Predicting embryonic patterning using mutual entropy fitness and in silico evolution
|
|
- Elinor McDonald
- 5 years ago
- Views:
Transcription
1 RESEARCH ARTICLE 2385 Development 137, (2010) doi: /dev Published by The Company of Biologists Ltd Predicting embryonic patterning using mutual entropy fitness and in silico evolution Paul François* and Eric D. Siggia SUMMARY During vertebrate embryogenesis, the expression of Hox genes that define anterior-posterior identity follows general rules: temporal colinearity and posterior prevalence. A mathematical measure for the quality or fitness of the embryonic pattern produced by a gene regulatory network is derived. Using this measure and in silico evolution we derive gene interaction networks for anterior-posterior (AP) patterning under two developmental paradigms. For patterning during growth (paradigm I), which is appropriate for vertebrates and short germ-band insects, the algorithm creates gene expression patterns reminiscent of Hox gene expression. The networks operate through a timer gene, the level of which measures developmental progression (a candidate is the widely conserved posterior morphogen Caudal). The timer gene provides a simple mechanism to coordinate patterning with growth rate. The timer, when expressed as a static spatial gradient, functions as a classical morphogen (paradigm II), providing a natural way to derive the AP patterning, as seen in long germ-band insects that express their Hox genes simultaneously, from the ancestral short germ-band system. Although the biochemistry of Hox regulation in higher vertebrates is complex, the actual spatiotemporal expression phenotype is not, and simple activation and repression by Hill functions suffices in our model. In silico evolution provides a quantitative demonstration that continuous positive selection can generate complex phenotypes from simple components by incremental evolution, as Darwin proposed. KEY WORDS: Hox genes, In silico evolution, Mutual entropy, Systems biology INTRODUCTION Numerical simulations of evolution have a long history in ecology and molecular evolution but are less used in cell and developmental biology. Evolutionary computations, in the latter context, face the technical challenges of defining the fitness to be optimized and inventing plausible mutations. To evolve properties of the cell, the selection used in ecology, i.e. reproductive success, is too far removed from the question and it is unclear how to translate mutation rates at the genome level into morphological change. In two previous papers we have evolved regulatory networks for segmentation and adaptation and confronted the problems of what fitness to optimize and how to chose mutation rates (Francois et al., 2007; Francois and Siggia, 2008). The fitness has to be specific to the process, e.g. reward segment number to evolve segmentation, yet be as general as possible because we can only hope to find networks common to phyla, not individual species. Detailed mutation rates became immaterial once it was shown that the fitness landscape was shaped like a funnel (defining better fitness to be lower), so that any mutational process that sampled all directions would move to the bottom of the funnel. This mathematics recapitulates Darwin s original insight that small changes in fitness can rapidly lead to the evolution of complex structures such as the eye (Nilsson and Pelger, 1994). Computational evolution functions like a genetic screen in that it enumerates in an unbiased way all models that can be built from a predefined set of parts to achieve a certain function. It favors Center for studies in Physics and Biology, The Rockefeller University, 1230 York Avenue, New York, NY, USA. *Author for correspondence (pfrancois@rockefeller.edu) Accepted 10 May 2010 models that can be built by incremental improvements in fitness, rather than via multiple neutral steps or transitions through less fit intermediates. Evolution is rapid when it can march along a fitness gradient. The early history of developmental patterning was rich in concepts, such as morphogen and selector genes, that lacked a molecular identity, yet informed many experiments (Crick and Lawrence, 1975), and it is to that level of description that we wish to return, but in a more quantitative way. There is extensive literature on homeotic mutants and homeotic genes, starting in the 1960s with the description of bithorax mutants (Lewis, 1963). In his pioneering work, Lewis proposed that fly segmental identities were directed by hypothetical bithorax substances, specific to a given segment. This idea was generalized to selector genes that had to be compartment specific, have an instructive role in development, and function combinatorially and cell-autonomously (Mann and Morata, 2000). The original selector genes were engrailed, which defines the anterior-posterior (AP) compartments within imaginal disks, and the Hox gene Ultrabithorax. Hox genes are major determinants in patterning the AP axis in bilaterians. Hox genes have been shown to be the crucial regulators of segmental identity in the fly (McGinnis and Krumlauf, 1992) and of vertebrae identity in vertebrates (Burke et al., 1995), such that Lewis further qualified them as master control genes (Lewis, 1992). Other examples of master control genes that direct cellular fates in different contexts at different stages of development include MyoD for muscles (Weintraub et al., 1991), Pax6 for eyes (Kozmik, 2005; Gehring and Ikeo, 1999) and Distal-less for legs (Gebelein et al., 2002; Pearson et al., 2005) and the so-called terminal selector genes, such as che-1, that determine ASE neuronal fates in C. elegans (Hobert, 2008). These master control genes are often embedded in feedback loops that lock commitment to a given cellular fate or identity (Weintraub et al., 1991; Zuber et
2 2386 RESEARCH ARTICLE Development 137 (14) al., 2003; Hobert, 2008), and transient activation, locked down via positive-feedback loops, appears to be a rule in developmental gene networks (Davidson et al., 2002; Oliveri et al., 2008). In both insects and vertebrates, the 3 to 5 arrangement of Hox genes on the chromosome matches the order of their anterior expression boundaries along the AP axis (McGinnis and Krumlauf, 1992), a property termed spatial colinearity. Furthermore, in vertebrates and short-germ insects, the temporal order of expression in the posterior region of the growing embryo follows the 3 to 5 genomic order (Kmita and Duboule, 2003; Ferrier and Minguillón, 2003; Wacker et al., 2004; Shippy et al., 2008), a phenomenon termed temporal colinearity. Hox function in the fly follows the posterior prevalence (or dominance) rule, whereby the most posterior Hox gene imposes its fate on all the anterior genes (McGinnis and Krumlauf, 1992; Kmita and Duboule, 2003). Loss-of-function mutations result in anterior homeotic transformations in which a parasegment(s) assumes the fate of the immediately anterior expressed Hox gene (Lewis, 1978). In gain-of-function experiments, a Hox gene that is ectopically expressed anterior to its normal position results in a posterior homeotic transformation, whereas expressed posteriorly it does nothing (Gibson and Gehring, 1988; González-Reyes and Morata, 1990; McGinnis and Krumlauf, 1992; Morata, 1993). The situation in vertebrates is similar, but more complex. There are four paralogous Hox clusters and the clearest phenotypes are observed when an entire Hox paralog group is removed. There is definitely combinatorial regulation among the paralog groups, in that adjacent Hox genes affect overlapping segments (Horan et al., 1994; Wellik and Capecchi, 2003; McIntyre et al., 2007; Wellik, 2007). However, the number of functional Hox combinations is a linear function of the number of genes, not an exponential one [e.g. see figure 2 in Iimura and Pourquie (Iimura and Pourquie, 2007)]. The boundaries between the major types of vertebrae coincide with Hox domains and are invariant among species, even when the number of vertebrae in each domain changes (Wellik, 2007). Posterior homeotic transformations have been observed by ectopic expression of genes anterior to their normal domains (Kessel et al., 1990; Lufkin et al., 1992). Our goal in this article is twofold. We first define quantitatively a fitness function (technically, the mutual entropy) that rewards complex patterning. This fitness is an explicit function of the concentration profiles of specific genes that define cellular identities (we will call them realizator genes) along the AP body axis. It favors diversity, i.e. there should be many such realizator genes present, each with a unique stable territory, and knowing the realizator it should be possible to infer AP position. A standard mutation-selection evolution algorithm then creates the network that allows for ordered domains of realizator gene expression. Mutual entropy (or information) has many mathematical properties that make it the natural fitness with which to evolve developmental networks in silico, generalizing its prior use in systems neuroscience (Rieke et al., 1999). We use this fitness to evolve networks to pattern the AP axis under general conditions that span those observed in arthropods and vertebrates: (1) a global morphogen gradient that disappears before the end of embryogenesis; and (2) a sliding morphogen that models patterning during growth (Francois et al., 2007; Peel et al., 2005; Iimura et al., 2009). Position is defined by exposure to the morphogen, but the networks are otherwise cellautonomous. We define the types of hierarchical networks that can be constructed by incremental improvements in fitness. For the sliding morphogen, which is appropriate to vertebrate Hox patterning, the pattern forms by means of a timer gene that measures the residence time in the posterior growth zone. Surprisingly, the evolved networks possess properties that are qualitatively similar to actual Hox gene networks, such as anterior homeotic transformations, posterior prevalence and temporal colinearity. The timer gene also naturally explains how to interconvert between static fly-like and dynamic morphogens without gross loss in fitness. Key aspects of Hox regulation simply follow from the exigencies of morphological evolution, suggesting that convergent evolution would channel variable molecular mechanisms towards the same phenotype. MATERIALS AND METHODS Mutual entropy as fitness We simulate networks of interacting genes and proteins as a system of differential equations, and we model an embryo as a linear array of L cells sharing the same genetic network. The fitness must be defined for any network, as we want to begin with networks that pattern poorly or not at all and evolve something better. We also seek to evolve patterning networks common to a phyla, so the fitness should be as generic, smooth and parameter free as possible (Francois et al., 2007; Francois and Siggia, 2008). We assume that, ultimately, a single gene (which may be the intersection of several conventionally defined selectors) defines or labels segmental identity (Lewis, 1963; Lewis, 1992). Since the fitness should be a property of the pattern of cell types, it will depend only on the spatial distribution of the label genes, henceforth called realizators (Mann and Morata, 2000). Computational evolution, as we will explain, has to discover the realizators as well as the genes and regulatory modules that control them. Fitness concepts Fitness should favor: (1) the diversity of genetic expression the fitness improves monotonically with the number of realizators; and (2) a unique cell fate one cell should express only a single master control gene for a given segmental identity. Mathematically, it is natural to measure diversity by entropy as is done in physics. If a system has N possible states available to it, but only resides in one of them, the entropy is zero, whereas if it spends equal time in each state the entropy is maximum and equals log(n). For the embryo, each realizator gene defines a state and the occupancy of each state is proportional to the integral of the realizator over the embryo. Thus, we define an entropy term, H(diversity), in the fitness that varies between zero when only one realizator is expressed, to log(n) when they are expressed equally. The second requirement of our fitness is naturally expressed as a conditional entropy, H(diversity position); namely, at a fixed position in the embryo we want the least diversity possible, i.e. the expression of a single realizator gene. Thus, our fitness requires us to optimize two contradictory constraints on the same function: maximizing entropy at the global scale and minimizing conditional entropy locally. To define the trade off between the two desiderata, we assume that duplicating a realizator gene while keeping its expression domain constant is a neutral event. Only one combination of our two entropies satisfies this condition (see Appendix S1 in the supplementary material) and we can define a unique fitness as: fitness H(diversity) + H(diversity position). (1) We have chosen signs so that fitness is to be minimized; for N realizators the optimal fitness is log(n) when each realizator is restricted to a single expression domain occupying 1/Nth of the embryo. [Our fitness is also called mutual information (Shannon and Weaver, 1998) and expresses how well the embryo can define position given concentrations of realizators.] The fitness has to be defined for any profile of the realizators and Fig. 1 illustrates several cases decomposed into the two components of the fitness. The most revealing case is illustrated in Fig. 1D,E. Allowing two realizators to overlap degrades fitness, although one might think that the
3 In silico evolution of embryonic pattern RESEARCH ARTICLE 2387 A C E B D F Fig. 1. Fitness diagram and gene expression profiles as a function of anterior-posterior (AP) position from cell 1 to 20 illustrate properties of the fitness. Only the realizator genes (solid lines) enter the fitness; other network genes are represented by dashed lines. (A) The two components of fitness are plotted with diagonal colored lines showing contours of constant total fitness (better fitness in red). B-F mark the fitness of subsequent panels. (B) For three genes ubiquitously expressed, both H(diversity) and conditional entropy H(diversity position) are high and equal, so the actual fitness is zero. (C) Each cell expresses a single gene resulting in zero conditional entropy, but gene 1 occupies most of the embryo, lowering the diversity, giving a fitness of log1.64. (D) Fitness is defined when realizators overlap, but neither the diversity nor the conditional entropy is optimal and the fitness is log1.78> log2. (E) The network in D can be improved by the addition of a new realizator 4 that accounts for the overlap of genes 2 and 3, giving a fitness of log2.33< log2. (F) Optimal configuration for three realizators; diversity is high (log3) and conditional entropy is zero, so the actual fitness is log3. overlap region conveys more positional information. However, we insist that evolution has to create a gene restricted to the overlap and to designate it as a realizator before the refined patterning of the axis is recognized by the fitness. Mathematical definition Let c ix be the concentration of realizator gene i in cell x. We can define a conditional probability for cell x to be in the realizator state i as: Note that: p i x =. (2) c kx p i x = 1, i and p i x 1 if one realizator is much larger than all the others. When only a single realizator is expressed, we are not concerned about its concentration as we assume its activity on downstream targets can be adjusted to ensure their expression. We define a probability p ix normalized over all cells and realizators as: where L is the number of cells in the embryo. From p ix, one can define a probability p i to find an realizator i anywhere in the embryo as: and a probability p x 1/L, which says that each cell x has equal weight. With these definitions, high diversity equates to large entropy, defined as: k H(diversity) is the usual Shannon entropy in information theory. This is maximum for all p i equal to 1/N for N selector genes, and therefore is lower or equal to its maximum value logn. c ix c ix p ix =, (3) L c kx k p i = p ix, (4) x H (diversity) = p i log p i. (5) i We also define a conditional entropy H(diversity position) as: H (diversity position) = p ix log p ix + p x log p x. (6) Minimization of H(diversity position) expresses the realizator gene hypothesis that only one realizator is expressed at a given position (cell) in the embryo. Thus, the fitness naturally resolves into the optimization of two functions: H(diversity) should be large and H(diversity position) should be small, a situation we have encountered before (Francois and Siggia, 2008). If we also impose the condition that duplication of a realizator is a fitness-neutral event, then only one combination of the two functions is allowed [see equations (6, 8) in Appendix S1 in the supplementary material], namely, the mutual entropy between position and realizators for the probability p ix : F ( p) = p i log p i + p x log p x p ix log p ix. (7) (Smaller fitness is better.) i x i,x Methods Our network evolution algorithm follows our earlier work (Francois and Hakim, 2004; Francois et al., 2007; Francois and Siggia, 2008) with some technical modifications specific to the problems treated here (see Appendix S1 in the supplementary material). Both the topology of the network [i.e. the nodes (genes) and the edges (interactions) connecting them] and all the numerical parameters for the expression rates are mutated and selected. The tags designating the realizators can move among the available genes and also be created and destroyed. Fig. 2 displays a summary of each generation of the algorithm. We evolve a population of networks. In one generation the half that is most fit is retained unaltered, and a copy of each is mutated and added back to the population. Therefore, the fitness of the best network can only improve or remain the same. When a morphogen is supplied as an input, all interactions are transcriptional and cell-autonomous. A transcription factor can act as an activator or repressor, depending on its target. Genes are off, i.e. non- ix x
4 2388 RESEARCH ARTICLE Development 137 (14) Fig. 2. Schematic of the evolutionary algorithm. Differential equations for each network are integrated (step 1). The fitness function is computed from the steady state of each network (step 2). The best half of the networks is retained (selection), copied (growth, step 3) and randomly mutated (mutation, step 4). Mutations change parameters (kinetics) or the network itself, as exemplified here. expressing, unless a transcriptional activator is supplied. A single activator suffices to turn a gene on, so that positive feedback of a gene on itself can result in bistability. Activators combine through the equivalent of OR functions. Similarly, one repressor is enough to suppress transcription and repressors work multiplicatively. Gene duplication is permitted and entails the replication of all interactions impinging on, and emanating from, the duplicated gene. If a realizator is duplicated, a new realizator tag is created and assigned to the new gene. The embryo consists of a line of L 20 cells, where cell x 1 is anterior. Although we do not consider molecular noise here, we modestly randomize the input values and select for an invariant (and static) final gene profile. When a morphogen is provided, either static or dynamic, to orient the embryo, we average c ix over all initial conditions and then compute p ix and the fitness. When two nearly optimal configurations are mixed in this way (or the realizator expression domains broken up in multiple ways) the fitness is clearly degraded. There are penalties imposed on pathological expression patterns that are not static at the end of the simulation or in which a cell expresses no realizators. Their precise form does not matter. For further details of the methods, see Appendix S1 in the supplementary material. The morphogen increases from anterior to posterior, in analogy with Caudal, which is conserved from insects to vertebrates and believed to be an ancestral morphogen in arthropods (Copf et al., 2004; Olesnicky et al., 2006). We define an AP order on genes, which potentially overlap in expression in the following way. A gene A is posterior (respectively anterior) to a gene B if the anterior (respectively posterior) boundary of A in space is posterior (respectively anterior) to that of B. For instance, in Fig. 1E, gene 1 is posterior to genes 2 and 3, whereas gene 2 is anterior to genes 1 and 3. To characterize network-derived patterns, we define a posterior index (respectively anterior index) by counting the number of repressions in which one gene is repressed by a more posterior (respectively anterior) gene. For example, in Fig. 1D, if gene 1 represses gene 2, then this repression counts for 1 in the posterior index. On the contrary, if gene 2 represses gene 1, then this repression counts for 1 in the anterior index. In practice, gene expression profiles are sharp enough that boundary positions can be assigned unambiguously, and we include all genes expressed at the final time in our index count. We display networks after applying a pruning procedure that eliminates all genes and interactions, the removal of which does not degrade the fitness. RESULTS We use the fitness function to evolve a patterning network in two cases that broadly exemplify what is seen in AP patterning in arthropods and vertebrates: (1) a static morphogen gradient that disappears before the fitness is measured; and (2) a sliding, or translating, morphogen, motivated by somitogenesis and Hox patterning (Francois et al., 2007; Dubrulle et al., 2001; Iimura et al., 2009). Since the network is cell-autonomous, AP fate is defined at the single-cell level, either from the morphogen level (experienced for a fixed time) or the length of time that the cell feels a fixed morphogen. These two problems become equivalent through the intermediary of a timer gene. With cell-cell interactions and no morphogen, our algorithm evolves lateral inhibition (see Appendix S1 and Figs S13, S14 in the supplementary material). Evolving with a disappearing morphogen gradient For each simulation, cells are initialized with an exponential morphogen gradient that is present for a fixed time and then removed rapidly (Fig. 3A). (This protocol defines an informative bridge between a morphogen that never disappears and a sliding morphogen tied to growth.) The fitness is computed some time after the morphogen disappears. Fig. 3 provides an example of a network that evolved under these conditions with our mutual entropy fitness. The
5 In silico evolution of embryonic pattern RESEARCH ARTICLE 2389 A B t < 1500 t = C D Fig. 3. A network evolved under the control of a static morphogen gradient. (A) Dynamics of the morphogen gradient, which is constant and then disappears. (B) Evolution of the fitness of the best network as a function of generation number. (C) Network topology; the nodes and edges are defined following the key in Fig. 2. (D) Steady-state profile of genes as a function of their position. Colors and numbers for a given gene correspond to those in C. Posterior index, 9; anterior index, 0; final fitness, log7.25. fitness clearly decreases with generation number, ending up close to log7.25, with eight realizators expressed at steady state defining eight slightly uneven domains. Movie 1 in the supplementary material shows the time course of embryonic development. For other examples of networks evolved under identical conditions, see Appendix S1 and Figs S1-S8 in the supplementary material. Despite some network-to-network variability, common structural features can be observed in the network topologies. All the realizator genes are self-sustaining in the final state (the morphogen is gone) and many are individually bistable. Bistability also plays a crucial role in pattern establishment because transient activation by upstream genes can push the realizator above the threshold that leads to a self-maintained high-activity state. This simple process has been described as the basic mechanism for stabilization of regulatory states in the sea urchin embryo (Davidson et al., 2002; Oliveri et al., 2008). Bistability also implies that gene repression can occur by transiently forcing a realizator below its autoactivating threshold, provided that no other activators are present. When a set of realizators are individually bistable, then supplying only a single repressive interaction between each pair of realizators is sufficient to stabilize just those configurations with at most one realizator active. This is most evident in the Boolean limit. Any configuration with two realizators on, would activate the repression between them and eliminate one. The sets of genes (8,4,2) and (1,8,4) in Fig. 3 are examples of this widely used arrangement. Another prominent feature of the evolved networks is the asymmetry in how the anterior versus posterior limits of the realizator domains are established due to the morphogen. Most posterior boundaries are defined by repression from genes expressed posterior to the one in question, rather than by the loss of an anteriorly expressed activator. Anterior boundaries are generally defined by activation thresholds, often in response to the morphogen. To quantify this asymmetry, we defined (see Materials and methods) network anterior/posterior indexes, the average values of which are 1.1 and 7.2, respectively, for all the networks in the main text and Appendix S1 that were generated by a disappearing morphogen gradient. An extreme case with anterior index 0 is provided by Fig. 3, in which genes are only repressed by genes posterior to them. As a consequence, the network itself is very hierarchical, and there is a correspondence between the position of a gene in this hierarchy and its domain of expression. For example, consider the subnetwork made of genes 2, 4, 8 and 1, and order them by the direction of the repressive links. Gene 2 is at the bottom of the hierarchy, being repressed by 4, 8 and 1, whereas gene 4 is repressed by genes 8 and 1, and gene 8 is repressed only by gene 1. Strikingly, this order in network hierarchy (2,4,8,1) is actually the order of gene expression from anterior to posterior at steady state, as can be seen in Fig. 3D. This property is general and can be seen in other evolved examples. So, the bias induced by the input gradient has a clear signature in the structure of the evolved network, imposing a hierarchy in which posterior genes are high and repress anterior genes, which occupy lower positions in the hierarchy. Gene duplication and mutational events To understand why there is such a bias in network structure, we looked at a typical evolutionary pathway that creates a new expression domain (Fig. 4). Gene duplication is central to the events pictured, but after all interactions are replicated for the new gene, several (e.g. the mutual activation of genes 1 and 3 in Fig. 4B) are superfluous and disappear. Then, while the expression domain of one copy is first kept essentially unchanged (gene 3 in Fig. 4C), the domain of expression of the other copy starts drifting to another position (improving the fitness) and becomes locked more posteriorly, new regulations being evolved to ensure that the domains do not overlap (Fig. 4D). Single neutral mutations and fitness-improving parameter changes suffice to traverse the entire pathway. A less
6 2390 RESEARCH ARTICLE Development 137 (14) A B C D Fig. 4. Example of a typical pathway going from fitness log2 to log3. (A-D) Starting with a network with two realizators and two domains of equal size, fitness is log2 (A); gene 1 is duplicated to create gene 3, with all incoming and outgoing interactions copied and no change in fitness (B). Parameter selection shifts the relative domains of the duplicated realizators, with fitness log2.1 (C). Eventually, the most posterior gene represses the anterior ones, confining gene 3 to the middle, each step improving fitness until finally, fitness is log3 (D). frequent pathway leading to an equivalent final state is shown in Fig. S15 in the supplementary material. If we freeze the topology of Fig. 4D, randomize the parameters and re-optimize with our fitness, the same hierarchical expression pattern re-emerges (see Fig. S16 in the supplementary material). Other frequent evolutionary pathways following gene duplication are shown in Fig. S17 in the supplementary material, leading to the same topology as in Fig. 4. Evolving with a sliding morphogen There is good evidence from somitogenesis in vertebrates that patterning occurs as cells emerge from a posterior growth zone and transit to lower levels of the posterior morphogens FGF and Wnt (Aulehla and Pourquié, 2010). Hox patterns develop contemporaneously (Aulehla and Pourquié, 2010; Iimura and Pourquie, 2006) with somitogenesis. In Xenopus, there are particularly clear data showing that Hox genes are expressed in a 3 to 5 temporal progression in the non-organizer mesoderm and acquire a fixed position when the cells converge into the organizer and then extend to create the AP axis (Wacker et al., 2004; Durston et al., 2010). Thus, to model Hox patterning coupled to growth, we assume a step-like morphogen profile that translates down a line of cells. High morphogen defines the posterior growth zone, and the step itself corresponds to the organizer, where the morphogen is withdrawn and cells assume a fixed fate. Thus, cells sense their distance from the rostral pole only once they are exposed to morphogen. Cell fate can be controlled by the exposure time to morphogen in the context of digit formation (Nelson et al., 1996), and possibly also during axis formation (Aulehla and Pourquié, 2010), although the process by which time is measured is completely unknown. Typical networks derived with these input dynamics are presented in Figs S9-S11 in the supplementary material. As for static gradients, realizators tend to auto-activate and be bistable so as to persist after the input disappears. Posterior boundaries are also controlled by repression from posterior genes. For the anterior boundaries, however, it is not possible just to read a morphogen level, but rather the gene has to measure the time that it is exposed to input. In several cases (e.g. see Fig. S11 in the supplementary material) this is accomplished by early-activated genes repressing those that appear later, i.e. setting their anterior boundaries. In general, it was harder with a sliding gradient than a static one to initiate multi-domain patterns starting from nothing. Using a timer gene To accelerate the evolution, we began with the small network shown in Fig. 5B. It is not unreasonable, biologically, to bias evolution in this way because the sliding morphogen really only patterns the trunk and posterior, not the head. Our initial network is common in developmental biology [e.g. the gsc/bra system (Green, 2002)] and was the generic two-domain network we found for a static input. One activator controls two genes with different thresholds, and the high-threshold gene represses the lowthreshold gene to make their expression domains disjoint. We generalize it slightly by adding a potential timer protein 3, which is activated by the input, to delay the activation of gene 1 by the morphogen. The subsequent evolution of this small network in shown in Fig. 5, along with the expression profile it generates. Another example of such evolution is shown in Fig. S12 in the supplementary material. The initial network bias and timer gene 3 facilitate the evolution of simple networks with many states that exhibit topological properties that are similar to those produced with a static input. Again, posterior index is high while anterior index is low. As with the static gradient, posterior boundaries are set up by repression by posterior genes. However, because there is no AP gradient, the mechanism of establishment of anterior boundaries is different, and relies heavily on the timer gene. In Fig. 5, gene 3 accumulates slowly and by virtue of graded activation thresholds, gene 3 directly activates genes 4 then 5 then 6, and indirectly controls the remaining realizators other than gene 2 (which is activated directly by the input and is repressed by gene 3 to restrict it to the anterior).
7 In silico evolution of embryonic pattern RESEARCH ARTICLE 2391 A B E C D F Fig. 5. Network evolved with a sliding morphogen beginning from a twodomain network. (A) The concentration of gene 0 recedes from anterior to posterior to model the coupling of patterning to growth. (B) Initial network topology and the evolved network topology after 5000 generations. (C) Steady-state profile for the evolved network. Posterior index, 5; anterior index, 0; fitness, log4.95. (D) Gene expression as a function of time in the posterior-most cell follows the AP order in C, with the exception of the one realizator (gene 8) that is repressed by the input. (E,F) We created two genes (shown by a common color) from each realizator as explained in the text and in Fig. S22 in the supplementary material. The dashed lines display the Hox-like genes of the pair with nested expression profiles, and the solid lines show the new realizator genes with non-overlapping expression domains. (E) Final pattern. (F) For a smoothed morphogen step, most of the genes display anterior spreading: they are first expressed posteriorly and then move anteriorly (see also Movie 6 in the supplementary material). As a consequence of these successive activations in response to the accumulating timer and in spite of the rather complex network topology, there is an almost perfect correspondence between the temporal order of expression in the posterior cells and the spatial order (Fig. 5C; see Movie 2 in the supplementary material). This property can be related to the so-called temporal colinearity of Hox genes and is therefore a direct consequence of evolution under the control of a timer gene. The common topological features of networks evolved under the control of static versus sliding morphogens allow an easy translation between the two cases. Since our networks act cell-autonomously, we can literally replace the static morphogen as in Fig. 3D with a timer gene that grows without saturation while exposed to morphogen, and then decays exponentially after the morphogen disappears from the cell in question. When this is done for the network in Fig. 3, the realizator expression order from anterior to posterior does not change (see Figs S19, S20 and Movie 3 in the supplementary material). Similarly, if we turn the timer gene into a static morphogen, the network of Fig. 5 patterns an embryo with the exact same anterior to posterior order of gene expression (see Fig. S21 and Movie 4 in the supplementary material). Such a change in morphogen dynamics could explain the evolution from short to long germ-band insects (Liu and Kaufman, 2005). Lastly, the existence of a timer gene suggests an easy way to couple growth of the embryo to the dynamics of patterning, a property necessary to explain the fact that embryos can develop normally at different rates, such as happens in amphibians at reduced temperature. If the dynamics of the timer gene scale with the growth rate (simulated by the speed of the sliding input), the embryo patterns properly, as shown in Movie 5 in the supplementary material. Connecting realizators to nested Hox pattern It is well known that Hox expression domains overlap considerably and are often nested, whereas their master gene activity is segmentally restricted. Unknown post-transcriptional events ensure that the activity of anterior Hox genes is repressed by posterior Hox genes, a property called phenotypic repression (or posterior dominance) in fly and posterior prevalence in vertebrates (Duboule and Morata, 1994; Kmita and Duboule, 2003). The network in Fig. 5 has manifest temporal colinearity in its realizators, but the remaining upstream genes 1, 6 and 9 are not nested in the typical Hox pattern. This is because we have made all of the genes multifunctional, i.e. simultaneously repressors and activators, so that we do not make any distinction between transcriptional and post-transcriptional activities. However, it is nevertheless possible to formally disentangle these two activities to retrieve a more usual Hox gene transcriptional pattern. For each realizator, we create a new upstream gene that captures all the activating inputs (including from itself). This new gene activates a realizator, which retains all the repressive connections of the original, and accounts for the actual master gene activity. Then, the bistable upstream genes will have Hoxlike nested expression domains, and the new realizators will retain the localized expression of the original ones (Fig. 5E). Fig. S24 in the supplementary material shows the complete network derived from Fig. 5B by this transformation; for further details, see Appendix S1 and Figs S22-S24 in the supplementary material. If we smooth our sliding input step to make the transition from off to on gradual, then our model can readily capture another feature of Hox patterning termed anterior spreading (Kmita and Duboule, 2003; Iimura et al., 2009). It is most obvious in chick,
8 2392 RESEARCH ARTICLE Development 137 (14) A B Fig. 6. Change in expression domains when a single gene 8 is forced to zero. (A) See Fig. 3C; (B) see Fig. 5C. In both cases, the gene directly anterior to 8 extends posteriorly, until it is repressed by the next posterior gene. and as the name implies, Hox genes first turn on in the posterior and are then expressed more anteriorly. When we simulate the network in Fig. S24 in the supplementary material and Fig. 5E, we see very evident anterior spreading (Fig. 5F; for the full time course for this network, see Movie 6 in the supplementary material). Simulation of anterior homeotic transformations The high posterior index that typifies hierarchical networks has a characteristic signature in a loss-of-function experiment when one gene is set to zero. In analogy with the anterior homeotic transformation seen with Hox gene loss of function (Horan et al., 1994; Wellik and Capecchi, 2003; McIntyre et al., 2007), the expression domain of the immediate anterior gene expands posteriorly to fill the hole left by the deactivated gene (Fig. 6), irrespective of whether the network was evolved under a static or sliding input. DISCUSSION Network hierarchy and posterior prevalence In silico evolution generates gene regulatory networks with properties similar to the Hox gene networks that pattern the AP body axis. Orientation is derived solely from the morphogen, be it static or sliding (our surrogate for patterning during growth); the gene networks are entirely cell-autonomous, which is not unreasonable biologically, as noted in the Introduction. Since the morphogen disappears before we assess the expression pattern of the realizator genes that define the fitness, the gene networks are inherently multi-stable and are directed towards the appropriate fate by the morphogen. Our networks were all hierarchical, as abstracted in the module in Fig. 4. The morphogen defines the anterior gene expression boundaries, whereas the posterior boundaries are defined by repression from other genes. The two-gene limit is well known (Green, 2002). We quantified the excess of repression from posterior versus anterior genes by the respective indices (as defined in the Materials and methods) and found, for the 11 networks described in the text and in Appendix S1 in the supplementary material that were evolved under the control of gradient or timer, averages of 6.9 and 1.1. The phenomenon of posterior prevalence is a direct consequence of repression from the posterior gene (Fig. 6). We obtained gene networks with the phenotypic properties of Hox genes and do not explicitly distinguish transcriptional and post-transcriptional regulation. The genes in the simulation may be composites of real genes. The classic nested Hox expression territories occurred when we segregated activator and repressor activities into separate genes (Fig. 5E). Our conclusions are largely insensitive to mutation parameters in the biologically plausible limit in which the rate of addition of new links/nodes in the network is much slower than parameter mutation and link/node removal. Repeated simulations for the fate of duplicated genes or parameter reoptimization with fixed network topologies (see Figs S16, S17 in the supplementary material) generally yielded the same outcome (Fig. 4). Changing mutation rates influences the speed of evolution, not its qualitative outcome, in agreement with previous findings (Francois et al., 2007). Only neutral or fitness-improving mutations survive selection and the fitness consists of plateaux separated by jumps when the topology changes and parameters are optimized in a few generations. The ease of evolving elaborate patterning networks suggests the fitness landscape is funnel-like, providing another argument for the parameter independence of our results. Morphogen, timer and temporal colinearity The correlation between the spatial, genomic, and (for vertebrates) temporal order of Hox expression across many species has motivated experiments for mechanistic explanations. Genomeordered Hox arrays are not required for proper AP expression (Seo et al., 2004); they may facilitate temporally ordered expression (Duboule, 1995), but genome order is not part of our phenotypic model. For mouse, experiments that disrupt one of four Hox clusters alter the temporal expression but do not disrupt the final spatial order (reviewed by Tschopp et al., 2009). Our model for vertebrates assumes that axial patterning occurs progressively as cells exit a region of high posterior morphogen (e.g. Wnt). In amniotes, this is coupled to axial growth from longterm progenitors in the tail bud (Tzouanacou et al., 2009). In amphibians, Hox patterning occurs as cells converge from the ventral-posterior mesoderm and pass through the organizer (Wacker et al., 2004; Durston et al., 2010). Both situations are modeled as a morphogen step that slides (translates) down a line of cells (there is no need to explicitly model cell proliferation or movements). The step inflection is analogous to the organizer. Our networks are cell-autonomous, so the only cue as to AP position comes from the residence time in the high-morphogen posterior region. In silico evolution connects time to AP position by creating a timer gene that builds up monotonically while the cells experience the morphogen and dies after they exit the morphogen. Cell fate records, through multi-stability, the highest value of the timer gene seen by that cell. Temporal colinearity of Hox expression in the undifferentiated posterior cells is one consequence of the timer gene. Temporal order does not itself generate spatial order, and morphogen versus temporal control is not an issue [except when we compare long and short germ-band insects (see below)]. Other biological properties, such as anterior spreading (Gaunt and Strachan, 1994), can be easily explained by translating a smoothed step.
9 In silico evolution of embryonic pattern RESEARCH ARTICLE 2393 A timer gene is a very natural way to coordinate growth and patterning, which is particularly important in amphibians, the embryonic development of which can vary by a factor of two with temperature. The vertebrate homolog of the posterior insect morphogen Caudal, Cdx (Duprey et al., 1988), has been shown to posteriorize Xenopus embryos in a dose-dependent manner (Pownall et al., 1996; Isaacs et al., 1998). Overexpression or downregulation of Cdx genes shifts multiple Hox domains in a graded way (van den Akker et al., 2002; Gaunt et al., 2008), indicating an upstream position in the global control of Hox genes that is suggestive of a role as a potential timer. Recently, overexpression of Hox genes has been shown to influence axial growth in mice (Young et al., 2009), which is beyond the scope of our model. However, the concept of a timer gene as a mediator between growth and axial patterning has not been proposed previously and we hope that our timer and wavefront model functions in an analogous role to the clock and wavefront model for somitogenesis. Transition from short to long germ-band insects There is now abundant evidence from the arthropod phylogeny that long germ-band segmental patterning arose from the ancestral short germ-band mode multiple times (Peel et al., 2005), and recent reviews focus mostly on segmentation (Peel, 2008; Rosenberg et al., 2009). Much less is known about Hox patterning in short as opposed to long germ-band insects, so we assume that its dynamics are qualitatively similar to those of vertebrates. Thus, we model the short to long germ-band transition as the transition from a sliding to static gradient. The timer gene in the short germ-band ancestor that converts residence time in the growth zone to a protein level simply becomes the new static morphogen (Fig. 7; see Fig. S21 and Movie 4 in the supplementary material), which could happen gradually as more nuclei become available in the blastula. What the timer gene concept accomplishes is to preserve unchanged the entire downstream gene hierarchy, which is necessary for a viable embryo. The fate of the Hox genes is seldom addressed in this radical developmental transition, although it has been proposed that the ancestral function of gap genes was to pattern Hox genes (reviewed by Peel, 2008). Interestingly, in view of vertebrate analogies, it has been suggested that the master morphogen controlling segmentation in the long germ-band insect Nasonia is Caudal in conjunction with Otd (Olesnicky et al., 2006; Lynch et al., 2006), and Caudal might be the timer in short germ-band insects. The temporal colinearity of expression that we observed for the sliding gradient is readily lost after the transition to static gradient patterning (see Movie 1 in the supplementary material). There is pressure (in both the simulation and the embryo) to make the Hox pattern rapidly, so that when a static morphogen is supplied the posterior genes turn on early and repress the initiation of the anterior genes in posterior territories, thus generating simultaneous temporal induction. Mutual entropy as a fitness and the role of gene duplications We used the mutual entropy between realizator genes and AP position to define a fitness for embryonic patterning. The same expression has been used to quantify information transmission in the presence of molecular noise for small genetic networks (Ziv et al., 2007; Tkacik et al., 2008; Tkacik et al., 2009). The measure used in those studies implies that combinatorial expression conveys Fig. 7. Model for AP patterning in vertebrates and short germband insects and the transition to a long germ-band insect. (Left) AP patterning in vertebrates and short germ-band insects. (Right) The transition to a long germ-band insect. The timer (green) accumulates while cells are exposed to the sliding posterior morphogen (blue) and then decays. Its maximum value in a cell defines the cell fate. The timer, when applied statically as a morphogen gradient (right), creates the same pattern, now simultaneously rather than sequentially. more information about position, whereas our fitness penalizes two realizators that overlap and it is only when a third realizator is created and confined to the overlap region that the fitness will improve. Our mutual entropy fitness offers a mathematical framework in which complex evolutionary events at the network level can be observed and quantified. Lewis proposed that Hox genes evolved by duplication, in which one copy keeps the original function while the other one is able to assume a new segmental identity (Lewis, 1992). However, we find a different scenario that is more symmetric between the two duplicated genes. They are expressed contiguously and perturb the expression domains of their immediate neighbors (Fig. 4). Some phylogenetic data on homeobox genes seem to support the idea that duplicated genes remain adjacent [for example, see figure 2 in Ryan et al. (Ryan et al., 2007), where Hox1/2, Hox6-8 and Hox9-14 respectively cluster together]. Incremental evolution and embryonic patterning Although a connection between posterior prevalence, temporal colinearity and anterior spreading has long been part of the Hox phenomenology, this is not equivalent to creating a differential equation model that expresses it. Nor was it obvious that the natural mathematical measure of diversity of gene expression along an axis could serve as the fitness, for which the properties of temporal colinearity and posterior prevalence could arise by incremental evolution. Duplication is the obvious route to multiple Hox genes, but we furnished a detailed path for how this can occur incrementally. Hox regulation during growth might be achieved by different combinations of molecular pathways in different species in analogy with the somite clock, i.e. the Wnt, Notch and FGF pathways may have different oscillatory properties in different species (Goldbeter and Pourquié, 2008; Giudicelli and Lewis, 2004), yet the phenomenon itself is invariant, and its ease of evolution by continuous improvements in fitness suggests an explanation for this.
10 2394 RESEARCH ARTICLE Development 137 (14) Acknowledgements We thank John Guckenheimer and Bill Bialek for discussions. Support was provided by the NSF under grant number DMR to E.D.S. Competing interests statement The authors declare no competing financial interests. Supplementary material Supplementary material for this article is available at References Aulehla, A. and Pourquié, O. (2010). Signaling gradients during paraxial mesoderm development. Cold Spring Harbor Perspect. Biol. 2, a Burke, A. C., Nelson, C. E., Morgan, B. A. and Tabin, C. (1995). Hox genes and the evolution of vertebrate axial morphology. Development 121, Copf, T., Schröder, R. and Averof, M. (2004). Ancestral role of caudal genes in axis elongation and segmentation. Proc. Natl. Acad. Sci. USA 101, Crick, F. H. and Lawrence, P. A. (1975). Compartments and polyclones in insect development. Science 189, Davidson, E. H., Rast, J. P., Oliveri, P., Ransick, A., Calestani, C., Yuh, C.-H., Minokawa, T., Amore, G., Hinman, V., Arenas-Mena, C. et al. (2002). A genomic regulatory network for development. Science 295, Duboule, D. (1995). Vertebrate hox genes and proliferation: an alternative pathway to homeosis? Curr. Opin. Genet. Dev. 5, Duboule, D. and Morata, G. (1994). Colinearity and functional hierarchy among genes of the homeotic complexes. Trends Genet. 10, Dubrulle, J., McGrew, M. J. and Pourquie, O. (2001). Fgf signaling controls somite boundary position and regulates segmentation clock control of spatiotemporal hox gene activation. Cell 106, Duprey, P., Chowdhury, K., Dressler, G. R., Balling, R., Simon, D., Guenet, J. L. and Gruss, P. (1988). A mouse gene homologous to the Drosophila gene caudal is expressed in epithelial cells from the embryonic intestine. Genes Dev. 2, Durston, A. J., Jansen, H. J. and Wacker, S. A. (2010). Time-space translation regulates trunk axial patterning in the early vertebrate embryo. Genomics 95, Ferrier, D. E. K. and Minguillón, C. (2003). Evolution of the hox/parahox gene clusters. Int. J. Dev. Biol. 47, Francois, P. and Hakim, V. (2004). Design of genetic networks with specified functions by evolution in silico. Proc. Natl. Acad. Sci. USA 101, Francois, P. and Siggia, E. D. (2008). A case study of evolutionary computation of biochemical adaptation. Phys. Biol. 5, Francois, P., Hakim, V. and Siggia, E. D. (2007). Deriving structure from evolution: metazoan segmentation. Mol. Syst. Biol. 3, 9. Gaunt, S. J. and Strachan, L. (1994). Forward spreading in the establishment of a vertebrate hox expression boundary: the expression domain separates into anterior and posterior zones, and the spread occurs across implanted glass barriers. Dev. Dyn. 199, Gaunt, S. J., Drage, D. and Trubshaw, R. C. (2008). Increased cdx protein dose effects upon axial patterning in transgenic lines of mice. Development 135, Gebelein, B., Culi, J., Ryoo, H. D., Zhang, W. and Mann, R. S. (2002). Specificity of distalless repression and limb primordia development by abdominal hox proteins. Dev. Cell 3, Gehring, W. J. and Ikeo, K. (1999). Pax 6, mastering eye morphogenesis and eye evolution. Trends Genet. 15, Gibson, G. and Gehring, W. (1988). Head and thoracic transformations caused by ectopic expression of antennapedia during Drosophila development. Development 102, 657. Giudicelli, F. and Lewis, J. (2004). The vertebrate segmentation clock. Curr. Opin. Genet. Dev. 14, Goldbeter, A. and Pourquié, O. (2008). Modeling the segmentation clock as a network of coupled oscillations in the notch, wnt and fgf signaling pathways. J. Theor. Biol. 252, González-Reyes, A. and Morata, G. (1990). The developmental effect of overexpressing a ubx product in Drosophila embryos is dependent on its interactions with other homeotic products. Cell 61, Green, J. (2002). Morphogen gradients, positional information, and Xenopus: Interplay of theory and experiment. Dev. Dyn. 225, Hobert, O. (2008). Regulatory logic of neuronal diversity: terminal selector genes and selector motifs. Proc. Natl. Acad. Sci. USA 105, Horan, G. S., Wu, K., Wolgemuth, D. J. and Behringer, R. R. (1994). Homeotic transformation of cervical vertebrae in hoxa-4 mutant mice. Proc. Natl. Acad. Sci. USA 91, Iimura, T. and Pourquie, O. (2006). Collinear activation of hoxb genes during gastrulation is linked to mesoderm cell ingression. Nature 442, Iimura, T. and Pourquie, O. (2007). Hox genes in time and space during vertebrate body formation. Dev. Growth Differ. 49, Iimura, T., Denans, N. and Pourquié, O. (2009). Establishment of hox vertebral identities in the embryonic spine precursors. Curr. Top. Dev. Biol. 88, Isaacs, H. V., Pownall, M. E. and Slack, J. M. (1998). Regulation of hox gene expression and posterior development by the Xenopus caudal homologue xcad3. EMBO J. 17, Kessel, M., Balling, R. and Gruss, P. (1990). Variations of cervical vertebrae after expression of a hox-1.1 transgene in mice. Cell 61, Kmita, M. and Duboule, D. (2003). Organizing axes in time and space; 25 years of colinear tinkering. Science 301, Kozmik, Z. (2005). Pax genes in eye development and evolution. Curr. Opin. Genet. Dev. 15, Lewis, E. B. (1963). Genes and developmental pathways. Am. Zool. 3, Lewis, E. B. (1978). A gene complex controlling segmentation in Drosophila. Nature 276, Lewis, E. B. (1992). The 1991 Albert Lasker medical awards. Clusters of master control genes regulate the development of higher organisms. JAMA 267, Liu, P. Z. and Kaufman, T. C. (2005). Short and long germ segmentation: unanswered questions in the evolution of a developmental mode. Evol. Dev. 7, Lufkin, T., Mark, M., Hart, C. P., Dollé, P., LeMeur, M. and Chambon, P. (1992). Homeotic transformation of the occipital bones of the skull by ectopic expression of a homeobox gene. Nature 359, Lynch, J. A., Brent, A. E., Leaf, D. S., Pultz, M. A. and Desplan, C. (2006). Localized maternal orthodenticle patterns anterior and posterior in the long germ wasp Nasonia. Nature 439, Mann, R. S. and Morata, G. (2000). The developmental and molecular biology of genes that subdivide the body of Drosophila. Annu. Rev. Cell Dev. Biol. 16, McGinnis, W. and Krumlauf, R. (1992). Homeobox genes and axial patterning. Cell 68, McIntyre, D. C., Rakshit, S., Yallowitz, A. R., Loken, L., Jeannotte, L., Capecchi, M. R. and Wellik, D. M. (2007). Hox patterning of the vertebrate rib cage. Development 134, Morata, G. (1993). Homeotic genes of Drosophila. Curr. Opin. Genet. Dev. 3, Nelson, C. E., Morgan, B. A., Burke, A. C., Laufer, E., DiMambro, E., Murtaugh, L. C., Gonzales, E., Tessarollo, L., Parada, L. F. and Tabin, C. (1996). Analysis of hox gene expression in the chick limb bud. Development 122, Nilsson, D. E. and Pelger, S. (1994). A pessimistic estimate of the time required for an eye to evolve. Proc. Biol. Sci. 256, Olesnicky, E. C., Brent, A. E., Tonnes, L., Walker, M., Pultz, M. A., Leaf, D. and Desplan, C. (2006). A caudal mrna gradient controls posterior development in the wasp Nasonia. Development 133, Oliveri, P., Tu, Q. and Davidson, E. H. (2008). Global regulatory logic for specification of an embryonic cell lineage. Proc. Natl. Acad. Sci. USA 105, Pearson, J. C., Lemons, D. and McGinnis, W. (2005). Modulating hox gene functions during animal body patterning. Nat. Rev. Genet. 6, Peel, A. D. (2008). The evolution of developmental gene networks: lessons from comparative studies on holometabolous insects. Philos. Trans. R. Soc. Lond. B Biol. Sci. 363, Peel, A. D., Chipman, A. D. and Akam, M. (2005). Arthropod segmentation: beyond the Drosophila paradigm. Nat. Rev. Genet. 6, Pownall, M. E., Tucker, A. S., Slack, J. M. and Isaacs, H. V. (1996). efgf, xcad3 and hox genes form a molecular pathway that establishes the anteroposterior axis in Xenopus. Development 122, Rieke, F., Warland, D., de Ruyter van Steveninck, R. and Bialek, W. (1999). Spikes: Exploring the Neural Code. Cambridge, MA: The MIT Press. Rosenberg, M. I., Lynch, J. A. and Desplan, C. (2009). Heads and tails: evolution of antero-posterior patterning in insects. Biochim. Biophys. Acta 1789, Ryan, J. F., Mazza, M. E., Pang, K., Matus, D. Q., Baxevanis, A. D., Martindale, M. Q., Finnerty, J. R. and Fay, J. (2007). Pre-bilaterian origins of the hox cluster and the hox code: evidence from the sea anemone, Nematostella vectensis. PLoS ONE 2, e153. Seo, H.-C., Edvardsen, R. B., Maeland, A. D., Bjordal, M., Jensen, M. F., Hansen, A., Flaat, M., Weissenbach, J., Lehrach, H., Wincker, P. et al. (2004). Hox cluster disintegration with persistent anteroposterior order of expression in Oikopleura dioica. Nature 431, Shannon, C. E. and Weaver, W. (1998). The Mathematical Theory of Communication. Urbana, IL: University of Illinois Press. Shippy, T. D., Ronshaugen, M., Cande, J., He, J., Beeman, R. W., Levine, M., Brown, S. J. and Denell, R. E. (2008). Analysis of the tribolium homeotic complex: insights into mechanisms constraining insect hox clusters. Dev. Genes Evol. 218,
Chapter 18 Lecture. Concepts of Genetics. Tenth Edition. Developmental Genetics
Chapter 18 Lecture Concepts of Genetics Tenth Edition Developmental Genetics Chapter Contents 18.1 Differentiated States Develop from Coordinated Programs of Gene Expression 18.2 Evolutionary Conservation
More informationFrom DNA to Diversity
From DNA to Diversity Molecular Genetics and the Evolution of Animal Design Sean B. Carroll Jennifer K. Grenier Scott D. Weatherbee Howard Hughes Medical Institute and University of Wisconsin Madison,
More informationMidterm 1. Average score: 74.4 Median score: 77
Midterm 1 Average score: 74.4 Median score: 77 NAME: TA (circle one) Jody Westbrook or Jessica Piel Section (circle one) Tue Wed Thur MCB 141 First Midterm Feb. 21, 2008 Only answer 4 of these 5 problems.
More informationWhy Flies? stages of embryogenesis. The Fly in History
The Fly in History 1859 Darwin 1866 Mendel c. 1890 Driesch, Roux (experimental embryology) 1900 rediscovery of Mendel (birth of genetics) 1910 first mutant (white) (Morgan) 1913 first genetic map (Sturtevant
More informationAxis Specification in Drosophila
Developmental Biology Biology 4361 Axis Specification in Drosophila November 6, 2007 Axis Specification in Drosophila Fertilization Superficial cleavage Gastrulation Drosophila body plan Oocyte formation
More informationHomeotic Genes and Body Patterns
Homeotic Genes and Body Patterns Every organism has a unique body pattern. Although specialized body structures, such as arms and legs, may be similar in makeup (both are made of muscle and bone), their
More information5/4/05 Biol 473 lecture
5/4/05 Biol 473 lecture animals shown: anomalocaris and hallucigenia 1 The Cambrian Explosion - 550 MYA THE BIG BANG OF ANIMAL EVOLUTION Cambrian explosion was characterized by the sudden and roughly simultaneous
More informationLecture 7. Development of the Fruit Fly Drosophila
BIOLOGY 205/SECTION 7 DEVELOPMENT- LILJEGREN Lecture 7 Development of the Fruit Fly Drosophila 1. The fruit fly- a highly successful, specialized organism a. Quick life cycle includes three larval stages
More information2/23/09. Regional differentiation of mesoderm. Morphological changes at early postgastrulation. Segments organize the body plan during embryogenesis
Regional differentiation of mesoderm Axial Paraxial Intermediate Somatic Splanchnic Chick embryo Morphological changes at early postgastrulation stages Segments organize the body plan during embryogenesis
More informationAxis Specification in Drosophila
Developmental Biology Biology 4361 Axis Specification in Drosophila November 2, 2006 Axis Specification in Drosophila Fertilization Superficial cleavage Gastrulation Drosophila body plan Oocyte formation
More informationMOLECULAR CONTROL OF EMBRYONIC PATTERN FORMATION
MOLECULAR CONTROL OF EMBRYONIC PATTERN FORMATION Drosophila is the best understood of all developmental systems, especially at the genetic level, and although it is an invertebrate it has had an enormous
More informationpurpose of this Chapter is to highlight some problems that will likely provide new
119 Chapter 6 Future Directions Besides our contributions discussed in previous chapters to the problem of developmental pattern formation, this work has also brought new questions that remain unanswered.
More information18.4 Embryonic development involves cell division, cell differentiation, and morphogenesis
18.4 Embryonic development involves cell division, cell differentiation, and morphogenesis An organism arises from a fertilized egg cell as the result of three interrelated processes: cell division, cell
More informationDrosophila melanogaster- Morphogen Gradient
NPTEL Biotechnology - Systems Biology Drosophila melanogaster- Morphogen Gradient Dr. M. Vijayalakshmi School of Chemical and Biotechnology SASTRA University Joint Initiative of IITs and IISc Funded by
More informationAxis Specification in Drosophila
Developmental Biology Biology 4361 Axis Specification in Drosophila July 9, 2008 Drosophila Development Overview Fertilization Cleavage Gastrulation Drosophila body plan Oocyte formation Genetic control
More informationDevelopmental genetics: finding the genes that regulate development
Developmental Biology BY1101 P. Murphy Lecture 9 Developmental genetics: finding the genes that regulate development Introduction The application of genetic analysis and DNA technology to the study of
More informationDevelopmental Biology 3230 Midterm Exam 1 March 2006
Name Developmental Biology 3230 Midterm Exam 1 March 2006 1. (20pts) Regeneration occurs to some degree to most metazoans. When you remove the head of a hydra a new one regenerates. Graph the inhibitor
More informationEvolution of Transcription factor function: Homeotic (Hox) proteins
Evolution of Transcription factor function: Homeotic (Hox) proteins Hox proteins regulate morphology in cellular zones on the anterior-posterior axis of embryos via the activation/repression of unknown
More informationUnicellular: Cells change function in response to a temporal plan, such as the cell cycle.
Spatial organization is a key difference between unicellular organisms and metazoans Unicellular: Cells change function in response to a temporal plan, such as the cell cycle. Cells differentiate as a
More informationEvolutionary Developmental Biology
Evolutionary Developmental Biology a.k.a. EVO-DEVO Paedomorphosis is common among salamanders. Note how this hellbender (top) and mudpuppy (bottom) both have gills, paddle tails, and weaker limbs... Top:
More informationThe Emergence of Modularity in Biological Systems
The Emergence of Modularity in Biological Systems Zhenyu Wang Dec. 2007 Abstract: Modularity is a ubiquitous phenomenon in various biological systems, both in genotype and in phenotype. Biological modules,
More informationDrosophila Life Cycle
Drosophila Life Cycle 1 Early Drosophila Cleavage Nuclei migrate to periphery after 10 nuclear divisions. Cellularization occurs when plasma membrane folds in to divide nuclei into cells. Drosophila Superficial
More informationUNIVERSITY OF YORK BIOLOGY. Developmental Biology
Examination Candidate Number: UNIVERSITY OF YORK BSc Stage 2 Degree Examinations 2017-18 Department: BIOLOGY Title of Exam: Developmental Biology Desk Number: Time allowed: 1 hour and 30 minutes Total
More informationA systems approach to biology
A systems approach to biology SB200 Lecture 7 7 October 2008 Jeremy Gunawardena jeremy@hms.harvard.edu Recap of Lecture 6 In phage lambda, cooperativity leads to bistability and hysteresis In HIV-1, sequestration
More information1. What are the three general areas of the developing vertebrate limb? 2. What embryonic regions contribute to the developing limb bud?
Study Questions - Lecture 17 & 18 1. What are the three general areas of the developing vertebrate limb? The three general areas of the developing vertebrate limb are the proximal stylopod, zeugopod, and
More informationDevelopmental processes Differential gene expression Introduction to determination The model organisms used to study developmental processes
Date Title Topic(s) Learning Outcomes: Sept 28 Oct 3 1. What is developmental biology and why should we care? 2. What is so special about stem cells and gametes? Developmental processes Differential gene
More informationPRACTICE EXAM. 20 pts: 1. With the aid of a diagram, indicate how initial dorsal-ventral polarity is created in fruit fly and frog embryos.
PRACTICE EXAM 20 pts: 1. With the aid of a diagram, indicate how initial dorsal-ventral polarity is created in fruit fly and frog embryos. No Low [] Fly Embryo Embryo Non-neural Genes Neuroectoderm Genes
More informationHomeotic genes in flies. Sem 9.3.B.6 Animal Science
Homeotic genes in flies Sem 9.3.B.6 Animal Science So far We have seen that identities of each segment is determined by various regulators of segment polarity genes In arthopods, and in flies, each segment
More informationAdaptation, Evolution & development
Adaptation, Evolution & development marie.semon@ens-lyon.fr CIGOGNE lab Evolution genes & shape - Innovation in our own time experimental evolution - New genes, new uses cis versus coding changes - The
More informationMorphogens in biological development: Drosophila example
LSM5194 Morphogens in biological development: Drosophila example Lecture 29 The concept of morphogen gradients The concept of morphogens was proposed by L. Wolpert as a part of the positional information
More informationGenetic transcription and regulation
Genetic transcription and regulation Central dogma of biology DNA codes for DNA DNA codes for RNA RNA codes for proteins not surprisingly, many points for regulation of the process DNA codes for DNA replication
More information!!!!!!!! DB3230 Midterm 2 12/13/2013 Name:
1. (10 pts) Draw or describe the fate map of a late blastula stage sea urchin embryo. Draw or describe the corresponding fate map of the pluteus stage larva. Describe the sequence of gastrulation events
More informationRole of Organizer Chages in Late Frog Embryos
Ectoderm Germ Layer Frog Fate Map Frog Fate Map Role of Organizer Chages in Late Frog Embryos Organizer forms three distinct regions Notochord formation in chick Beta-catenin localization How does beta-catenin
More informationChapter 11. Development: Differentiation and Determination
KAP Biology Dept Kenyon College Differential gene expression and development Mechanisms of cellular determination Induction Pattern formation Chapter 11. Development: Differentiation and Determination
More informationMBios 401/501: Lecture 14.2 Cell Differentiation I. Slide #1. Cell Differentiation
MBios 401/501: Lecture 14.2 Cell Differentiation I Slide #1 Cell Differentiation Cell Differentiation I -Basic principles of differentiation (p1305-1320) -C-elegans (p1321-1327) Cell Differentiation II
More informationDevelopmental Biology Lecture Outlines
Developmental Biology Lecture Outlines Lecture 01: Introduction Course content Developmental Biology Obsolete hypotheses Current theory Lecture 02: Gametogenesis Spermatozoa Spermatozoon function Spermatozoon
More information10/15/09. Tetrapod Limb Development & Pattern Formation. Developing limb region is an example of a morphogenetic field
Tetrapod Limb Development & Pattern Formation Figure 16.5(1) Limb Bud Formation derived from lateral plate (somatic) & paraxial (myotome) Fig. 16.2 Prospective Forelimb Field of Salamander Ambystoma maculatum
More information9/4/2015 INDUCTION CHAPTER 1. Neurons are similar across phyla Thus, many different model systems are used in developmental neurobiology. Fig 1.
INDUCTION CHAPTER 1 Neurons are similar across phyla Thus, many different model systems are used in developmental neurobiology Fig 1.1 1 EVOLUTION OF METAZOAN BRAINS GASTRULATION MAKING THE 3 RD GERM LAYER
More informationDrosophila Somatic Anterior-Posterior Axis (A-P Axis) Formation
Home Biol 4241 Luria-Delbruck 1943 Hershey-Chase 1952 Meselson-Stahl 1958 Garapin et al. 1978 McClintock 1953 King-Wilson 1975 Sanger et al. 1977 Rothberg et al. 2011 Jeffreys et al. 1985 Bacterial Genetics
More informationAxis determination in flies. Sem 9.3.B.5 Animal Science
Axis determination in flies Sem 9.3.B.5 Animal Science All embryos are in lateral view (anterior to the left). Endoderm, midgut; mesoderm; central nervous system; foregut, hindgut and pole cells in yellow.
More informationThree different fusions led to three basic ideas: 1) If one fuses a cell in mitosis with a cell in any other stage of the cell cycle, the chromosomes
Section Notes The cell division cycle presents an interesting system to study because growth and division must be carefully coordinated. For many cells it is important that it reaches the correct size
More information3/8/ Complex adaptations. 2. often a novel trait
Chapter 10 Adaptation: from genes to traits p. 302 10.1 Cascades of Genes (p. 304) 1. Complex adaptations A. Coexpressed traits selected for a common function, 2. often a novel trait A. not inherited from
More informationMolecular evolution - Part 1. Pawan Dhar BII
Molecular evolution - Part 1 Pawan Dhar BII Theodosius Dobzhansky Nothing in biology makes sense except in the light of evolution Age of life on earth: 3.85 billion years Formation of planet: 4.5 billion
More informationSCIENTIFIC EVIDENCE TO SUPPORT THE THEORY OF EVOLUTION. Using Anatomy, Embryology, Biochemistry, and Paleontology
SCIENTIFIC EVIDENCE TO SUPPORT THE THEORY OF EVOLUTION Using Anatomy, Embryology, Biochemistry, and Paleontology Scientific Fields Different fields of science have contributed evidence for the theory of
More informationHox Genes and Regional Patterning of the Vertebrate Body Plan
Hox Genes and Regional Patterning of the Vertebrate Body Plan Moises Mallo 1,2, Deneen M. Wellik 3, Jacqueline Deschamps 4 1 Instituto Gulbenkian de Ciência, Oeiras, Portugal, 2 Department of Histology
More informationLife Sciences For NET & SLET Exams Of UGC-CSIR. Section B and C. Volume-08. Contents A. BASIC CONCEPT OF DEVELOPMENT 1
Section B and C Volume-08 Contents 5. DEVELOPMENTAL BIOLOGY A. BASIC CONCEPT OF DEVELOPMENT 1 B. GAMETOGENESIS, FERTILIZATION AND EARLY DEVELOPMENT 23 C. MORPHOGENESIS AND ORGANOGENESIS IN ANIMALS 91 0
More informationCS-E5880 Modeling biological networks Gene regulatory networks
CS-E5880 Modeling biological networks Gene regulatory networks Jukka Intosalmi (based on slides by Harri Lähdesmäki) Department of Computer Science Aalto University January 12, 2018 Outline Modeling gene
More informationDevelopment of Drosophila
Development of Drosophila Hand-out CBT Chapter 2 Wolpert, 5 th edition March 2018 Introduction 6. Introduction Drosophila melanogaster, the fruit fly, is found in all warm countries. In cooler regions,
More informationNetworks in systems biology
Networks in systems biology Matthew Macauley Department of Mathematical Sciences Clemson University http://www.math.clemson.edu/~macaule/ Math 4500, Spring 2017 M. Macauley (Clemson) Networks in systems
More information56:198:582 Biological Networks Lecture 10
56:198:582 Biological Networks Lecture 10 Temporal Programs and the Global Structure The single-input module (SIM) network motif The network motifs we have studied so far all had a defined number of nodes.
More informationSegment boundary formation in Drosophila embryos
Segment boundary formation in Drosophila embryos Development 130, August 2003 Camilla W. Larsen, Elizabeth Hirst, Cyrille Alexandre and Jean Paul Vincent 1. Introduction: - Segment boundary formation:
More informationEnduring understanding 1.A: Change in the genetic makeup of a population over time is evolution.
The AP Biology course is designed to enable you to develop advanced inquiry and reasoning skills, such as designing a plan for collecting data, analyzing data, applying mathematical routines, and connecting
More informationChapter Chemical Uniqueness 1/23/2009. The Uses of Principles. Zoology: the Study of Animal Life. Fig. 1.1
Fig. 1.1 Chapter 1 Life: Biological Principles and the Science of Zoology BIO 2402 General Zoology Copyright The McGraw Hill Companies, Inc. Permission required for reproduction or display. The Uses of
More informationAP Curriculum Framework with Learning Objectives
Big Ideas Big Idea 1: The process of evolution drives the diversity and unity of life. AP Curriculum Framework with Learning Objectives Understanding 1.A: Change in the genetic makeup of a population over
More informationMajor questions of evolutionary genetics. Experimental tools of evolutionary genetics. Theoretical population genetics.
Evolutionary Genetics (for Encyclopedia of Biodiversity) Sergey Gavrilets Departments of Ecology and Evolutionary Biology and Mathematics, University of Tennessee, Knoxville, TN 37996-6 USA Evolutionary
More informationNIH Public Access Author Manuscript Phys Biol. Author manuscript; available in PMC 2013 October 01.
NIH Public Access Author Manuscript Published in final edited form as: Phys Biol. 2012 October ; 9(5): 056001. doi:10.1088/1478-3975/9/5/056001. Pareto Evolution of Gene Networks: An Algorithm to Optimize
More informationA A A A B B1
LEARNING OBJECTIVES FOR EACH BIG IDEA WITH ASSOCIATED SCIENCE PRACTICES AND ESSENTIAL KNOWLEDGE Learning Objectives will be the target for AP Biology exam questions Learning Objectives Sci Prac Es Knowl
More informationAP3162D: Lecture 4 - Basic modelling frameworks for developmental biology and cell-fate decisions
AP162D: Lecture 4 - Basic modelling frameworks for developmental biology and cell-fate decisions Hyun Youk Delft University of Technology (Dated: March 15, 2018) In this lecture, we will derive the Berg-Purcell
More informationSUPPLEMENTARY INFORMATION
doi:10.1038/nature11804 a Tailbud after cutting PSM after cutting b 3500 3000 2500 mean intensity 2000 1500 1000 ROI1 (TB) ROI2 (PSM) 500 0 0 1 2 3 4 5 6 7 8 9 time (h) Supplementary Fig.1 Lfng gene activity
More informationExam 1 ID#: October 4, 2007
Biology 4361 Name: KEY Exam 1 ID#: October 4, 2007 Multiple choice (one point each) (1-25) 1. The process of cells forming tissues and organs is called a. morphogenesis. b. differentiation. c. allometry.
More informationEvolutionary Games and Computer Simulations
Evolutionary Games and Computer Simulations Bernardo A. Huberman and Natalie S. Glance Dynamics of Computation Group Xerox Palo Alto Research Center Palo Alto, CA 94304 Abstract The prisoner s dilemma
More informationThere are 3 parts to this exam. Use your time efficiently and be sure to put your name on the top of each page.
EVOLUTIONARY BIOLOGY EXAM #1 Fall 2017 There are 3 parts to this exam. Use your time efficiently and be sure to put your name on the top of each page. Part I. True (T) or False (F) (2 points each). Circle
More informationPrinciples of Experimental Embryology
Biology 4361 Developmental Biology Principles of Experimental Embryology September 19, 2006 Major Research Questions How do forces outside the embryo affect its development? (Environmental Developmental
More informationBig Idea 1: The process of evolution drives the diversity and unity of life.
Big Idea 1: The process of evolution drives the diversity and unity of life. understanding 1.A: Change in the genetic makeup of a population over time is evolution. 1.A.1: Natural selection is a major
More informationChapter 16: Reconstructing and Using Phylogenies
Chapter Review 1. Use the phylogenetic tree shown at the right to complete the following. a. Explain how many clades are indicated: Three: (1) chimpanzee/human, (2) chimpanzee/ human/gorilla, and (3)chimpanzee/human/
More informationNeural development its all connected
Neural development its all connected How do you build a complex nervous system? How do you build a complex nervous system? 1. Learn how tissue is instructed to become nervous system. Neural induction 2.
More informationAnalysis and Simulation of Biological Systems
Analysis and Simulation of Biological Systems Dr. Carlo Cosentino School of Computer and Biomedical Engineering Department of Experimental and Clinical Medicine Università degli Studi Magna Graecia Catanzaro,
More informationarxiv: v1 [q-bio.qm] 23 Apr 2007
Converting genetic networ oscillations into somite spatial pattern K. I. Mazzitello, 1,2 C. M. Arizmendi, 2 and H. G. E. Hentschel 3 1 CONICET 2 Facultad de Ingeniería, Universidad Nacional de Mar del
More informationExercise 3 Exploring Fitness and Population Change under Selection
Exercise 3 Exploring Fitness and Population Change under Selection Avidians descended from ancestors with different adaptations are competing in a selective environment. Can we predict how natural selection
More informationDevelopmental regulation of the Hox genes during axial morphogenesis in the mouse
Review 2931 al regulation of the Hox genes during axial morphogenesis in the mouse Jacqueline Deschamps* and Johan van Nes Hubrecht Laboratory, Netherlands Institute for al Biology, Uppsalalaan 8, 3584
More informationGenes, Development, and Evolution
14 Genes, Development, and Evolution Chapter 14 Genes, Development, and Evolution Key Concepts 14.1 Development Involves Distinct but Overlapping Processes 14.2 Changes in Gene Expression Underlie Cell
More informationEvolution and Development Evo-Devo
Evolution and Development Evo-Devo Darwin wrote a book on barnacles. Plate 1 (Lepas), from A monograph on the sub-class Cirripedia, by Charles Darwin. Comparative embryology There is an obvious similarity
More information"PRINCIPLES OF PHYLOGENETICS: ECOLOGY AND EVOLUTION" Integrative Biology 200B Spring 2011
"PRINCIPLES OF PHYLOGENETICS: ECOLOGY AND EVOLUTION" Integrative Biology 200B Spring 2011 Evolution and development ("evo-devo") The last frontier in our understanding of biological forms is an understanding
More informationQuestion Set # 4 Answer Key 7.22 Nov. 2002
Question Set # 4 Answer Key 7.22 Nov. 2002 1) A variety of reagents and approaches are frequently used by developmental biologists to understand the tissue interactions and molecular signaling pathways
More information10/2/2015. Chapter 4. Determination and Differentiation. Neuroanatomical Diversity
Chapter 4 Determination and Differentiation Neuroanatomical Diversity 1 Neurochemical diversity: another important aspect of neuronal fate Neurotransmitters and their receptors Excitatory Glutamate Acetylcholine
More informationModelling Biochemical Pathways with Stochastic Process Algebra
Modelling Biochemical Pathways with Stochastic Process Algebra Jane Hillston. LFCS, University of Edinburgh 13th April 2007 The PEPA project The PEPA project started in Edinburgh in 1991. The PEPA project
More information10-810: Advanced Algorithms and Models for Computational Biology. microrna and Whole Genome Comparison
10-810: Advanced Algorithms and Models for Computational Biology microrna and Whole Genome Comparison Central Dogma: 90s Transcription factors DNA transcription mrna translation Proteins Central Dogma:
More informationChapter 27: Evolutionary Genetics
Chapter 27: Evolutionary Genetics Student Learning Objectives Upon completion of this chapter you should be able to: 1. Understand what the term species means to biology. 2. Recognize the various patterns
More informationAP Biology Gene Regulation and Development Review
AP Biology Gene Regulation and Development Review 1. What does the regulatory gene code for? 2. Is the repressor by default active/inactive? 3. What changes the repressor activity? 4. What does repressor
More informationGenetic assimilation can occur in the absence of selection for the assimilating phenotype, suggesting a role for the canalization heuristic
doi: 10.1111/j.1420-9101.2004.00739.x Genetic assimilation can occur in the absence of selection for the assimilating phenotype, suggesting a role for the canalization heuristic J. MASEL Department of
More informationSonic hedgehog (Shh) signalling in the rabbit embryo
Sonic hedgehog (Shh) signalling in the rabbit embryo In the first part of this thesis work the physical properties of cilia-driven leftward flow were characterised in the rabbit embryo. Since its discovery
More informationBiosc 41 9/10 Announcements
Biosc 41 9/10 Announcements v Genetics review: group problem sets Groups of 3-4 Correct answer presented to class = 2 pts extra credit Incorrect attempt = 1 pt extra credit v Lecture: Animal Body Plans
More informationLecture 8: Temporal programs and the global structure of transcription networks. Chap 5 of Alon. 5.1 Introduction
Lecture 8: Temporal programs and the global structure of transcription networks Chap 5 of Alon 5. Introduction We will see in this chapter that sensory transcription networks are largely made of just four
More informationCaenorhabditis elegans
Caenorhabditis elegans Why C. elegans? Sea urchins have told us much about embryogenesis. They are suited well for study in the lab; however, they do not tell us much about the genetics involved in embryogenesis.
More informationMap of AP-Aligned Bio-Rad Kits with Learning Objectives
Map of AP-Aligned Bio-Rad Kits with Learning Objectives Cover more than one AP Biology Big Idea with these AP-aligned Bio-Rad kits. Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4 ThINQ! pglo Transformation
More informationRevision Based on Chapter 25 Grade 11
Revision Based on Chapter 25 Grade 11 Biology Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A cell that contains a nucleus and membrane-bound organelles
More informationWritten Exam 15 December Course name: Introduction to Systems Biology Course no
Technical University of Denmark Written Exam 15 December 2008 Course name: Introduction to Systems Biology Course no. 27041 Aids allowed: Open book exam Provide your answers and calculations on separate
More informationBIOLOGY
Int. J. Dev. Biol. 53: 1469-1481 (2009) doi: 10.1387/ijdb.072276mm THE INTERNATIONAL JOURNAL OF DEVELOPMENTAL BIOLOGY www.intjdevbiol.com The road to the vertebral formula MOISÉS MALLO*,1, TÂNIA VINAGRE
More information5/31/17. Week 10; Monday MEMORIAL DAY NO CLASS. Page 88
Week 10; Monday MEMORIAL DAY NO CLASS Page 88 Week 10; Wednesday Announcements: Family ID final in lab Today Final exam next Tuesday at 8:30 am here Lecture: Species concepts & Speciation. What are species?
More informationConcepts and Methods in Molecular Divergence Time Estimation
Concepts and Methods in Molecular Divergence Time Estimation 26 November 2012 Prashant P. Sharma American Museum of Natural History Overview 1. Why do we date trees? 2. The molecular clock 3. Local clocks
More informationBasic modeling approaches for biological systems. Mahesh Bule
Basic modeling approaches for biological systems Mahesh Bule The hierarchy of life from atoms to living organisms Modeling biological processes often requires accounting for action and feedback involving
More informationLecture 7: Simple genetic circuits I
Lecture 7: Simple genetic circuits I Paul C Bressloff (Fall 2018) 7.1 Transcription and translation In Fig. 20 we show the two main stages in the expression of a single gene according to the central dogma.
More informationOutline. v Definition and major characteristics of animals v Dividing animals into groups based on: v Animal Phylogeny
BIOSC 041 Overview of Animal Diversity: Animal Body Plans Reference: Chapter 32 Outline v Definition and major characteristics of animals v Dividing animals into groups based on: Body symmetry Tissues
More informationReproduction and Evolution Practice Exam
Reproduction and Evolution Practice Exam Topics: Genetic concepts from the lecture notes including; o Mitosis and Meiosis, Homologous Chromosomes, Haploid vs Diploid cells Reproductive Strategies Heaviest
More informationv Scientists have identified 1.3 million living species of animals v The definition of an animal
Biosc 41 9/10 Announcements BIOSC 041 v Genetics review: group problem sets Groups of 3-4 Correct answer presented to class = 2 pts extra credit Incorrect attempt = 1 pt extra credit v Lecture: Animal
More information178 Part 3.2 SUMMARY INTRODUCTION
178 Part 3.2 Chapter # DYNAMIC FILTRATION OF VARIABILITY WITHIN EXPRESSION PATTERNS OF ZYGOTIC SEGMENTATION GENES IN DROSOPHILA Surkova S.Yu. *, Samsonova M.G. St. Petersburg State Polytechnical University,
More informationStudy of Life. Intro to AP Biology
Study of Life Intro to 2007-2008 Big Ideas Big Idea 1: The process of evolution drives the diversity and unity of life. Big Idea 2: Biological systems utilize free energy and molecular building blocks
More informationLesson Overview. Gene Regulation and Expression. Lesson Overview Gene Regulation and Expression
13.4 Gene Regulation and Expression THINK ABOUT IT Think of a library filled with how-to books. Would you ever need to use all of those books at the same time? Of course not. Now picture a tiny bacterium
More informationTHE THEORY OF EVOLUTION
THE THEORY OF EVOLUTION Why evolution matters Theory: A well-substantiated explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation
More information8/23/2014. Introduction to Animal Diversity
Introduction to Animal Diversity Chapter 32 Objectives List the characteristics that combine to define animals Summarize key events of the Paleozoic, Mesozoic, and Cenozoic eras Distinguish between the
More information