The mitogen-activated protein kinase (MAPK) signaling cascade, an evolutionarily conserved motif present in all eukaryotic cells, is involved in coordinating crucial cellular functions. While the asymptotic dynamical behavior of the pathway stimulated by a time-invariant signal is relatively well-understood, we show using a computational model that it exhibits a rich repertoire of transient adaptive responses to changes in stimuli. When the signal is switched on, the response is characterized by long-lived modulations in frequency as well as amplitude. On withdrawing the stimulus, the activity decays over long timescales, exhibiting reverberations characterized by repeated spiking in the activated MAPK concentration. The long-term persistence of such post-stimulus activity suggests that the cascade retains memory of the signal for a significant duration following its removal. The molecular mechanism underlying the reverberatory activity is related to the existence of distinct relaxation rates for the different cascade components. This results in the imbalance of fluxes between different layers of the cascade, with the reuse of activated kinases as enzymes when they are released from sequestration in complexes. The persistent adaptive response, indicative of a cellular “short-term” memory, suggests that this ubiquitous signaling pathway plays an even more central role in information processing by eukaryotic cells. Such networks mediate the response of a cell to a wide variety of extra- and intra-cellular signals, primarily through a sequence of enzyme-substrate biochemical reactions3. While the complexity of the entire signaling system is daunting4, it is possible to gain an insight into how it functions by focusing on a key set of frequently occurring motifs. These often take the form of linear signaling cascades, referred to as pathways. One of the best known of these pathways is the mitogen-activated protein kinase (MAPK) cascade that is present in all eukaryotic cells6. It is involved in regulating a range of vital cellular functions, including proliferation and apoptosis6, stress response7 and gene expression8. This signaling module comprises a sequential arrangement of three protein kinases, viz., MAPK, MAPK kinase (MAP2K) and MAPK kinase kinase (MAP3K). Modular function is initiated when extracellular signals stimulate membrane-bound receptors upstream of the cascade, with the information being relayed to MAP3K by a series of intermediaries. Activated kinases in each layer of the module function as enzymes for phosphorylating (and thereby activating) the kinase in the level immediately downstream, with the subsequent deactivation being mediated by corresponding dephosphorylating enzymes known as phosphatases (PPase). The terminal kinase in this cascade, i.e., MAPK, transmits the signal further downstream by phosphorylating various proteins, including transcription regulators9. Extensive investigations into the asymptotic dynamical behavior of the cascade have contributed towards an in-depth understanding of several emergent features including ultrasensitivity10, and oscillations12 that arise through retrograde propagation of activity15 or explicit feedback16. One of the striking features of the cascade is the occurrence of bistability, which allows the system to switch between two possible states corresponding to low and high activity20. This provides a post-transcriptional mechanism for obtaining a sustained response from transient signals, i.e., cellular memory22.Intra-cellular signaling networks are paradigmatic of complex adaptive systems that exhibit a rich repertoire of responses to stimuli21. This can arise in the cell through mechanisms such as auto-regulatory transcriptional positive feedback23 and nucleosomal modifications24. In the context of cell-fate determination, it has been shown that an irreversible biochemical response can be generated from a short-lived stimulus through feedback-based bistability22. This corresponds to a permanent alteration of the state of the system, thereby actively maintaining ‘memory’ of the signal. As bistability has also been observed to arise through multi-site phosphorylation in signaling modules, protein phosphorylation has been suggested as a plausible post-transcriptional mechanism for cellular memory26. In particular, there have been extensive investigations of the MAPK cascade as it integrates a large range of signals received by the cell in order to control numerous cellular decisions33. While majority of these investigations have considered the asymptotic dynamical behavior of the system, one may also observe transitory modulations in the response of the cascade in a changing environment35. The latter could encode information about prior stimuli to which the system was exposed, and can be a potential mechanism for imparting a form of “short-term” memory to the signaling cascade.Memory can be understood as long-term alterations in the state of a system in response to environmental changes, which allow the system to retain information about transient signals long after being exposed to themIn this paper we show that a linear MAPK cascade can indeed exhibit short-term memory through transient modulations in its response to an environmental change. Crucially, this can arise even in the absence of explicit feedback between different layers or cross-talk with other pathways. These modulations can persist long after the initial trigger, lasting for durations that are several orders of magnitude longer than the time-scales associated with phosphorylation-dephosphorylation processes. We demonstrate that this occurs both when a signal begins activating the MAPK cascade, as well as when it is withdrawn. On application of the stimulus, the module exhibits long-lived frequency and amplitude modulations in the activation profile of the constituent kinases. Following the withdrawal of stimulus, activity in the cascade decays over an extremely long time-scale, during which reverberatory dynamics, characterized by large-amplitude spiking in MAP Kinase activity, can be observed. We explain the emergence of such long-lived memory of the withdrawn stimulus in terms of the imbalance of fluxes between different layers of the cascade, which results from the diversity of relaxation time-scales of the cascade components, and the reuse of activated kinases as enzymes when they are released from sequestration. This phenomenon is seen to be robust with respect to variations in the model parameters, including the kinetic rate constants and the molecular concentrations of the constituent kinases and phosphatases. Our results reveal that a biochemical signaling module as simple as the MAPK cascade is capable of exhibiting short-term memory that is manifested as persistent modulations in the adaptive response of the system to changes in stimuli.10, schematically shown in Fig. S and that following its removal.For the results reported in this paper we consider the Huang-Ferrell model of the MAPK signaling cascade10, qualitatively similar behavior can be observed for many other parameter sets drawn from a physiologically plausible range, as explicitly shown in Figs Our results reveal that the transient dynamics can be unexpectedly long-lived, lasting for durations that are much longer compared to the time-scales associated with the phosphorylation and dephosphorylation processes in the cascade Fig. . While mWe first report the behavior of a cascade that is initially in the resting state (characterized by the absence of any phosphorylated components) when it is exposed to a signal. The transient activity that immediately follows exhibits several non-trivial features such as regular spiking in the activity of MAP2K and MAPK depending on the total concentrations of the kinases Fig.  and the An even more intriguing set of complex modulations is observed in the response of the cascade when the signal is withdrawn any time after the stimulated system has converged to the corresponding asymptotic state (which can be as short as a few minutes). Specifically, on switching off the signal, the cascade exhibits large-amplitude spiking behavior in the MAPK activity before eventually relaxing to the resting state Fig. . The durNFlux of a molecular species, i.e., its rate of growth expressed relative to the maximum rate of growth of MAPK**. We observe that the suppression of MAP2K** deactivation mentioned above results in its normalized chemical flux exceeding that of MAPK tot respectively. These regimes are characterized by relatively slow and rapid increases (respectively) in the recovery times with increasing [2K]tot, and appear to be related to the steady-state value attained by MAPK activity upon sustained stimulation of the cascade for the corresponding value of [2K]tot [Fig. K]tot for which ~17% of MAPK is activated for the parameter values used in Fig. As mentioned earlier, the emergence of long-lived reverberatory activity of MAPK following the withdrawal of an applied stimulus can be linked to the flux imbalance of different cascade components, which suggests significant differences in their rates of relaxation. As shown in Fig. tot Fig. . The croτPR on [2K]tot [Fig. K]tot, the recovery time decreases with increasing [3K]tot while the reverse trend is seen for higher values of [2K]tot. We have verified that increasing the stimulus amplitude S while keeping the total MAP3K concentration fixed has a similar effect on the relaxation behavior of activated MAPK (see Supplementary Information). As increasing total concentration of MAP2K results in increased steady-state activity of MAPK, we conclude that, in general, higher activity states of MAPK are associated with increasing relaxation time when either the signal or the substrate (MAP3K) is increased. Conversely, for states characterized by much lower MAPK activity, larger values of S or [3K]tot results in reduced relaxation periods.The distinct regimes are also observed in the dependence of the primary recovery time tot Fig. . As can Nr and the duration of the total memory time τm, the phenomenon of reverberatory activity following withdrawal of stimulation can be observed over a large range of the parameter space, underlining its robustness. We also observe that on increasing [3K]tot, the response of Nr to variation in [K]tot and [2K]tot becomes relatively homogeneous. Increasing the stimulus amplitude S tot, high values of Nr are observed to coexist with low values of τm tot being weak.Diverse cellular environments are characterized by different total concentrations of the various molecular components of the MAPK cascade. Thus, in order to determine the robustness of spiking and reverberatory activity following the removal of an applied stimulus, it is important to see how they are affected by varying total kinase concentrations. Such a study will also indicate the ease with which these phenomena can be experimentally observed. Figure ons Fig. . Note th τm Fig. . While iτr shows a more complex dependence on [K]tot [Fig. K]tot the MAPK activity following withdrawal of the stimulus shows Nr spikes over a duration of τr, then on increasing [K]tot the time-interval between the spikes increases (thereby resulting in an increase of τr) until a critical value beyond which the last of the Nr spike no longer appears. Thus, at this point Nr reduces by unity with a concomitant drop in τr. This series of events is repeated for steadily decreasing values of Nr as the total MAPK concentration is increased further. Each value of Nr is associated with a characteristic rate of increase in τr with [K]tot. With a reduction in Nr (as a result of increasing [K]tot), this rate is found to decrease as well, which suggests a saturation of the system response. These results are robust with respect to different choices of total MAP3K concentration as can be seen from Fig. As the total MAPK concentration is increased, we observe that while the primary recovery time increases almost linearly, the nature of the reverberatory dynamics as reflected in tot Fig. . If for Nr and the duration of total memory time τm depend on the total concentrations of the phosphatases MAPK PPase, MAP2K PPase, and MAP3K PPase. For larger values of the concentrations, viz., [PK], [PK2] and [PK3], respectively, the system operates in the low-amplitude response regime. As mentioned earlier, the reverberatory MAPK dynamics during recovery following withdrawal of the applied stimulus will not be seen in this regime. As the phosphatase concentrations are decreased, spiking behavior of MAPK activity is observed with both τm and Nr attaining high values in an optimal range. The large variation seen in τm [Fig. PK2]-[PK3] parameter space characterized by the same value of Nr are seen to exhibit a range of different values of τr and τPR  as is shown in Fig. PK] results also in decreased time for primary recovery τPR [Fig. τm on phosphatase availability. While this non-monotonicity is suggested in Fig. τm on PK [Fig. PK] over which reverberatory activity  occurs is demarcated by discontinuities in the functional dependence of τm on PK. For intermediate PK2 [Fig. PK2 [Fig. PK], reverberatory activity is observed over a broader range of [PK3]. While we have assumed that the same phosphatase acts on both the singly and doubly phosphorylated forms of the kinase in a particular layer of the cascade , we have explicitly verified that our results are not sensitively dependent on this.We have also investigated the role that phosphatase availability plays on the reverberatory activity of the cascade following the withdrawal of the stimulus. As is the case for total kinase concentrations shown in Fig.  τm Fig.  arises aτPR Fig. . For revτPR Fig. , which i PK Fig.  reveals Nr and the total duration of reverberatory activity τr depend on the signal strength S and the time interval P for which it is applied prior to withdrawal. From Fig. S and P the system operates in the high-amplitude response (H) regime. On lowering these stimulation parameters sufficiently a transition to an oscillatory dynamical regime (O) occurs. Further decrease in S and P results in yet another transition, this time to a low-amplitude response (L) regime. Note that, while reduction in the duration of stimulation can be compensated by increasing the signal strength in order to drive the system to the O or H regime starting from L, it appears that there is a critical value of S below which dynamical transitions cannot be achieved even if P is increased indefinitely.In addition to the effects of kinase and phosphatase concentrations considered above, we have studied how the reverberatory dynamics depends on the different extrinsic and intrinsic model parameters. Figure S–P parameter space. Intriguingly, the peak of reverberatory activity appears in the region corresponding to the boundary between these two dynamical regimes. This is analogous to critical slowing down in the response of physical systems which is manifested in the divergence of relaxation times near a phase transition36. However, there does not appear to be a simple relation between the asymptotic dynamical regimes observed on sustained stimulation of the cascade and the nature of the transient reverberatory activity, when we consider the dependence on intrinsic parameters such as the kinetic rate constants that govern the different reaction steps in the cascade. For example, in Fig. Nr and τr as a function of the rates kp1 and k3. As can be seen by comparing with the dynamical regimes in parameter space shown in Fig. Nr and τr as a function of the rates kp5 and k7 [Fig. Nr does appear to coincide with the boundary between the O and H regimes [Fig. τr dependence is more complex, showing a number of local maxima. The dependence of the reverberatory activity on several other reaction rates of the system are shown in Supplementary Information.As can be seen, the reverberatory MAPK dynamics following the withdrawal of the stimulus occurs only in the O and H regimes of the  k7 Fig. , the peames Fig. , while tNr, as well as, the total duration of reverberatory activity τr, the phenomena of post-stimulus repeated spiking in the activated MAPK concentration we report here is not confined to a very small region of the parameter space but can be seen for a wide variety of choices for the parameter values. Thus, these results establish the robust nature of the emergent “short-term” cellular memory.Apart from looking at the role that individual parameters play in the post-stimulus activity of the cascade, we have also considered how simultaneous variation of all of the parameters affect the reverberatory dynamics. This allows us to investigate whether the phenomena are robust, an essential property if they are to be observed experimentally, as environmental variations, polymorphisms or mutations can often cause multiple parameters of the signaling cascade to be altered. We have verified that the reverberations are not sensitively dependent on system parameters by simulating the dynamics of the cascade using a large number of different parameter sets, each being obtained by randomly sampling the parameter values from their respective physiologically plausible ranges. Figure 39. Thus, as the MAPK cascade is present in all eukaryotic cells6, the mechanism for short-term memory in such a signaling cascade that is presented here may hold for such cells in general. As the duration of MAPK** activity is critical for many cellular decisions40, e.g., the prolonged activation of ERK resulting in its translocation to the nucleus41, the persistent reverberatory activity seen here may play a non-trivial role in regulation of cellular functions. In addition, it has recently been shown that frequency modulation of ERK activity pulses can encode information controlling cellular proliferation42, suggesting that the pulsatile nature of the reverberatory MAPK activity shown here may need to be taken into account when considering such processes.In this paper we have shown that an isolated MAPK signaling module can serve as a fundamental motif in the intra-cellular signaling network for imparting a form of short-term memory to the cell. The emergence of long-lived reverberatory activity reported here arises from the diversity of relaxation timescales for the different components of the MAP Kinase cascade, which results in flux imbalance between activation of the MAPK layer and deactivation in the MAP2K layer. One may therefore expect to observe results qualitatively similar to what has been reported here whenever the system has disparate timescales regardless of the actual molecular concentrations and kinetic rates which can vary substantially across different cells43. We observe a crossover between two qualitatively distinct regimes of relaxation behavior of MAPK** occurring at a steady state that is characterized by relatively low proportion of activation of the available MAPK [~17% in Fig. τPR.The basal level activity of MAPK in a normal cell is maintained at a low proportion of the total MAPK concentration and serves several biological functions44. For the MAPK cascade investigated here, several of the kinetic rates associated with different reactions have never been measured experimentally. There are also a variety of values for the system parameters that have been reported in the literature11. For our investigations we have primarily used a reference set of parameter values (see SI for details) that differ only marginally from the base values originally used by Huang & Ferrell10, and yet which allow the cascade to exhibit three distinct dynamical regimes under different conditions. These are characterized by a time-invariant low-amplitude response (L), oscillatory dynamics (O) and a time-invariant high-amplitude response (H), respectively. We note that the phenomena we observe by using this reference parameter set in the cascade model is robust with respect to variations in the values of the parameters. Indeed, as reported above, the post-stimulus reverberatory activity of the cascade is observed for a large number of different parameter sets that have been randomly sampled from a physiologically plausible range.One of the most challenging aspects of computational modeling of the dynamics of biological networks is correctly assigning the values of the large number of parameters associated with these models28. Activation of MAPK by spaced stimulation is known to be responsible for morphological changes in dendrites27. Studies also suggest that the activation of the MAPK pathway is linked with associative learning in the mammalian nervous system, synaptic plasticity and neurological memory46. An intriguing possibility suggested by the results reported here is that the observed repeated spiking in MAPK activity may function as an effective temporally spaced signal to the nucleus of a neuron. This can then facilitate subsequent changes in the cell required for memory formation.It is known that ERK MAPK isoforms  are abundantly expressed in non-dividing terminally differentiated neurons48. The directionality of migration is known to persist for a certain duration, even if the chemical gradient is altered or becomes static. Studies show that the protein Moesin contributes to the long-lived rigidity of the cytoskeleton assembly that subsequently leads to the directional memory in polarized migrating cells48. However, the intra-cellular processes that underlie the persistent activity of Moesin in the absence of a gradient mediated signal are still largely unknown. Evidence suggests that the regulation of Moesin and other ERM proteins are linked with the activity of the MAPK pathway50. The long-term reverberatory activity of MAPK following the withdrawal of a stimulus that is reported here may be a possible mechanism underlying such persistent cellular behavior.Another well-known example of eukaryotic cellular memory is observed during chemotactic migration along the gradient of a chemical signalτPR) in order to observe the phenomenon reported here. It is of course possible that in the cellular milieu, coupling of the MAPK cascade to other intra-cellular signaling pathways, as well as, the possible presence of explicit feedback connections, may mask the response that is seen here in the case of an isolated MAPK cascade. Also, in vivo the cascade will be subject to a variety of signals that will often arrive in close succession. This will make it unlikely to observe extremely long-lived post-stimulus responses lasting over tens or hundreds of minutes. However, we hope that the results reported here will stimulate experiments specifically designed to test the existence of an emergent “short-term” memory in intra-cellular signaling.To the best of our knowledge the post-stimulus reverberatory activity described here is yet to be reported in the experimental literature. This could possibly be because, typically, during experiments, recording of ERK activity is stopped soon after the withdrawal of the stimulus. Note that in all cases where we observe reverberations, it was preceded by an apparent monotonic decay of MAPK activity immediately following the withdrawal of the stimulus. Experiments would necessarily have to be carried out for much longer durations beyond this initial decay of MAPK activity  a reversible step corresponding to the formation of the enzyme-substrate complex and (ii) an irreversible product formation step corresponding to the activation/deactivation of a kinase, as described in the Supplementary Information.The dynamics of the three layer MAPK signaling cascade has been simulated using the Huang-Ferrell modelMATLAB Release 2010b. Note that the quasi-steady-state hypothesis has not been invoked51. To ensure that initially all kinases are non-phosphorylated we prepare the initial resting state of the system by simulating it for a long duration (~106 mins) in the absence of any signal. Subsequently MAP3K is exposed to a stimulus of amplitude S and duration 5000 minutes. On using the base values for the parameter set as given in ref.10, the system exhibits ultrasensitivity (as reported earlier) which provides verification of the correct numerical implementation of the model (see Supplementary Information). Following the removal of the stimulus, we continue to simulate the system until it returns to the resting state or the simulation duration exceeds 104 minutes.The time-evolution of the molecular concentrations of the different components of the cascade are modeled using a set of coupled ordinary differential equations (see Supplementary Information) that are integrated using the stiff solver ode15s implemented in We have analyzed the long-lived reverberatory activity of the cascade after the removal of the stimulus by using the following measures:Rmax of MAPK** is recorded. On removing the stimulus, MAPK activity starts to decay. The time taken for MAPK** to monotonically decrease to half of Rmax is defined as the primary recovery time (τPR).Following the activation of the cascade by introducing a stimulus, the maximum concentration Rmax. The number of such spikes that are observed before the cascade reaches its resting state is designated as Nr.Following primary recovery, MAPK activity may exhibit a series of spikes, which are defined to be occurring whenever MAPK** concentration exceeds 70% of τr = tfinal − τPR. The time of the i th spike ti is defined as the instant when MAPK activity reaches maximum during that particular event. For 4 minutes.When spiking is observed in MAPK activity following the removal of the applied stimulus, the reverberatory activity duration is defined as the interval between the termination of primary recovery and the final spike event, i.e., τm = τPR + τr. Note that when the asymptotic dynamical behavior of the cascade in presence of the signal is oscillatory, on withdrawing the signal the activity may decay extremely rapidly resulting in τm ≈ 0.The total duration of memory activity following removal of the applied stimulus is defined as the sum of the primary recovery time and the total duration of reverberatory activity, i.e., τx for each constituent of the cascade. This is the time required by its concentration to evolve to the half-way point between the resting state and steady state values.For the situations where the steady state corresponds to a fixed-point attractor we define a relaxation time 10 is measured by the Total Parameter Variation (TPV)52: pi represents the value of the i-th parameter in the given sample and pi,HF is the corresponding base value . We have measured different characteristics of reverberatory activity, viz., Nr, τm and τr, for each realization of the cascade  and have observed them as a function of the TPV for four different values of the stimulus strength. We observe that qualitatively similar results to those reported here are observed for many different realizations.In order to investigate the robustness of the results reported here with respect to variations in the parameter values, we have performed simulations over an ensemble of cascade models whose parameter sets are obtained by uniform random sampling over a physiologically plausible range (see Supplementary Information). The deviation of such a randomly sampled parameter set from the base values used by Huang & FerrellSupplementary Information


Once biological systems are modeled by regulatory networks, the next step is to include external stimuli, which model the experimental possibilities to affect the activity level of certain network’s nodes, in a mathematical framework. Then, this framework can be interpreted as a mathematical optimal control framework such that optimization algorithms can be used to determine external stimuli which cause a desired switch from an initial state of the network to another final state. These external stimuli are the intervention points for the corresponding biological experiment to obtain the desired outcome of the considered experiment. In this work, the model of regulatory networks is extended to controlled regulatory networks. For this purpose, external stimuli are considered which can affect the activity of the network’s nodes by activation or inhibition. A method is presented how to calculate a selection of external stimuli which causes a switch between two different steady states of a regulatory network. A software solution based on Jimena and Mathworks Matlab is provided. Furthermore, numerical examples are presented to demonstrate application and scope of the software on networks of 4 nodes, 11 nodes and 36 nodes. Moreover, we analyze the aggregation of platelets and the behavior of a basic T-helper cell protein-protein interaction network and its maturation towards Th0, Th1, Th2, Th17 and Treg cells in accordance with experimental data. Organisms can be seen as molecular networks being able to react on external stimuli. Experiments are performed to understand the underlying regulating mechanisms within the molecular network. A common purpose for these efforts is to reveal mechanisms with which the molecular networks can be affected to achieve a desired behavior. To cover the complexity of life these models of molecular networks often need to be quite huge and need to have many cross connections between the different agents of the network that regulate the behavior of the network. A useful tool to structure this complexity are mathematical methods. Once the model based on experiments is set up the experimental data can be further processed by mathematical methods. As experiments are cumbersome, the present work provides a framework that can be used to systematically figure out intervention points in molecular networks to cause a desired effect. In this way promising intervention strategies can be obtained. For instance the process of obtaining new drugs for pharmacological modulation can be shortened as in the best case the calculated intervention strategy just has to be validated with one experiment and the time consuming procedure of searching an intervention strategy with several experiments can be saved. Biological networks are often formed by interacting proteins and molecules. Their change in time is often biologically regulated to adapt to different conditions. Detailed mathematical models describe changes of proteins, for instance their phosphorylation state or activity in general by differential equations. We analyze here in particular the question, how we can calculate the result of a pharmacological intervention and identify the best target points (receptors or downstream in the cascade or any other point in the network) to shift the network state into a new activity pattern as desired . Our approach thus allows the user to define the intervention points of choice and we then systematically calculate the optimal steering options the user has available to drive the network then into the desired state. We include the information how well the objective can be met with this choice.Mathematically speaking, regulatory networks are commonly modeled by a system of coupled ordinary differential equations (ODEs) . Then, aIn fact, we show in the present work that these external stimuli can cause a switch between an initial steady state of a network and a desired final steady state of the network. That means that we address the observation that a real system can change its quite stable state if an external perturbation is strong enough to cause this switch. A plausible example is the differentiation of stem cells. Different tissues are associated with different steady states of the corresponding regulatory network. Now, by applying agents which are the mentioned external stimuli, the stem cells differentiate to different tissues, corresponding to the external stimuli, see for example , 5. AnotOur approach provides a rational method to analyze networks with respect to the influence of external stimuli on the considered network, especially its steady states. For this purpose, for example Jimena , SQUAD  or 1] a a1] aim In Subsection “An extension of regulatory networks with external stimuli” (Methods), we give a mathematical description of the model presented in  and explIn the Discussion we compare our software package to alternative software dealing with the analysis of regulatory networks and explain how to combine different software packages to bunch it together to a great tool for network analysis and modeling with regulatory networks. Furthermore we discuss the sensitivity of the proposed method and how the method can be used for modeling taking systematically the external stimuli into account. We conclude the Discussion by illustrating the realization of our predictions. A conclusion completes the Discussion. Furthermore, besides the Matlab codes, supplementary material is provided with the present work where mathematical and algorithmic details of the used methods are explained.Here, we describe the basic ingredients of our framework. In the k ∈ {1, …, n} is described by the following ordinary differential equationk are elements of the subset {xj| j ∈ Ak ⊆ {1, …, n}} ⊆ {xk| k ∈ {1, …, n}} where Ak contains all the indices of {1, …, n} of the nodes which activate node k and the corresponding xj of node j to the total activation of node k. Analogously, the inhibitors of node k are elements of the subset {xj| j ∈ Ik ⊆ {1, …, n}} ⊆ {xk| k ∈ {1, …, n}} where Ik contains all the indices of {1, …, n} of the nodes which inhibit node k and the corresponding xj of node j to the total inhibition of node k. Furthermore, h > 0 where h models the cooperativity. If h is big, then the behavior of the equation is close to a switcher while small h are closer to a linear behavior of the activation level with respect to the input activation level. According to  and thus we do not have to multiply the activity stimulus by an additional term considering the maximum activity level of the node forcing the activating stimulus term to zero if the node’s activity level reaches its maximum. Furthermore, we equip PTP with an activating stimulus, ThromR with an inhibiting stimulus and Akt with an inhibiting stimulus. We use the output from Algorithm 3 for maxNum = 2, tol = 0.1, η = 0.5 and τ = 0.9 as an input for Algorithm 2 for α = 0.1 that converges here faster than the projected gradient method. From Algorithm 3, we obtain that applying stimulus u1 for 22 time units induces already a switch. From Algorithm 1, we also obtain that additionally external stimulus u2 steers the system towards irreversible platelet aggregation. This is in accordance with previous results  which serves as initial state for the network to Treg with the corresponding steady state , see Table 2 in [We use  50, see , Table 1η = 0.5 and τ = 0.9. We see that according to our model, inactivation of RORγt and activation of IL-2 and TGF-β for about 4.5 time units performs the desired switch. We take the result from Algorithm 3 as initial guess 0u for Algorithm 1 for the parameters α = 0.5, T = 20 and dt = 0.1. In u9 and IL-6R, u10 supports the switch, that means that the network switches faster to the Treg cell. Furthermore, we can deduce more structure from the model that first the inhibiting stimuli, u8, u9, u10 are active before the activating external stimuli u4 and u7 come into play. This can be interpreted in the way that activation of the T-cell by IL-2 and TGF-β is only efficient to induce the desired switch from Th17 to Treg if the specific Th17 expression pattern is knocked down to a certain degree. For this purpose it is sufficient to knock down RORγt that can be supported by the knock down of IL-6 and IL-6R. We stress that by virtue of the self activation of RORγt, a direct knock down of the node RORγt is necessary to induce the switch according to our model.In β, the ascites and TGF-β differed in that TGF-β alone induced IL-17A together with Foxp3 expression. Therefore, the cancer ascites must contain additional factors which suppress RORγt expression—as we show here a prerequisite to complete the switch from Th17 to Treg.A switch from Th17 to Treg has, indeed, been described e.g. in the tumor setting . Here, sγt or have interacting domains that are able to bind to sites of RORγt and thus biologically inactivate RORγt.Furthermore, our predictions, for example those of Figs In addition, we remark that the exact time curve in In our experiments which we perform with the network proposed in , we notiWe first discuss differences to other software existing to analyze regulatory networks and illustrate how to combine our provided software package with other tools. In particular, there is no calculation of optimal modulation of networks by external stimuli available. However, the selection of an optimal stimulus for a specified number of nodes to be modulated into a new state is central for pharmacological interventions. Moreover, planning of knockdowns, RNAi experiments for instance, or any kind of other inhibition, excitation or modulation of the network would highly profit from such an application and this is offered here. None of the tools currently available does this.On the other hand each of them allows an efficient description of the system state including suitable differential equations using either accurate or heuristic solutions. Iterative model refinement can be done including studying the effect of different receptor inputs, activations and inhibitions. However, none of these tools allows to directly calculate the optimal manipulation of the network for changing to a prespecified new system state. Instead there would be numerous trials and iterative steps necessary using any of the software below to achieve this.SQUAD (https://sbos.eu/docu/docu/SQUAD/doku.php.htm). One can utilize SQUAD to analyze steady states of a network once one has the topology of the network that means the interaction graph. Additionally, one can perturb the network for example by activating receptors or by changing decay or gain of a node’s activity. However, this software does not provide a systematical procedure how to search for perturbations to steer the network to a desired state. Therefore our concept of providing a framework to calculate perturbations by techniques of mathematical optimization to induce a switch between an initial steady state and a desired final steady state supplements the pioneering idea of SQUAD implemented in a software.We start with JIMENA (https://www.biozentrum.uni-wuerzburg.de/bioinfo/computing/jimena-c/) is a software package which focuses on an efficient numerical steady state analysis. Therefore, this package as well as SQUAD serves as an excellent tool to figure out the steady states of a network between which one would like to switch. Once the steady states are found, our framework proposed in the present work can be utilized for the calculation of the desired switch.CELL NET ANALYZER (https://www2.mpi-magdeburg.mpg.de/projects/cna/cna.html) provides, besides metabolic network analysis and steady state analysis, a method to calculate minimal intervention sets that provide a network with desired steady states. However, this means that one gets a list of knockins and knockouts of nodes of the network such that the network attains the desired steady states. This is a very important tool, especially in the case of lacking experimental information or conflicting information about the interaction of the considered agents, to design the topology of the network in order to obtain a network that provides the steady states sought. Thus this method is intended to change the topology of the network that means the interaction graph while our approach deals with a fixed topology of the network during all calculations. CELL NET ANALYZER is hence well suited for metabolic modeling, modeling of signalling networks and the upstream use of SQUAD or JIMENA to design an appropriate network but not for precalculation of the best and most efficient stimulus combination to achieve a desired switch between two different system states.ODEFY(https://www.helmholtz-muenchen.de/icb/software/odefy/index.html) is a tool in order to convert boolean networks into networks whose dynamic is described by ordinary differential equations (ODEs) which are the basic models in our framework. Therefore ODEFY is a key tool to transform network topologies into an ODE model which is essential for our framework, especially in the case of networks with many nodes and couplings between them. Thus ODEFY allows the swift formulation of the differential equation system, however, there is no systematic approach to identify the correct combination of external stimuli.j ∈ {1, …, m}, Other software applications (two examples given) allow to define differential equations for modeling biological systems flexibly. In principle pharmacological modeling is cumbersome in practice. For this purpose, we provide in addition a straight forward tool to 1) define and 2) apply functions COPASI toolbox (http://copasi.org/) focuses on the modeling and on simulating of biochemical reaction networks, especially simulation of time curves and steady states, parameter fitting of an underling model to experimental data, sensitivity analysis and dynamical behavior characterization. Besides steady state analysis, a further step of network analysis is to compare the simulated curves with experimental data. Therefore COPASI is a very important tool to analyze different models that fit the data best after fitting of the model’s parameters. Thus COPASI can have a big contribution to pharmacological modeling by first fitting parameters and then choose the model that fits the data best which is essential for dose rate calculations, for example. As our framework does not depend on special network equations that are set up from the interaction graph, our presented framework extends the great range of functions in a useful way. Moreover, COPASI is maybe even more powerful then ODEFY and wide ranges of parameters can be tested swiftly. Nevertheless, to find a proper combination of external stimuli to change the system state is a challenge, cumbersome and not systematic.Specifically, POTTERSWHEEL (http://www.potterswheel.de/Pages/index.php) can be used for modeling with ODEs and best parameter fit to experimental data. For this purpose, one can additionally include external driving functions or vary parameters. This can be used to adapt parameters of the system of ODEs with which one would like to model a particular real network such that the theoretical data fits best to the experimental data. Moreover, POTTERSWHEEL is very efficient in model testing and model refinement. However, for our task, pharmacological network modulation of the change of network state by the best, most efficient combination of external stimuli, the tool allows to quickly verify that a given combination is right, but to find it is difficult and needs numerous iterations. On the other hand, individual parameters are fast characterized regarding their sensitivity and importance for network behavior. Therefore, as COPASI, the software POTTERSWHEEL is also very helpful to figure out an appropriate model and can be extended by our framework with a further useful feature.The software tool uj, j ∈ {1, …, m} are time dependent while a parameter is constant. Therefore we extend the idea of parameter fit, which is a special application of mathematical optimal control theory, to a more general framework that also includes time dependent parameter fitting. In our case, the time dependence of the functions uj is important as they are switched on for a certain time and after the switch off, the network can relax to the desired state such that we can verify, after the application of certain external stimuli, that each node is close to its desired state which would not be possible with a constant parameter as the network could not relax with constitutively activated external stimuli.Next, we explain why there is a specific need for the software, mathematically speaking. The last two software packages are well known examples and perform, among other things, a fit of model parameters of a system of coupled ODEs. This is similar to our framework. However, the main difference between a parameter fit and our framework is, that the functions Our framework provides the most important external stimuli that are responsible for a desired switch. By this procedure, we can reduce the number of pharmacological intervention points to a small but very effective number which is in favor of pharmacological treatments. This issue is also not covered by classical parameter fitting that is provided by COPASI and POTTERSWHEEL. However, as we mentioned before, our framework of systematically finding external stimuli that steer the network from an initial steady state to a desired one is not restricted to a special type of ODE model. Therefore the provided Matlab files can also be integrated into existing software packages like COPASI or POTTERSWHEEL to extend their already great and helpful tools for model analysis with respect to experimental data.In the following we discuss some general properties of the proposed method. We first discuss the sensitivity of the proposed framework to model parameters that have to be concerned for modeling . We remaThe capability of the framework to reveal information in the model about external stimuli and their influence on the network is also a tool for validating a model. For example, if a certain set of external stimuli induces a switch in a real experiment, but this is not obtained by calculations with a corresponding model, it can be a hint that the model structure or its parameters are not set or fitted such that the model is sufficiently exact for the considered issue. Then one has a further option for testing the model by varying model parameters until the calculations give the same external stimuli that are found in the real experiment. If this is still not achievable, the model topology and components have to be reexamined and a new simulation cycle has to be started with a carefully revised model.We remark that the proposed framework systematically includes the external stimuli into the model. This is a very important brick for exact modeling by fitting software for the following reason. The data measured in experiments is usually the adaption of the observed system to external stimuli. That means the data is the variation of observed quantities upon external stimuli. These external stimuli can be set as time dependent functions and thus the information on the action of the external stimuli can be systematically and exactly included into the fitting process. By this way several data sets can be created in experiments such that a fitting software can calculate the model parameters such that the theoretical time curves fit best to the experimental time curves of the corresponding molecular agents. By measuring the distance between the theoretical time curves and the experimental ones, one can compare different models that all have been fitted to the same experimental data and take this one with the smallest distance. This model is the best fitting one and thus describes the considered experiment best which means contains the most reliable information about the considered biological system. Keep always in mind that there is more than just one possibility to fit the model to data. We illustrate one possibility where our proposed framework fits well in. In particular, model selection is not only based on the distance between data and model prediction, but also on the number of free parameters used to fit the data as quantified by information theoretical measures such as AIC (Akaike Information Criterion) or BIC (Bayesian Information Criterion).α in α one increases the costs for the action of an external stimulus. This means by solving the optimal control problem α filters out external stimuli whose input have the biggest influence on the desired switch. A systematical strategy for the choice of α in order to figure out only a small number and thus most effective external stimuli can be the following. We can increase α until the result consists of only non-active external stimuli. Then we can set α between the biggest value where there have been non-zero external stimuli and the smallest α where there are only non-active external stimuli in the solution of the corresponding optimal control problem. This can be repeated until the interval between these two numbers is below a given tolerance.Another important issue that needs to be discussed is the choice of the parameter γt is set to zero and the initial value for IL-2 and TGF-β is set to one according to the external stimuli proposed in γt is low while at the same time the expression level of IL-17 and IL-6 is high. This might not be possible as the transcription of IL-17 and IL-6 directly depends on the presence of RORγt, see We remark that perturbations by our external stimuli framework proposed in γt therapeutic targeting is per se more difficult. However, in case of RORγt with digoxin as an ‘old’ drug and with newly developed compounds like GSK805 specific inhibitors are available also for clinical use [For the experimental realization of our predictions, cytokines and cytokine receptors can be readily inhibited e.g. by monoclonal antibodies or the receptors stimulated by recombinant cytokines. For the T-cell lineage-specifying transcription factors like RORical use , 24. In A detailed mathematical extension of a regulatory network to controlled regulatory networks with external stimuli was presented. Different methods for a systematic calculation of the external stimuli inducing the desired switch were illustrated. A software tool was developed. The considerations presented in the presented work hold for any model consisting of well-posed ordinary differential equations, like chemical reaction networks –15. SincFurthermore, the proposed algorithm strategy directly calculates the best intervention points and strength of intervention. We show how it extends already available software such as Potterswheel, ODEFY or COPASI by an optimal targeting method allowing to calculate best combinations of external interactions. It has many applications for improved pharmacological treatment, recognition of the optimal target or drug combination as well as for molecular interventions.S1 File(PDF)Click here for additional data file.


Space debris removal from Earth orbit by using a satellite is an emergent technological challenge for sustainable human activities in space. In order to de-orbit debris it is necessary to impart a force to decelerate it, resulting in its atmospheric re-entry. A satellite using an energetic plasma beam directed at the debris will need to eject plasma in the opposite direction in a controlled manner in order to maintain a constant distance between it and the debris during the deorbiting mission. By employing a magnetic nozzle plasma thruster having two open source exits, bi-directional plasma ejection can be achieved using a single electric propulsion device. Both the forces exerted on the thruster and the target plate simulating the debris are simultaneously measured in a laboratory space simulation chamber showing that a force decelerating the debris and a zero net force on the thruster can be successfully obtained. These two forces can be individually controlled by external electrical parameters, resulting in the ability to switch the acceleration and deceleration modes of the satellite and the debris removal mode using a single electric propulsion device. Indeed, investigations into the mass distribution have shown a continuously increasing mass of debris5. To preserve a secure space environment and reduce the risk of collisions, the active removal, or de-orbiting of space debris is an emergent technological challenge. One of the important targets of the active removal is large space debris in the low Earth orbit (LEO), typically weighing about a ton and being a few meters in size6.Space debris orbiting around the Earth has become a serious problem over the past few decades7. Some concepts of space debris capture and removal have been proposed8; by using robotic arms and a tether net10, a laser-ablation-induced material ejection from the debris11, an orbit transfer using an electro-dynamic tether method12, and an ion-beam shepherd (IBS) method14 using two ion-beam sources.If remedial action is not taken in the near future, it will be difficult to prevent the mass of debris increasing, and the production rate of new debris resulting from collisions will exceed the loss rate due to natural orbital decayOrbiting space debris has an angular momentum where the centrifugal force is balanced against the gravitational force and a constant altitude is maintained if no drag forces act on the debris  and F1, respectively, where the positive force is defined as the rightward direction. According to an analysis in ref.13, a deorbit time of between 80 and 150 days for a 1 to 2 tonne object would require a thruster performance of about 60 mN and a specific impulse of about 1800 sec. A similar analysis performed in ref.16 has also shown similar requirement of about 30 mN thrust at 2.5–3 kW power level and discussed the beam divergence effect on the momentum transfer efficiency to the debris, considering a safe distance to the debris to be about 7 m, where typical beam divergence for the ion gridded thrusters and the Hall thrusters are about 10–20 and 40–50 degrees half angles, respectively17. Therefore, the active removal of the large size debris clearly requires the high power electric propulsion device operated at the thrust level of several tens of mN at the power level of about a few kW.In general, the thrust (which is a force) is given by the rate of the change of momentum, corresponding to the flux of momentum ejected from the satellite, which can be derived from the momentum conservation lawite Fig. , the netAnother key technology for debris removal by electric propulsion is the control of the acceleration and deceleration  have been investigated, where the high density plasma produced inside the source is transported to the source exit along magnetic field lines. Various types of plasma acceleration processes can occur, e.g., ion acceleration by a current-free double layer22 and electromagnetic acceleration by an electron diamagnetic current23. Using a magnetic nozzle to increase thrust has recently been demonstrated by measurement of the force exerted on the magnetic field lines24. Experiments and simulations have shown that the thrust force is also affected by the neutral density profiles which affect the plasma density profile26. Measurement of ion energy distribution functions in a basic laboratory device has shown the spontaneous generation of supersonic ion beams on both the upstream and downstream sides of the plasma source27.For long-term operation of satellite for space debris removal, the lifetime of the propulsion device is one of the most important considerations. Operations of the ion gridded thrusters and the Hall thruster are known to be significantly affected by erosion of the electrodes and walls exposed to the plasma, especially for their high power operations. To overcome this problem, electrodeless plasma thrusters using magnetic nozzles  and helicon plasma thrustersIn the present study a bi-directional plasma ejection from a magnetic nozzle rf plasma thruster having two open source exits Fig.  is demon28, where the source diameter is 9.5 cm and larger than a 6.5-cm-diameter source tube used in the present paper. More recent experiments show a higher performance giving a thrust of 65–70 mN for about 6 kW rf power with a specific impulse of 2000–3000 sec in the laboratory test, where the location of the gas injection port is changed and the thruster efficiency is increased up to 20%29. We have found that a 30 mN thrust level can be obtained with rf power less than 1.5 kW and a specific impulse of 1500 sec. It should be mentioned that the thruster is not operated in Xe but rather Ar, which has a cost advantage. Furthermore, very efficient rf amplifiers and impedance tuning systems are also now under development32. Previously performed basic laboratory experiments have shown that the ion beam accelerated by a potential drop formed in a magnetic nozzle has a divergence half angle of at most about 20 degrees, even at the edge of the beam plume35, being very similar to that in the ion gridded thruster. Furthermore, results in this paper shows similar values of thrust for the acceleration/deceleration modes and force to the debris in the debris removal modes, implying the operation mode can be changed while maintaining the effective utilization of the gas propellant and the rf power. Based on these published results of research and development, the system in this paper can potentially satisfy the requirements for the IBS mission with a single thruster.The proposed thruster can be scaled up in size. The previously reported maximum value of the thrust imparted by the single open end thruster has been about 55–60 mN for about 6 kW rf powerz = ±8.1 cm), and a rf antenna, the whole being attached to a pendulum thrust balance immersed in a 1 m diameter, 2 m long vacuum chamber. A schematic of the setup is shown in Fig. z = ±5 cm with a total mass flow rate of 100 sccm, where the mass flow rates from the left and right inlets (CArL and CArR) are individually controlled by two mass flow controllers. Two solenoids located near the two open source exits provide a magnetic field and the field configuration can be changed via the dc solenoid currents  as shown by the calculated magnetic field in Fig. 36 is situated at the axial center of the source tube (defined as z = 0) and powered from a 13.56 MHz, 1 kW rf generator; the power is primarily coupled to the electrons that ionise the argon gas by electron impact producing a high density plasma. Axial forces are imparted to the mechanical and magnetic structures of the thruster via momentum transfer by the ions interacting with the radial wall37 and by the Lorentz force on the magnetic field due to the plasma-induced electric current39. The thrust force exerted on the thruster by the plasma is obtained by measuring the displacement induced by the plasma ejection19. A 45-cm-diameter pendulum target plate simulating the debris is suspended from a pivot located at z = 35.9 cm downstream from and to the right of the thruster, and the force exerted on the target plate is obtained from its measured displacement combined with a calibration coefficient relating the displacement to the force40. The direction of both the forces and the displacements is defined as positive for the rightward direction with the detailed procedures for calibration of the two force measurements described in the Method section. An ion saturation current from an axially-movable and radially-facing Langmuir probe, which is proportional to a plasma density, is measured in addition to taking an image from a vacuum view port on the chamber side wall using a digital camera (where it should be mentioned that the target plate is not set in the chamber when taking the Langmuir probe data).The experiment is carried out with the magnetic nozzle rf plasma thruster having two open source exits on the left- and right-hand sides. The thruster comprises a 6.5-cm-inner-diameter 20-cm-long glass tube, two solenoids  = , , and , with the gas flow rates from the two gas inlets respectively set at 50 sccm yielding a total flow rate of 100 sccm. A brighter plasma plume is seen on the left and right sides for the  =  and  cases, respectively, while bi-directional plasma plumes are observed for the symmetric magnetic field configuration of the  =  case. The displacement signals of the thrust balance and the target plate for these conditions are shown in Fig. IBL, IBR) =  and  cases shown at the top and middle of Fig. IBL, IBR) = , a symmetric magnetic field configuration is produced; the target plate moves to the right while a zero displacement of the thruster is maintained ; when the current through one solenoid is changed, the current in the other solenoid is maintained at 8 A. It can be seen that for equal solenoid currents of 8 A (the symmetric magnetic field configuration), the thruster experiences a zero net force while a force of ~8mN is brought to bear on the target.Figure IBL, IBR) =  case and the thrusts for  =  and  cases are very similar in the range of 8–10 mN; implying that the operation modes can be switched while maintaining both the effective utilization of the gas propellant and the rf power.Interestingly, the force on the thruster can be changed, as seen in Fig. z = −35.9 cm.To understand the relation between the measured forces and the plasma behavior, measurement of the ion saturation current  is performed by two Langmuir probes mounted on an axially movable motor stage installed on the right side and on the fixed left side stage at z = ±35.9 cm are plotted in Fig. IBL, IBR) = , , and  as plotted in Fig. The ion saturation currents measured at 41 and the thrust force43. Here the measurements of the forces are performed for various ratios of the gas flow rates from the two gas inlets placed at z = ±5 cm, as plotted in Fig. IBL, IBR) =  providing a symmetric magnetic field configuration and the total gas flow rate CArL + CArR is maintained at 100 sccm. Setting equal gas flow rates from both the left and right gas inlets as  =  results in a zero net thrust force to the thruster and a right directed force to the target, while left and right directed forces to the thruster can be obtained by changing the ratio of the gas flow rates. The measured ion saturation currents at z = ±35.9 cm and the axial profiles as a function of the gas flow rates in Fig. It should be noted that previous analytical models, experiments, and simulations have shown that the spatial profile of the neutral density significantly affects the plasma density profileLaboratory experiments have shown that bi-directional plasma ejection from an open exits magnetic nozzle rf plasma thruster can impart a force to space debris whilst maintaining a zero net thrust force to the thruster (and satellite). The simultaneous measurements of the forces to the thruster and the target plate show that the two forces can be controlled by the magnetic field configuration and/or the gas flow rates from the left and right gas inlets respectively. Therefore, the system can be operational in three modes; the acceleration mode of the satellite, the deceleration mode of the satellite, and the space debris removal mode. These can be brought into play by simply switching electric signals to the solenoid current and the mass flow controller. As there is no movable mechanical structure this thruster configuration can provide new technology for the removal of space debris.40. Here application of this method to the present procedures for calibration of both forces is described:The thrust force and the force imparted to the target plate are obtained by multiplying the calibration coefficients to the measured displacements, following a method described previously in refs.F = mg cotθ, where m, g, and θ are the total mass of the weight put on the basket, the gravitational acceleration, and the angle between the two threads. The relation between the applied horizontal force and the displacement is obtained as plotted by the open circles in Fig. The coefficient relating the displacement to the force is obtained by measuring the displacement when applying a known force. A basket is tied to the back side of the thrust balance via a thin horizontal thread and a second thread attached to a support structure of the thrust stand as shown in Fig. Ical to the small solenoid, static and horizontal magnetic forces are exerted on both the permanent magnet and the solenoid, where the force to the permanent magnet is equal in magnitude and opposite in direction to that of the solenoid mounted on the target plate. Therefore, the magnitude of the magnetic force exerted to the target can be obtained from the signal of the load cell, which is input to a highly accurate differential amplifier with a gain of thousands and digitized by a 16 bit analog-digital convertor operated by a Labview program. The current Ical is very slowly swept between ±1.5 A for about 10 sec as shown in Fig. 40 indicating a good agreement between the thrust values independently measured by the thrust balance and by the target method.The coefficient relating the target displacement to the force imparted to the target is obtained by the known-force-induced displacement as well as the thrust balance, where the displacement is measured by a commercial light emitting diode (LED) sensor. A small permanent magnet is located at the bottom wall of the chamber, being used as a magnetic damper to damp the oscillation of the pendulum motion. A small solenoid is attached to the target plate as shown in Fig.


Surface plasmons polaritons are mixed electronic and electromagnetic waves. They have become a workhorse of nanophotonics because plasmonic modes can be confined in space at the nanometer scale and in time at the 10 fs scale. However, in practice, plasmonic modes are often excited using diffraction-limited beams. In order to take full advantage of their potential for sensing and information technology, it is necessary to develop a microscale ultrafast electrical source of surface plasmons. Here, we report the design, fabrication and characterization of nanoantennas to emit surface plasmons by inelastic electron tunneling. The antenna controls the emission spectrum, the emission polarization, and enhances the emission efficiency by more than three orders of magnitude. We introduce a theoretical model of the antenna in good agreement with the results. Developing a microscale ultrafast electrical source of surface plasmons is crucial for nanophotonic applications. Here, the authors report the design, fabrication and characterization of nanoantennas for emission and control of surface plasmons by inelastic electron tunneling. The corresponding electromagnetic field can be confined to nanometer scale and has a decay time on the order of 10 fs so that a new generation of devices can be designed5. SPPs are widely used for sensing and also for information technology11. An important limitation of surface plasmons is that in most cases, they are optically excited by a diffraction-limited beam so that the device size is larger than the wavelength. In order to fully benefit from the field confinement, it is necessary to generate SPPs in the near field with a subwavelength device. Electrical generation of surface plasmons has been demonstrated using LED-based platforms16 with time scales on the order of 1 ns. Ultrafast emission can be achieved using light emission by inelastic tunneling (LEIT) through a tunnel junction.Surface plasmon polaritons (SPPs) are mixed electronic and electromagnetic modes propagating along the interface between a metal and a dielectric17. This process is rather inefficient with a typical efficiency on the order of one photon per a million electrons. However, LEIT has important advantages. Firstly, it is intrinsically fast. The fundamental limit is given by the tunneling time19, which is on the order of h/eV where e is the electron charge, V the applied voltage on the order of 1 V and h is Planck’s constant yielding a time limit on the order of 4 fs. In practice, the limit is given by the circuit time constant RC. Photon sources based on LEIT have been operated at 1 GHz20. Secondly, LEIT can be a highly localized source. The source current density can be confined in a nanoantenna or in a metallic tip enabling electromagnetic excitation localized at the nanometer scale. Both photon21 and plasmon24 emission have been reported using scanning tunneling microscope (STM) tips. More recently, surface plasmon emission has been reported with metallic microstructures25 and molecular junctions26. Theoretical models are available for LEIT31, and for the role of the gap plasmon mode32. Hence, antenna surface plasmon emission by inelastic tunneling (ASPEIT) appears to be a suitable candidate for ultrafast and highly localized plasmon emission33.LEIT through a planar tunnel junction was discovered by Lambe and McCarthy36. Secondly, a resonant antenna can be designed in order to control both the polarization and the angular emission pattern38. Thirdly, a resonant plasmonic antenna contributes to the local density of states in the junction. If the contribution of the antenna mode is larger than the contribution of the non-radiative modes, it becomes possible to avoid quenching and therefore increase the radiative efficiency40 in a controlled and deterministic way. It is important to stress that there is no fundamental limit to the LEIT efficiency. We note in particular that in the microwave regime, the non-radiative modes can be suppressed using dissipation-less superconductors. Furthermore, impedance matching between the junction and a 50-Ω line can be achieved by microwave engineering so that photon emission in a 50-Ω line can reach very high efficiencies28. Photon emission in the visible by electrically driven optical antennas has been reported demonstrating a spectral control of the emission42 and also a directional control43. Spectral control of LEIT using resonant nanocubes has been demonstrated recently44 although only a small fraction of the tunneling current was affected by the antenna. These results demonstrate the potential of plasmonic nanoantennas to tailor LEIT. All these demonstrations deal with light emission. No antennas have been reported to emit surface plasmons so far. Reported surface plasmon sources are based on the use of a metallic tip24 or a planar junction26. While it is known that a localized gap plasmon takes place between the tip and the surface, no control of this mode using antennas has been reported.However, several issues need to be solved to use inelastic tunneling as a light source. It is required to control the emission spectrum, the angular emission pattern and to increase the emission efficiency. In order to tackle these issues, resonant nanoantennas can be used. The rationale for using an antenna is based on different properties. Firstly, a resonant antenna can select the frequency emissionThere are still many issues to be solved before developing electrical surface plasmon sources using inelastic tunneling assisted by antennas: (i) the tunnel barrier width, which plays a critical role in the success of the emission process, is not deterministically controlled in the reported experiments, (ii) the lifetime of the antenna is still an outstanding issue, (iii) LEIT is limited to very small power on the order of 1 fW for STM junctions or on the order of 10 fW for planar junctions while pW are needed for practical applications, (iv) the coupling between the antenna mode and the propagating plasmon mode has to be optimized, (v) a theoretical analysis of the emitted power as a function of the current fluctuations in the presence of an antenna is needed in order to analyze and optimize the emission.Here, we report the design, fabrication and characterization of antennas to emit surface plasmons propagating along an aluminum/air interface. We also report an original theoretical model introducing a figure of merit of the antenna showing that the relevant figure of merit is not the Purcell factor but the spatially averaged enhancement factor in the junction barrier. The antenna produces a narrow emission spectrum and provides an enhancement of the efficiency as compared to a planar junction larger than three orders of magnitude. The emitted power is on the order of 10 pW, four orders of magnitude larger than an STM tip.x interface  as a function of the applied voltage. The characteristic J(V) curve is depicted in Fig. 46 allows the estimation of the barrier thickness (3 nm) and the mean barrier height (2.01 ± 0.03 eV) using an effective mass of the electron of 0.23me47. As an additional check of the tunnel regime, we show in the Supplementary Note J(V) curve does not depend on temperature.The electrical surface plasmon source consists in a gold nanopatch antenna deposited on an Al/AlOsee Fig. . A plasmy45 Fig. . Due to x/Au junction is based on leakage radiation microscopy (LRM) using an inverted optical microscope. We use an oil objective (NA = 1.3) to collect the leakage of the emitted SPPs through the glass substrate when the junctions are biased. We show in Fig. y-axis. It is seen that on both sides of the array of antennas, light is also collected. This is due to radiative leakage of surface plasmons propagating away from the antennas. To prove the plasmonic character of the emitted light, we averaged the intensity along y in the area indicated by the dashed rectangle shown in Fig. x in Fig. 48. This value is known to be highly dependent on the deposition procedure48. To further check the plasmonic character of the emitted light, we recorded the far-field angular spectrum in the back focal plane as displayed in Fig. k0 = ω/c, a clear signature of surface plasmons propagating along an Al/air interface. An interesting non-uniform intensity pattern due to the antenna periodicity is observed as a function of the angle. To understand the data, we have developed a theoretical model of ASPEIT. A detailed derivation is given in Supplementary Note We now turn to the optical characterization of the emitted surface plasmons. The optical observation of the SPPs emitted by the Al/AlOeV/h  and by the antenna resonance. When repeating the simulation at 0 K as shown in Supplementary Fig. We now study the spectrum of the emitted field. To proceed, we collect the signal emitted toward the substrate and send it to a spectrometer (Andor Shamrock 750i). The data are shown in Fig. We now move to the study of the polarization emission properties of the antenna. Figure 6 photons per second by using ASPEIT (with a voltage bias of 1.6 V). Correcting for the collection efficiency, this corresponds to 1 × 108 photons emitted per second . It is interesting to compare with a STM tip22 , with a planar junction25 . The increased emitted power is both due to the larger size of our source (25 µm × 45 µm) and to the electron to photon conversion efficiency enhancement.An important figure of merit of an electrical source of surface plasmon is the emitted power. We detected 3.6 × 1035: (i) it provides a contribution to the local density of states larger than the non-radiative modes, (ii) its losses are dominated by radiative losses. We designed our antennas to fulfill these criteria. In order to measure the efficiency enhancement, we have compared the emission by the array of antennas with the emission of the same sample at a different position with no antennas , which is one order magnitude lower than the experimental value 1.6 × 10−6. We also find a difference for the antenna junction efficiency normalized by the planar junction efficiency. The experimental value is 2700 whereas the model predicts 400. We attribute this difference to the simplified model of the current fluctuation correlation function used. It has already been reported in the literature50 that this model underestimates the efficiency and it has been suggested that light emission could be due to hot electrons in the metal. We have computed this contribution and we found a marginal change. We thus conclude that the origin of the discrepancy is due to the simplified correlation function of the current density. In summary, the antenna appears to be a powerful tool to enhance the efficiency of LEIT, which has been known for decades to be an inefficient light emission process. Nonetheless, the experimental electron to plasmon conversion efficiency (~10−5) is still low. We now discuss how it could be improved. As shown in Supplementary Fig. −5) so that the electron to plasmon efficiency could be on the order of 10−4.As shown before, the theoretical model predicts correctly the emission spectrum, the angular emission pattern and the polarization. However, the photon per electron efficiency is only qualitatively predicted. The theoretical model predicts an antenna efficiency of 1.1 × 10−4 plasmons per electron. This raises the prospect of an efficient, ultrafast and highly localized electric surface plasmon source.In conclusion, we have reported ASPEIT. We have shown that the emission spectrum can be tuned by varying the width of the antenna. An important feature of the antenna is its ability to enhance the efficiency of the coupling between electrons and plasmons. We have demonstrated a more than three orders of magnitude enhancement of the electron to photon conversion efficiency when comparing with a planar junction. The ASPEIT operates in the 10 pW regime, four orders of magnitude above the fW regime of a STM-based junction. We have introduced a theoretical model of ASPEIT that accounts for the observed spectrum, polarization structure and is able to predict the efficiency enhancement. This model provides guidance to further improve the efficiency. Using the model, we find that a silver/alumina/silver junction could reach an efficiency at 10x layer. The Au top electrode is fabricated by using an electron-beam lithography (Nanobeam NB4) system. All the detailed fabrication processes can be found in Supplementary Note The ASPEIT tunnel junctions are fabricated on a standard coverslip . The bottom Al electrode is fabricated by UV photolithography via a mask aligner (MJB4). An Ebeam evaporator  is employed to do the Al deposition. After the lift-off, a dry thermal oxidation process in a furnace is used to generate an ultrathin AlOThe electrical characterization of our junction is performed via a source meter (Agilent B2902A). The IV measurements are conducted by a Quick IV Measurement software provided by keysight technologies website. For all experiments, the Au electrodes are grounded and the Al electrodes are biased. To avoid any possible dielectric breakdowns, each IV curve is within ±1.8 V. To avoid heating the junction, we use a time period of 1.5 ms for every voltage step. When performing the electroluminescence (EL) measurement, we apply a lower voltage (<1.6 V) to maintain a longlife measurement (larger than 10 h).The optical characterization of our devices is based on an inverted optical microscope (Olympus X71). An EMCCD (iXon 885) and a spectrometer (Andor Shamrock 750i) are used to capture the EL images and spectra, respectively. Detailed information is provided in Supplementary Note 51 to numerically compute the electric field in the tunnel junction barrier. The dielectric constants for Al are taken from ref. 52 and the Au data from ref. 53. The refractive indexes of the glass substrate and alumina layer are set at 1.5 and 1.76, respectively. The modes of the patch antenna in Fig. 54. For that purpose, a vertically polarized  dipole source is inserted in the middle of the alumina layer along the z-axis and 30 nm off-center along the x-axis. More details can be found in Supplementary Note The far-field angular distributions and the emitted spectra are calculated based on the reciprocity theorem model described in Supplementary Note Supplementary informationPeer Review File


Most human energy budget models consider a person to be approximately cylindrical in shape when estimating or measuring the amount of radiation that they receive in a given environment. Yet, the most commonly used instrument for measuring the amount of radiation received by a person is the globe thermometer. The spherical shape of this instrument was designed to be used indoors where radiation is received approximately equally from all directions. But in outdoor environments, radiation can be strongly directional, making the sphere an inappropriate shape. The international standard for measuring radiation received by a person, the Integral Radiation Measurement (IRM) method, yields a measure of the Mean Radiant Temperature (Tmrt). This method uses radiometers oriented in the four cardinal directions, plus up and down. However, this setup essentially estimates the amount of energy received by a square peg, not a cylinder. This paper identifies the errors introduced by both the sphere and the peg, and introduces a set of two new instrument that can be used to directly measure the amount of radiation received by a vertical cylinder in outdoor environments. The Cylindrical Pyranometer measures the amount of solar radiation received by a vertical cylinder, and the Cylindrical Pyrgeometer measures the amount of terrestrial radiation received. While the globe thermometer is still valid for use in indoor environments, these two new instruments should become the standard for measuring radiation received by people in outdoor environments. Global Climate Change (GCC) and Urban Heat Island Intensification (UHII) combined produce urban environments that are often hotter than the surrounding countryside. This can have negative effects on both chronic and acute health of urban residents. People are less likely to walk in overheated environments ,2 and thThere are many models of outdoor thermal comfort and they have taken several different approaches. Johansson et al.  has callJohansson et al.  identifiThorsson et al.  reportedJohansson et al.  identifiHumans arguably are neither square pegs nor spherical globes, but are more typically cylindrical in shape  and theyThese three different shapes of instruments in the same environment will yield different values of solar and terrestrial radiation received. The Cylindrical Radiation Thermometer (CRT) has a shape that most closely resembles a typical human, but it relies on an empirical heat flux equation  that canThe goal of this paper was therefore twofold: (1) To compare, through the use of three-dimensional geometrical analysis, the radiation received by square pegs, spheres, and cylinders in outdoor environments; and (2) to identify a more accurate and precise method of measuring the radiation received by people in outdoor environments.The three instrument shapes  were assessed in terms of their geometry and how their shape influences the measurement of solar and terrestrial radiation. For these tests, the up and down directions will not be included. Similarly, diffused and reflected radiation will not be included. The goal was not to provide a complete assessment of the radiant environment, but rather to illustrate situations that cause errors. Each instrument was placed first in a theoretical horizontal flat plane with no objects to obstruct or reflect the solar radiation, and secondly with a sun-warmed wall to (i) the north of the instrument; and (ii) to the north-east of the instrument. The wall was heated by incident solar radiation during the day and emitted terrestrial radiation. The amount of solar and terrestrial radiation received by each shape at test times of the day and with the wall in test locations are calculated and the results from the different shaped instruments are compared.−2 of beam radiation on a vertical flat plate, the IRM pyranometer facing directly toward the east will record 400 Wm−2, while the other three instruments—facing south, west, and north—will all record 0 Wm−2 beam radiation. The average amount of beam radiation received by the four vertical faces is 100 Wm−2 Φ = flux density at the surface ΦΘ = angle between beam and normal to the surfaceHigh Sun Angle: When the sun is directly south of the instruments at solar noon, the south-facing instrument will receive radiation according to Lambert’s Cosine Law :Φ = Φ0 c−2 of beam radiation with an elevation angle of 45° above the horizon, the south-facing instrument will receive 707 Wm−2 of directional radiation, while the other three radiometers will receive 0. The average amount received will be 177 Wm−2.In the case of a very clear day when the sun is providing 1000 Wm−2 was received when the sun was 15° east of south, then the east-facing instrument will receive 707 cos(90−15) = 183 Wm−2 while the south-facing instrument will receive 707 cos(90−75) = 682 Wm−2. The west- and north-facing instruments will receive 0. The average amount of beam radiation measured will be 216 Wm−2. This is a 22% difference from the same amount of radiation received directly from the south  A wall to the north of the instruments, and (b) a wall to the north-east of the instruments. The two walls are considered to be the same temperature as heated up by absorbed solar radiation and are the same distance from the instruments. The location of the wall will have a similar impact on the amount of terrestrial radiation received by a person in that location in a landscape and the orientation of the instrument or the wall does not influence the result.For this test example, the ground is considered to be covered with grass and is at 25 °C; the wall fills 50% of the sky hemisphere and is 50 °C, while clear sky fills the other 50% of the sky hemisphere. For illustration purposes, the emissivity of surfaces is assumed to be 1.0 for all cases.4 × 5.67 × 10−8 = 618 Wm−2. The ground at 25 °C will be emitting 448 Wm−2 and the radiation from the sky can be estimated from Equation [If the wall to the north of the instrument has a surface temperature of 50°C, according to the Stefan-Boltzmann equation, it will be emitting (273.15 + 50)Equation :Lsky = 2−2. The north-facing pyrgeometer will register 618 Wm−2 while the south, east, and west facing pyrgeometers will record 0.5 × 448 + 0.5 × 350.5 = 399 Wm−2. Averaging the four values yields 454.75 Wm−2  + (0.5 × 350.5) = 484.25 Wm−2. The average of these two values is 466.1 Wm−2. The location of the wall relative to the globe does not change this value  + (0.5 × 618) = 484.25. The average will be 466.1 Wm−2 and as with the globe, the location of the wall relative to the cylinder does not change the amount of terrestrial radiation received (Considering the sphere of influence on the cylinder, half of the terrestrial radiation will be received from the ground and half from the sky hemisphere. The ground portion will be 448 Wmreceived c.The different amounts of terrestrial radiation yielded by the three different shaped instruments is shown in As reported in the literature ,10 measuThis study proposes two new radiometers based on the same principles as the standard pyranometer and pyrgeometer; however, rather than measuring the radiation on a horizontal flat plate, they measure the amount of radiation received by a cylinder.−2.The Cylindrical Pyranometer  consists−2.The Cylindrical Pyrgeometer  consistsInstruments such as these radiometers will have a built-in uncertainty. It can be expected that these two instruments will have uncertainties similar to that of high-quality flat plate pyranometers and pyrgeometers, which are in the range of 3% to 5%.Instruments that are currently being used to measure and estimate radiation received by a person in outdoor environments yield incorrect results. Two new radiometers, a cylindrical pyranometer and a cylindrical pyrgeometer, will provide more accurate and precise measurements of the radiation a person receives in a landscape.With more than 80% of the American population and more than 50% of people worldwide living in cities, it is critical that urban environments be designed to provide thermally comfortable environments for people. Radiation is a critical component of the energy budget of people in urban outdoor areas, particularly during extreme heat events, and it is important that design and planning decisions are made based on accurate and precise measurements.The two instruments described in this study have been registered and are “patent pending”.


Intra-aneurysmatic flow diverters offer an endovascular treatment option for broad-based intracranial aneurysms without the need for neck bridging devices  placed in the parent artery. Experience with the Woven EndoBridge (WEB) device , as the only established intra-aneurysmatic flow diverter, is rapidly growing with promising angiographic and clinical results over the past years , 2.Coil migration is a well-known complication in the endovascular treatment of intracranial aneurysms treated by standard coiling, which occurs in up to 6% of the cases. Several endovascular rescue strategies address the problem of partly or totally dislocated platinum coils ranging from oral antiplatelet therapy to dedicated devices especially designed for the retrieval of dislocated coils –5.Here, we describe a case of a secondarily displaced WEB device during the treatment of an internal carotid artery aneurysm followed by successful withdrawal from the middle cerebral artery with an Alligator retrieval device .A 64-year-old female patient was referred to our hospital with an aneurysm of the right internal carotid artery bifurcation. The aneurysm was diagnosed by magnetic resonance angiography (MRA) performed at the referring hospital after an episode of impaired vision. Using a diagnostic digital subtraction angiography (DSA) including a rotational 3D angiography the aneurysm morphology could be visualized in detail. Additional aneurysms were ruled out. The average aneurysm diameter was 2.9 mm with a maximum diameter of 3.1 mm measured in the lateral projection. The maximum aneurysm height was 3.2 mm  and Navien™ 072  were positioned in the cervical segment of the right internal carotid artery. Size selection of the WEB device resulted from exact calibrated measurements of the aneurysm in two orthogonal projections based on a 3D rotational angiographic dataset according to the established standards described in the literature [Now a Rapid Transit microcatheter  was advanced towards the dislocated WEB device with a Traxcess EX microwire (Microvention). The microwire was pulled back and the Alligator retrieval device was inserted into the microcatheter and pushed forward. Once the closed jaws of the device reached the distal marker of the microcatheter both the microcatheter and the device were pushed towards the struts of the WEB device. Now the Alligator retrieval device was slightly advanced and the microcatheter was held in place, which resulted in an opening of the four jaws of the Alligator device at the level of the dislocated WEB. The microcatheter was then slightly advanced under permanent distally directed tension of the Alligator retrieving device in order to close the jaws. At this point the ensemble of the microcatheter with the Alligator was gently pulled back with the WEB device trapped between the jaws Fig. .Fig. 4ThA final angiographic run proved an unchanged situation especially without suspicion of a dissection followed by the described maneuver. The procedure was finished without a final treatment of the aneurysm and 5 days later the aneurysm was occluded with coils using the remodeling technique.The endovascular treatment options for broad-based intracranial aneurysms are nowadays various ranging from stent-assisted coiling to extra-aneurysmal or intra-aneurysmal flow diversion. The identification of the optimal treatment strategy in a particular case can be challenging. Growing experience with a new technique, and especially its potential limitations, helps to identify the appropriate indications.With respect to the literature published to date a complete dislocation of a WEB device outside an aneurysm is a unique complication of this technique. The reason for this complication finally remains unclear but some possible explanations are hypothesized as follows: we followed the recommendation to oversize the width of the WEB device with a compensatory undersizing of its height in order to clamp the device inside the aneurysm according to the so-called +1/−1 rule , 6. ThesAs documented in Fig. The distal marker of the VIA microcatheter was advanced towards the WEB device in order to cover the detachment zone and promote the detachment process, as recommended by the manufacturer. Regarding this advice, awareness of the peculiar position of the distal marker on the VIA microcatheter is important since it does not indicate the exact end of the catheter but is placed 1 mm proximal to the definite end of the catheter. These technical features might explain the dislocation of the WEB in our case. The close contact of the proximal marker of the WEB with the distal end of the VIA microcatheter might in combination with the tight angle between the WEB and the microcatheter have caused an interlocking of both followed by a mobilization of the WEB device during the withdrawal of the microcatheter.Several endovascular devices address the problem of dislocated material ranging from snares to stent retrievers –11. The Detachment of the WEB device and withdrawal of the microcatheter should be performed with caution especially in complex anatomies with tight angles between the aneurysm and the parent artery. The position of the distal marker on the VIA microcatheter might be misleading.