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Communication between and within brain regions is essential for information processing within functional networks. The current methods to determine the influence of one region on another are either based on temporal resolution, or require a predefined model for the connectivity direction. However these requirements are not always achieved, especially in fMRI studies, which have poor temporal resolution. We thus propose a new graph theory approach that focuses on the correlation influence between selected brain regions, entitled Dependency Network Analysis (DEPNA). Partial correlations are used to quantify the level of influence of each node during task performance. As a proof of concept, we conducted the DEPNA on simulated datasets and on two empirical motor and working memory fMRI tasks. The simulations revealed that the DEPNA correctly captures the network's hierarchy of influence. Applying DEPNA to the functional tasks reveals the dynamics between specific nodes as would be expected from prior knowledge. To conclude, we demonstrate that DEPNA can capture the most influencing nodes in the network, as they emerge during specific cognitive processes. This ability opens a new horizon for example in delineating critical nodes for specific clinical interventions.

Regulatory gene circuit motifs play crucial roles in performing and maintaining vital cellular functions. Frequently, theoretical studies of gene circuits focus on steady-state behaviors and do not include time delays. In this study, the inclusion of time delays is shown to entirely change the time-dependent dynamics for even the simplest possible circuits with one and two gene elements with self and cross regulations. These elements can give rise to rich behaviors including periodic, quasi-periodic, weak chaotic, strong chaotic and intermittent dynamics. We introduce a special power-spectrum-based method to characterize and discriminate these dynamical modes quantitatively. Our simulation results suggest that, while a single negative feedback loop of either one- or two-gene element can only have periodic dynamics, the elements with two positive/negative feedback loops are the minimalist elements to have chaotic dynamics. These elements typically have one negative feedback loop that generates oscillations, and another unit that allows frequent switches among multiple steady states or between oscillatory and non-oscillatory dynamics. Possible dynamical features of several simple one- and two-gene elements are presented in details. Discussion is presented for possible roles of the chaotic behavior in the robustness of cellular functions and diseases, for example, in the context of cancer.

Cellular plasticity during cancer metastasis is a major clinical challenge. Two key cellular plasticity mechanisms -Epithelial-to-Mesenchymal Transition (EMT) and Mesenchymal-to-Amoeboid Transition (MAT) - have been carefully investigated individually, yet a comprehensive understanding of their interconnections remains elusive. Previously, we have modeled the dynamics of the core regulatory circuits for both EMT (miR-200/ZEB/miR-34/SNAIL) and MAT (Rac1/RhoA). We now extend our previous work to study the coupling between these two core circuits by considering the two microRNAs (miR-200 and miR-34) as external signals to the core MAT circuit. We show that this coupled circuit enables four different stable steady states (phenotypes) that correspond to hybrid epithelial/mesenchymal (E/M), mesenchymal (M), amoeboid (A) and hybrid amoeboid/mesenchymal (A/M) phenotypes. Our model recapitulates the metastasis-suppressing role of the microRNAs even in the presence of EMT-inducing signals like Hepatocyte Growth Factor (HGF). It also enables mapping the microRNA levels to the transitions among various cell migration phenotypes. Finally, it offers a mechanistic understanding for the observed phenotypic transitions among different cell migration phenotypes, specifically the Collective-to-Amoeboid Transition (CAT).

Metastasis is the major cause for cancer patients' death, and despite all the recent advances in cancer research it is still mostly incurable. Understanding the mechanisms that are involved in the migration of the cells in a complex environment is a key step towards successful anti-metastatic treatment. Using experimental data-based modeling, we focus on the fundamentals of metastatic invasion: motility, invasion, proliferation and metabolism, and study how they may be combined to maximize the cancer's ability to metastasize. The modeled cells' performance is measured by the number of cells that succeed in migration in a maze, which mimics the extracellular environment. We show that co-existence of different cell clones in the tumor, as often found in experiments, optimizes the invasive ability in a frequently-changing environment. We study the role of metabolism and stimulation by growth factors, and show that metabolism plays a crucial role in the metastatic process and should therefore be targeted for successful treatment.

Metastasizing tumor cells migrate through the surrounding tissue and extracellular matrix toward the blood vessels, in order to colonize distant organs. They typically move in a dense environment, filled with other cells. In this work we study cooperative effects between neighboring cells of different types, migrating in a maze-like environment with directional cue. Using a computerized model, we measure the percentage of cells that arrive to the defined target, for different mesenchymal/amoeboid ratios. Wall degradation of mesenchymal cells, as well as motility of both types of cells, are coupled to metabolic energy-like resource level. We find that indirect cooperation emerges in mid-level energy, as mesenchymal cells create paths that are used by amoeboids. Therefore, we expect to see a small population of mesenchymals kept in a mostly-amoeboid population. We also study different forms of direct interaction between the cells, and show that energy-dependent interaction strength is optimal for the migration of both mesenchymals and amoeboids. The obtained characteristics of cellular cluster size are in agreement with experimental results. We therefore predict that hybrid states, e.g. epithelial-mesenchymal, should be utilized as a stress-response mechanism.

Metastatic carcinoma cells exhibit at least two different phenotypes of motility and invasion - amoeboid and mesenchymal. This plasticity poses a major clinical challenge for treating metastasis, while its underlying mechanisms remain enigmatic. Transitions between these phenotypes are mediated by the Rac1/RhoA circuit that responds to external signals such as HGF/SF via c-MET pathway. Using detailed modeling of GTPase-based regulation to study the Rac1/RhoA circuit's dynamics, we found that it can operate as a three-way switch. We propose to associate the circuit's three possible states to the amoeboid, mesenchymal and amoeboid/mesenchymal hybrid phenotype. In particular, we investigated the range of existence of, and the transition between, the three states (phenotypes) in response to Grb2 and Gab1 - two downstream adaptors of c-MET. The results help to explain the regulation of metastatic cells by c-MET pathway and hence can contribute to the assessment of possible clinical interventions.

Sporulation vs. competence provides a prototypic example of collective cell fate determination. The decision is performed by the action of three modules: 1) A stochastic competence switch whose transition probability is regulated by population density, population stress and cell stress. 2) A sporulation timer whose clock rate is regulated by cell stress and population stress. 3) A decision gate that is coupled to the timer via a special repressilator-like loop. We show that the distinct circuit architecture of this gate leads to special dynamics and noise management characteristics: The gate opens a time-window of opportunity for competence transitions during which it generates oscillations that are turned into a chain of transition opportunities - each oscillation opens a short interval with high transition probability. The special architecture of the gate also leads to filtering of external noise and robustness against internal noise and variations in the circuit parameters.

The relationship between a market index and its constituent stocks is complicated. While an index is a weighted average of its constituent stocks, when the investigated time scale is one day or longer the index has been found to have a stronger effect on the stocks than vice versa. We explore how this interaction changes in short time scales using high frequency data. Using a correlation-based analysis approach, we find that in short time scales stocks have a stronger influence on the index. These findings have implications for high frequency trading and suggest that the price of an index should be published on shorter time scales, as close as possible to those of the actual transaction time scale.

Understanding correlations in complex systems is crucial in the face of turbulence, such as the ongoing financial crisis. However, in complex systems, such as financial systems, correlations are not constant but instead vary in time. Here we address the question of quantifying state-dependent correlations in stock markets. Reliable estimates of correlations are absolutely necessary to protect a portfolio. We analyze 72 years of daily closing prices of the 30 stocks forming the Dow Jones Industrial Average (DJIA). We find the striking result that the average correlation among these stocks scales linearly with market stress reflected by normalized DJIA index returns on various time scales. Consequently, the diversification effect which should protect a portfolio melts away in times of market losses, just when it would most urgently be needed. Our empirical analysis is consistent with the interesting possibility that one could anticipate diversification breakdowns, guiding the design of protected portfolios.

Bacterial colonies must often cope with unfavourable environmental conditions. To do so, they have developed sophisticated modes of cooperative behaviour. It has been found that such behaviour can cause bacterial colonies to exhibit complex growth patterns similar to those observed during non-equilibrium growth processes in non-living systems; some of the qualitative features of the latter may be invoked to account for the complex patterns of bacterial growth. Here we show that a simple model of bacterial growth can reproduce the salient features of the observed growth patterns. The model incorporates random walkers, representing aggregates of bacteria, which move in response to gradients in nutrient concentration and communicate with each other by means of chemotactic 'feedback'. These simple features allow the colony to respond efficiently to adverse growth conditions, and generate self-organization over a wide range of length scales.