Limits...
Dynamical properties of gene regulatory networks involved in long-term potentiation.

Nido GS, Ryan MM, Benuskova L, Williams JM - Front Mol Neurosci (2015)

Bottom Line: Differential gene co-expression analysis further highlighted the importance of the Egr family and found a rapid enrichment in connectivity at 20 min, followed by a systematic decrease, providing a potential explanation for the down-regulation of gene expression at 24 h documented in our preceding studies.We also found that the architecture exhibited by a control and the 24 h LTP co-expression networks fit well to a scale-free distribution, known to be robust against perturbations.These results suggest that a new homeostatic state is achieved 24 h post-LTP.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer Science, University of Otago Dunedin, New Zealand ; Brain Health Research Centre, University of Otago Dunedin, New Zealand.

ABSTRACT
The long-lasting enhancement of synaptic effectiveness known as long-term potentiation (LTP) is considered to be the cellular basis of long-term memory. LTP elicits changes at the cellular and molecular level, including temporally specific alterations in gene networks. LTP can be seen as a biological process in which a transient signal sets a new homeostatic state that is "remembered" by cellular regulatory systems. Previously, we have shown that early growth response (Egr) transcription factors are of fundamental importance to gene networks recruited early after LTP induction. From a systems perspective, we hypothesized that these networks will show less stable architecture, while networks recruited later will exhibit increased stability, being more directly related to LTP consolidation. Using random Boolean network (RBN) simulations we found that the network derived at 24 h was markedly more stable than those derived at 20 min or 5 h post-LTP. This temporal effect on the vulnerability of the networks is mirrored by what is known about the vulnerability of LTP and memory itself. Differential gene co-expression analysis further highlighted the importance of the Egr family and found a rapid enrichment in connectivity at 20 min, followed by a systematic decrease, providing a potential explanation for the down-regulation of gene expression at 24 h documented in our preceding studies. We also found that the architecture exhibited by a control and the 24 h LTP co-expression networks fit well to a scale-free distribution, known to be robust against perturbations. By contrast the 20 min and 5 h networks showed more truncated distributions. These results suggest that a new homeostatic state is achieved 24 h post-LTP. Together, these data present an integrated view of the genomic response following LTP induction by which the stability of the networks regulated at different times parallel the properties observed at the synapse.

No MeSH data available.


Results of the RBN dynamical stability analysis. (A) Derrida plots for the LTP networks previously identified by Ryan et al. (2011, 2012) at different times post-LTP induction (20 min, 5 h, 24 h in green, orange, and blue, respectively) and the yeast transcriptional network (black). The left plot corresponds to the initial Hamming distance H(0) plotted against the Hamming distance after 1 iteration, H(1). Hence, only the nearest-neighbor interactions (local motifs) affect the dynamics. The right plot depicts H(0) vs H(5), where long-distance indirect influences between genes have an effect on the dynamics. Longer dynamics allow to reveal the influence of the overall network structure on its stability. The earlier networks (20 min and 5 h) are more unstable than the 24 h network, and the curve corresponding to the latter lies near the diagonal of the plot, which represents the border between the chaotic (white background) and the ordered regime (gray background). (B) Average time evolution of perturbed fixed points starting from Hamming distance H(0) = 1. This small difference tends to be amplified in these biological networks. The latest network recruited following LTP induction (24 h, blue), shows a less pronounced tendency to amplify the perturbation. Furthermore, from t = 2 to t = 5 the Hamming distance shows a slight decrease. The yeast transcriptional network (black dashed line) lies between the earlier LTP networks and the 24 h. (C) Derrida plots for each LTP network and to ensembles of random networks. The same stability profile shown in (A) for H(0) vs H(5) is shown separately for each of the temporal networks. The range of stability exhibited by the two ensembles of random networks (red shade: same number of nodes randomly connected by the same number of edges; blue shade: same number of nodes, same number of edges, and same in- and out-degree). These contrasts allow to isolate the effect of the specific degree sequence from the effect of the average degree (blue shade vs. red shade). In addition, it shows that if an evolutionary constraint were to act on the degree sequence, the real networks choose the less unstable option among all the possible network architectures with the same degree sequence (namely identical local motifs, blue shade). Each point in the plots is the average over 1000 random rule assignments for 100 random initial conditions (increasing these numbers has no effect on the results). Shades for random networks (red) and rewired networks (blue) correspond to the ranges observed using 100 topologies for each. Hamming distances are normalized by the number of nodes.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4528166&req=5

Figure 1: Results of the RBN dynamical stability analysis. (A) Derrida plots for the LTP networks previously identified by Ryan et al. (2011, 2012) at different times post-LTP induction (20 min, 5 h, 24 h in green, orange, and blue, respectively) and the yeast transcriptional network (black). The left plot corresponds to the initial Hamming distance H(0) plotted against the Hamming distance after 1 iteration, H(1). Hence, only the nearest-neighbor interactions (local motifs) affect the dynamics. The right plot depicts H(0) vs H(5), where long-distance indirect influences between genes have an effect on the dynamics. Longer dynamics allow to reveal the influence of the overall network structure on its stability. The earlier networks (20 min and 5 h) are more unstable than the 24 h network, and the curve corresponding to the latter lies near the diagonal of the plot, which represents the border between the chaotic (white background) and the ordered regime (gray background). (B) Average time evolution of perturbed fixed points starting from Hamming distance H(0) = 1. This small difference tends to be amplified in these biological networks. The latest network recruited following LTP induction (24 h, blue), shows a less pronounced tendency to amplify the perturbation. Furthermore, from t = 2 to t = 5 the Hamming distance shows a slight decrease. The yeast transcriptional network (black dashed line) lies between the earlier LTP networks and the 24 h. (C) Derrida plots for each LTP network and to ensembles of random networks. The same stability profile shown in (A) for H(0) vs H(5) is shown separately for each of the temporal networks. The range of stability exhibited by the two ensembles of random networks (red shade: same number of nodes randomly connected by the same number of edges; blue shade: same number of nodes, same number of edges, and same in- and out-degree). These contrasts allow to isolate the effect of the specific degree sequence from the effect of the average degree (blue shade vs. red shade). In addition, it shows that if an evolutionary constraint were to act on the degree sequence, the real networks choose the less unstable option among all the possible network architectures with the same degree sequence (namely identical local motifs, blue shade). Each point in the plots is the average over 1000 random rule assignments for 100 random initial conditions (increasing these numbers has no effect on the results). Shades for random networks (red) and rewired networks (blue) correspond to the ranges observed using 100 topologies for each. Hamming distances are normalized by the number of nodes.

Mentions: Consistent with our hypothesis, the output of the RBN analysis (Figure 1) demonstrates that the network identified 24 h following LTP induction is considerably more ordered than either of the earlier networks (20 min and 5 h) or the RBN benchmark, the yeast transcriptional network. The curve corresponding to the late (24 h) network lies underneath the others, which means that the average outcomes of perturbations to the gene expression levels do not spread across the network to the same extent (Figure 1A; τ = 1). This observation is even more apparent if the simulations are evolved for more iterations, allowing the new values for the gene expression to be used as inputs for next iteration (Figure 1A; τ = 5) before plotting the Hamming distances H(0) vs H(τ). This amplification of the differences between the temporal networks with longer dynamics indicates that both local motifs and long-distance interactions contribute to the differential stability observed between the temporal networks.


Dynamical properties of gene regulatory networks involved in long-term potentiation.

Nido GS, Ryan MM, Benuskova L, Williams JM - Front Mol Neurosci (2015)

Results of the RBN dynamical stability analysis. (A) Derrida plots for the LTP networks previously identified by Ryan et al. (2011, 2012) at different times post-LTP induction (20 min, 5 h, 24 h in green, orange, and blue, respectively) and the yeast transcriptional network (black). The left plot corresponds to the initial Hamming distance H(0) plotted against the Hamming distance after 1 iteration, H(1). Hence, only the nearest-neighbor interactions (local motifs) affect the dynamics. The right plot depicts H(0) vs H(5), where long-distance indirect influences between genes have an effect on the dynamics. Longer dynamics allow to reveal the influence of the overall network structure on its stability. The earlier networks (20 min and 5 h) are more unstable than the 24 h network, and the curve corresponding to the latter lies near the diagonal of the plot, which represents the border between the chaotic (white background) and the ordered regime (gray background). (B) Average time evolution of perturbed fixed points starting from Hamming distance H(0) = 1. This small difference tends to be amplified in these biological networks. The latest network recruited following LTP induction (24 h, blue), shows a less pronounced tendency to amplify the perturbation. Furthermore, from t = 2 to t = 5 the Hamming distance shows a slight decrease. The yeast transcriptional network (black dashed line) lies between the earlier LTP networks and the 24 h. (C) Derrida plots for each LTP network and to ensembles of random networks. The same stability profile shown in (A) for H(0) vs H(5) is shown separately for each of the temporal networks. The range of stability exhibited by the two ensembles of random networks (red shade: same number of nodes randomly connected by the same number of edges; blue shade: same number of nodes, same number of edges, and same in- and out-degree). These contrasts allow to isolate the effect of the specific degree sequence from the effect of the average degree (blue shade vs. red shade). In addition, it shows that if an evolutionary constraint were to act on the degree sequence, the real networks choose the less unstable option among all the possible network architectures with the same degree sequence (namely identical local motifs, blue shade). Each point in the plots is the average over 1000 random rule assignments for 100 random initial conditions (increasing these numbers has no effect on the results). Shades for random networks (red) and rewired networks (blue) correspond to the ranges observed using 100 topologies for each. Hamming distances are normalized by the number of nodes.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4528166&req=5

Figure 1: Results of the RBN dynamical stability analysis. (A) Derrida plots for the LTP networks previously identified by Ryan et al. (2011, 2012) at different times post-LTP induction (20 min, 5 h, 24 h in green, orange, and blue, respectively) and the yeast transcriptional network (black). The left plot corresponds to the initial Hamming distance H(0) plotted against the Hamming distance after 1 iteration, H(1). Hence, only the nearest-neighbor interactions (local motifs) affect the dynamics. The right plot depicts H(0) vs H(5), where long-distance indirect influences between genes have an effect on the dynamics. Longer dynamics allow to reveal the influence of the overall network structure on its stability. The earlier networks (20 min and 5 h) are more unstable than the 24 h network, and the curve corresponding to the latter lies near the diagonal of the plot, which represents the border between the chaotic (white background) and the ordered regime (gray background). (B) Average time evolution of perturbed fixed points starting from Hamming distance H(0) = 1. This small difference tends to be amplified in these biological networks. The latest network recruited following LTP induction (24 h, blue), shows a less pronounced tendency to amplify the perturbation. Furthermore, from t = 2 to t = 5 the Hamming distance shows a slight decrease. The yeast transcriptional network (black dashed line) lies between the earlier LTP networks and the 24 h. (C) Derrida plots for each LTP network and to ensembles of random networks. The same stability profile shown in (A) for H(0) vs H(5) is shown separately for each of the temporal networks. The range of stability exhibited by the two ensembles of random networks (red shade: same number of nodes randomly connected by the same number of edges; blue shade: same number of nodes, same number of edges, and same in- and out-degree). These contrasts allow to isolate the effect of the specific degree sequence from the effect of the average degree (blue shade vs. red shade). In addition, it shows that if an evolutionary constraint were to act on the degree sequence, the real networks choose the less unstable option among all the possible network architectures with the same degree sequence (namely identical local motifs, blue shade). Each point in the plots is the average over 1000 random rule assignments for 100 random initial conditions (increasing these numbers has no effect on the results). Shades for random networks (red) and rewired networks (blue) correspond to the ranges observed using 100 topologies for each. Hamming distances are normalized by the number of nodes.
Mentions: Consistent with our hypothesis, the output of the RBN analysis (Figure 1) demonstrates that the network identified 24 h following LTP induction is considerably more ordered than either of the earlier networks (20 min and 5 h) or the RBN benchmark, the yeast transcriptional network. The curve corresponding to the late (24 h) network lies underneath the others, which means that the average outcomes of perturbations to the gene expression levels do not spread across the network to the same extent (Figure 1A; τ = 1). This observation is even more apparent if the simulations are evolved for more iterations, allowing the new values for the gene expression to be used as inputs for next iteration (Figure 1A; τ = 5) before plotting the Hamming distances H(0) vs H(τ). This amplification of the differences between the temporal networks with longer dynamics indicates that both local motifs and long-distance interactions contribute to the differential stability observed between the temporal networks.

Bottom Line: Differential gene co-expression analysis further highlighted the importance of the Egr family and found a rapid enrichment in connectivity at 20 min, followed by a systematic decrease, providing a potential explanation for the down-regulation of gene expression at 24 h documented in our preceding studies.We also found that the architecture exhibited by a control and the 24 h LTP co-expression networks fit well to a scale-free distribution, known to be robust against perturbations.These results suggest that a new homeostatic state is achieved 24 h post-LTP.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer Science, University of Otago Dunedin, New Zealand ; Brain Health Research Centre, University of Otago Dunedin, New Zealand.

ABSTRACT
The long-lasting enhancement of synaptic effectiveness known as long-term potentiation (LTP) is considered to be the cellular basis of long-term memory. LTP elicits changes at the cellular and molecular level, including temporally specific alterations in gene networks. LTP can be seen as a biological process in which a transient signal sets a new homeostatic state that is "remembered" by cellular regulatory systems. Previously, we have shown that early growth response (Egr) transcription factors are of fundamental importance to gene networks recruited early after LTP induction. From a systems perspective, we hypothesized that these networks will show less stable architecture, while networks recruited later will exhibit increased stability, being more directly related to LTP consolidation. Using random Boolean network (RBN) simulations we found that the network derived at 24 h was markedly more stable than those derived at 20 min or 5 h post-LTP. This temporal effect on the vulnerability of the networks is mirrored by what is known about the vulnerability of LTP and memory itself. Differential gene co-expression analysis further highlighted the importance of the Egr family and found a rapid enrichment in connectivity at 20 min, followed by a systematic decrease, providing a potential explanation for the down-regulation of gene expression at 24 h documented in our preceding studies. We also found that the architecture exhibited by a control and the 24 h LTP co-expression networks fit well to a scale-free distribution, known to be robust against perturbations. By contrast the 20 min and 5 h networks showed more truncated distributions. These results suggest that a new homeostatic state is achieved 24 h post-LTP. Together, these data present an integrated view of the genomic response following LTP induction by which the stability of the networks regulated at different times parallel the properties observed at the synapse.

No MeSH data available.