Recent Progress on the Analysis of Power-law Features in Complex Cellular Networks

Complex interactions between different kinds of bio-molecules and essential nutrients are responsible for cellular functions. Rapid advances in theoretical modeling and experimental analyses have shown that drastically different biological and non-biological networks share a common architecture. That is, the probability that a selected node in the network has exactly k edges decays as a power-law. This finding has definitely opened an intense research and debate on the origin and implications of this ubiquitous pattern. In this review, we describe the recent progress on the emergence of power-law distributions in cellular networks. We first show the internal characteristics of the observed complex networks uncovered using graph theory. We then briefly review some works that have significantly contributed to the theoretical analysis of cellular networks and systems, from metabolic and protein networks to gene expression profiles. This prevalent topology observed in so many diverse biological systems suggests the existence of generic laws and organizing principles behind the cellular networks.     

Inherent size constraints on prokaryote gene networks due to “accelerating” growth

Networks exhibiting “accelerating” growth have total link numbers growing faster than linearly with network size and either reach a limit or exhibit graduated transitions from non-stationary-to-stationary statistics and from random to scale-free to regular statistics as the network size grows. However, if for any reason the network cannot tolerate such gross structural changes then accelerating networks are constrained to have sizes below some critical value. This is of interest as the regulatory gene networks of single-celled prokaryotes are characterized by an accelerating quadratic growth and are size constrained to be less than about 10,000 genes encoded in DNA sequence of less than about 10 megabases. This paper presents a probabilistic accelerating network model for prokaryotic gene regulation which closely matches observed statistics by employing two classes of network nodes (regulatory and non-regulatory) and directed links whose inbound heads are exponentially distributed over all nodes and whose outbound tails are preferentially attached to regulatory nodes and described by a scale-free distribution. This model explains the observed quadratic growth in regulator number with gene number and predicts an upper prokaryote size limit closely approximating the observed value.     

Transient and steady state phase response curves of limit cycle oscillators

The experiment of phase shifts resulting from discrete perturbations of stable biological rhythms has been carried out to study entrainment behavior of oscillators. There are two kinds of phase response curves, which are measured in experiments, according to as one measures the phase shifts immediately or long after the perturbation. The former is the first transient phase response curve and the latter is the steady state phase response curve. We redefine both curves within the framework of dynamical system theory and homotopy theory. Several topological properties of both curves are clarified. Consequently, it is shown that we must compare the shapes of both two phase response curves to investigate the inner structures of biological oscillators. Moreover, we prove that a single limit cycle oscillator involving only two variables cannot simulate transient resetting behavior reported by Pittendrigh and Minis (1964). In other words, the circadian oscillator of Drosophila pseudoobscura does not consist of a single oscillator of two variables. Finally we show that a model which consists of two limit cycle oscillators is able to simulate qualitatively the phase response curves of Drosophila.     

Ground-based methods reproduce space-flight experiments and show that weak vibrations trigger microtubule self-organisation

The effect of weightlessness on physical and biological systems is frequently studied by experiments in space. However, on the ground, gravity effects may also be strongly attenuated using methods such as magnetic levitation and clinorotation. Under suitable conditions, in vitro preparations of microtubules, a major element of the cytoskeleton, self-organise by a process of reaction–diffusion: self-organisation is triggered by gravity and samples prepared in space do not self-organise. Here, we report experiments carried out with ground-based methods of clinorotation and magnetic levitation. The behaviour observed closely resembles that of the space-flight experiment and suggests that many space experiments could be carried out equally well on the ground. Using clinorotation, we find that weak vibrations also trigger microtubule self-organisation and have an effect similar to gravity. Thus, in some in vitro biological systems, vibrations are a countermeasure to weightlessness.     

A regression model of the relationship between locust seedling growth and soil conditions

The relationship between locust (Robinia pseudoacacia L.) biomass and soil physico-chemical properties can be expressed by a multivariate regression equation. The best equation formed through a stepwise regression method indicated that acidity and available P were the main factors which influenced plant growth. The role of available P reflected its cooperative relationship with available Mo and available K separately. Available N, available K and CaCO₃ also played very important roles and the concerted effects of available Mo with CaCO₃, CO₂ and total N separately had obviously cooperative effects to promote plant growth. Greater locust growth occurred in neutral, low calcareous and weakly acid soil, poorer growth occurred in the strongly acid and the highly calcareous soils.     

Dynamics of pattern formation in biomimetic systems

This paper is an attempt to conceptualize pattern formation in self-organizing systems and, in particular, to understand how structures, oscillations or waves arise in a steady and homogenous environment, a phenomenon called symmetry breaking. The route followed to develop these ideas was to couple chemical oscillations produced by Belousov-Zhabotinsky reaction with confined reaction environments, the latter being an essential requirement for any process of Life. Special focus was placed on systems showing organic or lipidic compartments, which represent more reliable biomimetic matrices.     

Transitory behaviors in diffusively coupled nonlinear oscillators

We study collective behaviors of diffusively coupled oscillators which exhibit out-of-phase synchrony for the case of weakly interacting two oscillators. In large populations of such oscillators interacting via one-dimensionally nearest neighbor couplings, there appear various collective behaviors depending on the coupling strength, regardless of the number of oscillators. Among others, we focus on an intermittent behavior consisting of the all-synchronized state, a weakly chaotic state and some sorts of metachronal waves. Here, a metachronal wave means a wave with orderly phase shifts of oscillations. Such phase shifts are produced by the dephasing interaction which produces the out-of-phase synchronized states in two coupled oscillators. We also show that the abovementioned intermittent behavior can be interpreted as in-out intermittency where two saddles on an invariant subspace, the all-synchronized state and one of the metachronal waves play an important role.     

Comparable ecological dynamics underlie early cancer invasion and species dispersal, involving self-organizing processes

Occupancy of new habitats through dispersion is a central process in nature. In particular, long-distance dispersal is involved in the spread of species and epidemics, although it has not been previously related with cancer invasion, a process that involves cell spreading to tissues far away from the primary tumour.Using simulations and real data we show that the early spread of cancer cells is similar to the species individuals spread and we suggest that both processes are represented by a common spatio-temporal signature of long-distance dispersal and subsequent local proliferation. This signature is characterized by a particular fractal geometry of the boundaries of patches generated, and a power-law scaled, disrupted patch size distribution. In contrast, invasions involving only dispersal but not subsequent proliferation (“physiological invasions”) like trophoblast cells invasion during normal human placentation did not show the patch size power-law pattern. Our results are consistent under different temporal and spatial scales, and under different resolution levels of analysis.We conclude that the scaling properties are a hallmark and a direct result of long-distance dispersal and proliferation, and that they could reflect homologous ecological processes of population self-organization during cancer and species spread. Our results are significant for the detection of processes involving long-range dispersal and proliferation like cancer local invasion and metastasis, biological invasions and epidemics, and for the formulation of new cancer therapeutical approaches.     

Male powerlifting performance described from the viewpoint of complex systems

This paper reflects on the factors that condition performance in powerlifting and proposes that the result-generating process is inadequately described by the allometric equations commonly used. We analysed the scores of 1812 lifters belonging to all body mass categories, and analysed the changes in the results achieved in each weight category and by each competitor. Current performance-predicting methods take into account biological variables, paying no heed to other competition features. Performance in male powerlifting (as in other strength sports) behaves as a self-organised system with non-linear interactions between its components. Thus, multiple internal and external elements must condition changes in a competitor's score, the most important being body mass, body size, the number of practitioners, and the concurrency of favourable factors in one individual. It was observed that each behaved in a specific form in the high level, according to the individuals’ circumstances, which make up the main elements of the competitive system in every category. In powerlifting, official weight categories are generally organised in three different groups: light (<52.0 to <60 kg), medium (<67.5 to <90.0 kg) and heavy (<100 to >125 kg) lifter categories, each one of them with specific allometric exponents. The exponent should be revised periodically, especially with regard to the internal dynamics of the category, and adjusted according to possible changes affecting competition.     

Electron states of semiconductor quantum ring with geometry and size variations

Heterostructured semiconductor quantum rings (QR) are studied by a three-dimensional model in a single sub-band approach with energy dependent electron effective mass. Nonlinear confinement energy problem is numerically solved by the finite element method. Effects of boundary conditions corresponding to various QR/substrate configurations are analyzed. General relation for the size dependence of the QR confined energy is derived. The contribution to confinement energy due to the presence of external magnetic field is compared with the effect of variation of QR geometrical parameters. Applicability of the model is tested by comparison with experimental data.     

Local network parameters can affect inter-network phase lags in central pattern generators

Weakly coupled phase oscillators and strongly coupled relaxation oscillators have different mechanisms for creating stable phase lags. Many oscillations in central pattern generators combine features of each type of coupling: local networks composed of strongly coupled relaxation oscillators are weakly coupled to similar local networks. This paper analyzes the phase lags produced by this combination of mechanisms and shows how the parameters of a local network, such as the decay time of inhibition, can affect the phase lags between the local networks. The analysis is motivated by the crayfish central pattern generator used for swimming, and uses techniques from geometrical singular perturbation theory.     

A Life Table Regression Analysis for Complex Survey Data

A methodology for obtaining maximum likelihood estimates of life table regression coefficients from complex survey data is presented. Certain of the issues of writing a likelihood for survey data are presented and discussed. The proposed methodology includes consideration of the sampling design in any inference by using design based variance estimates for the parameters. An example is given using data from the 1973 United States National Survey of Family Growth.     

“Turn off–on” phosphorescent biosensors for detection of DNA based on quantum dots/acridine orange

A “turn off–on” switch mode was established by using the interaction between acridine orange (AO) and DNA as an input signal and using the room temperature phosphorescence (RTP) reversible change of 3-mercaptopropionic acid (MPA)-capped Mn-doped ZnS quantum dots (QDs) as an output signal in biological fluids. AO was absorbed into the surface of Mn-doped ZnS QDs via electrostatic attraction and, thus, formed a ground-state complex through photoinduced electron transfer (PIET). This complex quenched the phosphorescence of Mn-doped ZnS QDs and then rendered the system into the “turn-off” mode. Along with the addition of DNA and embedded binding with DNA, AO was competitively induced to fall off from the surface of Mn-doped ZnS QDs and embed into the double helix structure of DNA. As a result, the RTP of Mn-doped ZnS QDs was recovered and the system consequently was rendered into “turn-on” mode. In this case, a new biosensor for DNA detection was built and has a detection limit of 0.033 mg L⁻¹ and a detection range from 0.033 to 20 mg L⁻¹. What is more, this kind of biosensor does not require complex pretreatments and is free from the interference from autofluorescence and scattering light. Thus, this biosensor can be used to detect DNA in biological fluids.