steady-state, bacillary cells grow exponentially by extending length L only, but their constant width W is larger at shorter τ's or longer C's, in proportion to the number of chromosome replication positions n (= C/τ), at least in Escherichia coli and Salmonella typhimurium. Extending C by thymine limitation of fast-growing thyA mutants result in continuous increase of M, associated with rising W, up to a limit before branching. A set of such puzzling observations is qualitatively consistent with the view that the actual cell mass (or volume) at the time of replication-initiation Mi (or Vi), usually relatively constant in growth at varying τ's, rises with time under thymine limitation of fast-growing, thymine-requiring E. coli strains. The hypothesis will be tested that presumes existence of a minimal distance lmin between successive moving replisomes, translated into the time needed for a replisome to reach lmin before a new replication-initiation at oriC is allowed, termed Eclipse E. Preliminary analysis of currently available data is inconsistent with a constant E under all conditions, hence other explanations and ways to test them are proposed in an attempt to elucidate these and other results. The complex hypothesis takes into account much of what is currently known about Bacterial Physiology: the relationships between cell dimensions, growth and cycle parameters, particularly nucleoid structure, replication and position, and the mode of peptidoglycan biosynthesis. Further experiments are mentioned that are necessary to test the discussed ideas and hypotheses.

Aggregation kinetics of a simulated telechelic polymer.

We investigate the aggregation kinetics of a simulated telechelic polymer gel. In the hybrid molecular dynamics (MD)/Monte Carlo (MC) algorithm, aggregates of associating end groups form and break according to MC rules, while the position of the polymers in space is dictated by MD. As a result, the aggregate sizes change over time. In order to describe this aggregation process, we employ master equations. They define changes in the number of aggregates of a certain size in terms of reaction rates. These reaction rates indicate the likelihood that two aggregates combine to form a large one, or that a large aggregate splits into two smaller parts. The reaction rates are obtained from the simulations for a range of temperatures. Our results indicate that the rates are not only temperature dependent, but also a function of the sizes of the aggregates involved in the reaction. Using the measured rates, solutions to the master equations are shown to be stable and in agreement with the aggregate size distribution, as obtained directly from simulation data. Furthermore, we show how temperature-induced variations in these rates give rise to the observed changes in the aggregate distribution that characterizes the sol-gel transition.

Eigenvalue spectra of spatial-dependent networks.

Many real-life networks exhibit a spatial dependence; i.e., the probability to form an edge between two nodes in the network depends on the distance between them. We investigate the influence of spatial dependence on the spectral density of the network. When increasing spatial dependence in Erdös-Rényi, scale-free, and small-world networks, it is found that the spectrum changes. Due to the spatial dependence the degree of clustering and the number of triangles increase. This results in a higher asymmetry (skewness). Our results show that the spectrum can be used to detect and quantify clustering and spatial dependence in a network.

Changes of initiation mass and cell dimensions by the 'eclipse'.

The minimum time (E) required for a new pair of replication origins (oriCs) produced upon initiating a round of replication to be ready to initiate the next round after one cell mass doubling, the 'eclipse', is explained in terms of a minimal distance (l(min)) that the replication forks must move away from oriC before oriCs can 'fire' again. In conditions demanding a scheduled initiation event before the relative distance l(min)/L(0.5) (L being the total chromosome length) is reached, initiation is presumably delayed. Under such circumstances, cell mass at the next initiation would be greater than the usual, constant Mi (cell mass per copy number of oriC) prevailing in steady state of exponential growth. This model can be tested experimentally by extending the replication time C using thymine limitation at short doubling times tau in rich media to reach a relative eclipse E/C < l(min)/L(0.5). It is consistent with results obtained in experiments in which the number of replication 'positions'n (= C/tau) is increased beyond the natural maximum, causing the mean cell size to rise continuously, first by widening, then by lengthening, and finally by splitting its poles. The consequent branching is associated with casting off a small proportion of normal-sized cells and lysing DNA-less cells. Whether or how these phenomena are related to peptidoglycan composition and synthesis are moot questions.

DNA-membrane interactions can localize bacterial cell center.

In actively growing bacterial cells, the DNA exerts stress on the membrane, in addition to the turgor caused by osmotic pressure. This stress is applied through coupled transcription/translation and insertion of membrane proteins (so-called "transertion" process). In bacillary bacteria, the strength of this interaction varies along cell length with a minimum at its midpoint, and hence can locate the cell's equator for the assembly of the FtsZ-ring.

Bacterial debris-an ecological mechanism for coexistence of bacteria and their viruses.

A model of bacteria and phage survival is developed based on the idea of shielding by bacterial debris in the system. This model is mathematically formulated by a set of four nonlinear difference equations for susceptible bacteria, contaminated bacteria, bacterial debris and phages. Simulation results show the possibility of survival, and domains of existence of stable and unstable solutions

Bacteriophage T4 development in Escherichia coli is growth rate dependent.

Three independent parameters (eclipse and latent periods, and rate of ripening during the rise period) are essential and sufficient to describe bacteriophage development in its bacterial host. A general model to describe the classical "one-step growth" experiment [Rabinovitch et al. (1999a) J. Bacteriol.181, 1687-1683] allowed their calculations from experimental results obtained with T4 in Escherichia coli B/r under different growth conditions [Hadas et al. (1997) Microbiology143, 179-185]. It is found that all three parameters could be described by their dependence solely on the culture doubling time tau before infection. Their functional dependence on tau, derived by a best-fit analysis, was used to calculate burst size values. The latter agree well with the experimental results. The dependence of the derived parameters on growth conditions can be used to predict phage development under other experimental manipulations.