СИСТЕМНАЯ БИОЛОГИЯ

Первые попытки применения теории систем к биологии относятся к 30-м годам XX в. Так, в 1932 г. Уолтер Кэнон, декан факультета физиологии Гарвардского университета, в своей книге «Мудрость тела» («The wisdom of the body») описал термином «гомеостаз» способность организмов поддерживать большое число физиологических величин на постоянном уровне, несмотря на непрерывные изменения условий внешней среды. В 1943 г. американский математик Норберт Винер вместе с соавторами предположил, что отрицательные обратные связи могут играть центральную роль в поддержании стабильности живых систем, связав, тем самым, концепции контроля и оптимума с динамикой биологических систем.В последние годы интерес к системному подходу в биологии был вызван прорывом в технологиях секвенирования и, как результат, расшифровке геномов, траскриптомов и протеомов человека и других организмов. Наличие мощных вычислительных ресурсов (суперкомпьютеров) и скоростных Интернет-соединений также значительно облегчило доступ к огромным массивам молекулярно-биологических данных и обеспечило возможность их анализа, что в значительной степени стало основанием для современной системной биологии. Об активном развитии этой области биологии в последнее время говорит следующий факт: количество статей, представленных PubMed и содержащих фразу «systems biology», увеличилось со 140 в 2003 г. до более 10 000 в 2013 г

The relationship between node degree and dissipation rate in networks of diffusively coupled oscillators and its significance for pancreatic beta cells

Self-sustained oscillatory dynamics is a motion along a stable limit cycle in the phase space, and it arises in a wide variety of mechanical, electrical, and biological systems. Typically, oscillations are due to a balance between energy dissipation and generation. Their stability depends on the properties of the attractor, in particular, its dissipative characteristics, which in turn determine the flexibility of a given dynamical system. In a network of oscillators, the coupling additionally contributes to the dissipation, and hence affects the robustness of the oscillatory solution. Here, we therefore investigate how a heterogeneous network structure affects the dissipation rate of individual oscillators. First, we show that in a network of diffusively coupled oscillators, the dissipation is a linearly decreasing function of the node degree, and we demonstrate this numerically by calculating the average divergence of coupled Hopf oscillators. Subsequently, we use recordings of intracellular calcium dynamics in pancreatic beta cells in mouse acute tissue slices and the corresponding functional connectivity networks for an experimental verification of the presented theory. We use methods of nonlinear time series analysis to reconstruct the phase space and calculate the sum of Lyapunov exponents. Our analysis reveals a clear tendency of cells with a higher degree, that is, more interconnected cells, having more negative values of divergence, thus confirming our theoretical predictions. We discuss these findings in the context of energetic aspects of signaling in beta cells and potential risks for pathological changes in the tissue. Self-sustained oscillators are models of naturally oscillating objects, and as such they embrace many concepts in physics, biology, and engineering. Stable dissipative oscillatory dynamics results from the flow of energy or matter through a nonlinear system. If the energy is supplied to the system at a rate at which it is dissipated, ordered, and stable, self-organized oscillations may occur. In general, the stability and robustness of such a dynamical state depend on the dissipative properties of individual oscillators, which in turn determine the important dynamical features, such as synchronization and entraining capability. However, in ensembles of interconnected oscillators, the coupling itself can also significantly affect both robustness and dissipation. Motivated by the fact that many real-life systems are composed of coupled dissipative elements that exhibit complex connectivity patterns, in the present study, we therefore analyze the impact of a heterogeneous network structure on the dissipation rates of oscillators. To this effect, we first examine theoretically and numerically the relationship between node degree and average dissipation of oscillators and show that for networks of diffusively coupled oscillators this relation is linear. Next, we validate this result experimentally by measuring the activity of coupled beta cells within intact mouse pancreatic tissue by means of confocal imaging. On the basis of the measured cellular signals, we extract the intercellular functional connectivity patterns and calculate the average dissipation of individual cells. Our results reveal a clear tendency of cells in the network with a higher node degree having higher dissipation rates, which corroborates and in fact confirms our theoretical predictions. Moreover, our findings point out that the intercellular communication quite noticeably contributes to the energy needs of beta cells, which encompasses important aspects of structural and functional performance of beta cell networks in health and disease

Network Dynamics Mediate Circadian Clock Plasticity

A circadian clock governs most aspects of mammalian behavior. Although its properties are in part genetically determined, altered light-dark environment can change circadian period length through a mechanism requiring de novo DNA methylation. We show here that this mechanism is mediated not via cell-autonomous clock properties, but rather through altered networking within the suprachiasmatic nuclei (SCN), the circadian “master clock,” which is DNA methylated in region-specific manner. DNA methylation is necessary to temporally reorganize circadian phasing among SCN neurons, which in turn changes the period length of the network as a whole. Interruption of neural communication by inhibiting neuronal firing or by physical cutting suppresses both SCN reorganization and period changes. Mathematical modeling suggests, and experiments confirm, that this SCN reorganization depends upon GABAergic signaling. Our results therefore show that basic circadian clock properties are governed by dynamic interactions among SCN neurons, with neuroadaptations in network function driven by the environment

Modeling the seasonal adaptation of circadian clocks by changes in the network structure of the suprachiasmatic nucleus

The dynamics of circadian rhythms needs to be adapted to day length changes between summer and winter. It has been observed experimentally, however, that the dynamics of individual neurons of the suprachiasmatic nucleus (SCN) does not change as the seasons change. Rather, the seasonal adaptation of the circadian clock is hypothesized to be a consequence of changes in the intercellular dynamics, which leads to a phase distribution of electrical activity of SCN neurons that is narrower in winter and broader during summer. Yet to understand this complex intercellular dynamics, a more thorough understanding of the impact of the network structure formed by the SCN neurons is needed. To that effect, we propose a mathematical model for the dynamics of the SCN neuronal architecture in which the structure of the network plays a pivotal role. Using our model we show that the fraction of long-range cell-to-cell connections and the seasonal changes in the daily rhythms may be tightly related. In particular, simulations of the proposed mathematical model indicate that the fraction of long-range connections between the cells adjusts the phase distribution and consequently the length of the behavioral activity as follows: dense long-range connections during winter lead to a narrow activity phase, while rare long-range connections during summer lead to a broad activity phase. Our model is also able to account for the experimental observations indicating a larger light-induced phase-shift of the circadian clock during winter, which we show to be a consequence of higher synchronization between neurons. Our model thus provides evidence that the variations in the seasonal dynamics of circadian clocks can in part also be understood and regulated by the plasticity of the SCN network structure

Modeling the Seasonal Adaptation of Circadian Clocks by Changes in the Network Structure of the Suprachiasmatic Nucleus

<div><p>The dynamics of circadian rhythms needs to be adapted to day length changes between summer and winter. It has been observed experimentally, however, that the dynamics of individual neurons of the suprachiasmatic nucleus (SCN) does not change as the seasons change. Rather, the seasonal adaptation of the circadian clock is hypothesized to be a consequence of changes in the intercellular dynamics, which leads to a phase distribution of electrical activity of SCN neurons that is narrower in winter and broader during summer. Yet to understand this complex intercellular dynamics, a more thorough understanding of the impact of the network structure formed by the SCN neurons is needed. To that effect, we propose a mathematical model for the dynamics of the SCN neuronal architecture in which the structure of the network plays a pivotal role. Using our model we show that the fraction of long-range cell-to-cell connections and the seasonal changes in the daily rhythms may be tightly related. In particular, simulations of the proposed mathematical model indicate that the fraction of long-range connections between the cells adjusts the phase distribution and consequently the length of the behavioral activity as follows: dense long-range connections during winter lead to a narrow activity phase, while rare long-range connections during summer lead to a broad activity phase. Our model is also able to account for the experimental observations indicating a larger light-induced phase-shift of the circadian clock during winter, which we show to be a consequence of higher synchronization between neurons. Our model thus provides evidence that the variations in the seasonal dynamics of circadian clocks can in part also be understood and regulated by the plasticity of the SCN network structure.</p> </div