Transhumeral amputees face substantial difficulties in efficiently controlling their prosthetic limb, leading to a high rate of rejection of these devices. Actual myoelectric control approaches make their use slow, sequential and unnatural, especially for these patients with a high level of amputation who need a prosthesis with numerous active degrees of freedom . While surgical muscle-reinnervation is becoming a generic solution for amputees to increase their control capabilities over a prosthesis, research is still being conducted on the possibility of using the surface myoelectric patterns specifically associated to voluntary Phantom Limb Mobilization (PLM), appearing naturally in most upper-limb amputees without requiring specific surgery. The objective of this study was to evaluate the possibility for transhumeral amputees to use a PLM-based control approach to perform more realistic functional grasping tasks. Two transhumeral amputated participants were asked to repetitively grasp one out of three different objects with an unworn eight-active-DoF prosthetic arm and release it in a dedicated drawer. The prosthesis control was based on phantom limb mobilization and myoelectric pattern recognition techniques, using only two repetitions of each PLM to train the classification architecture. The results show that the task could be successfully achieved with rather optimal strategies and joint trajectories, even if the completion time was increased in comparison with the performances obtained by a control group using a simple GUI control, and the control strategies required numerous corrections. While numerous limitations related to robustness of pattern recognition techniques and to the perturbations generated by actual wearing of the prosthesis remain to be solved, these preliminary results encourage further exploration and deeper understanding of the phenomenon of natural residual myoelectric activity related to PLM, since it could possibly be a viable option in some transhumeral amputees to extend their control abilities of functional upper limb prosthetics with multiple active joints without undergoing muscular reinnervation surgery. People with an upper arm amputation represent a significant part of the major upper-limb amputees in western countries , and their still counter-intuitive and sequential control that limit their actual use .To overcome these limitations, pattern-recognition approaches have been developed since the late 60s/70s  execution. Indeed, voluntary PLM have recently been shown to be controlled as intact limb movements  with a unilateral transhumeral amputation of traumatic origin were selected to participate to the study. Three healthy participants (in the 25–27 age range) were recruited as a control group to perform the grasp and release task through a simplified computer GUI control. This study was carried out in accordance with the recommendations of the Université Paris Descartes ethic committee CERES (N°IRB 20151900001072), which had approved the protocol. All participants provided written informed consent to participate in the study, and both patients gave written permission for publication of photographs for scientific and educational purposes. The protocol was performed in accordance with the Declaration of Helsinki.© elbow, an active wrist rotator and a polydigital hand , controlled by two electrodes placed over his biceps and triceps muscle (the control-switching between joints being achieved through a co-contraction of both muscles). Table The selection of the two amputated participants was based on the level of amputation , their control ability of a mobile phantom limb , the absence of phantom and residual limb pain, and the availability of the participants during the recording period. The first participant P1), because of an injured plexus brachial leading to limited muscle contraction amplitudes, has never been fitted with a myoelectric prosthesis. On the contrary, the second participant (P2) is daily using a myoelectric prosthesis composed of a motorized Utah, becauseThe amputated participants were followed-up at the Louis Pierquin Centre of the Regional Institute of Rehabilitation, Nancy, France. Their voluntary mobilization of phantom limb had been explored through a questionnaire and a preliminary evaluation in order to make clear distinctions between residual limb sensations, phantom pain, phantom sensations, and most importantly, between mobility of the residual limb and that of the phantom limb , and a Robolimb polydigital hand from Touch Bionics© possessing 6 active joints (one per finger flexion plus the thumb rotation). This prototype was attached directly to a dedicated support frame made of aluminum profiles, which was adjusted to place the prosthetic elbow close to the phantom elbow joint position. The overall prosthetic system was controlled by an embedded Raspberry Pi 3 which drives the elbow and wrist joints through a dedicated position/velocity motor controller (Roboclaw Motor Controller from Ion Motion Control©), and the polydigital hand through a generic serial connection. A dedicated C++ program was developed (running at a frequency of 100 Hz on the Jessie OS© from Debian Linux©) to receive movement instructions (received from a wifi socket connection), to control the active joints accordingly (with respect to a set of predefined parameters like joint velocities), to monitor the kinematic activity and to store recorded data in files.The upper limb prosthetic used for this experiment  was placed over the prosthetic hand. Thanks to a dedicated calibration phase (performed once for each patient), the prosthetic fingers activity were recorded at 25 Hz. This glove was also fitted with two Inertial Measurement Units  allowing us to track both the elbow flexion and wrist rotation kinematics at a similar frequency.To monitor the kinematic activity of the upper-limb prosthetic, a motion capture dataglove  with bipolar shielded channels at 24-bit resolution was used to record sEMG muscle activities from the participant's residual limb at a 1 kHz frequency. Because of the variability in residual limb length and muscle anatomy due to the level of amputation, the scheme of electrodes placement had to be adapted for each participant  were initially placed on each participant to measure activity on various parts of the residual biceps, triceps, deltoid and sometimes trapezoidal and pectoralis major muscles. No specific skin preparation was used before placing the active electrodes on the residual limb.A dedicated electrophysiological signal-recording system . A filter approach exploiting the properties of the Principal Component Analysis  was used to classify the myoelectric activities. The features were computed from the sEMG using a 512-ms-sliding analysis window with a 128-ms-overlap between successive windows. Among the wide variety of features that have been investigated in the literature  and Extension (EE), Wrist Pronation (WP) and Supination (WS), hand, resp. Pinch Closing  and Opening  with a few seconds of rest after each movement. This sequence was repeated once to get 2 demonstrations per movement. The experimenter was in charge of verbally asking the subject to execute a given movement and thus determined the rythm of the performance. No instruction was given about the amplitude and the velocity of the gesture, only the need of repeatability was mentioned. It is important to highlight that this brief initial individual training of the classifier was then used for the whole experiments.*8 for P1  PLM was performed with intermediate resting periods of a few minutes every 20 movements.After a rapid data treatment, the training phase of the classifier was followed by a preliminary assessment of the classifier performance. During this phase, while the online classification algorithm was running, the participant was asked to induce given movements of the prosthesis through the phantom limb mobilization. The participant performed a randomized set of PLM (12 repetitions of the 8 selected gestures) during which the movements of the prosthesis reflected the PLM that were detected by the classifier. Once the movement instruction provided by the experimenter, the participant had 5 s to perform the task. Within this time period, a failed trial could be followed by a second one. Once a trial was considered as successful, or when it lasted more than 5 s, the experimenter asked the participant to relax before giving the next PLM to perform. In order to avoid incompatible successions of actions, a pseudo-randomized list of 12After 10–15 min of passive recovery, the protocol ended by a grasping task performance with the arm prosthesis that included a randomized set of 3 grasping repetitions of 3 different objects . The object had to be reached, grasped, detached from its support (velcro fixation requiring approximatively a 3 N force to be detached), brought back to the extended-arm posture and released in a dedicated bucket. Before the start of each trial, the prosthesis was automatically brought back to a standardized initial posture, i.e., elbow fully extended, wrist in pronosupination with the hand palm aligned with the saggital plane, and fully open hand. The final/release positions was similar, i.e., elbow fully extended and hand opened but without particular constraint over the wrist orientation. The participants had the opportunity to perform two trials with each object to train before the real grasping task phase started. The object presentation was not randomized and always started with the simplest object to grasp (cylinder) and finish with the toughest (clothespin).In order to appreciate the performance obtained by the patients with such a control and setup, which remains very different from a natural limb control , the three healhty participants were asked to perform the exact same experiment but with the prosthesis being controlled through the use of a graphical interface on a computer screen and a mouse . So, no classification of EMG was necessary to control the prothesis.© script to automatically determine within the 5 s interval allocated to each task , the exact starting time of the participant action (when the classifier detected a change from the inactivity with a confidence over 95%) and its end (last time instant of the classifier output detection of an activity until the end of the 5 s time period). The confusion percentages were then calculated over these previously selected times of action, based on the ratio between the time of action and the time during which the correct movement was performed.The online performance during the preliminary assessment of the classification and PLM-based control was analyzed using a MatlabFor the grasping tasks, the prosthetic arm joints were extracted from the worn motion capture glove: the embedded wrist IMU was used to compute both elbow flexion and wrist prono-supination angles. Full elbow extension was defined as a null flexion angle, while the palm parallel to the saggital plane (with the thumb pointing forward) defined the 0°posture for the wrist prono-supination. The hand closing level was averaged by the closing level of the three last fingers (from medium to little). The pinch closing level was defined as the closing level between the thumb and the index (which came into contact at around 30% of the pinch closing level because of the associated thumb rotation).Task duration was defined as the time elapsed since the first activation detection by the control architecture (different from the “resting state”) until the object impact after falling into the receiving container.The confusion matrices for the participants to the preliminary evaluation of online control of the prosthesis are shown in Figure Representative scenarios of participant P1 (one of the three repetitions) of the three grasping tasks are shown in Figure The duration of the first grasping phase and the total task duration  are shown in Figures Although the total grasp-and-release time is shorter for the controls than for the patients, the relation between the total grasp-and-release time and the needed number of actions to complete the task is rather similar. Indeed, Figure Figure The optimal sequences of motor actions to perform the grasping-releasing tasks of the three objects are shown in Table The amputees control of the prosthesis was suboptimal compared to the control group performance  Figure . For theTwo transhumeral amputated participants have been asked to repetitively grasp three different objects with an unworn active eight-DoF prosthetic arm and release them in a dedicated drawer, thanks to a prosthesis control based on phantom limb mobilization and myoelectric pattern recognition techniques, with a classifier trained using only two repetitions of each PLM. The participants successfully achieved the tasks, even if the completion times were increased (in comparison with the performances obtained by a control group using a simple GUI control) and the control strategies required numerous corrections.The recognition rate averaged over all movements revealed to be rather high (on the average 86.4% for the two amputated participants) indicating that they were able to control 8 different prosthetic movements with a limited set of 6 electrodes placed over their residual upper-arm limb. The main confusions appeared between the hand and pinch actions. However, this confusion did not directly alter the grasp and release performances since even the precise clothespin grasping could be performed with the whole hand instead of a pinch.Although successful, this online recognition and control rate remains slightly lower than the latest classification rate of over 90% reported in the literature  sessions usually required in upper-limb amputees to master a simple (but constraining in terms of muscular contraction amplitudes) myoelectric control of active wrist and hand prostheses. Their kinematic strategies  than for the control participants (simply acting over a mouse), and, moreover, prolonged phantom limb mobilization induces fatigue , to manage the rather complex interaction between their PLM, the associated actions of the prosthesis and, through it, their physical interaction with objects and the environment. The PLM-based control revealed to be rather intuitive. This is confirmed by the fact that the patients never used their PLM in daily life and still were able to control the prosthesis without any beforehand training. Moreover, the patients instinctively tried to correct unplanned actions generated at the prosthesis level with adapted phantom movements (as we do with intact limbs) but unfortunately not known by the classifier. This intrinsic limitation of the pattern recognition techniques that can only recognize specific and known (trained) PLM, still limits the intuitiveness and naturalness of the approach.Obviously, in the current state of the control architecture, the control performance can be expected to be reduced with a worn prosthesis. Indeed, the current limited robustness of pattern recognition techniques is a major obstacle, particularly when they have to be used in realistic scenarios including a worn prosthesis. This will generate additional constraints such as pressure and sweating, along with a mobile residual limb generating non-“phantom limb related” muscle contractions. These factors will affect the sEMG signals and thus decrease the PLM detection rate. Yet, this is a generic problem in the field of pattern recognition of electro-physiological signals, and numerous solutions are actually developed that could compensate for the listed issues. Examples of these solutions are (1) robustness to electrodes shift  myoelectric control can offer. While TMR is now becoming a generic solution for transhumeral amputees to increase their control capabilities over  prosthesis with more than 2 active DoF , the preliminary results obtained in this study and other research teams exploiting the natural myoelectric activity related to PLM, pushes toward a reconsideration of the possibility of extracting more control signals without undergoing invasive surgical procedures. Obviously, TMR is providing an interesting way of stabilizing and reinforcing the myoelectric patterns related to PLM. This eases the decoding of myoelectric activities and is possibly one major key to overcome the issue of the perturbations generated by the wearing of the prosthesis. Nonetheless, recent “realistic” use of TMR in transhumeral amputees, controlling a 3-active-DoF-prosthesis through pattern recognition , with exponential velocity and smoothened acceleration profiles to restore human-like movement properties (isochrony and minimization of the jerk (Viviani and Flash, NJ, EdM, JdG, CN, AT designed the protocol. EdM, FR, and NJ built the experimental platform, and EdM collected the data with the healthy participants. AT, NM, and JP contacted the amputated participant and organized the experimental session. NJ, CN, JdG, EdM, and AT participated in the experimental session with the amputated participant. NJ, JdG, CN, and AT analyzed the data, and wrote the present report.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Microneedles (MNs) have been established as promising medical devices as they are minimally invasive, cause less pain, and can be utilized for self-administration of drugs by patients. There has been rapid development in MNs for transdermal monitoring and diagnostic systems, following the active research on fabrication methods and applications for drug delivery. In this paper, recent investigations on bio-sensing using MNs are reviewed in terms of the applicability to continuous glucose monitoring system (CGMS), which is one of the main research focuses of medical engineering technologies. The trend of the functionalized MNs can be categorized as follows: (i) as a sensing probe, and (ii) as a biological fluid collector. MNs as in vivo sensors are mainly integrated or coated with conductive materials to have the function as electrodes. MNs as fluid collectors are given a certain geometrical design, such as a hollow and porous structure aided by a capillary action or negative pressure, to extract the interstitial fluids or blood for ex vivo analysis. For realization of CGMS with MNs, a long-term accurate measurement by the MN-based sensing probe or a fluidic connection between the MN-based fluid collector and the existing microfluidic measurement systems should be investigated. Diagnostic systems using bio-sensing technologies have been the main focus of research for the last few decades owing to the high demand for more rapid, precise, and easy-to-use applications for the well-being of society. One of the aims in the development of recent diagnostic devices is to achieve a shorter time period of analysis with a reduced amount of the required biological samples by microfluidic and electrochemical components realized by new fabrication technologies, such as the CMOS and MEMS. However, in spite of the advantages of such diagnostic systems, called micro total analysis systems (pTASs), the methodologies of body fluid sampling is limited to conventional methods such as hypodermic needles.Conventional needles have several disadvantages such as the associated unavoidable pain, and requirement of a high level of skilled training of the medical professionals, even though they extract too much amount of the body fluids for pTASs. Hence, microneedles (MNs) have attracted significant attention as next-generation devices to access biological tissues through the skin without pain due to their microsized dimension, e.g. typically a length of less 1 mm and diameter of less 500 pm. Subsequent to the reports of MNs being novel tools to penetrate the skin and to deliver drugs and vaccines with a minimal invasion and pain, a wide range of research has focused on the methods of their fabrication, supported by micromachining technologies and the applications for transdermal, self-administration of drugs .In addition to the medical drug delivery, MNs, e.g., dissolvable MN patches, are also well known as commercialized cosmetic products for skin treatments , 14 nowa+ and Na+ ions, nitrogen oxide, and glucose, the analysis, as well as that of blood . I. I66]. IAn alternative way to access biological information is to extract body fluids through the micro pores punctured by the MNs. In this category, the MNs are defined as biological fluid collectors creating a transdermal fluidic path at the interface between the inner tissue including the dermis and the outer part of the skin. The MNs collecting biological fluids such as blood and ISF have attracted the interest of researchers as they have the potential to be utilized in the existing ex vivo diagnostic systems including pTAS devices. However, it is necessary for the MN-based collector to collect at least a few pL of liquid for a reliable measurement of the analytes –74, wherResearch on the application of hollow MNs for the collection of biological fluid was initiated earlier than that of other types of MNs, probably due to their suitability to the sampling of a sufficient amount of the biological fluid in a manner similar to conventional hypodermic needles. The hollow MNs extract ISF or blood into their bores by a capillary action or external negative pressure. As the hollow MNs were put to use as micro injection needles for localized drug delivery into the skin at the initial stage of the development of research in MNs , 75, thex-immobilized paper channel. The glucose level is observed by comparing the colorimetric change of the paper (Fig.  The Jung’s group presented a vacuum-pressure aided blood extraction system with Ni hollow MN for a colorimetric glucose sensor . They coper Fig. b, which per Fig. c. In terAn alternative method to the collection of ISF by using an MN array is to employ swelling materials for the body for the MN. It has been demonstrated that hydrogel MNs are capable to extract ISF by swelling, which results in a fluidic conduit –97, as wISF is absorbed in the dry hydrogel MNs by diffusion, after their penetration into the skin, which has to be followed by the process of separation of the sampled ISF from the MN array, by using centrifugation, either with or without immersion into a solvent. Although the swelling MNs intrinsically need the additional process to remove the analytes, the main fabrication process by mold casting is relatively simple and they have the ability to collect ISF efficiently due to the relatively large capacity of the sampling volume. This approach is also applied to the measurement of glucose levels , 97.Although the porous MNs were widely considered as drug delivery devices , 102–106The first successful study of a porous MN array for ISF collection and a fluidic connection to a external measurement system was reported by the Nishizawa’s group , 110. AsConsidering the research history of the micro-sized glucose sensors, MNs functionalized for bio-sensing systems are comparatively recent. Hence, there are still challenges to be faced in the development of MN-based bio-sensing devices, especially for CGMS.As discussed above, the MN-based electrodes, especially MNs coated with conductive layers, have been successfully indicated to monitor the blood glucose level continuously. This is because the MN-based electrodes are in direct contact with a sufficient amount of fluids beneath the skin for a reliable measurement of glucose, in a similar manner to conventional implantable sensors. However, from the perspective of the application of CGMS devices, the MN-based electrodes have certain drawbacks. One is a common problem of implantable sensors, that is, the loss of the sensitivity owing to surface fouling and enzyme inactivation induced by proteins and immune response –115. ThiOn the other hand, the use of MNs as biological fluid collectors have an advantage over their use as sensing probes because of the developed technology of ex vivo analysis of extracted biological samples. In particular, pTAS devices meet the purpose of the MN-based fluid collector by achieving a small amount of direct flow of ISF or blood from inside the skin to measurement systems. From this perspective, the hydrogel-forming swellable MNs have a disadvantage of the requirement of an additional step to separate the absorbed ISF from the MN array. As microfluidic CGMS devices composed of microchannels have already been proposed using infrared light , viscosiIn this paper, the applicabilities of functionalized MNs to CGMS were discussed. The MN-based in vivo sensors have been applied to diagnostic systems even in a clinical experiment level, by being functionalized as electrodes, especially for glucose measurement. However, the MNs as sensing probes have been facing the challenges similar to those of the implantable sensors, such as the impaired sensitivity and the limited measurement methodology. On the other hand, the MN-based trans-dermal fluidic channels can be highlighted with the potential to be combined with recently developed pTAS technologies. Therefore, the use of MNs as biological fluid collectors should be investigated for integration with the existing ex vivo diagnostic systems and for a more efficient sampling mechanism of ISF. The development of functionalized MNs in those ways will contribute to the realization of commercially available CGMS devices in a minimally invasive manner instead of conventional glucose monitoring devices with pain.


Developmental neuroscience, the study of the processes that shape and reshape the maturing brain, is a growing field still in its nascent stages. The developmental application of functional and effective connectivity techniques, which are tools that measure the interactions between elements of the brain, has revealed insight to the developing brain as a complex system. However, this insight is granted in discrete windows of consecutive time. The current review uses dynamic systems theory as a conceptual framework to understand how functional and effective connectivity tools may be used in conjunction to capture the dynamic process of change that occurs with development. Billions of neurons form intricate patterns that can flexibly integrate based on shared function, forming networks that are constrained by, but not limited to, direct structural connections of the brain . FunctioIncreasingly, researchers in the field of developmental cognitive neuroscience are implementing connectivity techniques, making methodological and conceptual strides in the understanding of the developing brain e.g., . These sdynamic systems is a theoretical approach that describes the behavior of complex networks  and its response to the external environment . The brain's intrinsic architecture is defined as the spontaneous fluctuations between elements of the neural system in the absence of an explicit task, which can be assessed through the acquisition of functional data such as resting-state. This intrinsic architecture may provide a framework for the moment-to-moment responses that the external world evokes . Extrinsprocess of change. Given that the intrinsic and extrinsic architectures of the brain shape each other throughout the nested milliseconds and years of developmental time, perhaps a more precise picture of developmental change can be captured through the use of functional and effective connectivity tools in conjunction.Understanding the ways in which these multiple influences interact, not only with each other, but across time, is at the heart of the complexity of developmental science. The second tenet of dynamic systems theory is that development can only be understood as nested processes that unfold over many timescales. For example, neural excitation occurs on the order of a millisecond. Every neural event is the initial condition for the next slice of time. Developmental change occurs over weeks, months, and years. The coherence of time dictates that the dynamics of the smallest timescale  are nested within the dynamics of all other timescales . Thus, in the study of development, we must be concerned with the interaction of different timescales. Although connectivity techniques have given researchers unprecedented insight to the brain as a complex system, this insight is limited to glimpses of change through discrete windows of developmental time, either on the scale of milliseconds (effective connectivity) or lifetime processes . Comparisons among snapshots of the brain throughout developmental time may not effectively capture the In the current review, the functional examination of intrinsic connectivity is described through resting-state, which is a form of data acquisition during functional magnetic resonance imaging (fMRI). Effective connectivity and subsequent extrinsic architecture is discussed using dynamic causal modeling (DCM) as an example, which is an analytic technique applied to fMRI data. It is worthwhile to mention that psychophysiological interactions (PPI) is a task-based non-directional connectivity technique that has been used widely but is not covered in this review. Graph theory, an analytic technique that can be applied to functional or effective connectivity data, is discussed to provide a framework for understanding large-scale networks. The principles and methodology of each technique will be reviewed, as well as their developmental applications; the limitations and developmental considerations of each approach will be discussed. Finally, current extensions of the technology will be summarized and future directions for the field are proposed. The reader is referred to 22.1Brain regions that often work together form a functional network with a high level of ongoing, strongly correlated spontaneous neuronal activity, without the presence of a task or stimulus . RestingBiswal and colleagues first demonstrated that ongoing neural activity occurs at rest throughout functionally connected regions of the brain when they revealed a high correlation between the blood oxygen level dependent (BOLD) time-series of the left and right hemispheric regions of the primary motor network in the absence of a task . SeveralThe acquisition of resting-state simply involves collecting functional imaging data from participants as they lay in the MRI scanner, fixating on a cross-hair or with eyes closed, while refraining from engaging in any specific cognitive task. One study demonstrated that the BOLD response differed when participants fixated on a cross-hair compared to closing their eyes , which eOnce data are collected, one form of analysis to examine the functional connections of a particular brain region is the seed method. Seed-based ROI analyses correlate the resting-state time-series of an a priori brain region of interest against the time-series of all other brain regions, resulting in a functional connectivity map fcMap; . The fcMTo examine whole-brain connectivity patterns, methods designed to evaluate general patterns of connectivity have been introduced. There are several model-free methods, though the most widely used are independent component analysis (ICA) and clustering. ICA methods require that the investigator choose the number of components, and then a search is conducted for the existence of spatial sources of resting-state signals that vary together over time and are maximally distinguishable from other sets of signals . Among tSince the emergence of resting-state, these methods have been used to identify major functional networks, such as the primary motor, visual, and auditory networks, in addition to higher order cognitive systems . Of partThe use of resting-state in general and the examination of the default mode network in particular can be conducted independent of task performance. This may be advantageous, as differentiating changes in brain activation related to task performance compared to those related to brain maturation has been a challenge in developmental research . However2.2Though the technique is still in its infancy, the increasingly widespread application of resting-state has begun to clarify and reveal important principles of functional brain development. The use of resting-state has not only detected the presence of a stable visual network in infants as young as three months old , it has Several resting-state studies have demonstrated that in the development of large-scale brain systems, functional connectivity shifts from a local to distributed architecture. For example, intrahemispheric connectivity within local circuits precedes the development of longer-range interhemispheric connectivity . Others 2.3In the study described above , the groAdditionally, raw resting-state data is influenced by physiological noise . ResearcResting-state is still a novel method, and acquisition and analysis techniques undergo continual standardization and refinement. Although the conclusions drawn from resting-state data appear to be relatively robust, only time will tell the extent of potentially spurious findings due to motion as researchers continue to search for the most effective preprocessing for raw resting-state data. The technique, though still evolving, provides invaluable information on the intrinsic functional architecture of the developing brain.33.1Advancements in the area of effective connectivity allow for an examination of co-activation between neural regions during performance of a task or experimental manipulation ; specifin interacting neural regions  to create a simple model of neural dynamics in a network of  regions . This dy regions , a numbe regions . This mex1 are caused by activity in another node x2 (uj) embodies influences of experimental manipulations that cause perturbations of neural states in these nodes. The inputs to the model are denoted by u and the C-Matrix indexes the direct influences on an area  of that network.A network's topological patterns are evaluated using the key properties of graph theory: clustering coefficient, characteristic path length, node degree, centrality, and modularity . The cluNeuroimaging research applying graph theory on resting-state data has revealed small-world architecture of functional brain networks across development . In otheSmall-world network organization is an efficient organization for flow of information . While b4.2The ontogeny of the large-scale functional organization of the brain is still not well understood, though studies have begun to use network analyses to reveal that children and adults display similar small-world architecture at a global level to maximize efficiency, with specific group differences in hierarchical organization and interregional connectivity . For insAdditionally, more mature brains exhibit greater hierarchical organization, with more regions involved in longer-distance clusters of activity. Networks with greater hierarchy are characterized by high degree nodes, which exhibit low clustering. Hierarchical networks contain small densely connected clusters that combine to form large, less interconnected clusters, which further combine to form larger and lesser interconnected clusters . HierarcFinally, the development of large-scale neural networks is characterized by a weakening of short-range functional connectivity and a strengthening of long-range functional connectivity. Functional connectivity between more proximal anatomical regions is significantly higher in children, whereas functional connectivity between more distal anatomical regions is significantly higher in adults . This su4.3Such emerging findings use graph theory to provide important insight into the development of functional neural systems; however, limitations must be addressed. The functional network of the brain is comprised of neurons and columns, physical elements that have a limited ability of being accurately measured and defined in humans. For graph theory analyses, inferences must be made when nodes are defined as voxels, or anatomically- or functionally-defined regions of interest. Definitions of nodes are particularly difficult in developmental research, as the nodes are likely not the same across the sample. The use of graph theory requires careful selection of nodes and an understanding that obtained graphs are only as accurate as the nodes. Given that it is impossible to fully know the true definition of functional nodes in the human brain, graphs likely contain some amount of distortion .5The implementation of graph theory to resting-state data has demonstrated that the brain is a remarkable and complex hierarchy of multiple subsystems within one dynamic system. It is important to note that graph theory may also be applied to effective connectivity data, and as an increasing number of developmental studies begin to use DCM, a directional understanding of the influence of functional regions within the context of the larger system may be possible . The groThe development of the brain is influenced by multiple elements, with no one element taking priority. This means that no single element  drives development; rather, it is the interaction between elements that is important. The use of functional connectivity techniques such as resting-state captures the intrinsic and stable functional networks of the brain, while effective connectivity assesses the moment-to-moment influence of one element of the system over another. In the same way that a dynamic system may generate novelty through interactions between individual elements of the system, the combined implementation and interpretation of connectivity techniques may have the potential to reveal new insight that has not yet been attained through use of these tools individually. Specifically, examining functional and effective connectivity data in conjunction may capture the process of change and the emergence of novel patterns that may arise from activity within the system itself . We specPrevious examinations of coupling between the extrinsic and intrinsic architecture of the brain has been done through the use of large-scale meta-analytic approaches . While tThere are no conflicts of interest to report.


Metabolic networks comprise thousands of enzymatic reactions functioning in a controlled manner and have been shaped by natural selection. Thanks to the genome data, the footprints of adaptive (positive) selection are detectable, and the strength of purifying selection can be measured. This has made possible to know where, in the metabolic network, adaptive selection has acted and where purifying selection is more or less strong and efficient. We have carried out a comprehensive molecular evolutionary study of all the genes involved in the human metabolism. We investigated the type and strength of the selective pressures that acted on the enzyme-coding genes belonging to metabolic pathways during the divergence of primates and rodents. Then, we related those selective pressures to the functional and topological characteristics of the pathways. We have used DNA sequences of all enzymes (956) of the metabolic pathways comprised in the HumanCyc database, using genome data for humans and five other mammalian species. We have found that the evolution of metabolic genes is primarily constrained by the layer of the metabolism in which the genes participate: while genes encoding enzymes of the inner core of metabolism are much conserved, those encoding enzymes participating in the outer layer, mediating the interaction with the environment, are evolutionarily less constrained and more plastic, having experienced faster functional evolution. Genes that have been targeted by adaptive selection are endowed by higher out-degree centralities than non-adaptive genes, while genes with high in-degree centralities are under stronger purifying selection. When the position along the pathway is considered, a funnel-like distribution of the strength of the purifying selection is found. Genes at bottom positions are highly preserved by purifying selection, whereas genes at top positions, catalyzing the first steps, are open to evolutionary changes. These results show how functional and topological characteristics of metabolic pathways contribute to shape the patterns of evolutionary pressures driven by natural selection and how pathway network structure matters in the evolutionary process that shapes the evolution of the system. Metabolism is the set of enzymatic reactions that allows the synthesis, degradation and transformation of the biochemical components necessary for the maintenance and reproduction of a cell. Understanding the evolution of a system whose functioning arises from the interplay of many cellular components, is important both, for understanding the biology of the cell and for unraveling general principles of evolution of complex biological systems.The origin and evolution of metabolic pathways is a difficult problem and several ideas have been proposed (reviewed in ). Among A full understanding of the evolution of metabolism also requires the understanding of the functional evolution of the enzymes. This can be achieved by investigating the selective pressures that have been acting on the genes that code for the enzymes (metabolic genes), and trying to understand their evolutionary dynamics in relation to the molecular systems they participate. An interesting approximation is the study of the selective pressures over the network structure of molecular systems; this can be achieved through the study of the relationship between parameters of the evolutionary histories of the enzyme-coding genes and the topological properties of their gene products within a network. Connectivity, which is the number of links of a node in a network, in a metabolic network represents the number of metabolic interactions and it is an initial measure for the topological description of each node.Selective pressures are at the base of understanding adaptation and two main types have to be distinguished. By one hand purifying selection, which is the force that eliminates genetic variants that impair the function and, by the other, positive selection, in which one  variants show a better adaptation and the frequency in the population will increase, reaching eventually fixation.dN/dS when comparing the genomes from different species. A negative correlation between connectivity and the evolutionary rates have been reported in the Drosophila and yeast genome-scale metabolic networks. In these networks, highly connected genes have been shown to evolve at slower rates, indicating selective constraints acting on them [These evolutionary pressures may be detected and measured through  on them ,12. Henc on them .This same approach, which couples the molecular evolution of genes with the knowledge of the interaction networks of their gene-products, has been also applied to study specific metabolic pathways, and the influence of the local network structure (that is the structure of only the metabolic pathway) is studied. This may reveal local strategies of adaptation that may be found different from the constraints imposed by the whole metabolic network, as well as it may shed light on network constraints specific to only specific pathways. In these works, the analysis at the network level initially seeks differences in the strength of the selection on genes located upstream versus those located downstream in the pathway, in order to detect whether the position of a gene along the pathway may constrain gene evolution. In plant biosynthetic pathways, it has been found that upstream genes tend to evolve slower than those downstream due to a stronger selective constraint –18. The All these studies suggest the idea that a part of the variation of evolutionary rates in metabolic pathways can be accounted for by the structure of their functional network, both the local metabolic pathway and the global whole-cell metabolic network. However, in the case of single metabolic pathways, different patterns have been found for different pathways and different species sets and no general pattern has emerged from these few cases. A large number of pathways and an overall vision of the metabolic network should be analyzed to reveal whether there exist general patterns in their evolutionary history and to better understand the distribution of selective pressures in the network, both in terms of constraints or adaptations. Here, we address the relationship between the topology of the whole set of human metabolic pathways during the time of divergence of primate and rodents and relate it to the evolutionary behavior of each gene in terms of natural selection (purifying and adaptive). Its relationship may help understand the distribution of evolutionary forces within complex biomolecular networks.The data set is composed of the metabolic pathways comprised in the HumanCyc database, release 18.1. The number of human pathways present in HumanCyc 18.1 is 325. Of these, 13 pathways were not considered in the present study because they are signaling or protein modification pathways. Two pathways (morphine biosynthesis and melatonin degradation III) could not be used because their reactions are not associated to any annotated human gene. The final total number of considered metabolic pathways for the analysis is then 310. Of these, 275 are base pathways (comprised of reactions only) while 35 are super-pathways, which are comprised of one or more pathways, plus possible additional reactions. These super-pathways were treated separately in the analysis because they add redundant information. A full list of the pathways can be found in The election of HumanCyc may requires justification. Even if there are other sources of reconstruction of human metabolism –23, in oThe total number of enzymatic reactions comprised in the 310 pathways that are associated to at least one annotated gene is 879.The total number of genes that encodes enzymes that take part in the annotated pathways is 956. Genes were functionally classified by assigning them to the functional class of the pathway in which they participate. Two different classification schemes were considered since there are different criteria according to which pathways can be assigned to distinct functional groups. The first classification scheme used, the ontology-based scheme, relies on the HumanCyc Pathway-ontology that aims at classifying pathways into a tree-based structure (as a gene ontology). We used the top level of the tree  as classes to assign pathways. We used 7 of the 9 parent classes just after the root of the HumanCyc pathways ontology, excluding the two classes for non-metabolic pathways, “Macromolecule Modifications” and “Signal transduction pathways”. The basic criteria of this ontology rely on the metabolic mode of the pathway, for example biosynthesis versus degradation. The second classification schema, compound-based, is based on the kind of compounds that are primarily transformed in the pathway, for example nucleotide versus fatty acids . When absent, orthologous sequences were predicted, if possible, through a similarity search of the human gene sequence against the genome assembly, followed by subsequent gene prediction by GeneWise , in a prdN/dS over the entire tree and sequence length (model M0). Each maximum-likelihood estimation, including likelihood ratio tests, was carried out 5 times, each with 3 different initial dN/dS values: 0.1, 1 and 2 to check for stability of the results to repeated runs and different initial conditions. Final results of the likelihood ratio tests were corrected through a False Discovery Rate (FDR) method [Evolutionary rates were computed using the codeml program of the PAML package . Two lik) method . PositivGiven the strong impact of alignment errors in generating spurious signals of positive selection, the alignments corresponding to genes with P < 0.05 in the likelihood ratio test for positive selection were inspected visually. Alignment regions containing evident errors  were manually masked and then evolutionary rates and positive selection tests were then recomputed.Metabolic pathways were derived from HumanCyc. The classical representation of metabolic pathways, also used in HumanCyc, is through the substrate graph, in which nodes represent metabolites and edges represent reactions that transform metabolites. Here we represent pathways as reaction graphs , in whicTopological measures within the directed graphs built for each pathway independently were computed through build-in functions of the NetworkX Python package. Four centrality measures were computed: closeness, betweenness, and in-degree and out-degree centrality. Centrality measures for the corresponding undirected graphs were also computed.simple_cycles function of the NetworkX package applied to the directed graph. This variable was only computed for pathways of more than one reaction.A Boolean variable was derived for each pathway to detect whether the pathway contains loops. This computation has been achieved through the For each pathway, nodes were assigned to three different classes depending whether they are at the beginning of the pathway , at the end  or in any other position in between (“intermediate”). The uppermost positions (top positions), are the first reaction steps of the pathway, corresponding to initial reactions. At bottom positions there are the reactions that produce the final products of the pathway. Reactions in any other position in between of these two are assigned to the same class (intermediate). Beside these three classes, a fourth class has been added for nodes (reactions) that become isolated when the substrate graph is transformed into the corresponding reaction graph. This is the case for pathways for which the reaction graph comprises more than one connected component. These reactions have the feature of directly catalyzing the end products of the pathway starting from the initial substrates, thus being at the beginning (first step) and at the end (last step) at the same time.To evaluate the importance of relationship between evolutionary estimates and the different descriptive network properties, we performed a multivariate analysis, through an automated linear modeling routine implemented in SPSS software. The automated linear modeling created a single standard model to explain the relationship between fields. The adopted linear modeling also included codon bias, protein length and CG content as explanatory variables. Before the linear modeling missing values were replaced. No variable selection method was used and all variables entered into the model were assessed. The automated linear modeling allows also for detecting outliers. However, outliers were not excluded of the analysis. To compare groups, non-parametric methods were used. To correct for multiple testing, False Discovery Rate (FDR) methods were applied .Genes considered under positive selection were compared to the whole set of metabolic genes for several centrality measures using a permutation test. For every centrality measure, the mean score of the genes under positive selection was compared to the distribution of the mean scores of a set of randomly selected genes from the whole set of metabolic genes with the same sample size, using a permutation test (10.000 permutations).The total number of pathways used for the analysis is 310, with 275 base pathways and 35 super pathways see . A full NAGK, GGCT, SRR, TYW4, GGT1, EBP, SC5DL, DHCR7, DHCR24, CCBL1, OPLAH, CNDP2, CCBL2) are associated to reactions that are uniquely present in super pathways. Of the 956 genes, 335 encode proteins that carry out their enzymatic activity within protein complexes while 621 genes encode proteins that are themselves the functional enzymes.The total number of genes associated to the reactions in the pathways is 956. 943 out of the 956 gens participate in base pathways, while 13 genes (FASN (fatty acid synthase), CYP2A6 (a type of cytochrome P450), UGT2B11 (a type of UDP-glucuronosyltransferase), SCMOL (a methylsterol monooxygenase) DIO3 , ALOX5 (arachidonate 5-lipoxygenase) and ALDH3A2 .The relationship between enzymatic activities and enzymes is not one-to-one: on the one hand, each gene encodes an enzyme (or an enzymatic subunit) that may carry out more than one catalytic activity and, on the other hand, the same catalytic activity can be served by more than one enzyme (isoenzymes) that are encoded by different genes. Within this scenario, 71% of the genes (677 out of 956) code for enzymes (or enzymatic subunits) that carry out only one metabolic function, 26% of the genes (247 out of 956) are associate to a number of reactions between 2 and 5, and the remaining 3% of the genes (32 out of 956) are associated to more than 5 reactions. The genes whose encoded enzymes are associated to the biggest number of reactions are: dS), the non-synonymous evolutionary rate (dN) and their ratio (dN/dS), which provides the direction of the action of the selection and an overall estimation of the strength of the purifying selection that have acted on each gene. The distribution of the evolutionary rates can be seen in dN/dS values lower than 0.5.The evolutionary rates have been computed for 927 genes  considering the full set of six species : the synonymous evolutionary rate , HDC , CES1 , DPM2 , SPAM1  and AKR1C1 .CYP2E1 is a member of the cytochrome 450 family of enzymes involved in the inactivation of drugs and xenobiotics. The HDC gene codes for histidine decarboxylase, which converts L-histidine into histamine, a biogenic amine involved in different physiological processes such as neurotransmission, gastric acid secretion, inflammation and regulation of circadian rhythm. CES1 codes for a carboxylesterase involved in the hydrolysis of various xenobiotics and drug clearance in liver. DPM2 encodes for the regulatory subunit of the dolichol-phosphate mannose (DPM) synthase complex whose main function is recognition on the cellular surface. SPAM1encodes for a hyaluronidase located on the human sperm surface that enables sperm to penetrate through the hyaluronic acid-rich envelope of the oocyte. AKR1C1 belongs to a superfamily of aldo-keto reductases and catalyzes the reaction of progesterone to the inactive form 20-alpha-hydroxy-progesterone.The quality control of the alignments which involve the removal of bad quality regions from the computation of the evolutionary rates might have led to an underestimation of the positive selection events, however it guarantees the reliability of the events found.dN, and dN/dS (with dS close to significance).Beside the evolution of specific genes under positive selection, we investigated different levels of selective constraint between functional classes by comparing evolutionary rates of genes participating in pathways performing different functions. A Kruskal-Wallis (KW) test was used to test differences in evolutionary rates between genes belonging to different functional classes of pathways. For both ontology-based and compound-based classification, we find significant differences among different functional classes in the evolutionary rates dN/dS reveals relaxed constraints  for external routes (“Detoxification”), and strong constraints (low dN/dS), for routes of the core metabolism (“Generation of precursor metabolites”). We also find that biosynthesis routes are more constrained than degradation ones. These differences in the strength of purifying selection can reflect the need of making the biosynthesis of very specific metabolites, but degradation of a broad range of external compounds, most likely unknown and toxic.When we consider the ontology-based classification , differedN/dS separate those with highest values, Steroid, Secondary metabolism and Detoxification, and those with the lowest, mainly Glycolysis/TCA/PentoseP, which corresponds to the inner core of the metabolic network. In particular, the detoxification class, the one with the highest dN/dS, contains pathways with enzymes able to recognize a broad range of metabolites. Thus, both classification schemes show that genes participating in peripheral routes have evolved under relaxed constraint, while stronger selective constraint has acted on the genes whose encoded enzymes have roles within the central metabolism.When we consider the compound-based classification , values dN and dN/dS) than the ones in the second layer which, in turn, are more constrained than those of the more peripheral layer  we compared the selective pressures that have acted on genes that encode for unique enzymes, to that of genes that encode for enzymes for which isoenzymes exist. The existence of isoenzymes indicates that alternative proteins could be recruited to perform the same metabolic function, whereas the presence of a unique enzyme is critical for their specific metabolic function to be served. Interestingly, we find no difference in selective constraint between these two classes of genes. A Mann-Whitney U test shows no significant differences: P = 0.066 for In order to investigate whether and how the organization into metabolic networks imposes constraints on the evolution of the enzyme-coding genes, we carried out automated linear modeling to reveal possible linear relationships between evolutionary rates and topological features of reactions . Among tdN/dS) a significant linear relationship is found with topological parameters, showing that the evolutionary rates suffer the influence of the position and the role of gene products within the pathways. In particular a highly significant negative correlation is found between both dN and dN/dS and in-degree centrality, meaning that genes that have high in-degree centralities are highly constrained in their evolution with a strong purifying selection, while genes that have low in-degree centralities are free to evolve under relaxed constraints and accumulate non-synonymous substitutions at a faster rate. This result holds for pathways of different topologies regardless of whether the structure presents loops or not.As seen in In order to analyze the possible relationship of topological centrality measures and the position within the specific metabolic pathways, we took advantage of the physiological directionality of metabolic pathways and we generated a new categorical variable to account for position. Three different classes of reactions have been defined according to their position within the pathway: reactions that catalyze the first enzymatic step in the pathway (top position); reactions that catalyze the last step in the pathway (bottom position); all the in-between steps are assigned to same class (intermediate). A fourth class has been introduced for reactions that catalyze the first and last step at the same time, being, for example the only reaction of one branch of a branched pathway that directly converts the initial substrates into the final products. Genes are assigned to the class of the reaction catalyzed by the enzyme they encode. It should be noted that this classification on position is correlated with in-degree centrality: nodes at top positions are those with no incoming links  and those at bottom positions are defined solely on the basis of out-degree . This new variable, even if correlated with in-degree, encodes different positional information that is not fully captured by the in-degree centrality.dN/dS (P = 0.001) and dN (P = 0.001) while no significant differences are found in dS (P = 0.151). Both cases of dN/dS and dN pairwise comparisons show that the intermediate class has a lower dN and dN/dS than the top (0.022 for dN/dS and 0.010 for dN) and one-step (0.010 for dN/dS and 0.005 for dN) classes. This means that genes whose encoded enzymes catalyze reactions at top positions have undergone more relaxed evolution and faster non-synonymous substitution rates than genes at intermediate position. Genes belonging to the one-step class have the highest evolutionary rates.We analyzed whether genes whose encoded enzymes catalyze reactions belonging to these four classes have evolved under different selective pressures. Evolutionary rates for these four classes are shown in dN for the three classes of top-intermediate-bottom with P-value of 0.008. Non-significant P-values for the linear relationship are instead found for dN/dS (0.072) and for dS (0.481). This means that a statistically significant gradient in the rate of non-synonymous substitution is found along metabolic pathways with genes in top positions having experienced faster non-synonymous substitution rates.Given that the last three classes  constitute an ordered variable of the position along the pathway, we carried out a trend test to test whether a linear relationship exists of the evolutionary rates and these positional classes. A significant linear relationship is found for dN/dS (P = 0.023) and dN (P = 0.005) between the four classes considered, while no significant differences are found in dS (P = 0.300). When looking at pairwise comparisons we find that dN/dS of genes of the one-step class have a significantly higher dN/dS than those belonging to the intermediate (P = 0.035) and to the bottom (P = 0.019) class, and the dN of genes belonging to the one-step class are significantly different from dN of the remaining three classes: top (P = 0.034), intermediate (P = 0.006), bottom (P = 0.004).Given that the top/bottom position implies directionality for the pathway, we repeated the analysis in the subset of 208 pathways that have no loops thus have a marked directional structure . As befoIn summary, the stringent KW test clearly highlighted differences between the rates of functional evolution of the genes belonging to the one-step class and those belonging to the other classes, pointing to their relaxed evolutionary constraint. This implies a gradient of non-synonymous substitution rates along metabolic pathways with genes at top-positions allowed to evolve at a faster rate than genes at intermediate and bottom positions, and with genes at intermediate and bottom positions being more tightly constrained to fix non-synonymous substitutions at a slower rate.We measured the differences in the mean of the four centrality measures  between genes with signatures of positive selection and the whole set of metabolic genes. We tested two sets: genes under positive selection with and without multiple testing correction. When only the six genes under positive selection after multiple testing correction were considered, no statistical significance is observed, even though genes under positive selection show higher out-degree and higher closeness than the average (0.33 vs. 0.22 for the out-degree and 0.38 vs. 0.28 for the closeness). Given the small number of positively selected genes (six genes), this same analysis was also repeated with all genes (49 genes) that have a p-value smaller than 0.05 in the positive selection test before the multiple test correction. The aim of this analysis is to test if there is any difference in the centrality measures values for the genes that belong to the tail of the positive selection test distribution. When these two groups are compared, higher out-degree  and higher closeness  values are found for positively selected genes with an increase of 32% in the average value of out-degree and of 21% in closeness in genes under positive selection compared to the whole set of metabolic genes. This result shows that the tail of positive selection distribution is enriched by genes with higher out degree and higher closeness.These results indicate that genes encoding enzymes with a greater number of reactions that make use of their products in the human metabolic pathways are more likely to present signals of positive selection than those with fewer enzymes using their products. Genes under positive selection have also higher closeness than the average and hence shorter path lengths to other nodes in the pathway.Linking the action of natural selection in the evolution of genes to the network structure and topology is an interesting approach to understand the constraints that the network structure may have on the evolution of complex molecular systems such as metabolism. Here, we have carried out a comprehensive molecular evolutionary study of human metabolism by investigating the selective pressures that acted on the enzyme-coding genes during the divergence of primates and rodents, and their relationships with functional and topological features of the pathways that constitute the system. Extensive studies have made possible the reconstruction of the biochemical pathways that constitute the metabolism; here we use this information to investigate the influence of the local network topology of the metabolic pathways in its evolutionary behavior by analyzing the distribution on the network of selective forces, be they in form of innovations (positive or adaptive selection) or in the strength of conservation (purifying selection).The analysis of individual metabolic pathways instead of the whole metabolic network has several advantages: i) it allows the study of the influence onto the evolution of metabolic genes of their local relevant environment, that is, the context of the gene products in which the metabolic task is achieved; ii) it allows to separately study the functional units responsible for the different metabolic tasks, classify and compare them, and study the distribution of selective pressures within each functional unit; these functional units are particularly relevant because are likely to approximate the “molecular phenotypes” targeted by selection; and iii) it allows an intermediate analysis between the single enzyme and the whole metabolic network in the line of considering the hierarchical and topological structure of the pathways. However, the partitioning of the metabolic network into pathways is a somehow arbitrary process, the most arbitrary decision being the definition of pathway boundaries. Criteria for the definition of a pathway have been analyzed and compared ,31 and tThe final dataset under study was composed of 927 genes, whose products are integrated in 310 pathways. The species that have been considered are human, chimpanzee, gorilla, orangutan, mouse and rat, and thus the analysis embraces the divergence time of both primates and rodents. The tools for detecting positive selection and for measuring the strength of purifying selection see  are baseThe detection of genes that underwent positive selection, and that are thus at the base of innovative changes, have resulted in a very small number of genes, six out of the 927 genes. These genes are: CYP2E1, a member of the cytochrome 450 family; HDC, a histidine decarboxylase; CES1, a carboxylesterase; DPM2, a subunit of the dolichol-phosphate mannose synthase complex; SPAM1, a hyaluronidase; and AKR1C1 an aldo-keto reductase. Two of the six genes that show sequence signature of positive selection, CYP2E1 and CES1, encode for detoxification enzymes and contribute to the solubility of molecules that must be expelled from the cell as fast as possible. Therefore, response to xenobiotic molecules has likely been a target of adaptive selection during primate and rodent divergence.i.e. secondary metabolism), which shows the most relaxed selective constraint. We have shown that the stronger selective constraint has acted on the genes whose encoded enzymes have roles within the inner core of metabolism; pathways comprised in this inner layer are involved in the transformations of small precursor metabolites for cell maintenance. These pathways are the oldest, the more phylogenetically conserved [i.e. higher kcat and kcat/KM) than secondary metabolism enzymes [The main selective force in metabolism is the maintenance of the system through purifying selection; we have calculated this strength for each gene and analyzed the context according to biochemical and network properties. We observed a steep gradient of selective constraints that goes from genes serving functions within the inner core of intermediary metabolism (the most constrained), through those of a second layer of intermediary metabolism, to the outer peripheral layer of metabolism  and here we have considered their direction. So, in our representation edges are indeed arrows and the resulting graph is a directed graph. By encoding metabolic pathways through directed graphs, we are able to take into account the physiological direction of the reactions in the cell.Even in absence of specific information about the metabolic pathways for all the considered species, the relatively shallow phylogenetic divergence considered and the well-known conservation of metabolism among mammals ensures the use of a unique structure of pathways and function of all enzymes. The influence of the local network topology over gene’s evolution was investigated for both positive and purifying selection.The influence of the local network topology over gene’s evolution had been previously investigated in few cases of specific metabolic pathways. The comprehensive analysis carried out here allowed revealing that this influence is pervasive and general patterns can be found. When positive selection has been considered we have found that positively selected genes have higher out-degree centralities than non-adaptive genes. Genes with high out-degree are not involved in the production of the final products of the metabolic task and, at the same time, are those whose products are subsequently transformed by a high fraction of different reactions in the pathway. Here we see that genes in these positions are preferentially targeted by adaptive evolution.When purifying selection has been considered, in-degree centrality has been identified as the strongest topological factor constraining metabolic gene’s sequence evolution. Genes characterized by higher in-degree connectivities have evolved under stronger purifying selection. Within the context of biochemical reaction graphs in which each node represents a biochemical reaction, in-degree reflects the number of reactions that directly precede the given one, that is, the number of reactions that produce metabolites that are then taken as substrates by the given reaction. This means that in-degree centrality is higher for reaction with many incoming links and lower for reactions with few incoming links.Besides the encoding of topological information through centrality measures we also used topological features that encode the position along the pathway  of each enzyme. When this topological information was considered for plant biosynthetic pathways –18 a proi.e. prokaryotic) stages of evolution and that are involved in the synthesis of a small set of metabolic precursors linking the synthesis and degradation of essential biomolecules, namely sugars, lipids, amino acids and nucleotides. A more relaxed selection has been found for enzymes that manage higher levels of chemodiversity. This is the case of detoxification of xenobiotics or the biosynthesis of a wide spectrum of secondary metabolites that, by definition, are not directly involved in the survival of the organism, but rather in its ecological and behavioral traits.The comprehensive analysis of the whole set of human metabolic pathways revealed that both adaptive and purifying selection are not evenly distributed among the genes encoding the enzymes involved in metabolic pathways. Adaptive selection has targeted a small number of genes during the divergence of primates and rodents and adaptive genes are mainly involved in detoxification functions. Purifying selection has been a pervasive selective force dominating the evolution of metabolic genes during the divergence of primates and rodents. It has acted with different strengths according to the layer of metabolism over which it acts, with the inner core of metabolism being strongly conserved and with little or no room left for evolutionary innovation. From these results, it is tempting to conclude that it is less likely to innovate on pathways that were established in the early (S1 Table(DOC)Click here for additional data file.S1 Fig(DOCX)Click here for additional data file.S2 Fig(DOCX)Click here for additional data file.S3 Fig(DOCX)Click here for additional data file.S4 Fig(DOCX)Click here for additional data file.


Whole-brain computational modeling based on structural connectivity has shown great promise in successfully simulating fMRI BOLD signals with temporal coactivation patterns that are highly similar to empirical functional connectivity patterns during resting state. Importantly, previous studies have shown that spontaneous fluctuations in coactivation patterns of distributed brain regions have an inherent dynamic nature with regard to the frequency spectrum of intrinsic brain oscillations. In this modeling study, we introduced frequency dynamics into a system of coupled oscillators, where each oscillator represents the local mean-field model of a brain region. We first showed that the collective behavior of interacting oscillators reproduces previously shown features of brain dynamics. Second, we examined the effect of simulated lesions in gray matter by applying an in silico perturbation protocol to the brain model. We present a new approach to map the effects of vulnerability in brain networks and introduce a measure of regional hazardousness based on mapping of the degree of divergence in a feature space. Computational modeling of the brain enables us to test different hypotheses without any experimental complication, and it provides us with a platform for improving our understanding of different brain mechanisms. In this study, we proposed a new macroscopic computational model of the brain oscillations for resting-state fMRI. Optimizing model parameters using empirical data was performed based on several measures of functional connectivity and instantaneous coherence. We simulated the effect of malfunction in a brain region by changing that region’s dynamics to evoke noisy behavior. Together with presenting a new paradigm for local vulnerability mapping in the brain connectome, we evaluated the hazard rate induced after perturbing a brain region by measuring divergence of the perturbed model from the original model in feature space. The analysis of hazard rates induced by primary failures of individual brain regions provides relevant insights not only into the size of the damage inflicted on the connectome by a particular failure, but also into the potential origins of disease. Furthermore, we proposed a spatial brain map that is associated with the regional hazardousness rates, which is in good agreement with the known pathophysiologic roles of malfunction in different functional systems in the brain. The human connectome is a complex network that is made up of interactive systems encompassing a large number of regions. Regions communicate with each other in order to share and process information providing the structural and functional basis for complex cognitive processes. Understanding the network architecture of the human brain in the context of its Several resting-state studies have shown that there exist spontaneous fluctuations in coactivation patterns of distributed brain regions , usually by a set of differential equations  or all connections of an individual region from the network  that are based on ongoing brain activity . Resting-state fMRI data were collected in two sessions, each session including two runs with phase encoding in either left-to-right or right-to-left directions. For our analysis, we used a single resting-state run, collected during 14.4 min with temporal resolution of 0.72 s. The entire dataset consisted of 1,200 image volumes.The primary data source for this study was the Human Connectome 500-subject release  was applied to parcellate the cortical surface of T1-weighted images into 68 anatomically segregated gyral-based regions of interest  as an indirect measure of brain activity acquired by the MR scanner, whereas the imaginary part serves as the hidden state of the system that is unobservable.Nonlinear dynamic models with stable limit cycles describe systems with self-sustained oscillations . The nonlinear system described above is easier to analyze if we rewrite The next step is to embed the local dynamics for each node as postulated in j with standard deviation of β = 0.02 and implemented as Wiener process) was added to the differential equation of each oscillator to simulate the effect of random processes that occur in brain , as well as inputs from sensory systems that have not been explicitly modeled  peak frequency of the mean (across voxels) BOLD signal.We describe the dynamics of angular frequency for every area Notably, in this study we introduce the possibility of frequency modulation of each oscillator, where the oscillating frequency can be modulated by its neighbors . Thus, by combining the previous model of whole-brain dynamics . The phase of each oscillator (denoted by θi) was calculated as the inverse tangent  of the quotient of dividing the imaginary part by the real part of the system variable (zi). Schematic overview of whole-brain modeling is illustrated in In our model, frequency modulation is achieved through the structural connectivity matrix so that for each oscillator it limits the inclusion of oscillators in the neighbor ensemble to the ones that are directly structurally connected to that particular oscillator  of whole-brain network, assuming the abovementioned functional networks  are the brain network’s modules.Modularity quantifies the degree to which a network can be divided into the groups of nodes  with stronger intramodule connections and weaker intermodule connections. For an FC matrix with positive weights, modularity is defined astan−1) of the quotient formed by dividing the imaginary part by the real part of the BOLD signal.Here, we applied the Hilbert transformation to the regional BOLD signals to derive the analytic representation of the real-valued BOLD signals. We calculated the instantaneous phase of the analytic signal by computing the four-quadrant inverse tangent (Computing the instantaneous phase synchrony (phase coherence) as a measure of time-varying FC offers single time point resolution and has gained considerable attention in the recent literature  to the noise-driven fluctuations. With regard to investigating the effects from perturbations, we took advantage of the mathematical representation of the brain network as a graph with a set of nodes symbolizing brain regions and edges denoting the mutual interactions among nodes Newman, .a = −2. An increasing fraction of regions, as denoted by f, were selected and perturbed, followed by measuring the size of largest strongly connected component  formed in the network  while the random number generator was reseeded at each iteration. (b) Simulating targeted attacks by applying perturbations to an increasing fraction of regions that were already sorted according to their degree of centrality in the structural connectivity matrix. That is, regions with a higher centrality were targeted for perturbation before the remaining regions. The degree of centrality of each region was measured as a composite hub score that was calculated by averaging the unity-based normalized measures of nodal strength, betweenness centrality, and closeness centrality  Simulating random failures by applying perturbations to an increasing fraction of regions that were randomly selected. This procedure was repeated many times  was computed by averaging FCs among all node pairs belonging to different functional networks  random null model. Aforementioned measures were computed for the model of healthy brain  as well as for 68 models of the impaired brain . Each measure was unity normalized across 69 observations. Subsequently, static FC-based measures were recruited to create a 13-dimensional feature vector for every simulated perturbed/unperturbed set of whole-brain signals. The vector space associated with these 69 feature vectors is called the feature space. In a similar way, we created a 3-dimensional feature space for instantaneous phase-based measures.If we apply a perturbation to any region of the brain, it is likely to cause a feature space divergence from the optimal simulated brain network. We refer to the relationship between the location of each perturbation and the level of distance in feature space as hazard mapping, while the measured distance indicates the degree of hazardousness for that particular location. We computed the pairwise Euclidean distance between the feature vectors obtained from the simulated perturbation sets and the feature vector of simulated healthy brain to investigate how every region’s failure contributes to increasing the dissimilarity between the simulated impaired brain and the simulated healthy brain. The level of distance was separately computed for the static FC-based measures and instantaneous phase-based measures. In the case of dynamic connectivity pattern, the Kolmogorov-Smirnoff distance was used as the numerical difference of their values. Afterwards, the two Euclidean distance measures were unity-based normalized and then summed together to create one distance measure for every perturbation.A region shows a significant level of hazardousness if applying the perturbation to that particular region causes a substantial level of dissimilarity between the measures obtained from the simulated perturbation set and with the measures calculated for the simulated healthy brain. A brain region with the highest level of hazardousness may be interpreted as the region with the lowest level of fault tolerance.λ ranged from 0.2 to 1 with a step size of 0.2. The grid search for the global coupling G included 15 evenly distributed values in the interval of 0.002 to 0.03. The spanning range for the global bifurcation a included 71 values in the range from minus to plus 0.07.The parameters of the model  were estimated in a grid-search framework, extended to a four-dimensional space. We performed a grid search in two steps using a different granularity in each step. First, we used a coarse-grained search that spanned a wide range of values for each parameter. Then, we used the results from the first search to perform a second, more fine-grained search for the optimal choices of a, G, λ, and m. From the first search, we found evidence supporting our hypothesis that the resting brain operates at the edge of a critical point of bifurcation, with bifurcation parameters being close to 0 producing a better fit of the model. In the fine-grained grid search, frequency modulation coefficient m ranged from 0.1 to 0.2 in 11 steps, and frequency lethargy λ, and frequency modulation m is shown as a white asterisk in the first panel of j when the net phase of its neighbor ensemble ψj = ∑ Cijθi reaches its extremums. On the other hand, the phase of each neighbor oscillator (denoted by θi) is related to the activity of that particular oscillator . j starts to decline, the net phase of the neighbor ensemble (ψj) begins to grow until the overall neighborhood activity passes 0 and starts to regrow again. Therefore, the net phase of the neighbor ensemble (ψj) reaches its maximum value at the point where the overall neighborhood activity is at the minimum level. In conclusion, the frequency of an oscillator undergoes the highest change when the net activity of its neighbor ensemble is in the vicinity of 0, so that the speed of frequency changes reaches its maximum positive value (speedup) when the net neighborhood activity gets close to passing the zero line, whereas it gets its maximum negative value (slowdown) when the net neighborhood activity has just started to grow.In the proposed model of the brain oscillations, the frequency of each oscillator is modulated by the net phase of the neighbor ensemble. f fraction of regions. The size of the giant component at every value of f was divided by the actual size of the giant component, which provides a relative measure of giant component size. From As a measure of network robustness, Applying an in silico perturbation protocol to our proposed model enabled us to quantify network vulnerability in the form of hypo-/hyper-connectivity risk rate for either different brain regions (p = 0.008), degree , and strength . Measure of association with hazardousness for the local efficiency was not significant . Reported p values are FDR-corrected across four comparisons.Finally, we examined the effects of malfunctions in different brain regions when a combination of local and global measures of brain network were taken into account (hazardousness mapping). The results of the hazardousness mapping are shown in The analysis of the size of the damage inflicted on the network by applying perturbation to individual nodes showed that the superior parietal cortex  and the left cuneus cortex, and to a lesser extent the precuneus cortex and the entorhinal cortex, were the most critical regions for maintaining adequate network communication. In addition, we observed a high level of hazardousness for some regions in the right hemisphere such as the inferior parietal cortex , the isthmus cingulate cortex, the middle frontal gyrus, the insular cortex, and the caudal anterior cingulate cortex. Upon closer inspection, the medial orbital frontal cortex and the right posterior cingulate cortex, as well as the left postcentral gyrus and right parahippocampal gyrus, had some level of hazardousness, too . MalfuncBased on our constructed model, the oscillatory frequencies undergo the highest change when the activity in the neighborhood is in the vicinity of 0 . In otheOf note, we know from the literature that the frequency spectrum of intrinsic oscillations of the brain has a time-varying nature  by perturbing regions in silico. Removing nodes or links  is the most commonly used method for investigation of brain robustness. Since hub scores were calculated based on the actual structural connectome and perturbations were simulated by applying bifurcation-induced shifts in the dynamical regime, this finding may further validate the model and the recruited perturbation strategy presented here.The hazard rates induced by primary failures of individual nodes provide relevant insights not only into the size of the damage inflicted on the network by individual nodes, but also into the potential origins of disease. Our results regarding nodal hazardousness rates are interesting in the context of the question of why failures in some cases might lead to long-lasting impairment and disease, while others might not. To this end, we observed the highest level of hazardousness for the CONT/dATT system, which mainly covers the superior parietal cortex, the right caudal middle frontal gyrus, and the bilateral rostral middle frontal gyrus, as well as for the posteromedial subsystem of the DM network . In addition, the LIM system, in particular the entorhinal cortex, was found to be a hazardous region. The SAL/vATT system  was also found to cause substantial levels of damage in case of malfunction . These rβ deposition in the prominent hubs located in posteromedial cingulate, lateral temporal, lateral parietal, and medial/lateral prefrontal cortices , we observed that functional connections of our brain are obviously more susceptible to hyper-connectivity than hypo-connectivity, particularly in brain regions with high connectedness. Previous studies have repeatedly reported increased functional connectivity after traumatic brain injury as a compensatory brain response to make up for physiological disturbances . On the other hand, we found that the medial visual network, regions of the right parietal lobe , as well as regions of the frontal lobe  had noticeable risks of hypo-connectivity.Our results regarding the vulnerability of intersystem connections are also in line with the published literature on the effects of injury to brain networks. For example, a previous study of mild traumatic brain injury has reported functional hyper-connectivity for the FC of posterior cingulate cortex with the frontal eye fields, the dorsolateral prefrontal cortex, the associative visual cortex, the somatosensory association cortex, and the premotor cortex, as well as for the FC of occipital lobe with the frontal lobe  with the DM, CONT/dATT, SOM, and VIS systems, as well as strong hyper-connectivity between the VIS and LIM systems. Moreover, previous reports of the hyper-connectivity within the frontal lobe , funded by the 16 NIH institutes and centers that support the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. The authors thank Behzad Iravani for his valuable methodological advice.https://doi.org/10.1162/netn_a_00104.Supporting information for this article is available at Neda Kaboodvand: Conceptualization; Data curation; Formal analysis; Investigation; Methodology; Project administration; Resources; Software; Validation; Visualization; Writing – Original Draft; Resources; Writing – Review & Editing. Martijn P. van den Heuvel: Data curation; Formal analysis; Resources; Writing – Review & Editing. Peter Fransson: Conceptualization; Funding acquisition; Project administration; Resources; Supervision; Validation; Writing-Orginal Draft; Writing – Review & Editing.http://dx.doi.org/10.13039/501100004359), Award ID: 2016-03352. Peter Fransson: Swedish e-Science Research Center. Martijn P. van den Heuvel, Mental Health and Quality of Life (MQ). Martijn P. van den Heuvel, Netherlands Organisation for Scientific Research (NWO), VIDI grant (452-16-015). Martijn P. van den Heuvel, Netherlands Organisation for Scientific Research (NWO), ALW open grant (ALWO179).Peter Fransson, Swedish Research Council (Click here for additional data file.


Circular synthetic aperture radar (CSAR) has a 360° observation capability on the central observation scenario. A typical way to process CSAR imaging is to cut data into small sub-apertures because most targets are only coherent at a very small observation angle. There are many sub-aperture imaging methods after development in recent years. The back-projection algorithm is widely used because it is simple and can be applied to an arbitrary trajectory. Because of the limitation of the Nyquist sampling frequency and influence of the antenna sidelobe, azimuth ambiguity is a phenomenon that may occur in the radar imaging process. The existing researches typically choose the back-projection (BP) imaging area according to the SAR platform flight path and the antenna beam width. The limitation of the CSAR imaging area and its azimuth ambiguity region are rarely analyzed theoretically. This paper focus on the sub-aperture imaging of CSAR, based on the BP algorithm, which derives the relationship of azimuth ambiguity with CSAR parameters such as the pause repeat frequency (PRF), slant range angle, velocity of radar platform, etc. This paper proposes an equation for the calculation of the azimuth ambiguity region and analyzes the limitations, which provides theoretical support for CSAR parameter design, imaging area selection, and azimuth ambiguity analysis. Circular synthetic aperture radar (CSAR) is a special imaging mode of SAR whose radar platform moves along a circular track. Compared with traditional SAR, CSAR can provide higher resolution and all-around information on targets. Additionally, CSAR has the potential for three-dimensional imaging . Due to There are several imaging methods for CSAR imaging. The frequency-domain processor, based on the analysis of the three-dimensional Green’s function, is proposed , which iBecause of the limitations of the Nyquist sampling theorem, the azimuth ambiguity phenomenon may also occur during CSAR imaging. In the past few years, the theoretical study on CSAR emphasizes a concentric circle containing the center of the scene, which is in the 360° beam irradiation. In this assumption, pause repeat frequency (PRF) is supposed to be larger than the instant Doppler bandwidth of the concentric circle . ActuallThis study, we focus on the azimuth ambiguity of CSAR and analyze the relationship between azimuth ambiguity and CSAR parameters, providing the expression for the ambiguity area based on the back-projection imaging algorithm. In addition, we provide a better parameter design method that can offer an arbitrarily selected area in the entire reference height plane and avoid azimuth ambiguity.The remainder of the article is organized as follows: In An ideal imaging geometry is shown in According to , after dusing is :(3)I or just given by the reference height plane.Consider an arbitrary point target In the CSAR geometry, there is not any exact solution for Then, we consider the center point Notice that Solve Equation (9) and substitute the solution Furthermore, points on the straight line In Equation (12), Here we focus on the constant If If Next, we consider In the traditional method , an area theorem . We tranThis section we first take the ideal point at First, substitute the parameters for simulation to Equation (9); Because the azimuth ambiguity problem is relative, targets in the ambiguity area also affect the target at These CSAR data were collected by the Aerospace Information Research Institute, Chinese Academy of Sciences, in 2017. Most parameters are very similar to the above simulation parameters, except real PRF is 1179 Hz, trajectory is not an ideal circle, and velocity is not a constant. The experimental scene includes an area whose sea level is roughly zero. This article emphasizes the area choice of BP imaging, so we only select a small sub-aperture. For this real data, parameters are designed reasonably, and the fuzzy phenomenon can be avoided by setting limits of beam width. However, we can still study azimuth ambiguity for CSAR using the whole sub-aperture ignoring the beam limit. In the real data experiment, we can decrease the sampling rate by 10 times to meet extremely poor-quality conditions. From Equation (15) we can get the conclusion that there are at least 40 solutions. From Equations 13) and (14) we can infer that the azimuth ambiguity area is not too defocusing like  and (14)This paper introduces a theoretical analysis of ambiguity regions that may occur using the back-projection algorithm. The fundamental analysis is based on the reason that on the reference height plane, there exist points that have a similar distance history to the real targets. This is the difference using the time domain algorithm instead of the frequency domain algorithm. Nevertheless, the traditional method only refers that the system sampling is supposed to satisfy the sampling theorem. In the case of under-sampling, the analysis of the azimuth ambiguity is not mentioned. We discover that due to the geometry of trajectory in CSAR, the azimuth ambiguity area has an exact solution to the ideal point target. The exact solution explains the reason that the ambiguity is defocused and the shape of the ambiguity area on the whole reference height. Furthermore, because the distance history similarity is relative, the solution contributes to the explanation of the effect caused by strong scattering targets received by the antenna sidelobe on the interested targets, which is located in the scene center.In summary, this article expounds the occurrence of azimuth ambiguity when observing the whole reference height plane using the back-projection algorithm. The work mainly focuses on the analysis of an ideal point target. More complex objects and situations can be discussed following the rules described in the article.