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

Preface to the Princeton Landmarks in Biology Edition vii Preface xi Symbols Used xiii 1. The Importance of Islands 3 2. Area and Number of Speicies 8 3. Further Explanations of the Area-Diversity Pattern 19 4. The Strategy of Colonization 68 5. Invasibility and the Variable Niche 94 6. Stepping Stones and Biotic Exchange 123 7. Evolutionary Changes Following Colonization 145 8. Prospect 181 Glossary 185 References 193 Index 201

The Theory of Island Biogeography

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

Complex networks: Structure and dynamics

https://www.tau.ac.il/%7Eklafter1/258.pdf

The random walk's guide to anomalous diffusion: a fractional dynamics approach

We consider percolation in two dimensions as a fractal growth problem, and apply to it the theory of fractal growth based on the fixed-scale transformation approach developed for diffusion-limited aggregation and the dielectric breakdown model. This represents an important test for this new theoretical method based on an additional invariance property with respect to the renormalization group. We compute the fractal dimension of the percolating cluster including terms up to third order. The result is D=1.8830 for the square lattice and D=1.8650 for the triangular lattice. These values are in excellent agreement with the universal exact result D= 91 48 =1.8958 and also show the potential of this new method for standard problems.

Percolation as a fractal growth problem

The nonadiabatic regime of the electron-phonon interaction leads to behaviors of some physical measurable quantities qualitatively different from those expected from the Migdal-Eliashberg theory. Here we identify in the Pauli paramagnetic susceptibility χ one of such quantities and show that the nonadiabatic corrections reduce χ with respect to its adiabatic limit. We also show that the nonadiabatic regime induces an isotope dependence of χ, which in principle could be measured.

Pauli susceptibility of nonadiabatic Fermi liquids

Although Camacho and Arenas
 1 raise potentially interesting points, we believe that some of their arguments are flawed or undermined by poor statistics, and therefore that they do not invalidate our results2.

Food-web topology: universal scaling in food-web structure? (reply)

Diversity is a fundamental feature of ecosystems, even when the concept of ecosystem is extended to sociology or economics Diversity can be intended as the count of different items, animals, or, more generally, interactions There are two classes of stylized facts that emerge when diversity is taken into account The first are Diversity explosions: evolutionary radiations in biology, or the process of escaping 'Poverty Traps' in economics are two well known examples The second is nestedness: entities with a very diverse set of interactions are the only ones that interact with more specialized ones In a single sentence: specialists interact with generalists Nestedness is observed in a variety of bipartite networks of interactions: Biogeographic, macroeconomic and mutualistic to name a few This indicates that entities diversify following a pattern Since they appear in such very different systems, these two stylized facts point out that the build up of diversity is driven by a fundamental probabilistic mechanism, and here we sketch its minimal features We show how the contraction of a random tripartite network, which is maximally entropic in all its degree distributions but one, can reproduce stylized facts of real data with great accuracy which is qualitatively lost when that degree distribution is changed We base our reasoning on the combinatoric picture that the nodes on one layer of these bipartite networks can be described as combinations of a number of fundamental building blocks The stylized facts of diversity that we observe in real systems can be explained with an extreme heterogeneity (a scale-free distribution) in the number of meaningful combinations in which each building block is involved We show that if the usefulness of the building blocks has a scale-free distribution, then maximally entropic baskets of building blocks will give rise to very rich behaviors

Luciano Pietronero

Papers

Percolation as a fractal growth problem

Pauli susceptibility of nonadiabatic Fermi liquids

Food-web topology: universal scaling in food-web structure? (reply)

The Build-Up of Diversity in Complex Ecosystems

Fractal universe and cosmic acceleration in a Lemaître–Tolman–Bondi scenario