Phylodynamics of Infectious Disease Epidemics

We present a formalism for unifying the inference of population size from genetic sequences and mathematical models of infectious disease in populations. Virus phylogenies have been used in many recent studies to infer properties of epidemics. These approaches rely on coalescent models that may not be appropriate for infectious diseases. We account for phylogenetic patterns of viruses in susceptible–infected (SI), susceptible–infected–susceptible (SIS), and susceptible–infected–recovered (SIR) models of infectious disease, and our approach may be a viable alternative to demographic models used to reconstruct epidemic dynamics. The method allows epidemiological parameters, such as the reproductive number, to be estimated directly from viral sequence data. We also describe patterns of phylogenetic clustering that are often construed as arising from a short chain of transmissions. Our model reproduces the moments of the distribution of phylogenetic cluster sizes and may therefore serve as a null hypothesis for cluster sizes under simple epidemiological models. We examine a small cross-sectional sample of human immunodeficiency (HIV)-1 sequences collected in the United States and compare our results to standard estimates of effective population size. Estimated prevalence is consistent with estimates of effective population size and the known history of the HIV epidemic. While our model accurately estimates prevalence during exponential growth, we find that periods of decline are harder to identify.COALESCENT theory has found wide applications for inference of viral phylogenies (Nee et al. 1996; Rosenberg and Nordborg 2002; Drummond et al. 2005) and estimation of epidemic prevalence (Yusim et al. 2001; Robbins et al. 2003; Wilson et al. 2005), yet there have been few attempts to formally integrate coalescent theory with standard epidemiological models (Pybus et al. 2001; Goodreau 2006). While epidemiological models such as susceptible–infected–recovered (SIR) consider the dynamics of an entire population going forward in time, the coalescent theory operates on a small sample of an infected subpopulation and models the merging of lineages backward in time until a common ancestor has been reached. The original coalescent theory was based on a population of constant size with discrete generations (Kingman 1982a,b). Numerous extensions have been made for populations with overlapping generations in continuous time, exponential or logistic growth (Griffiths and Tavare 1994), and stochastically varying size (Kaj and Krone 2003). However, infectious disease epidemics are a special case of a variable size population, often characterized by early explosive growth followed by decline that leads to extinction or an endemic steady state.If superinfection is rare and if mutation is fast relative to epidemic growth, each lineage in a phylogenetic tree corresponds to a single infected individual with its own unique viral population. An infection event viewed in reverse time is equivalent to the coalescence of two lineages and every transmission of the virus between hosts can generate a new branch in the phylogeny of consensus viral isolates from infected individuals. Recently diverged sequences should represent transmissions in the recent past, and branches close to the root of a tree should represent transmissions from long ago. Consequently, branching patterns provide information about the frequency of transmissions over time (Wilson et al. 2005). The correspondence between transmission and phylogenetic branching is easiest to detect for viruses such as human immunodeficiency virus (HIV) and hepatitis C virus that have a high mutation rate relative to dispersal. Underlying SIR dynamics also apply to other pathogens, although in some cases it may be more difficult to reconstruct the transmission history.We examined the properties of viral phylogenies generated by the most common epidemiological models based on ordinary differential equations (ODEs). We are able to fit epidemiological models to a reconstructed phylogeny for sampled viral sequence data and make inferences regarding the size of the corresponding infected population. Our solution takes the form of an ODE analogous to those used to track epidemic prevalence and thereby provides a convenient link between commonly used epidemiological models and phylodynamics. Virtually all coalescent theory to date has been expressed in terms of integer-valued stochastic processes. Our motivation for using differential equations to describe the coalescent process is a desire to formalize a link with standard epidemiological models that are also expressed in terms of differential equations.We use our method to calculate the distribution of coalescent times for samples of viral sequences, fit SIR models to a viral phylogeny, and calculate median time to the most recent common ancestor (MRCA) of the sample. Our method also provides equations that describe the time evolution of the cluster size distribution (CSD)—the distribution of the number of descendants of a lineage over time. Clusters of related virus are often interpreted as epidemiologically linked. For example, clusters of acute HIV infections may represent short transmission chains between high-risk individuals (Yerly et al. 2001; Hue et al. 2005; Pao et al. 2005; Goodreau 2006; Brenner et al. 2007; Drumright and Frost 2008; Lewis et al. 2008). Because our model reproduces the moments of the cluster size distribution, it can be used to predict the level of clustering as a function of epidemiological conditions. The moments could be directly compared to empirical values or they could be used to reconstruct the entire CSD, whereupon standard statistical tests could be used for comparing distributions.Although our equations describe the macroscopic properties of the population distribution of cluster sizes, we generalize our method to the case of a small cross-sectional sample of sequences. This allows us to develop a likelihood-based approach to fitting SIR models to observed sequences.By considering variable degrees of incidence and the size of the infected population, our solution sheds light on the relationship between coalescent rates and epidemic dynamics. Coalescent rates are low near peak prevalence, but higher when there is a large ratio of incidence to prevalence. This can occur early on, when the epidemic is entering its expansion phase, as well as late if the epidemic has multiple periods of growth.     

Strabismus regulates asymmetric cell divisions and cell fate determination in the mouse brain

The planar cell polarity (PCP) pathway organizes the cytoskeleton and polarizes cells within embryonic tissue. We investigate the relationship between PCP signaling and cell fate determination during asymmetric division of neural progenitors (NPs) in mouse embryos. The cortex of Lp/Lp (Loop-tail) mice deficient in the essential PCP mediator Vangl2, homologue of Drosophila melanogaster Strabismus (Stbm), revealed precocious differentiation of neural progenitors into early-born neurons at the expense of late-born neurons and glia. Although Lp/Lp NPs were easily maintained in vitro, they showed premature differentiation and loss of asymmetric distribution of Leu-Gly-Asn–enriched protein (LGN)/partner of inscuteable (Pins), a regulator of mitotic spindle orientation. Furthermore, we observed a decreased frequency in asymmetric distribution of the LGN target nuclear mitotic apparatus protein (NuMa) in Lp/Lp cortical progenitors in vivo. This was accompanied by an increase in the number of vertical cleavage planes typically associated with equal daughter cell identities. These findings suggest that Stbm/Vangl2 functions to maintain cortical progenitors and regulates mitotic spindle orientation during asymmetric divisions in the vertebrate brain.     

Crystal Structure of Human Collagen XVIII Trimerization Domain: A Novel Collagen Trimerization Fold

Collagens contain a unique triple-helical structure with a repeating sequence -G-X-Y-, where proline and hydroxyproline are major constituents in X and Y positions, respectively. Folding of the collagen triple helix requires trimerization domains. Once trimerized, collagen chains are correctly aligned and the folding of the triple helix proceeds in a zipper-like fashion. Here we report the isolation, characterization, and crystal structure of the trimerization domain of human type XVIII collagen, a member of the multiplexin family. This domain differs from all other known trimerization domains in other collagens and exhibits a high trimerization potential at picomolar concentrations. Strong chain association and high specificity of binding are needed for multiplexins, which are present at very low levels.     

On Primordial Sense–Antisense Coding

The genetic code is implemented by aminoacyl-tRNA synthetases (aaRS). These 20 enzymes are divided into two classes that, despite performing same functions, have nothing common in structure. The mystery of this striking partition of aaRSs might have been concealed in their sterically complementary modes of tRNA recognition that, as we have found recently, protect the tRNAs with complementary anticodons from confusion in translation. This finding implies that, in the beginning, life increased its coding repertoire by the pairs of complementary codons (rather than one-by-one) and used both complementary strands of genes as templates for translation. The class I and class II aaRSs may represent one of the most important examples of such primordial sense–antisense (SAS) coding (Rodin and Ohno, Orig Life Evol Biosph 25:565–589, 1995). In this report, we address the issue of SAS coding in a wider scope. We suggest a variety of advantages that such coding would have had in exploring a wider sequence space before translation became highly specific. In particular, we confirm that in Achlya klebsiana a single gene might have originally coded for an HSP70 chaperonin (class II aaRS homolog) and an NAD-specific GDH-like enzyme (class I aaRS homolog) via its sense and antisense strands. Thus, in contrast to the conclusions in Williams et al. (Mol Biol Evol 26:445–450, 2009), this could indeed be a “Rosetta stone” gene (Carter and Duax, Mol Cell 10:705–708, 2002) (eroded somewhat, though) for the SAS origin of the two aaRS classes.     

Cooperation between catalytic and DNA binding domains enhances thermostability and supports DNA synthesis at higher temperatures by thermostable DNA polymerases

We have previously introduced a general kinetic approach for comparative study of processivity, thermostability, and resistance to inhibitors of DNA polymerases [Pavlov, A. R., et al. (2002) Proc. Natl. Acad. Sci. U.S.A.99, 13510-13515]. The proposed method was successfully applied to characterize hybrid DNA polymerases created by fusing catalytic DNA polymerase domains with various sequence-nonspecific DNA binding domains. Here we use the developed kinetic analysis to assess basic parameters of DNA elongation by DNA polymerases and to further study the interdomain interactions in both previously constructed and new chimeric DNA polymerases. We show that connecting helix-hairpin-helix (HhH) domains to catalytic polymerase domains can increase thermostability, not only of DNA polymerases from extremely thermophilic species but also of the enzyme from a faculatative thermophilic bacterium Bacillus stearothermophilus. We also demonstrate that addition of Topo V HhH domains extends efficient DNA synthesis by chimerical polymerases up to 105 °C by maintaining processivity of DNA synthesis at high temperatures. We found that reversible high-temperature structural transitions in DNA polymerases decrease the rates of binding of these enzymes to the templates. Furthermore, activation energies and pre-exponential factors of the Arrhenius equation suggest that the mechanism of electrostatic enhancement of diffusion-controlled association plays a minor role in binding of templates to DNA polymerases.     

Mitochondrial DNA signals of late glacial recolonization of Europe from near eastern refugia

Human populations, along with those of many other species, are thought to have contracted into a number of refuge areas at the height of the last Ice Age. European populations are believed to be, to a large extent, the descendants of the inhabitants of these refugia, and some extant mtDNA lineages can be traced to refugia in Franco-Cantabria (haplogroups H1, H3, V, and U5b1), the Italian Peninsula (U5b3), and the East European Plain (U4 and U5a). Parts of the Near East, such as the Levant, were also continuously inhabited throughout the Last Glacial Maximum, but unlike western and eastern Europe, no archaeological or genetic evidence for Late Glacial expansions into Europe from the Near East has hitherto been discovered. Here we report, on the basis of an enlarged whole-genome mitochondrial database, that a substantial, perhaps predominant, signal from mitochondrial haplogroups J and T, previously thought to have spread primarily from the Near East into Europe with the Neolithic population, may in fact reflect dispersals during the Late Glacial period, ～19-12 thousand years (ka) ago.     

Expression, purification and preliminary biochemical and structural characterization of the leucine rich repeat namesake domain of leucine rich repeat kinase 2

Mutations in leucine-rich repeat kinase 2 (LRRK2) are the most common cause of familial Parkinson's disease. Much research effort has been directed towards the catalytic core region of LRRK2 composed of GTPase (ROC, Ras of complex proteins) and kinase domains and a connecting COR (C-terminus of ROC) domain. In contrast, the precise functions of the protein-protein interaction domains, such as the leucine-rich repeat (LRR) domain, are not known. In the present study, we modeled the LRRK2 LRR domain (LRR(LRRK2)) using a template assembly approach, revealing the presence of 14 LRRs. Next, we focused on the expression and purification of LRR(LRRK2) in Escherichia coli. Buffer optimization revealed that the protein requires the presence of a zwitterionic detergent, namely Empigen BB, during solubilization and the subsequent purification and characterization steps. This indicates that the detergent captures the hydrophobic surface patches of LRR(LRRK2) thereby suppressing its aggregation. Circular dichroism (CD) spectroscopy measured 18% α-helices and 21% β-sheets, consistent with predictions from the homology model. Size exclusion chromatography (SEC) and dynamic light scattering measurements showed the presence of a single species, with a Stokes radius corresponding to the model dimensions of a protein monomer. Furthermore, no obvious LRR(LRRK2) multimerization was detected via cross-linking studies. Finally, the LRR(LRRK2) clinical mutations did not influence LRR(LRRK2) secondary, tertiary or quaternary structure as determined via SEC and CD spectroscopy. We therefore conclude that these mutations are likely to affect putative LRR(LRRK2) inter- and intramolecular interactions.     

Atomistic models of ion and solute transport by the sodium-dependent secondary active transporters

The recent determination of high-resolution crystal structures of several transporters offers unprecedented insights into the structural mechanisms behind secondary transport. These proteins utilize the facilitated diffusion of the ions down their electrochemical gradients to transport the substrate against its concentration gradient. The structural studies revealed striking similarities in the structural organization of ion and solute binding sites and a well-conserved inverted-repeat topology between proteins from several gene families. In this paper we will overview recent atomistic simulations applied to study the mechanisms of selective binding of ion and substrate in LeuT, Glt, vSGLT and hSERT as well as its consequences for the transporter conformational dynamics. This article is part of a Special Issue entitled: Membrane protein structure and function.