From sequence to consequence and back

AbstractThe genotype–phenotype relation is at the core of theoretical biology. It is argued why a mathematically based explanatory structure of this relation is in principle possible, and why it has to embrace both sequence to consequence and consequence to sequence phenomena. It is suggested that the primary role of DNA in the chain of causality is that its presence allows a living system to induce perturbations of its own dynamics as a function of its own system state or phenome, i.e. it capacitates living systems to self-transcend beyond those morphogenetic limits that exist for non-living open physical systems in general. Dynamic models bridging genotypes with phenotypic variation in a causally cohesive way are shown to provide explanations of genetic phenomena that go well beyond the explanatory domains of statistically oriented genetics theory construction. A theory originally proposed by Rupert Riedl, which implies that the morphospace that is reachable by the standing genetic variation in a population is quite restricted due to systemic constraints, is shown to provide a foundation for a mathematical conceptualization of numerous evolutionary phenomena associated with the phenotypic consequence to sequence relation. The paper may be considered a call to arms to mathematicians and the mathematically inclined to rise to the challenge of developing new formalisms capable of dealing with the deep defining characteristics of living systems

The mathematics of tanning

<p>Abstract</p> <p>Background</p> <p>The pigment melanin is produced by specialized cells, called melanocytes. In healthy skin, melanocytes are sparsely spread among the other cell types in the basal layer of the epidermis. Sun tanning results from an UV-induced increase in the release of melanin to neighbouring keratinocytes, the major cell type component of the epidermis as well as redistribution of melanin among these cells. Here we provide a mathematical conceptualization of our current knowledge of the tanning response, in terms of a dynamic model. The resolution level of the model is tuned to available data, and its primary focus is to describe the tanning response following UV exposure.</p> <p>Results</p> <p>The model appears capable of accounting for available experimental data on the tanning response in different skin and photo types. It predicts that the thickness of the epidermal layer and how far the melanocyte dendrites grow out in the epidermal layers after UV exposure influence the tanning response substantially.</p> <p>Conclusion</p> <p>Despite the paucity of experimental validation data the model is constrained enough to serve as a foundation for the establishment of a theoretical-experimental research programme aimed at elucidating the more fine-grained regulatory anatomy underlying the tanning response.</p

Carotenoid dynamics in Atlantic salmon

BACKGROUND: Carotenoids are pigment molecules produced mainly in plants and heavily exploited by a wide range of organisms higher up in the food-chain. The fundamental processes regulating how carotenoids are absorbed and metabolized in vertebrates are still not fully understood. We try to further this understanding here by presenting a dynamic ODE (ordinary differential equation) model to describe and analyse the uptake, deposition, and utilization of a carotenoid at the whole-organism level. The model focuses on the pigment astaxanthin in Atlantic salmon because of the commercial importance of understanding carotenoid dynamics in this species, and because deposition of carotenoids in the flesh is likely to play an important life history role in anadromous salmonids. RESULTS: The model is capable of mimicking feed experiments analyzing astaxanthin uptake and retention over short and long time periods (hours, days and years) under various conditions. A sensitivity analysis of the model provides information on where to look for possible genetic determinants underlying the observed phenotypic variation in muscle carotenoid retention. Finally, the model framework is used to predict that a specific regulatory system controlling the release of astaxanthin from the muscle is not likely to exist, and that the release of the pigment into the blood is instead caused by the androgen-initiated autolytic degradation of the muscle in the sexually mature salmon. CONCLUSION: The results show that a dynamic model describing a complex trait can be instrumental in the early stages of a project trying to uncover underlying determinants. The model provides a heuristic basis for an experimental research programme, as well as defining a scaffold for modelling carotenoid dynamics in mammalian systems

Characterisation of a novel paralog of scavenger receptor class B member I (SCARB1) in Atlantic salmon (Salmo salar)

<p>Abstract</p> <p>Background</p> <p>Red flesh colour is a unique trait found in some salmonid genera. Carotenoid pigments are not synthesized <it>de novo </it>in the fish, but are provided by dietary uptake. A better understanding of the molecular mechanisms underlying the cellular uptake and deposition of carotenoids could potentially be used to improve the low muscle deposition rate that is typically found in farmed Atlantic salmon. In addition, from an evolutionary point of view, the establishment and maintenance of this trait is still poorly understood. It has been demonstrated in several species that scavenger receptor class B, member 1 (<it>SCARB1</it>) is involved in intestinal absorption of carotenoids, which makes this gene a possible source of genetic variation in salmonid flesh pigmentation.</p> <p>Results</p> <p>In this study, a novel paralog of <it>SCARB1 (SCARB1-2) </it>was detected through screening for genetic variation in Atlantic salmon <it>SCARB1</it>. Full length <it>SCARB1-2 </it>encodes a protein with 89% identity to Atlantic salmon <it>SCARB1</it>, except for the C-terminal cytoplasmic tail that shows only 12% identity. The most prominent site of <it>SCARB1 </it>mRNA expression was in the mid gut, while a five-fold lower level was detected in Atlantic salmon skeletal muscle and liver. The <it>SCARB1-2 </it>mRNA was equally expressed in liver, muscle and mid gut, and at a lower level than <it>SCARB1 </it>mRNA. A total of seven different <it>SCARB1-2 </it>alleles comprising repetitive enhancer of zeste motifs (EZH2) were identified in the founding parents of a resource Atlantic salmon population. We mapped the <it>SCARB1-2 </it>paralog to a region on Atlantic salmon chromosome 1, containing a putative QTL for flesh colour. Addition of the <it>SCARB1-2 </it>marker increased the significance of this QTL, however the large confidence interval surrounding the QTL precludes confirmation of <it>SCARB1-2 </it>as a causative gene underlying variation in this trait.</p> <p>Conclusion</p> <p>We have characterised a novel paralog of <it>SCARB1 (SCARB1-2)</it>, have mapped it to Atlantic salmon chromosome 1 and have described its expression in various tissues. Mapping with <it>SCARB1-2 </it>alleles added further evidence for a QTL affecting flesh colour on this chromosome, however further studies are needed to confirm a functional role for this gene in flesh colour pigmentation.</p

Towards a quantitative understanding of the MITF-PIAS3-STAT3 connection

<p>Abstract</p> <p>Background</p> <p>Expression of the two transcription factors microphthalmia-associated transcription factor (MITF) and signal transducer and activator of transcription 3 (STAT3) are tightly connected to cell proliferation and survival, and are important for melanocyte development. The co-regulation of MITF and STAT3 via their binding to a common inhibitor Protein Inhibitor of Activated STAT3 (PIAS3) is intriguing. A better quantitative understanding of this regulation is likely to be important for elucidation of the melanocyte biology.</p> <p>Results</p> <p>We present a mathematical model describing the MITF-PIAS3-STAT3 signalling network. A default parameter set was developed, partly informed by the literature and partly by constraining the model to mimic reported behavioural features of the system. In addition, a set of experiment-specific parameters was derived for each of 28 experiments reported in the literature. The model seems capable of accounting for most of these experiments in terms of observed temporal development of protein amounts and phosphorylation states. Further, the results also suggest that this system possesses some regulatory features yet to be elucidated.</p> <p>Conclusions</p> <p>We find that the experimentally observed crosstalk between MITF and STAT3 via PIAS3 in melanocytes is faithfully reproduced in our model, offering mechanistic explanations for this behaviour, as well as providing a scaffold for further studies of MITF signalling in melanoma.</p

Electrodiffusive model for astrocytic and neuronal ion concentration dynamics

Electrical neural signalling typically takes place at the time-scale of milliseconds, and is typically modeled using the cable equation. This is a good approximation for processes when ionic concentrations vary little during the time course of a simulation. During periods of intense neural signalling, however, the local extracellular K+ concentration may increase by several millimolars. Clearance of excess K+ likely depends partly on diffusion in the extracellular space, partly on local uptake by- and intracellular transport within astrocytes. This process takes place at the time scale of seconds, and can not be modeled accurately without accounting for the spatiotemporal variations in ion concentrations. The work presented here consists of two main parts: First, we developed a general electrodiffusive formalism for modeling ion concentration dynamics in a one-dimensional geometry, including both an intra- and extracellular domain. The formalism was based on the Nernst-Planck equations. It ensures (i) consistency between the membrane potential and ion concentrations, (ii) global particle/charge conservation, and (iii) accounts for diffusion and concentration dependent variations in resistivities. Second, we applied the formalism to model how astrocytes exchange ions with the ECS, and identified the key astrocytic mechanisms involved in K+ removal from high concentration regions. We found that a local increase in extracellular K\textsuperscript{+} evoked a local depolarization of the astrocyte membrane, which at the same time (i) increased the local astrocytic uptake of K\textsuperscript{+}, (ii) suppressed extracellular transport of K+, (iii) increased transport of K+ within astrocytes, and (iv) facilitated astrocytic relase of K+ in extracellular low concentration regions. In summary, these mechanisms seem optimal for shielding the extracellular space from excess K+.Comment: 19 pages, 5 figures, 1 table (Equations 37 & 38 and the two first equations in Figure 2 were corrected May 30th 2013

Allele Interaction – Single Locus Genetics Meets Regulatory Biology

Background: Since the dawn of genetics, additive and dominant gene action in diploids have been defined by comparison of heterozygote and homozygote phenotypes. However, these definitions provide little insight into the underlying intralocus allelic functional dependency and thus cannot serve directly as a mediator between genetics theory and regulatory biology, a link that is sorely needed. Methodology/Principal Findings: We provide such a link by distinguishing between positive, negative and zero allele interaction at the genotype level. First, these distinctions disclose that a biallelic locus can display 18 qualitatively different allele interaction sign motifs (triplets of +, – and 0). Second, we show that for a single locus, Mendelian dominance is not related to heterozygote allele interaction alone, but is actually a function of the degrees of allele interaction in all the three genotypes. Third, we demonstrate how the allele interaction in each genotype is directly quantifiable in gene regulatory models, and that there is a unique, one-to-one correspondence between the sign of autoregulatory feedback loops and the sign of the allele interactions. Conclusion/Significance: The concept of allele interaction refines single locus genetics substantially, and it provides a direct link between classical models of gene action and gene regulatory biology. Together with available empirical data, our results indicate that allele interaction can be exploited experimentally to identify and explain intricate intra- and inter-locu

Nonlinear regulation enhances the phenotypic expression of trans-acting genetic polymorphisms

<p>Abstract</p> <p>Background</p> <p>Genetic variation explains a considerable part of observed phenotypic variation in gene expression networks. This variation has been shown to be located both locally (<it>cis</it>) and distally (<it>trans</it>) to the genes being measured. Here we explore to which degree the phenotypic manifestation of local and distant polymorphisms is a dynamic feature of regulatory design.</p> <p>Results</p> <p>By combining mathematical models of gene expression networks with genetic maps and linkage analysis we find that very different network structures and regulatory motifs give similar <it>cis</it>/<it>trans </it>linkage patterns. However, when the shape of the <it>cis-</it>regulatory input functions is more nonlinear or threshold-like, we observe for all networks a dramatic increase in the phenotypic expression of distant compared to local polymorphisms under otherwise equal conditions.</p> <p>Conclusion</p> <p>Our findings indicate that genetic variation affecting the form of <it>cis</it>-regulatory input functions may reshape the genotype-phenotype map by changing the relative importance of <it>cis </it>and <it>trans </it>variation. Our approach combining nonlinear dynamic models with statistical genetics opens up for a systematic investigation of how functional genetic variation is translated into phenotypic variation under various systemic conditions.</p

Disruption of vitellogenin gene function in adult honeybees by intra-abdominal injection of double-stranded RNA

BACKGROUND: The ability to manipulate the genetic networks underlying the physiological and behavioural repertoires of the adult honeybee worker (Apis mellifera) is likely to deepen our understanding of issues such as learning and memory generation, ageing, and the regulatory anatomy of social systems in proximate as well as evolutionary terms. Here we assess two methods for probing gene function by RNA interference (RNAi) in adult honeybees. RESULTS: The vitellogenin gene was chosen as target because its expression is unlikely to have a phenotypic effect until the adult stage in bees. This allowed us to introduce dsRNA in preblastoderm eggs without affecting gene function during development. Of workers reared from eggs injected with dsRNA derived from a 504 bp stretch of the vitellogenin coding sequence, 15% had strongly reduced levels of vitellogenin mRNA. When dsRNA was introduced by intra-abdominal injection in newly emerged bees, almost all individuals (96 %) showed the mutant phenotype. An RNA-fragment with an apparent size similar to the template dsRNA was still present in this group after 15 days. CONCLUSION: Injection of dsRNA in eggs at the preblastoderm stage seems to allow disruption of gene function in all developmental stages. To dissect gene function in the adult stage, the intra-abdominal injection technique seems superior to egg injection as it gives a much higher penetrance, it is much simpler, and it makes it possible to address genes that are also expressed in the embryonic, larval or pupal stages

A computational analysis of the long-term regulation of arterial pressure

The asserted dominant role of the kidneys in the chronic regulation of blood pressure and in the etiology of hypertension has been debated since the 1970s. At the center of the theory is the observation that the acute relationships between arterial pressure and urine production—the acute pressure-diuresis and pressure-natriuresis curves—physiologically adapt to perturbations in pressure and/or changes in the rate of salt and volume intake. These adaptations, modulated by various interacting neurohumoral mechanisms, result in chronic relationships between water and salt excretion and pressure that are much steeper than the acute relationships. While the view that renal function is the dominant controller of arterial pressure has been supported by computer models of the cardiovascular system known as the “Guyton-Coleman model”, no unambiguous description of a computer model capturing chronic adaptation of acute renal function in blood pressure control has been presented. Here, such a model is developed with the goals of: 1. representing the relevant mechanisms in an identifiable mathematical model; 2. identifying model parameters using appropriate data; 3. validating model predictions in comparison to data; and 4. probing hypotheses regarding the long-term control of arterial pressure and the etiology of primary hypertension. The developed model reveals: long-term control of arterial blood pressure is primarily through the baroreflex arc and the renin-angiotensin system; and arterial stiffening provides a sufficient explanation for the etiology of primary hypertension associated with ageing. Furthermore, the model provides the first consistent explanation of the physiological response to chronic stimulation of the baroreflex