The authors would like to thank the reviewers for their helpful comments to improve the manuscript. For detailed responses highlighted by blue font to the points raised by the reviewers, please see below: Referee: 1 Comments to the Author The authors have addressed my comments on the first version of this paper extensively and thoroughly. The revised paper is definitely improved. I have only a few comments left: -The authors answered the first part of my question 2 (why networks become more random during stroke recovery, see also question 6, referee no 3); however it seems they did not explicitly address the second part of question 2 on increasing betweenness centrality in more random networks. We apologize for not providing an explicit answer to this question in our previous response. Thank you for providing us with an opportunity to provide our interpretation of the relationship between betweenness centrality and network randomness found in this study. We agree with the reviewer that there may exist an inherent association between betweenness centrality and network configuration. To investigate it, we simulated the evolutionary process in which a regular network becomes a random network by rewiring each edge with probability P from 0 to 1 with an increment of 0.01(Figure 1) as per Watts and Strogatz (1998). The initial regular network had 20 nodes and 40 edges where, on average, each node is connected by four edges. In addition to betweenness centrality used in the main text, we also specified closeness centrality, clustering coefficient and degree to quantify local properties of nodes in a graph. The value of closeness centrality is obtained via the following equation: Ci = (n-1)/sum(dij) (Sporns et al., 2007), where n denotes the number of nodes in a graph and dij is the shortest path length from node i to node j. The closeness centrality quantifies the connectivity of a node to all other nodes of a network and is directly proportional to global efficiency as defined by Latora and Marchiori (2001). The last two indices (i.e. clustering coefficient and degree) are the most general measurements in graph analysis (for the detailed definitions on the measures involved, please also see a recent review by Rubinov and Sporns (2009)). Figure 2 shows the average changes over all nodes in all measurements of regional properties as a function of P. As the value of P increases, we found that the network configuration gradually moves toward a random 1 configuration (Figure 1) and, on average, the betweenness centrality and clustering coefficient values show reductions, whereas closeness centrality increased. Since the number of nodes and edges are not changed in the graph, the average degree for each node is relatively stable over the range of changes in the value of P. From visual examination of the formula for determining closeness centrality, the distance functions involved in the calculation allow one to determine which nodes are, on average, closest to all other nodes. Increasing the rewiring probability of the edges leads to the appearance of an increasingly random organization pattern and further reduces the shortest path length in the graph. Given the inversely proportional relationship between closeness centrality and shortest path length, we think it is unsurprising to find increases in closeness centrality when P is increased. Similarly, decreases in clustering coefficient are also unsurprising because this measure assesses the degree to which nodes tend to cluster together and a random graph is expected to show low clustering coefficient. In contrast, the relationship between betweenness centrality and P is difficult to be determined. Although in this simulation, the mean values of betweenness centrality showed reductions with P, we are at a loss to predict how this measure will change as a function of P in every scenario, because both denominator and nominator in the equation of betweenness centrality involve shortest path length. In spite of the lack of a direct relationship between P and betweenness centrality, we feel it is worth noting that the reduction in the mean betweenness centrality displayed in this figure did not reflect reduced betweenness centrality in all regions, but show differential effects, with reductions and increases in betweenness centrality dependent upon nodes. Therefore, although in our study of stroke cases we observed both increased betweenness centrality in the ipsilesional primary motor area (and contralesional cerebellum) and a gradual shift towards a more random organization, there is no necessary association between the two findings. Moreover, in this study the ipsilesional cerebellum showed decreased betweenness centrality during stroke recovery, which further suggest that the relationship between increasing betweenness and more random networks may not hold in every case. Latora V, Marchiori M (2001) Efficient behavior of small-world networks. Phys Rev Lett 87:198701. Rubinov M, Sporns O (2009) Complex network measures of brain connectivity: Uses and interpretations. NeuroImage: in press. Sporns O, Honey CJ, Kotter R (2007) Identification and classification of hubs in brain networks. PLoS ONE 2:e1049. Watts DJ, Strogatz SH. Collective dynamics of 'small-world' networks. Nature 1998; 393: 440-2. 2 Figure 1. Random rewiring procedure from a regular ring lattice to a random network without altering the number of vertices or edges in the graph. Figure 2. Changes in measures of regional properties as a function of rewiring probability P. -my main problem remains the way the correlation matrices are converted to graphs (question 7, see also question 5 by referee 3): The authors new give better arguments why the chosen 'cost' is likely to results (mainly) in significant connections. However, fixing the cost (or the degree), while resulting in networks with the same N and k, really can produce networks with different thresholds in terms of significance. The validity of the main results would have been strengthened if at least the most important findings could be reproduced with fixed threshold as well. Please 3 note that determining this threshold in terms of significance has to take into account the effect of multiple comparisons (an arbitrary threshold is not enough). We agree with the reviewer’s comments that fixing the cost will lead to different thresholds used to construct a network. As the reviewer suggested, we also used different correlation values (from 0.2 to 0.55) to directly threshold functional connectivity in order to build functional networks for each subject in each session. To adjust for multiple comparisons, a false discovery rate (FDR) procedure (Genovese et al., 2002) was performed (corrected statistical threshold α = 0.05). Figure S3 illustrates the effect of changes in significance levels on Gamma. The P values surviving the multiple comparison correction were marked by black arrows. We found that Gamma was significantly reduced between the correlation range of 0.3 - 0.5. As the reviewer mentioned, such a result did strengthen our previous finding of reduced Gamma in the main text. The new result has been added in the revised supplementary materials (see page 2). Figure S3. Changes in P values corresponding to statistical tests on Gamma during stroke recovery. Genovese CR, Lazar NA, Nichols T (2002) Thresholding of statistical maps in functional neuroimaging using the false discovery rate. NeuroImage 15:870-878. -with respect to the minor comment, relating to page 11 of the original manuscript: I agree that setting the distance between disconnected vertices to infinity solves the problem for the pathlength, at least if a harmonic mean is used. However, what will happen to the clustering coefficient based upon Barrat's formula? 4 In this study, the strength of functional connectivity between two regions was considered as the weight of an edge connecting the two regions. In general, the distance of an edge was defined as the inverse of the edge weight, considering the notion that a path length is inversely proportional to a weight, i.e. lij =1/wij if wij ≠ 0, and lij =+∞ if wij = 0 (Achard and Bullmore, 2007; Rubinov et al., 2009; Stam et al., 2009). The formula of the harmonic mean used to compute weighted shortest path length in the main text eventually reflect the inversely proportional relation: the denominator in the equation is related to the weights in a graph. Specifically, Lw N ( N 1) N N 1 l i 1 j i ij (where, lij min (sum (d ij )) and d ij 1 / wij mentioned in the i j main text) could be equivalently converted to Lw N ( N 1) N N max( w i 1 j i ij ) if the weights of disconnection between nodes are directly set to zero, i.e. lij =+∞ if wij = 0 where node i is unconnected to node j. In contrast, given that weighted clustering coefficient is generally proportional to weights of edges, the computation of clustering coefficient based on Barrat's formula was preserved. The same processing has been widely used in graph theoretical approaches and investigations of complex brain networks (Rubinov et al., 2009; Stam et al., 2009). In addition, a recent review on network measures also illustrated the manipulation (Rubinov and Sporns, 2009). Achard S, Bullmore ET (2007) Efficiency and Cost of Economical Brain Functional Networks. PLoS Comput Biol 3:e17. Rubinov M, Sporns O (2009) Complex network measures of brain connectivity: Uses and interpretations. NeuroImage: in press. Stam CJ, de Haan W, Daffertshofer A, Jones BF, Manshanden I, van Cappellen van Walsum AM, Montez T, Verbunt JP, de Munck JC, van Dijk BW, Berendse HW, Scheltens P (2009) Graph theoretical analysis of magnetoencephalographic functional connectivity in Alzheimer's disease. Brain 132:213-224. -the authors indicate that analysis of the whole network (in contrast to the motor network) did not show significant differences in graph indices; could this mean that the non motor network showed opposite changes? 5 This is an excellent question; the question of whether abnormalities in a functional subsystem can spread to the whole brain is an excellent research topic that, as far as we know, has yet to be addressed. We speculated that the reviewer’s comments may arise from considerations about bucking effect, since the observations of significant changes in functional subnetwork topological organization and nonsignificant changes in that of the whole network easily allow one to imagine that changes in non-motor network may show opposite direction to that of motor network and then lead to an appearance of the bucking effect. As is well-known, however, stroke recovery involves more complex processes, such as axonal degeneration, axonal sprouting and neurogenesis. Although the subcortical infarctions in patients of this study in general were mainly involved in motor pathways, we cannot guarantee that the brain lesions only affected the motor pathway in all patients. If other functional subnetworks were impaired by stroke lesions, how topological patterns in these subnetworks might change over time may also depend on the extent to which the involved regions had been affected in individual patient. Therefore, although analysis of the whole network did not show significant differences in graph indices compared to the motor network, it was more difficult to generally claim that the non motor networks showed opposite changes to that of the motor network. We think the lack of significant changes in the whole brain network may at least partially explained by the involved brain regions being not large enough to bring a significant results in the terms of the whole brain analysis. In addition, our recent study has demonstrated that the topological organization of specific functional brain networks cannot be captured by examining the network properties of the whole brain (He et al., 2009), which may, at least in part, account for our findings. Although in this study we mainly focused on changes in the topological organization in a set of motor-related regions during stroke recovery, it would be interested in investigating whether and how abnormalities in a functional subsystem could spread to the whole brain. Future studies using a simulated injury model are needed to explore this important issue. He Y, Wang J, Wang L, Chen ZJ, Yan C, Yang H, Tang H, Zhu C, Gong Q, Zang Y, Evans AC (2009) Uncovering intrinsic modular organization of spontaneous brain activity in humans. PLoS ONE 4:e5226. Referee: 2 Comments to the Author 6 From the changes made it may be concluded that other reviewers had comments on the methods. For myself it remains unclear what this application of graph theory has as advantages in comparison to other connectivity measures (such as Granger causality, Learning Bayesian networks etc.). I am not ´saying that others are better but we don’t really understand and can interprete those datas, so why start with new techniques. This makes interpretation somehow difficult and although the wordening has become more cautious now, the manuscript may offer some alternative explanations. We apologize for not providing a clear account of the features that distinguish graph theory approaches from other connectivity measures. In the revised manuscript, we have added relevant descriptions of this topic to the Introduction section (see pages 3-5) and relevant discussions as one of several potential limitations (see page 24) of the revised manuscript. The Introduction section: In recent years, graph theory has been introduced as a novel method of studying functional networks in the central nervous system (for a recent review, see Bullmore and Sporns, 2009). This approach, based on an elegant representation of nodes (vertices) and links (edges) between pairs of nodes, describes important properties of complex systems by quantifying topologies of network representations (Boccaletti et al., 2006). Nodes in large-scale brain networks usually represent anatomically-defined brain regions, while links represent functional or effective connectivity (Friston, 1994). Functional connectivity corresponds to magnitudes of temporal correlations in activity (Friston et al., 1993) and may occur between pairs of anatomically unconnected regions. Depending on the measure, functional connectivity may reflect linear or nonlinear interactions (Zhou et al., 2009), which can be estimated using many methods such as linear correlation (Fox et al., 2005; Horwitz et al., 1998; Salvador et al., 2005), coherence (Sun et al., 2004), synchronization likelihood (Stam and van Dijk, 2002), (constrained) principal (Friston et al., 1993; Woodward et al., 2006) or independent component analysis (McKeown and Sejnowski, 1998) and partial least squares (McIntosh et al., 1996). Effective connectivity represents direct or indirect influences that one brain region exerts over another one (Friston, 1994), quantified by various mathematical models, such as structural equation modeling (McIntosh and GonzalezLima, 1994), Granger causality (Roebroeck et al., 2005), multivariate autoregressive modeling (Harrison et al., 2003), dynamic causal modeling (Friston et al., 2003) and Bayesian networks (Zheng and Rajapakse, 2006). The above mentioned methods can really introduce measures describing the relationships between nodes. Based on these measures, graph theoretical methods 7 can build abundant models of complex networks to further characterize connection patterns within the brain from a perspective of topological organization. It has been generally believed that functional segregation and integration are two major organizational principles of the human brain. An optimal brain requires a balance between local specialization and global integration of brain functional activity (Tononi et al., 1998). This is properly supported by graph indices [e.g. clustering coefficients (an index of functional segregation) and path length (an index of functional integration)] used in analysis of functional brain networks (Bassett and Bullmore, 2006; Stam and Reijneveld, 2007). The resultant coordinated patterns with high clustering coefficients and short path length, known as a small-world network model (Watts and Strogatz, 1998), reflect the need of the brain networks to satisfy the competitive demands of local and global processing (Kaiser and Hilgetag, 2006). In addition, graph theoretical methods also allow one to evaluate regional centrality in a graph using measures of centrality in contrast to the connectivity methods mentioned above. The Discussion section: In this study, Pearson correlation was employed to estimate the relationships between brain regions. However, in recent years, computational methods of neuroimaging have made enormous advances and provided various approaches mentioned above to perform the estimation. In future studies, it would be worthwhile to investigate the effect of different methods on topological characteristics of the brain networks in order to better understand the relations between network structure and the processes taking place on these networks. Bassett DS, Bullmore E. Small-world brain networks. Neuroscientist 2006; 12: 512-23. Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang DU. Complex networks: Structure and dynamics. Physics Reports 2006; 424: 175-308. Bullmore E, Sporns O. Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci 2009; 10: 186-98. Fox MD, Snyder AZ, Vincent JL, Corbetta M, Van Essen DC, Raichle ME. The human brain is intrinsically organized into dynamic, anticorrelated functional networks. Proc Natl Acad Sci U S A 2005; 102: 9673-8. Friston K. Functional and effective connectivity in neuroimaging: A synthesis. Human Brain Mapping 1994; 2: 56-78. Friston KJ, Frith CD, Liddle PF, Frackowiak RS. Functional connectivity: the principalcomponent analysis of large (PET) data sets. J Cereb Blood Flow Metab 1993; 13: 5-14. 8 Friston KJ, Harrison L, Penny W. Dynamic causal modelling. Neuroimage 2003; 19: 1273-302. Harrison L, Penny WD, Friston K. Multivariate autoregressive modeling of fMRI time series. Neuroimage 2003; 19: 1477-91. Horwitz B, Rumsey JM, Donohue BC. Functional connectivity of the angular gyrus in normal reading and dyslexia. Proc Natl Acad Sci U S A 1998; 95: 8939-44. Kaiser M, Hilgetag CC. Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems. PLoS Comput Biol 2006; 2: e95. McIntosh AR, Bookstein FL, Haxby JV, Grady CL. Spatial pattern analysis of functional brain images using partial least squares. Neuroimage 1996; 3: 143-57. McIntosh AR, Gonzalez-Lima F. Structural equation modeling and its application to network analysis in functional brain imaging. Human Brain Mapping 1994; 2: 2-22. McKeown MJ, Sejnowski TJ. Independent component analysis of fMRI data: examining the assumptions. Hum Brain Mapp 1998; 6: 368-72. Roebroeck A, Formisano E, Goebel R. Mapping directed influence over the brain using Granger causality and fMRI. Neuroimage 2005; 25: 230-42. Salvador R, Suckling J, Coleman MR, Pickard JD, Menon D, Bullmore E. Neurophysiological architecture of functional magnetic resonance images of human brain. Cereb Cortex 2005; 15: 1332-42. Stam CJ, Reijneveld JC. Graph theoretical analysis of complex networks in the brain. Nonlinear Biomed Phys 2007; 1: 3. Stam CJ, van Dijk BW. Synchronization likelihood: an unbiased measure of generalized synchronization in multivariate data sets. Physica D: Nonlinear Phenomena 2002; 163: 236-251. Sun FT, Miller LM, D'Esposito M. Measuring interregional functional connectivity using coherence and partial coherence analyses of fMRI data. Neuroimage 2004; 21: 647-58. Tononi G, Edelman GM, Sporns O. Complexity and coherency: integrating information in the brain. Trends in Cognitive Sciences 1998; 2: 474-484. Watts DJ, Strogatz SH. Collective dynamics of 'small-world' networks. Nature 1998; 393: 440-2. Woodward TS, Cairo TA, Ruff CC, Takane Y, Hunter MA, Ngan ET. Functional connectivity reveals load dependent neural systems underlying encoding and maintenance in verbal working memory. Neuroscience 2006; 139: 317-25. Zheng X, Rajapakse JC. Learning functional structure from fMR images. Neuroimage 2006; 31: 1601-13. 9 Zhou D, Thompson WK, Siegle G. MATLAB toolbox for functional connectivity. Neuroimage 2009; 47: 1590-607. The authors refer to some changes in the “ipsilesional” hemisphere in stroke patients, which indeed may represent changes in location of maxima (e.g.; “lateral extension” of motor representation) and still don’t use fMRI based ROIs. Despite all this I judge this as very valid and interesting data In our previous response, we have provided several reasons for not using explicit tasks to indentify ROIs. In the new revised manuscript, we have added this point and other potential issues as limitations of this study (see page 25). Referee: 3 Comments to the Author The paper has substantially improved after revision. The authors have rephrased and toned down some of their statements regarding functional ‘importance’ of the resting state data (e.g., on p.14) and rephrased the conclusions (p.23). The interpretation that ‘progressive network randomization’ is a substrate of recovery after stroke and that this might be due to outgrowth of suboptimal axonal connections is interesting. However, I am not convinced about the time scale. Axonal outgrowth takes time, especially if axons need to reach new targets. There are still many questions open regarding whether or not those connections are functionally meaningful. According to figure 2, gamma values decrease, at least in some patients, within the first 10-14 days after stroke. Is there any evidence that axonal sprouting can result in novel connections that affect the large-scale network so fast? In this period of time, I would assume that an axon will not sprout more than a couple of 100 µm (at best). To some extent, the timing issue also relates to the fact that in the acute stage there are no differences between stroke patients and controls. If one argues that axonal sprouting might influence Gamma within 10-14 days, then it is surprising that the tremendous changes in the acute phase after the ischemia do not affect the network. Acute changes are not restricted to local neuronal assemblies as we know from diaschisis findings or from neurophysiological phenomena in the penumbra. Finally, if I understand the data of Honey and Sporns (2008) and of Alstott et al. (2009) correctly, 10 focal lesions resulted in non-local, disturbed interactions among regions by deleting central nodes and edges. This would be a reason to expect Gamma changes in the acute phase, wouldn’t it? Thank you for raising an important issue. We agree with the reviewer’s opinion that axonal sprouting cannot propagate quickly enough (within 7-14 days) to affect the network characteristics. In the revised manuscript, we have re-organized this part and toned down some of statements while interpreting the results (see page 19). On a cellular level, one of major regenerative events occurring in periinfarct cortex involves axons sprouting new connections and establishing novel projection patterns (Carmichael, 2006; Carmichael, 2008). Meanwhile, stroke induces a unique permissive environment for axonal sprouting, when neurons activate growth-promoting genes in successive waves and many growthinhibitory molecules are not yet activated (Carmichael, 2006; Carmichael, 2008). Many animal studies suggested that axonal sprouting after stroke progresses through specific biological time points: trigger (1-3 days after stroke) (Carmichael and Chesselet, 2002), initiation and maintenance (7-14 days after stroke) (Leon et al., 2000; Stroemer et al., 1995) and maturation (28 days after stroke) phases (Carmichael et al., 2001). Moreover, the time points might be prolonged after stroke in the human brain. In addition, computational neuroscience has indicated that synaptic formation can be described as a process with random outgrowth patterns (Kaiser et al., 2009). This evidence suggests that new axonal outgrowth may partly account for the randomized network organization found in patients during stroke recovery. However, caution must be taken when interpreting the results on this level. Since a few of the patients did show reduced Gamma within the first 10-14 days after stroke (Figure 2), the interpretation mentioned above can only, at best, partially account for the results because novel connections could not lead to the changes in the large-scale networks found during this early time period based on the estimated time points mentioned above. Hence, axonal outgrowth may be one reason for network randomization but it cannot be the only one. After stroke, other changes in structural and functional plasticity (Schaechter et al., 2006) may also contribute to the continued randomization of the network configuration. In addition, we agree with the reviewer’s comments regarding the data from Honey and Sporns (2008) and Alstott et al. (2009) regarding focal lesions resulting in non-local, disturbed interactions among regions through the deletion of central nodes and edges. In these studies, the central nodes were mainly comprised of association cortex, whereas the central edges were 11 believed to correspond to the corpus callosum connecting bilateral homogenous regions of cortex. In this regard, these studies differed from ours, although they all focused on the effect of brain lesions on brain networks. Some of the relevant differences are: 1) in our study, patients with subcortical motor pathway stroke were recruited. Such a lesion damages only a few connections (such as the corticospinal tract) within the executive motor network, rather than cutting off all connections, while the two previous studies mentioned above simulated the process of removing edges by cutting off all connections in corpus callosum. Thus, it remains unclear how the network organization would be changed if only part of anatomical connections was removed; 2) it has been suggested that the subcortical infarction may further impair the structural anatomy of the ROIs (such as primary motor cortex) through the process of axonal degeneration. Although the two previous studies demonstrated that instantly removing primary cortices would show very little effect on network organization, the effect of these subsequently degenerative changes on network configuration were not investigated in those studies. We feel that the longitudinal design of our study complemented these studies by investigating the dynamic changes in network structure over the stroke recovery continuum, as many of the apparent contradictions can be explained by the differences in study design. In the revised manuscript, we have re-organized this part and explained the differences in the results across these studies (see pages 20-21). Alstott J, Breakspear M, Hagmann P, Cammoun L, Sporns O. Modeling the impact of lesions in the human brain. PLoS Comput Biol 2009; 5: e1000408. Carmichael ST. Cellular and molecular mechanisms of neural repair after stroke: making waves. Ann Neurol 2006; 59: 735-42. Carmichael ST. Themes and strategies for studying the biology of stroke recovery in the poststroke epoch. Stroke 2008; 39: 1380-8. Carmichael ST, Chesselet M-F. Synchronous Neuronal Activity Is a Signal for Axonal Sprouting after Cortical Lesions in the Adult. J Neurosci 2002; 22: 6062-6070. Carmichael ST, Wei L, Rovainen CM, Woolsey TA. New patterns of intracortical projections after focal cortical stroke. Neurobiol Dis 2001; 8: 910-22. Honey CJ, Sporns O. Dynamical consequences of lesions in cortical networks. Hum Brain Mapp 2008; 29: 802-9. Leon S, Yin Y, Nguyen J, Irwin N, Benowitz LI. Lens injury stimulates axon regeneration in the mature rat optic nerve. J Neurosci 2000; 20: 4615-26. 12 Schaechter JD, Moore CI, Connell BD, Rosen BR, Dijkhuizen RM. Structural and functional plasticity in the somatosensory cortex of chronic stroke patients. Brain 2006; 129: 272233. Stroemer RP, Kent TA, Hulsebosch CE. Neocortical neural sprouting, synaptogenesis, and behavioral recovery after neocortical infarction in rats. Stroke 1995; 26: 2135-44. The authors have responded to the problem of using only few ROIs. Nevertheless, the risk of false negative results remains, e.g., by shifting of hot spots, and needs to be explicitly addressed in the discussion as a limitation of the study. The approach of using 12 mm spheres in addition to the main analysis with 10 mm spheres is helpful, as is the additional analysis to rule out influences of non-cortical structures (see response to reviewer 1). In the revised manuscript, we have added a discussion of the problem as a limitation of this study as per the reviewer’s comments and provided relevant discussion involving using other methods to reduce the influence. For instance, we created ROIs with 12 mm diameter spheres and repeatedly computed network parameters (Gamma and Lambda). Significant reductions in Gamma but non-significant changes in Lambda were observed again, which did repeat previous results in motor-related network constructed based on ROIs with 10 mm diameter. See the revised manuscript for detailed descriptions (see pages 25). The new supplementary material is helpful. Thank you for this comment. The validation with the Hanakawa coordinates is reassuring. Thank you for this comment. The clinical data in Table S1 of the revised supplementary materials are helpful. Thank you for this comment. 13