The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them. 
Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network. 
The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other. 
The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.

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Statistical mechanics of complex networks

Many complex systems display a surprising degree of tolerance against errors. For example, relatively simple organisms grow, persist and reproduce despite drastic pharmaceutical or environmental interventions, an error tolerance attributed to the robustness of the underlying metabolic network1. Complex communication networks2 display a surprising degree of robustness: although key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network. The stability of these and other complex systems is often attributed to the redundant wiring of the functional web defined by the systems' components. Here we demonstrate that error tolerance is not shared by all redundant systems: it is displayed only by a class of inhomogeneously wired networks, called scale-free networks, which include the World-Wide Web3,4,5, the Internet6, social networks7 and cells8. We find that such networks display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected even by unrealistically high failure rates. However, error tolerance comes at a high price in that these networks are extremely vulnerable to attacks (that is, to the selection and removal of a few nodes that play a vital role in maintaining the network's connectivity). Such error tolerance and attack vulnerability are generic properties of communication networks.

Error and attack tolerance of complex networks

The study of networks pervades all of science, from neurobiology to statistical physics. The most basic issues are structural: how does one characterize the wiring diagram of a food web or the Internet or the metabolic network of the bacterium Escherichia coli? Are there any unifying principles underlying their topology? From the perspective of nonlinear dynamics, we would also like to understand how an enormous network of interacting dynamical systems-be they neurons, power stations or lasers-will behave collectively, given their individual dynamics and coupling architecture. Researchers are only now beginning to unravel the structure and dynamics of complex networks.

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Exploring complex networks

A key aim of postgenomic biomedical research is to systematically catalogue all molecules and their interactions within a living cell. There is a clear need to understand how these molecules and the interactions between them determine the function of this enormously complex machinery, both in isolation and when surrounded by other cells. Rapid advances in network biology indicate that cellular networks are governed by universal laws and offer a new conceptual framework that could potentially revolutionize our view of biology and disease pathologies in the twenty-first century.

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Network biology: understanding the cell's functional organization

Improved approaches for the detection of common epithelial malignancies are urgently needed to reduce the worldwide morbidity and mortality caused by cancer. MicroRNAs (miRNAs) are small (≈22 nt) regulatory RNAs that are frequently dysregulated in cancer and have shown promise as tissue-based markers for cancer classification and prognostication. We show here that miRNAs are present in human plasma in a remarkably stable form that is protected from endogenous RNase activity. miRNAs originating from human prostate cancer xenografts enter the circulation, are readily measured in plasma, and can robustly distinguish xenografted mice from controls. This concept extends to cancer in humans, where serum levels of miR-141 (a miRNA expressed in prostate cancer) can distinguish patients with prostate cancer from healthy controls. Our results establish the measurement of tumor-derived miRNAs in serum or plasma as an important approach for the blood-based detection of human cancer.

/pdf/circulating-micrornas-as-stable-blood-based-markers-for-3iuj944mh7.pdf

Circulating microRNAs as stable blood-based markers for cancer detection

Cellular functions, such as signal transmission, are carried out by 'modules' made up of many species of interacting molecules Understanding how modules work has depended on combining phenomenological analysis with molecular studies General principles that govern the structure and behaviour of modules may be discovered with help from synthetic sciences such as engineering and computer science, from stronger interactions between experiment and theory in cell biology, and from an appreciation of evolutionary constraints

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From molecular to modular cell biology.

The events of the cell cycle of most organisms are ordered into dependent pathways in which the initiation of late events is dependent on the completion of early events. In eukaryotes, for example, mitosis is dependent on the completion of DNA synthesis. Some dependencies can be relieved by mutation (mitosis may then occur before completion of DNA synthesis), suggesting that the dependency is due to a control mechanism and not an intrinsic feature of the events themselves. Control mechanisms enforcing dependency in the cell cycle are here called checkpoints. Elimination of checkpoints may result in cell death, infidelity in the distribution of chromosomes or other organelles, or increased susceptibility to environmental perturbations such as DNA damaging agents. It appears that some checkpoints are eliminated during the early embryonic development of some organisms; this fact may pose special problems for the fidelity of embryonic cell division.

https://science.sciencemag.org/content/sci/246/4930/629.full.pdf

Checkpoints: controls that ensure the order of cell cycle events

Multiple genetic changes occur during the evolution of normal cells into cancer cells. This evolution is facilitated in cancer cells by loss of fidelity in the processes that replicate, repair, and segregate the genome. Recent advances in our understanding of the cell cycle reveal how fidelity is normally achieved by the coordinated activity of cyclin-dependent kinases, checkpoint controls, and repair pathways and how this fidelity can be abrogated by specific genetic changes. These insights suggest molecular mechanisms for cellular transformation and may help to identify potential targets for improved cancer therapies.

https://science.sciencemag.org/content/sci/266/5192/1821.full.pdf

Cell cycle control and cancer

Mitotic cell division in eukaryotes is accomplished through a highly reproducible temporal sequence of events that is common to almost all higher organisms. An interval of time, Gl, separates the previous cell division from the initiation of DNA synthesis. Ohromosome replication is acco’mplished during the DNA synthetic period, S, which typically occupies about a third of the cell cycle. Another interval of time, G2, separates the completion of DNA synthesis from prophase, the beginning of mitosis, M. A dramatic sequence of changes in chromosome structure and of chromosome ,movement characterizes the brief mitotic period that results in the precise separation of sister chromatids to daughter nuclei. Mitosis is followed by cytokinesis, the partitioning of the cytoplasm into two daughter cells with separate plasma membranes. In some organisms the cycle is completed by cell wall separation. Each of these events occurs during the cell division cycle of the yeast, Saccharomyces cerevisiae (I) (Fig. 1) . However, two features which distinguish the cell cycle of S. cerevisiae from most other eukaryotes are particularly useful for an analysis of the gene functions that control the cell division cycle. First, the fact that both haploid and diploid cells undergo mitosis permits the isolation of recessive mutations in haploids and their analysis by complementation in diploids. Second, the daughter cell is recognizable at an early stage of the cell cycle as a bud on the surface of the parent cell. Since the ratio of bud size to parent cell size increases progressively during the cycle, this ratio pro-

https://science.sciencemag.org/content/sci/183/4120/46.full.pdf

Genetic Control of the Cell Division Cycle in Yeast

Cell division is arrested in many organisms in response to DNA damage. Examinations of the genetic basis for this response in the yeast Saccharomyces cerevisiae indicate that the RAD9 gene product is essential for arrest of cell division induced by DNA damage. Wild-type haploid cells irradiated with x-rays either arrest or delay cell division in the G2 phase of the cell cycle. Irradiated G1 and M phase haploid cells arrest irreversibly in G2 and die, whereas irradiated G2 phase haploid cells delay in G2 for a time proportional to the extent of damage before resuming cell division. In contrast, irradiated rad9 cells in any phase of the cycle do not delay cell division in G2, but continue to divide for several generations and die. However, efficient DNA repair can occur in irradiated rad9 cells if irradiated cells are blocked for several hours in G2 by treatment with a microtubule poison. The RAD9-dependent response detects potentially lethal DNA damage and causes arrest of cells in G2 until such damage is repaired.

https://science.sciencemag.org/content/sci/241/4863/317.full.pdf

Leland H. Hartwell

Papers

From molecular to modular cell biology.

Checkpoints: controls that ensure the order of cell cycle events

Cell cycle control and cancer

Genetic Control of the Cell Division Cycle in Yeast

The RAD9 Gene Controls the Cell Cycle Response to DNA Damage in Saccharomyces cerevisiae