抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

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.

/pdf/statistical-mechanics-of-complex-networks-1zfjpvxipu.pdf

Statistical mechanics of complex networks

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

/pdf/the-structure-and-function-of-complex-networks-34deompc9l.pdf

The Structure and Function of Complex Networks

http://www.maths.qmul.ac.uk/%7Elatora/report_06.pdf

Complex networks: Structure and dynamics

http://brainimaging.waisman.wisc.edu/~chung/neuro.processing/literature/rubinov.2010.NI.network.pdf

Complex network measures of brain connectivity: uses and interpretations.

Background: eQTL analysis is a powerful method that allows the identification of causal genomic alterations, providing an explanation of expression changes of single genes. However, genes mediate their biological roles in groups rather than in isolation, prompting us to extend the concept of eQTLs to whole gene pathways. Methods: We combined matched genomic alteration and gene expression data of glioblastoma patients and determined associations between the expression of signaling pathways and genomic copy number alterations with a non-linear machine learning approach. Results: Expectedly, over-expressed pathways were largely associated to tag-loci on chromosomes with signature alterations. Surprisingly, tag-loci that were associated to under-expressed pathways were largely placed on other chromosomes, an observation that held for composite effects between chromosomes as well. Indicating their biological relevance, identified genomic regions were highly enriched with genes having a reported driving role in gliomas. Furthermore, we found pathways that were significantly enriched with such driver genes. Conclusions: Driver genes and their associated pathways may represent a functional core that drive the tumor emergence and govern the signaling apparatus in GBMs. In addition, such associations may be indicative of drug combinations for the treatment of brain tumors that follow similar patterns of common and diverging alterations.

/pdf/genome-wide-associations-of-signaling-pathways-in-23p8fuf0hi.pdf

Genome-wide associations of signaling pathways in glioblastoma multiforme

A sandpile model with stochastic toppling rule is studied The control parameters and the phase diagram are determined through a MF approach, the subcritical and critical regions are analyzed The model is found to have some similarities with directed percolation, but the existence of different boundary conditions and conservation law leads to a different universality class, where the critical state is extended to a line segment due to self-organization These results are supported with numerical simulations in one dimension The present model constitute a simple model which capture the essential difference between ordinary nonequilibrium critical phenomena, like DP, and self-organized criticality

Self-organized criticality and directed percolation

Infectious disease outbreaks are expected to grow exponentially in time but their initial dynamics is less known. Here I derive analytical expressions for the infectious disease dynamics with a gamma distribution of generation intervals. Excluding the exponential distribution, the outbreak grows as a power law at short times. At long times the dynamics is exponential with a growth rate determined by the basic reproductive number and the parameters of the generation interval distribution. These analytical expressions can be deployed to do better estimates of infectious disease parameters.

/pdf/exact-solution-of-infection-dynamics-with-gamma-distribution-3tzyrhfmag.pdf

Exact solution of infection dynamics with gamma distribution of generation intervals

A large part of the recent development of the interest in complex networks has been triggered by the observation of particular characteristics of real world networks, such as the small-world properties or the heavy-tailed distributions of degrees. Many datasets are, however, the result of an incomplete sampling of the underlying real networks, and it has been argued that sampling procedures might introduce uncontrolled biases in the statistical properties of the sampled graph. In this paper, we explore this issue in the case of the Internet, which is generally mapped from a limited set of sources by using traceroute-like probes. The origin of the biases introduced by such a sampling process is investigated and related with the global topological properties of the underlying network. We complement the analytical discussion with a thorough numerical investigation of simulated mapping strategies in network models with different topologies.

/pdf/sampling-of-networks-with-traceroute-like-probes-56n7tira1b.pdf

Sampling of Networks with Traceroute-Like Probes

Mapping the Internet generally consists in sampling the network from a limited set of sources by using traceroute-like probes. This methodology has been argued to introduce uncontrolled sampling biases that might produce statistical properties of the sampled graph which sharply differ from the original ones. Here we explore these biases and provide a statistical analysis of their origin. We derive a mean-field analytical approximation for the probability of edge and vertex detection that allows us to relate the global topological properties of the underlying network with the statistical accuracy of the sampled graph. In particular we show that shortest path routed sampling allows a clear characterization of underlying graphs with scale-free topology. We complement the analytical discussion with a throughout numerical investigation of simulated mapping strategies in different network models.

Alexei Vazquez

Papers

Genome-wide associations of signaling pathways in glioblastoma multiforme

Self-organized criticality and directed percolation

Exact solution of infection dynamics with gamma distribution of generation intervals

Sampling of Networks with Traceroute-Like Probes

Traceroute-like exploration of unknown networks : A statistical analysis