Elizabeth M. Forbes's research works | The University of Queensland and other places

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Calcium and cAMP Levels Interact to Determine Attraction versus Repulsion in Axon Guidance

Article

May 2012

51 Reads

58 Citations

Neuron

Correct guidance of axons to their targets depends on an intricate network of signaling molecules in the growth cone. Calcium and cAMP are two key regulators of whether axons are attracted or repelled by molecular gradients, but how these molecules interact to determine guidance responses remains unclear. Here, we constructed a mathematical model for the relevant signaling network, which explained a large range of previous biological data and made predictions for when axons will be attracted or repelled. We then confirmed these predictions experimentally, in particular showing that while small increases in cAMP levels promote attraction large increases do not, and that under some circumstances reducing cAMP levels promotes attraction. Together, these results show that a relatively simple mathematical model can quantitatively predict guidance decisions across a wide range of conditions, and that calcium and cAMP levels play a more complex role in these decisions than previously determined.

Schematic showing how Dscam1 is believed to facilitate neuronal self-avoidance. (A) There are a large number ( 20,000) of possible Dscam1 isoforms. (B) Each neuron stochastically expresses a small subset of the isoforms ( isoforms). (C) When processes from the same neuron encounter one another, the isoforms homophilically bind. This binding generates repulsion. (D) However, when processes from different neurons encounter one another, they are unlikely to be expressing the same isoforms, so homophilic binding does not occur and the processes do not repel.

(A) The maximum number of distinct neurons n that can be created while maintaining a 95% probability that all neuron pairs are distinct as a function of the total number of isoforms i as calculated by equation 5.1. We show the results when there are m=30 isoforms per neuron and when varying degrees of sharing are allowed before neurons are no longer considered distinct. Both axes are log scale. In the wild type animal, 20,000 (2e4). The Hattori simulation line was plotted using values from Hattori et al. (2009) with 10% sharing and m=30. It is clear that these values are consistent with the values generated by equation 5.1. (B) The number of distinct neurons that can be created with a probability of 95% that all contacting neurons will have a distinct identity when neurons contact with a likelihood u. This is calculated for several values of i with m=30 isoforms per neuron and 20% sharing allowed.

The minimum percentage (A) and absolute number (B) of isoform sharing that would need to be tolerated in order to maintain a 95% probability that all mushroom body neurons are distinct. We show the degree of sharing required for the situation in which Hattori et al. (2009) found proper self-avoidance (i=4752 total isoforms) and for the situation in which they found improper self-avoidance (i=1152 total isoforms). Bumps and nonmonotonicity in the graph are due to the number of isoforms that are shared, changing discretely as m is increased.

The relationship between the number of isoforms expressed on each neuron m1 and m2 and the probability that the pair of neurons has one or more isoforms in common. Calculated with i=5000 isoforms in total.

(A) The probability distribution of the difference in the number of isoforms expressed between two neurons if each neuron expresses a number of isoforms m chosen independently from a discrete uniform distribution with a range [10, 30]. It is much more likely that a randomly chosen pair of neurons differs in the number of isoforms they express than that they do not. (B) The number of possible distinct neurons with a probability of 95% that the neurons are unique when each neuron expresses exactly m=30 isoforms (unadjusted, triangles) and when the number of isoforms expressed by each neuron is chosen stochastically (adjusted, circles). In these calculations, neurons are allowed to share up to k=4 isoforms while still being considered distinct. In the wild type animal, .

The Combinatorics of Neurite Self-Avoidance

November 2011

26 Reads

8 Citations

During neural development in Drosophila, the ability of neurite branches to recognize whether they are from the same or different neurons depends crucially on the molecule Dscam1. In particular, this recognition depends on the stochastic acquisition of a unique combination of Dscam1 isoforms out of a large set of possible isoforms. To properly interpret these findings, it is crucial to understand the combinatorics involved, which has previously been attempted only using stochastic simulations for some specific parameter combinations. Here we present closed-form solutions for the general case. These reveal the relationships among the key variables and how these constrain possible biological scenarios.

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... Elevation of intracellular calcium can convert repulsion into attraction [82]. Moreover, the effect of the cAMP-dependent or cGMP-dependent pathways can be mediated by protein kinase A (PKA) or protein kinase G (PKG), which can modulate the synthesis of cytoskeleton-associated proteins [83]. Many experiments have confirmed that reducing cAMP or cGMP levels switches attraction to repulsion, while increasing cAMP or cGMP favors converting a repulsive response to an attractive one [42,80,82,84]. ...
Reference:
Roles of Fibroblast Growth Factors in the Axon Guidance