Our findings define a mechanistic framework for the biophysical implementation of dopamine neuron firing patterns in the intact brain.The in vivo firing patterns of ventral midbrain dopamine neurons are controlled by afferent and intrinsic activity to generate sensory cue and prediction error signals that are essential for reward-based learning. Given the absence of in vivo intracellular recordings during the last three decades, the subthreshold membrane potential events that cause changes in dopamine neuron firing patterns remain unknown. To address this, we established in vivo whole-cell recordings and obtained over 100 spontaneously active, immunocytochemically-defined midbrain dopamine neurons in isoflurane-anaesthetized adult mice. We identified a repertoire of subthreshold membrane potential signatures associated with distinct in vivo firing patterns. Dopamine neuron activity in vivo deviated from single-spike pacemaking by phasic increases in firing rate via two qualitatively distinct biophysical mechanisms: 1) a prolonged hyperpolarization preceding  The in vivo firing patterns of ventral midbrain dopamine neurons are controlled by afferent and intrinsic activity. The authors identified biophysical membrane potential signatures associated with distinct in vivo firing patterns in whole-cell recordings of spontaneously active midbrain dopamine neurons. Loss or dysregulation of dopamine neuron subpopulations located in the substantia nigra pars compacta (SNc) and ventral tegmental area (VTA) perturbs crucial circuits leading to major brain disorders, including Parkinson Disease (PD)5, schizophrenia6, depression7, and addiction8. However, describing the dynamics of subthreshold ionic conductances that cause dopamine neuron spiking activity in vivo has remained a challenge.The midbrain dopamine system is necessary for essential brain functions related to reward-based learning, motivation, action, and cognition10. Individual dopamine neurons signal prediction errors by transient, sub-second changes in their firing rates. A recent study also suggested that prediction error coding by dopamine neurons might occur in a distributed manner11. Transient cue- or reward-associated increases in firing rate – from a low tonic background firing frequency (in the range of about 1–8 Hz) – are thought to encode positive reward prediction errors (RPEs), while transient reductions or pauses in baseline firing are believed to encode negative RPEs, induced for instance by the omission of an expected reward. Increasingly, experimental evidence points to additional dopamine functions, such as signaling salience, novelty and action control13, as well as aversion14. This functional diversity might also be reflected by the emerging molecular16, cellular, and anatomical diversity of the midbrain dopamine system23. Even within canonical RPE signaling, the interpretation of the transient burst has become more complex. It is currently divided into a short-latency component, which might signal the sensory characteristics of the stimulus (e.g. intensity); and a long-latency component, which might represent the predictive properties of the stimulus10. In addition, recent progress has been made in characterizing the underlying arithmetic of single dopamine neuron activity in the context of RPE signaling24.Single-unit extracellular recordings from non-human primates and rodents have provided major insights into the computational roles of dopamine neuron firing, most prominently in the context of reward-based learning25, thereby dynamically tuning its intrinsic pacemaker activity. This process enables the generation of burst-pause firing patterns, which in turn contribute to temporally resolved extracellular dopamine concentration transients in axonal target regions26. However, how inputs are integrated in dopamine neurons in vivo has remained unknown for the last three decades due to the lack of available tools. While the in vivo extracellular recording method does reveal spontaneous firing patterns of dopamine neurons, it is blind to the causal subthreshold processes that drive them. Intracellular recordings are unique in their ability to directly monitor and manipulate membrane potentials with full temporal resolution. Yet, the only available in vivo intracellular data on dopamine neurons came from the pioneering studies by Grace and Bunney31 in the early eighties. Here, we provide the first large dataset on subthreshold membrane potential properties of identified dopamine neurons in vivo by establishing a robust method for deep in vivo patch-clamp recordings in anesthetized adult mice. Our dataset comprises 110 spontaneously active, immunocytochemically identified dopamine neurons, which were mapped to their respective anatomical positions within the SNc and VTA. We discovered two qualitatively distinct subthreshold membrane potential signatures associated with transient high-frequency firing, which we named rebound and plateau bursting. Moreover, we demonstrate that in vivo pacemaking of dopamine neurons exhibits tightly controlled action potential thresholds, while rebound and plateau bursts are characterized by opposing shifts in action potential thresholds. Thus, our study provides a framework for mechanistic studies into in vivo firing patterns of midbrain dopamine neurons.To approach in vivo electrophysiology from the perspective of the dopamine neuron, it is reasonable to assume that it integrates excitatory and inhibitory inputs that are derived from heterogeneous afferentsStable in vivo whole-cell recordings of immunocytochemically identified dopamine neurons reveal subthreshold membrane potential.n = 110, N = 78; Fig. n = 100, N = 73) and female  mice from two different C57BL/6 substrains  and C57BL/6J . We also used two different variants of the internal pipette solution with a small difference in estimated free calcium concentrations of 40 nM  and 80 nM . As there were no significant differences in the mean firing rates (FR) and firing variabilities (quantified as coefficient of variation (CV) of interspike intervals (ISI)) among these data sets, they were pooled  = 446.6 (301.3–656.7) MΩ; n = 71, N = 11; see Supplemental Table 33. In addition, subthreshold membrane potential responses to in vivo hyperpolarizing current injections were recorded in a subset of cells, which revealed a diversity reminiscent of previous in vitro studies , were again comparable to extracellular recordings using the same anaesthesia19  of each ISI, i.e., the most hyperpolarized membrane potential between two action potentials  for each ISI, i.e., the action potential threshold .To best utilize the direct readout of subthreshold membrane potentials provided by in vivo whole-cell recordings, we focused on a systematic investigation of the subthreshold membrane potentials associated with distinct firing patterns. To achieve this with an unbiased approach, we focused on the overall variability of firing (i.e. coefficient of variation (CV)) to characterize the activity of the recorded cell. As shown in Fig. Vmin  and showed a clear bimodal distribution  captured by in vivo patch-clamp recordings might be related to spike train statistics. Indeed, when comparing the Vmin CV versus the variability of spike firing pattern (i.e. ISI CV) of the entire dopamine neuron population, a strong positive correlation was detected . Moreover, Vmin CV scaled with ISI CV over the entire dynamic range. The variability of the threshold potentials also displayed a clear correlation with spike train regularity . Other parameters of subthreshold membrane potentials (mean of Vmin and Vthr) and their distributions (skewness and kurtosis of Vmin and Vthr) did not correlate well with the ISI CV . In summary, in vivo spike train variability of dopamine neurons was well-correlated, not just with the overall variability of Vmin and Vthr, but more specifically with the bimodality coefficient of the Vmin and Vthr distributions. Like the spike train variability itself, the bimodality coefficient was distributed as a spectrum for the recorded dopamine neuron population . Similar to the example neuron illustrated in Fig. Vmin and Vthr distributions of this neuron displayed unimodal distributions  had a mean Vmin BC of 0.29 ± 0.02 and mean Vthr BC of 0.32 ± 0.05 . To further examine the relationship between these subthreshold membrane properties and spike firing properties, individual Vmin and Vthr were plotted against their respective ISI durations  firing patterns of in vivo dopamine neurons, which were now identified by their low BC (lower 10% of the population). Figure ons Fig. . As the Vmin and Vthr distributions, we utilized event-triggered averaging by superimposing pacemaking spikes , or repolarization (Min dV/dt) speeds across the sequence of three action potentials among all low Vmin BC dopamine neurons (ΔVthr: spike 1 vs spike 2 median (IQR) = −0.002 (−0.0043 to 0.0012) mV, spike 2 vs 3 = 0.0016 (−0.0035 to 0.0043) V; Δmax dV/dt: spike 1 vs 2 = −0.0124 (−0.021 to 0.13) V/s, spike 2 vs 3 = −0.0174 (−0.0387 to 0.002) V/s; p = 0.0.375, 0.2324, 0.4316, and 0.02 for all comparisons; n = 10, N = 9; range of 3-spike sequences per cell = 78–691; Fig. For a more detailed insight, we analyzed the phase plots of action potentials in these pacemaker firing sequences. Figure Rebound bursts are characterized by bimodal distribution in voltage minima and hyperpolarizing shift in action potential threshold at the beginning of the burst.Vmin BC was in the top 10% (Vmin BC range = 0.66–0.83). A representative recording and images of immunocytochemistry of such a dopamine neuron located in the SNc is shown in Fig. Vmin from a bursting dopamine neuron was well-described by a bimodal Gaussian distribution  = 2.7 ± 1.6 mV; Mode 2 Vmin mean = −37.9 ± 3.7 mV, SD = 1.5 ± 0.4; n = 10, N = 10). As in Fig. Vthr distribution was also unimodal . When plotting the individual ISIs against the corresponding Vmin, the more hyperpolarized membrane potentials  followed by membrane depolarization back to threshold. The rebound firing occurring after large hyperpolarizations was associated with a transient increase in firing in the beta frequency range. Accordingly, we termed these events rebound bursts. In contrast, event-triggered averaging of spikes following the Mode 2 Vmin events did not result in a stereotypical low-variability subthreshold waveform. The frequency distribution associated with the rebound burst significantly widened the range of dopamine neuron firing , both on the level of individual cells and, in particular, on the level of dopamine neuron populations  = −3.1 (−5.6 to −2.4) mV, spike 2 vs 3 = 1.0 (0.9–1.1) mV; Δmax dV/dt: spike 1 vs 2 = 16.3 (13.6–21.9) V/s, spike 2 vs 3 = −5.3 (−8.3 to −3.2) V/s; p =  0.02 for all comparisons; n = 10, N = 10; range of 3-spike sequences per cell = 9–95; Fig. Vmin, which widen their frequency range, and their observed threshold dynamics occur at burst onset.The phase plot of the rebound burst action potentials shows different dynamics compared to that of pacemaking Fig. . In partPlateau bursts are characterized by bimodal distribution in action potential threshold and depolarizing shift in action potential threshold at the end of the burst.Vthr. To explore the features of this particular subthreshold membrane potential signature, we analyzed the dopamine neurons in the top 10% of Vthr BC. An example trace and its corresponding immunocytochemical images of an identified VTA dopamine neuron are shown in Fig. Vthr was clearly bimodal , a unique feature that is not observed in pacemaking or rebound bursting. In this particular example, the distribution of Vmin also displayed a high BC and bimodal distribution . When plotting the ISI durations against their respective Vthr  = 0.39 (−0.35–0.92) mV, p = 0.19; spike 2 vs 3 = 4.66 (3.62–4.43) mV, p = 0.002; Δmax dV/dt: spike 1 vs 2 = −0.5 (−3.25–0.11) V/s, p = 0.11; spike 2 vs 3: −14.38 (−17.95 to −6.73) V/s, p = 0.02, n = 10, N = 10; range of 3-spike sequences per cell = 4–89; Supplemental Table n = 455; 3 spikes, n = 48; 4 spikes; n = 11, N = 11). In essence, our unbiased exploration of subthreshold membrane voltages from dopamine neurons in vivo uncovered two unique subthreshold burst signatures featuring opposing threshold dynamics, each associated with a distinct and non-overlapping frequency range.When plotting the action potential trajectories of plateau bursts, in contrast to rebound bursts, we found no change in the action potential threshold voltage or waveform properties at the onset of plateau bursts Fig. . This imDopamine neurons in vivo fire both Plateau and Rebound bursts during a single recording.Vmin and Vthr  = −2.3 (−2.6 to −1.8) mV, spike 2 vs 3 = 0.6 (0.5–0.9) mV; Δmax dV/dt: spike 1 vs 2 = 7.18 (6.04–8.98) V/s, spike 2 vs 3 = −1.91 (−2.79 to −1.13) V/s; p = 4.88 × 10−4 for all comparisons; n = 12, N = 12; range of 3-spike sequences per cell = 1–15; Fig. In this dopamine neuron firing in a mixed pattern, the phase plot of action potentials in rebound bursts shows similar properties compared to that of dopamine neurons locked in a rebound burst mode Fig. . Again, In summary, the first systematic in vivo patch-clamp study of identified midbrain dopamine neurons demonstrated the presence of two qualitatively distinct burst firing mechanisms, identified by their bimodal subthreshold distributions, with contrasting subthreshold membrane potential signatures and diametrically-opposing action potential threshold dynamics. These findings present the first framework of how predictive coding might be biophysically implemented in midbrain dopamine neurons.Vmin) and maxima (Vthr) in the subthreshold membrane potential range. In addition, we demonstrate that bimodality in the distributions of Vmin and Vthr enabled the identification of unique subthreshold signatures associated with distinct burst patterns. We defined (1) a prolonged membrane potential hyperpolarization leading to rebound bursts, which were associated with a hyperpolarizing shift in action potential threshold at the onset of the burst; and (2) a fast depolarization leading to plateau bursts, which were associated with a depolarizing shift in the action potential threshold at the end of the burst. While plateau bursts were strongly coupled to short, high-frequency (gamma range) discharge, rebound bursts occurred at lower frequencies (beta range), some of which would not have been detected by traditional heuristics.For the first time in nearly four decades, our study provides new intracellular in vivo recordings of identified midbrain dopamine neurons. By establishing deep in vivo whole-cell patch-clamp recordings in anaesthetized mice with no noticeable perturbations on firing activity, our large dataset allowed the first systematic analysis of the subthreshold membrane potential range of dopamine neurons in the intact brain. We show that the overall regularity of action potential discharge, captured by the coefficient of variation (CV) of the spike train, correlated well with the CV of the minima  balance. Indeed, our previous dynamic clamp studies in vitro revealed similar threshold and action potential waveform behavior when the E/I balance rapidly shifts toward more excitation or disinhibition31. In addition, it was only now possible to determine that the in vivo intracellular recordings did not alter the firing pattern of intact cells – both by on-cell recordings in this study and by comparison to previous in vivo extracellular recordings of identified dopamine neurons36. Importantly, all dopamine neurons included in our study were filled, recovered, and identified as TH-immunopositive. Given these quality control measures and the size of the dataset, we can begin to also address the in vivo subthreshold diversity of dopamine neurons. The previously reported differences in in vitro intrinsic subthreshold properties39, such as sag amplitudes and rebound latencies, were also evident in our in vivo dataset, although dopamine neurons in the paranigral aspect of the VTA were underrepresented. Also, our present in vivo patch-clamp study does not provide information about axonal projections of the recorded dopamine neurons. However, the observed diversity might contribute to subpopulation-specific computations, as also recently identified by in vivo GCaMP imaging during a complex behavioral task40.While the in vivo intracellular recordings with sharp microelectrodes of identified dopamine neurons from the 1980s did not provide systematic analyses of the subthreshold membrane potential range in relation to firing patterns, those results are mostly in accordance with our findings. There is, however, one important exception. Input resistances in our in vivo patch-clamp recordings of dopamine neurons are about 10-fold higher than those reported previously, indicating that the in vivo “high conductance” state might have been overestimated and, in part, be caused by impaling dopamine neurons with sharp microelectrodesA, GABAB, dopamine receptor D2 (D2R), or metabotropic glutamate receptors (mGluR) coupled to small conductance calcium-activated potassium (SK) channels46. In addition, the rebound kinetics are likely to be controlled by intrinsic conductances in the subthreshold range. Here, rebound depolarization accelerating (e.g. HCN channels38) and delaying (e.g. Kv4 channels47) conductances are likely to be relevant. Some dopamine neurons even respond to the termination of a hyperpolarizing current injection with a robust recruitment of T-type calcium channels48. The plateau burst, on the other hand, is driven by a rapid onset depolarization, which is likely to be caused by a rapid change in the E/I balance44. Fundamentally, rebound and plateau bursts represent responses within dopamine neurons comprised of a sequence of synaptic inputs that are active at any moment in the intact brain in addition to the intrinsic cellular processes that are particular to the individual neuron. Future studies exploring detailed intrinsic biophysical properties of in vivo dopamine neurons in the context of synaptic input will be necessary to determine the degree to which synaptic inputs contribute to rebound and plateau bursts in dopamine neurons. In addition, dynamic clamp and pharmacological manipulations could be performed to further characterize intrinsic activity underlying these burst patterns. In essence, in vivo patch-clamp studies will facilitate future mechanistic studies of dopamine neuron firing in anaesthetized as well as awake behaving animals.Despite the strengths, our study has a limitation in that we recorded under anaesthesia and were therefore unable to study subthreshold membrane potential signatures of dopamine neuron firing patterns in response to sensory cues or reward-related signals. However, the stability of brain states in controlled anaesthesia is also an advantage as it enabled the unbiased identification of subthreshold membrane potential signatures. Another limitation of our study is that we did not go beyond the identification of subthreshold patterns to explicitly target underlying synaptic and intrinsic biophysical mechanisms. For instance, the deep hyperpolarization that precedes rebound bursting could be activated by different types of synaptic input involving distinct receptors ranging from GABAC57BL/6N (Charles River Laboratories and Janvier Labs) and C57BL/6J (Jackson Laboratories) mice  were used for the experiments. Mice were maintained on a 12-h light/dark cycle with food and water available ad libitum. All experimental procedures were approved by the German Regional Council of Darmstadt (TVA 54-19c20/15-F40/28) or the University of Texas at San Antonio Institutional Animal Care and Use Committees.For head-plate implantations, animals were anaesthetized with isoflurane  and placed in a stereotaxic frame (David Kopf Instruments). The body temperature was maintained at 37–38 °C with a heating blanket, and the breathing rate at 1–2 Hz. Small indentations were made above the VTA  or SNc  as a reference for later craniotomies. Customized head-plates were anchored to the skull with superglue and dental cement , as well as with screws mounted on the skull.2, 0.1 EGTA, 0.075 CaCl2 (variant 1) or no added CaCl2 (variant 2), 5 ATP (Na), and 1 GTP (Li), neurobiotin  or biocytin (0.3%), at pH 7.35. The estimated free calcium concentrations based on a calcium contamination of 15 µm  were about 80 nM for variant 1 and ~40 nM for variant 2 . Recording electrodes were made with borosilicate glass capillaries  pulled with a pipette puller .Electrophysiology was performed using glass electrodes (5–10 MΩ) filled with internal solution containing (in mM): 135 K-gluconate, 10 HEPES, 5 KCl, 5 MgClI = 0) with a series resistance range of 20–130 MΩ–using long taper (10 mm) pipettes to reach the ventral midbrain – for a median duration of approximately 5 min  including spontaneous activity and current-injection protocols. Responses to hyperpolarizing current injections were then obtained in current-clamp mode to measure sag and rebound delay. Recording signals were obtained with a patch-clamp amplifier  and the data were acquired with PatchMaster software (HEKA) or Axograph software (Axograph) at a sampling rate of 20 kHz.Animals were maintained under isoflurane  and head-fixed to a customized recording platform (Luigs & Neumann). The body temperature (37–38 °C) and breathing rate (1-2 Hz) were continuously monitored. Craniotomies and duratomies were performed at the reference locations. The electrode was lowered down to ~200 µm above the region of interest with a positive pressure of 600–1000 mbar. The pressure was gradually lowered and kept in a range between 40 and 70 mbar during probing for cells in the VTA (DV: 4.0–5.2 mm) and SNc (DV: 3.8–5.2 mm). A tone generator  was used to monitor the pipette resistance during probing and sealing. A fluctuating 20–50% increase in the pipette resistance indicated a cell was nearby. Once reaching proximity, pressure was released to achieve a GΩ seal. On-cell recordings were obtained for some neurons prior to breaking in. After breaking into the whole-cell mode with a small suction, cell capacitance and series resistance were estimated. Whole-cell recordings of spontaneous activity were recorded in current-clamp mode with zero holding current  and transcardially perfused with PBS followed by 4% paraformaldehyde (wt/vol) and 15% picric acid (vol/vol) in phosphate-buffered saline. Collected brains were post-fixed in 4% paraformaldehyde and 15% picric acid overnight and then stored in PBS at 4 °C. Coronal slices were collected at 50-μm-thick using a vibratome. Collected slices were washed with PBS and then incubated in blocking solution , 0.5% Triton X-100 (vol/vol), 0.2% BSA (vol/vol)) for 2 h at room temperature. For the tyrosine hydroxylase (TH) staining, polyclonal rabbit antibody  was used as the primary antibody diluted in carrier solution  overnight at 4 °C on a shaker. Slices were then rinsed 3 times in 1X PBS and incubated for 2 h in AlexaFluor-488 goat anti-rabbit IgG  diluted in the carrier solution previously described as the secondary antibody. Neurobiotin and biocytin were visualized with AlexaFluor-568 streptavidin conjugate . Sections were washed 5x in PBS and then mounted on slides  using Prolong Gold Antifade Reagent  mounting media, and visualized under a light microscope  and a laser-scanning microscope .Imaged brain sections were registered to the Allen Mouse Brain Common Coordinate Framework (CCF) using an automated section-to-atlas registration in Neuroinfo software (MBF Bioscience). Registration of imaged sections results in a transform that has assigned image pixels to brain regions in the Allen Reference Atlas (Allen Institute for Brain Science). The location of neurobiotin- or biocytin-labeled neurons are marked within the registered sections and cell locations are transformed into CCF. The resulting transforms of cell locations provides exact coordinates for each recorded cell within a 3-dimensional reference brain.V/dt threshold : First, the minimal value of dV/dt must be <−5 mV/ms. Second, the maximal value of voltage must be within 30 mV of the highest voltage in the entire trace. Last, the difference between the maximal voltage and the voltage at the dV/dt-threshold crossing (spike height) must be >5 mV. In some cases, these parameters were modified to improve spike detection performance.A spike peak was detected if the following three conditions were met within a 3-ms window after crossing a d2V/dt2 crossing certain thresholds. To make the algorithm flexible and robust, these thresholds were indexed to the maximal values of the first and second voltage derivative for each detected spike. Specifically, the spike threshold is detected when the following conditions are met within a 2-ms window ending at the spike peak: Both first and second derivative of voltage cross 5% of their respective within-window maximal values for two consecutive samples. This ensured that spike threshold determination was adjusted for each spike. The phase of the spike being detected as threshold was visually verified and was found to be very consistent. Similar to the above algorithm, the numeric parameters were tunable.Detection of spike threshold was dependent on the dV/dt and dVmin distribution of neurons with the highest (top 10%) Vmin BC values. The voltage value midway between the crossing point of the two individual Gaussians and the peak of the leftward Gaussian was chosen as the threshold for classifying Vmin values as deep hyperpolarizations. If either of the two ISIs following a deep hyperpolarization were faster than the cell’s median firing rate, they were identified as a rebound burst. The burst was said to be terminated when the instantaneous firing rate fell below the median. In non-bimodal cells, deep hyperpolarizations showed up as outliers in the ISI vs Vmin scatter plot. As such, we used Tukey’s method to detect outlier ISI and Vmin values. If a Vmin was more hyperpolarized than q1-2.5x (q3-q1), where q1 = 25th quantile and q3 = 75th quantile in the Vmin distribution; and if the corresponding ISI was longer than q3 + 2.5x (q3-q1), where q1 = 25th quantile and q3 = 75th quantile in the ISI distribution, it was classified as a deep hyperpolarization. Identification of the subsequent burst followed the same criteria as for bimodal cells. The factor 2.5 was derived from analysis of bimodal cells and to optimize detection in non-bimodal cells.Rebound bursts: a Gaussian mixture model with two Gaussians was fitted to the Vthr BC, the voltage criterion for classifying Vthr values as plateau potentials was calculated in a similar way to deep hyperpolarizations, with the only difference being that it was calculated on Vthr distributions and the second Gaussian in the Vthr distribution lay to the right of the main Gaussian. All ISIs whose Vthr values were higher than this criterion were considered part of the plateau burst. In non-bimodal cells, plateau potentials were detected in a parallel fashion to deep hyperpolarizations, with 2.5 used as the factor for Vthr outlier detection and 0.5 as the factor for ISI outlier detection, in addition to the Vthr being 3.5 mV more depolarized than its immediate predecessor for it to be identified as a plateau burst. Also, the corresponding ISI has to be shorter than q1-0.5x (q3-q1), where q1 = 25th quantile and q3 = 75th quantile in the ISI distribution. Similar to rebound burst detection, these criteria were derived from bimodal cells and with an aim to optimize detection in non-bimodal cells.Plateau bursts: For dopamine neurons with the highest (top 10%) 34. Measurements of effect size were also calculated50. Parametric data were presented as mean ± standard deviation. Non-parametric data were presented as median with interquartile range. Wilcoxon rank-sum test and Wilcoxon sign rank tests were used for unpaired and paired data. Adjusted R squared values are reported for linear correlation.Data processing and quantifications were performed using MATLAB (MathWorks). Wilcoxon rank-sum tests were used to determine statistical differences using MATLAB (MathWorks). Graphs and maps were created using MATLAB or Prism 6. Bimodality coefficient was used for dual process detectionFurther information on research design is available in the Supplementary InformationPeer Review FileReporting Summary


With the development of Internet technology, the speed of information dissemination and accelerated updates result in frequent discussion of topics and expressions of public opinion. In general, multi-dimensional discussion topics related to the same event are often generated in the network, and the phenomenon of multi-dimensional public opinion polarization is formed under the mutual influence of groups. This paper targets the phenomenon of multi-dimensional public opinion polarization under topic-derived situations as the research object. Firstly, this paper identifies the factors influencing multi-dimensional public opinion polarization, including the mutual influence of different topic dimensions and the interaction of viewpoints within the same topic. Secondly, the topic correlation coefficient is introduced to describe the correlation among topics in different dimensions, and the individual topic support degree is used to measure the influence of topics in different dimensions and that of information from external intervention on individual attitudes. Thirdly, a multi-dimensional public opinion polarization model is constructed by further integrating multi-dimensional attitude interaction rules. Finally, the influence of individual participation, topic status, topic correlation coefficient and external intervention information on the multi-dimensional public opinion polarization process is analyzed through simulation experiments. The simulation results show that: (1) when there is a negative correlation between multi-dimensional topics, as the number of participants on different dimensional topics becomes more consistent, the conflict between multi-dimensional topics will weaken the polarization effect of overall public opinion. However, the effect of public opinion polarization will be enhanced alongwith the enhancement in the confidence of individual opinions. (2) The intervention of external intervention information in different dimensions at different times will further form a multi-dimensional and multi-stage public opinion polarization, and when the multi-dimensional topics are negatively correlated, the intervention of external intervention information will have a stronger impact on the multi-dimensional and multi-stage public opinion polarization process. Finally, the rationality and validity of the proposed model are verified by a real case. After the outbreak of an event, relevant information will spread rapidly on the Internet. Affected by information with multiple tuples, netizens’ comments are multidimensional, meaning the comments are made from various perspectives or vary over time, thus leading to multidimensional topics. The interaction of viewpoints about multidimensional topics makes public opinion escalate to a climax, resulting in multidimensional public opinion polarization. In real life, most hot events show multi-dimensional characteristics, such as the “Liu Qiangdong sexual assault incident”. Netizens’ views on the event show multiple dimensions. At the beginning, most netizens criticized Liu Qiangdong’s sexual assault. Since then, with more disclosure of information, netizens have talked about its derivative subject:“Liu had been framed”, “Sino-US trade war trap”. With the development of events, the multidimensional public opinion polarization phenomenon is formed, and thus led to a pattern of network violence, impacting on social harmony and stability. Based on this, it is of great theoretical and practical significance to study the multi-dimensional public opinion polarization process in the topic derivation context.There is limited study on the multi-dimensional public opinion polarization phenomenon in a topic-derived context, while most studies conduct research from a single dimension of network public opinion topics and use macro statistics ,2 or a mThe structure of this paper is as follows: The concept of group polarization was first proposed by American scholar Sunstein  in 1961,At present, the research on unidimensional public opinion polarization is mainly analyzed from its internal and external influencing factors. The representative results are as follows. Chen et al.  studied In addition, there are studies about the impacts of external factors on public opinion polarization. Some typical literature is as follows. Lee and Choi  found thThe literature on the public opinion polarization phenomenon is mostly based on the single dimension of network public opinion topics, starting from the internal and external factors that affect public opinion polarization, and exploring the formation of the public opinion polarization process; although to a certain extent the study reveals the formation mechanism, it omits public opinion from the multidimensional discussion of the formation of polarization. With further disclosure of information related to the event, discussion topics of multiple dimensions will gradually emerge in the network, and individuals’ participation in topics of different dimensions will form their multidimensional attitudes, and the polarization of online public opinions will be promoted to present multi-dimensional characteristics through interaction with individual neighbors . Due to At present, some scholars have made a preliminary discussion on the process of multi-dimensional public opinion polarization. By combining social judgment theory with the multi-agent model, Li and Xiao  proposedTo sum up, most of the current research on the polarization of public opinion considers network public opinion from a single dimension, and merely studies multi-dimensional public opinion polarization from the perspective of topic derivation. In fact, in the evolution of online public opinion, the outbreak of a social hot event usually gives rise to discussion from multiple dimensions, and individuals’ participation in topics of different dimensions will form their multi-dimensional attitudes towards the event. At the same time, an individual’s attitude will change under the influence of internal and external aspects of the topic he or she participates in. Among these influences, internal influence comes from the views of neighbors within the same dimension of the topic, while external influence comes from the influence of other dimensions of the topic and external intervention information. Based on this, this paper first introduces the topic correlation coefficient and the influence intensity index of different dimensions of topics to describe the mutual influence among multi-dimensional topics, and defines the index of individual topic support, comprehensively reflecting the influence of different dimensions of topics and external intervention information on individual attitudes. Secondly, based on the model proposed by Jager and Amblard , a multi1, x2, x3, …, xn), which is a point in n-dimensional space. The xn belongs to the interval , and xn obeys N ~ , mapping in the interval . Set attitude (<0) as 0 and the attitude (>1) as 1. In this way, the initial attitude of most individuals is relatively neutral, while only a few individuals hold extreme attitudes. This assumption is consistent with the attitude distribution of groups in the real world towards certain kinds of events.In this paper, modeling is carried out based on Monte Carlo the multi-agent method. Agents are used to represent individual nodes in the network. The network scale is set as N, i.e., there are N netizen nodes in the network. The individual’s initial attitude is –(12).Step10: Randomly select agent Step11: Repeat step4–10 until the end of the evolution time.i to the nth dimensional topic. On the one hand, it is affected by the individual’s attitude value towards the nth dimensional topic; On the other hand, it will be influenced by other dimensional topics and external intervention information. Based on this, its expression is as follows (Equation (1)):nth dimensional topic.Because of the differences in social background and the style of thinking, even when facing the same social hot event, individuals have different attention and acceptance for different dimensional topics . The attn will be affected by C(i) (C(i)∈), the opinion confidence of individual i. The larger value of C(i) indicates that the individuals are more confident and less likely to be affected by other dimensional topics.The impact of topic m on topic nth dimensional topic, so its attitude value is 0.With the change of individual topic support, their attitude value will also change. Generally speaking, the higher an individual’s support for a certain dimension of the topic, the greater his attitude towards that topic will be. Based on this, the conversion rules between an individual’s support degree and an individual attitude value are defined as follows (Equation (2)):For multi-dimensional topics derived from the same event, there is usually a relatively complex relationship among them, which will have an important impact on the evolution process of multi-dimensional public opinions. Therefore, this paper refers to the Pearson correlation coefficient  to descrmth dimensional topic on the nth dimensional topic, which is affected by total group attitude for the mth dimensional topic and the number of individuals taking part in the nth dimensional topic. The ratio of these two represents the average influence of the comprehensive attitude tendency of the mth dimensional topic on the individuals participating in the nth dimensional topic, which can reflect the influence degree of the mth dimensional topic on the nth dimensional topic.mth dimensional topic on the nth dimensional topic , mapping in the interval . In order to observe the evolution of multi-dimensional public opinions, the correlation of topics in different dimensions is set to be strongly negative, with the evolution time T = 50. In this paper, the evolution results of three-dimensional topics are taken as an example for analysis, and the conclusion can be extended to other multi-dimensional situations.Combined with the multi-dimensional public opinion polarization model mentioned above, the initial parameters of model evolution are set. In order to describe the distribution of extreme attitude, individuals with attitude values greater than 0.9 are called strongly positive individuals, individuals with attitude value less than 0.1 are called strongly negative individuals, and the proportion of extreme individuals in the group is called the polarization rate. This can be divided into When a multi-dimensional topic is derived from a hot event, individuals tend to participate in part or full in the discussion according to their interests and cognition. The number of different individuals participating in the topic discussion will be different, and this difference in selection will impact on the multi-dimensional public opinion polarization. Based on this, this section will analyze the situations in which individuals participate in discussion on different numbers of topics, and the results are shown in As can be seen from In order to further analyze the influence of the number of individuals participating in the topic discussion on multi-dimensional public opinion polarization, based on the above analysis, a form of random distribution is designed. To facilitate the control of variables, the following rules are made: (1) when individuals only participate in the discussion of one topic, it is assumed that the individual participates in the topic in dimension 1; (2) when individuals participate in the discussion of two topics, it is assumed that they participate in the topics in dimension 1 and 2; (3) When individuals participate in the discussion of three topics, it is assumed that they participate in the topics in dimension 1, 2 and 3. 100 times tests are carried out respectively; in each test, a different topic number of individuals is randomly generated and assembled into different social networks . The proportion rate of each combination is recorded and a 4D scatter plot  is drawn. The results are shown in It can be seen from In the process of multi-dimensional public opinion evolution, individuals’ participation in derivative topics will change dynamically under the influence of opinion leaders and related topics. This section will study the dynamic changes in the number of topics that individuals participate in. First, this paper searched for opinion leaders according to the concept of degree in a social network, calculated the degree of each node and ranked it, and selected opinion leaders from high to low. Because opinion leaders have advantages in thinking mode and information acquisition, it is assumed that opinion leaders will participate in the discussion of three topics at the initial moment, while ordinary individuals only participate in the discussion of one-dimensional topics. In the process of public opinion evolution, ordinary individuals under the influence of opinion leaders will choose to participate in discussions of more dimensional topics, so as to observe the influence of opinion leaders on the number of topics that ordinary individuals participate in. To facilitate the control of variables, 30% of the nodes are selected as opinion leaders, and 70% of the nodes are ordinary individuals . The results are shown in In The above analysis can explain the factors affecting the change in individuals from participating in the discussion of single dimensional topics to multi-dimensional topics. The following will further analyze the factors affecting this change in combination with the topic correlation coefficient. Under the initial conditions, all individuals were set to participate in the discussion of topics in three dimensions, and the number of topics that individuals participated in was observed to change with the topic correlation coefficient. The results are shown in As can be seen from The interaction among the topics of each dimension will have an important influence on the multi-dimensional public opinion polarization process, while individual factors will reduce or enlarge the effect between topics, and then have an influence on the multi-dimensional public opinion polarization process . TherefoIn order to describe the confidence of different opinions held by different individuals, the confidence of individual opinions C is subject to N~ and mapped to , indicating that the individual viewpoint confidence is generally low, that is, it is easy to be affected by other dimensional topics. C is subject to N~ and mapped to , indicating a generally high level of individual viewpoint confidence. C is subject to N~ and mapped to , indicating a general level of individual viewpoint confidence. C is subject to U~ to describe the situation where the number of individuals with different individual viewpoint confidence is roughly the same in the network. At this point, it is set that all individuals participate in the discussion of three dimensional topics, and the results are shown in C is subjected to N ~ , the distribution of group attitudes of various dimensions presents the polarization state, and the number of individual attitude values around 0 is significantly higher than those around 1. Meanwhile, the corresponding attitude polarization is around 35%, suggesting that when C is low, individuals are easily influenced by other dimensional topics, and thus weaken their own attitude. However, when C is subject to N ~ , individuals’ opinion confidence is generally high, and individuals are not easily affected by other dimensional topics. Therefore, the distribution of group attitude is around 1, and the polarization rate is around 55%, which is significantly higher. When the individuals’ viewpoint confidence is relatively general or more evenly distributed, that is, when C is subject to N ~  and U ~ , their attitude polarization rate increases compared with that of individuals with low confidence. Therefore, it can be concluded that when there is a negative correlation between multi-dimensional topics, with the increase of the confidence of an individual’s point of view, its restraining effect on the influence of other dimensional topics will be enhanced, thus promoting the effect of multi-dimensional public opinion polarization, and vice versa.From As an important part of individual attitude renewal, the individual interaction process plays an important role in the formation and polarization of multi-dimensional public opinion. The number of interactions between individuals is usually regarded as the depth of their opinion communication, and the deeper the communication between individuals, the easier it is to reach consensus, which is of great significance for the formation of multi-dimensional public opinion polarization. The results are shown in As can be seen from From the above analysis, it can be seen that both individual opinion confidence and individual interaction times have an impact on the effect of multi-dimensional public opinion polarization. As two important factors affecting public opinion polarization at the individual level, it will be further analyzed in the form of a combination of factors. Here, only the evolution results of the first dimensional topic are analyzed, and the results of other dimensions are basically consistent with them, as shown in As can be seen from The topic correlation coefficient will have an impact on the interaction between topics of different dimensions, which includes two aspects: first, the topic correlation, which affects the direction of the interaction between them; second, the degree of topic correlation, which affects the intensity of interaction between each other. The following will analyze the influence of the topic correlation coefficient on the multi-dimensional public opinion polarization process.In order to analyze the interaction mechanism between different dimensional topics, this section will combine the concept of topic correlation coefficient defined above to analyze the influence of topic correlation on multi-dimensional public opinion polarization . To faciIt can be seen from At the same time, it can be seen from When there is a certain correlation between multi-dimensional topics, they will influence each other and enhance or weaken the effect of multi-dimensional public opinion polarization. However, the degree of mutual influence among topics of different dimensions will be influenced by the degree of topic correlation. The stronger the degree of correlation, the stronger the mutual influence will be. The following will analyze the influence of topic correlation degree on the multi-dimensional public opinion polarization process, and the results are shown in x-axis represents the degree of correlation between topics in different dimensions, which can be divided into negative correlation , mutual independence, and positive correlation , y-axis represents the dimension of topics , and z-axis represents the polarizability. It can be seen from In In order to comprehensively analyze the role of the topic correlation coefficient in the process of multi-dimensional public opinion polarization, the following content sets the correlation coefficient between topics in different dimensions through the form of random distribution and observes the change of topic polarizability in each dimension. 200 trials were conducted respectively, and each trial randomly generated the correlation coefficient between two topics . The polarizability of each combination is recorded, and a four-dimensional scatter plot of the polarizability is drawn, . The results are shown in The After the outbreak of a hot event, with the release of external intervention information in different dimensions, individuals’ attitudes towards topics in different dimensions will change accordingly, which will lead to the change of public opinion polarization direction and the extension of the public opinion evolution process. Therefore, this section will comprehensively analyze the influence of external intervention information on the multi-dimensional public opinion polarization process.The intervention of external information in different dimensions at different times usually promotes the derivation of public opinion topics. Analyzing the influence of external intervention information in the process of the derivation of public opinion topics is of great significance for the research of multi-dimensional public opinion polarization. First of all, in the initial state, it is assumed that there is only one hot topic transmission in the public opinion field, and external intervention information of different dimensions is released at different times to observe the derivation of public opinion topics. For the convenience of research, the topic in the initial state is called the original topic, and the topic emerging with external intervention information is called the derived topic. The results are shown in It can be seen from In real life, due to the “authenticity” of network information, with the release of authoritative information the polarization process of network public opinion tends to take on a multi-stage form. The following is a study of multi-dimensional and multi-stage public opinion polarization phenomenon, and the results are shown in It can be seen from f1 = 0.5 of the first dimensional topic at time between 0 and 50, and f2 and f3 at time between 50 and 100 are set as −0.8, −0.6, −0.4, −0.2, 0, 0.2, 0.4, 0.6 and 0.8, respectively, so as to discuss the changes of multi-dimensional public opinion polarization process when the external information of topic 2 and topic 3 at time between 50 and 100 is involved simultaneously. The setting of other parameters is the same as above, and the result is shown in In addition, the multi-dimensional polarization process of external information intervention in any single dimension is discussed above. In the evolution process of public opinion, there are usually multiple dimensions of external information intervention, which will have more complex influences on the process. The external information intensity f2 and f3, the attitude polarizability of topic 1 decreased sharply, while that of topic 2 and 3 increased accordingly. This indicates that the intervention of external information in different dimensions at different times will further form the multi-dimensional and multi-stage polarization of public opinion, and the more relevant topics and information intensity released by the information means that extent of public opinion inversion is greater. Therefore, in public opinion control, relevant departments should release authoritative information in a timely fashion about hot events, guide the public opinion to a certain correct dimension, and avoid the continuous impact caused by the event.As can be seen from f1 is set to 0.5. At the time moments between 50 and 100, the external information intensity f3 is set to 0.2, 0.4, 0.6 and 0.8, respectively, to observe the change of the polarizability of topic attitude in each dimension. In order to simplify the simulation process, only the situation when external positive information involved is analyzed here, and the conclusion can be extended to other cases. The results are shown in When there is a certain correlation between multi-dimensional topics, the external information intervention of any dimensional topic will have an impact on its related topics. Therefore, combined with the topic correlation coefficient, it is very important to analyze the influence of external intervention information on the multi-dimensional public opinion polarization process. Here, at the time moments between 0 and 50, the external information intensity x-axis is the external information intensity of topic 3, y-axis is the topic correlation coefficient, and z-axis is the polarizability. With the decrease of the topic correlation coefficient, the attitude polarizability of topics in all dimensions decreases gradually. When the topic correlation coefficient is greater than 0, as its value increases, the attitude polarizability of topics in all dimensions keeps rising and tends to be stable. At this time, with the enhancement of the external positive information intensity of topic 3, the attitude polarizability of topic 1 and topic 2 does not change significantly, while that of topic 3 increases significantly. This shows that when there is a positive correlation between multi-dimensional topics, the intervention of external information on any dimensional topic will only have an impact on itself, with relatively small impact on its related topics. However, when the topic correlation coefficient is less than 0, with the enhancement of the external positive information intensity of topic 3, the polarizability of topic 1 and 2 decreases continuously, while the polarizability of topic 3 increases significantly. Therefore, when there is a negative correlation between multi-dimensional topics, the intervention of positive information outside the related topics will have a positive impact on itself and a negative impact on the related topics. On the whole, the topic correlation coefficient has a stronger influence on the multi-dimensional public opinion polarization process, and the influence of external intervention information on other dimensional topics will be constrained by the topic correlation coefficient.In This paper selects a typical case “Tencent sues Laoganma” to verify the multi-dimensional public opinion polarization model constructed in this paper.On 30 June 2020, Tencent requested the court to seize 16.24 million Yuan as “property preservation” due to an unpaid advertising fee. The news aroused strong attention among netizens. Laoganma responded that it “has no business cooperation with Tencent and called the police”. On 1 July, Guizhou police issued a notice saying that “someone pretended to be Laoganma and signed a cooperation agreement with Tencent, resulting in Tencent’s prosecution.” Relevant information caused hot discussion in multiple dimensions, such as: “Laoganma is faithless, defaulting huge advertising fee”, “Tencent were cheated”, “Nanshan District court freezes tens of millions”. Multi-dimensional discussion was carried out which can be summarized under the following three aspects: (1) relevant evaluation of Tencent; (2) relevant evaluation of The Godmother; (3) relevant evaluation of Nanshan District Court in Shenzhen. Based on this, this event is selected as an empirical case in this paper. Python crawler technology was used to obtain Weibo information published in “Toutiao”, “The Paper”, “CCTV news” and other media released between 30 June and 3 July 2020. There are total of 50,000 Weibo comments, including the publisher’s ID, posting time, number of followers, number of comments, number of likes, etc. The results are shown in Since the acquired raw data contains a large amount of useless information, and the Chinese text data contains various error encoding information, the raw data needs to be processed. The specific steps are as follows:Step1: Data cleaning. Python data cleaning tools are used to eliminate raw data containing large amounts of incorrect garbage, emoticons, missing or duplicate redundant information. In total, there are more than 30,000 useful pieces of information left.Step2: Text classification. By observing the data obtained, it can be seen that netizens’ comments on the event are roughly divided into three dimensions. However, because the dataset is large and messy, it needs to be classified as text. By comparing the three text classification methods of Recurrent Neural Network (RNN) , FastTexStep3: Text Sentiment Scoring. The raw data crawled is the comment information in Chinese texts, and in order to correspond to the model, the Chinese texts need to be processed for sentiment scoring to quantify the sentiment tendency of individuals. Based on Step2, the “other irrelevant comments” category is excluded here, and more than 20,000 comments are selected. The sentiment score was processed by the natural language processing tool SnowNLP ,42, the 30,000 comments selected by convolutional neural network are divided into four categories, among which the comments “related to Tencent” account for 39% of the total, indicating that under the influence of related information, netizens have made many comments on Tencent’s behavior. Second, “Related to Laoganma” accounts for 21% of the comments, indicating that netizens have also paid great attention to “Laoganma”. At the same time, Shenzhen Nanshan District Court played an important role in the process of freezing Laoganma’s property, and due to the contradiction of relevant information before and after, many netizens questioned the behavior of Nanshan District Court and made many comments on it. Finally, other comments that had “nothing to do with the incident” accounted for 29%. In general, netizens usually comment on an event from multiple dimensions, which indirectly explains the actual value of the multi-dimensional public opinion polarization model constructed in this paper.On this basis, this paper eliminated the category of “other irrelated comments” and selected a total of more than 20,000 comment data. Through SnowNLP, a natural language processing tool, emotion scoring was conducted to obtain the emotion value of each Weibo comment by quantification. The results are shown in The evolution process of this event is dominated by three pieces of external information. First, “Tencent asked the court to seize Laoganma’s tens of millions on the grounds that it owed a huge amount of advertising fee”. This news immediately attracted the attention of some netizens and gave Tencent “support and sympathy”. Secondly, as the news broke that Laoganma had “no cooperation with Tencent”, netizens paid more attention to this information and began to show “sympathy” to Laoganma, while condemning Tencent’s behavior. Finally, with the announcement of the Guizhou police and the release of the “Tencent was cheated” information, many netizens began to question the Nanshan District Court’s freezing of Laoganma’s property. As can be seen from f1 = 0.2  was set in the simulation. f2 = 0.5 ; f3 = 0.1 . At the same time, the correlation of topics in three dimensions is set as follows: the topic of “Tencent” and “Laoganma” shows strongly negative correlation; the topic of “Laoganma” and “Nanshan District Court” shows strongly negative correlation; the topic of “Tencent” and “Nanshan District Court” shows moderately positive correlation. Other parameters are set as follows: the individual point confidence C is subject to N ~  and mapped to , indicating that most individuals’ point confidence is general. d1 = 0.15, d2 = 1.15, μ = 0.35, β = 0.15; Interaction time T = 20; the result is shown in The following is the simulation of the event according to the multi-dimensional public opinion polarization model proposed in this paper. Due to the large amount of data and the comprehensive consideration of visualization, this paper sets the network size of the simulation as 1000, and sets the initial group size in the simulation according to the proportion of the three types of comments. Since the event was dominated by three external pieces of intervention information, It can be seen from In order to further compare the differences with other models, a model in the literature  was usedAlthough the literature  describeIn order to reveal the evolution mechanism of the polarization of multidimensional public opinion based on a topic derivative situation, this article considers the interaction mechanism between different dimensions of subject and multidimensional interaction rules, and builds a multidimensional public opinion polarization model so as to analyze the influence of individual participation status, individual opinion confidence, topic correlation coefficient, and external intervention information on the polarization process of multidimensional public opinion.When there is a negative correlation among multi-dimensional topics, as the opinion of participants from different dimensions is gradually the same, the conflict between multi-dimensional topics will weaken the overall polarization effect of public opinion, while when there is a positive correlation between multi-dimensional topics, the polarization effect of public opinion will be correspondingly enhanced.When there is a negative correlation between multi-dimensional topics, with the increase of opinion confidence of an individual, the interaction between topics of different dimensions will weaken accordingly, thus enhancing the effect of public opinion polarization.When multi-dimensional topics are positively correlated, the participation of a certain proportion of opinion leaders can promote more individuals to participate in the discussion of multi-dimensional topics. However, when multi-dimensional topics are negatively correlated, the interaction between different dimensional topics will cause individuals to give up their support for a certain dimensional topic, thus reducing their participation in multi-dimensional topics.The intervention of external intervention information in different dimensions at different times will further form the multi-dimensional and multi-stage public opinion polarization phenomenon; however, the influence of external intervention information on multi-dimensional topics is constrained by the topic correlation coefficient, i.e., when multi-dimensional topics are negatively correlated, the intervention of external intervention information has a stronger influence on the multi-dimensional public opinion polarization process.The following conclusions can be drawn from the simulation experiments:Although this paper considers the interaction between topics in different dimensions and defines the topic correlation coefficient to describe it, it does not give a specific calculation method, so it is necessary to artificially determine the correlation coefficient between topics in different dimensions. Therefore, in follow-up research, big data and AI technology can be used to comprehensively analyze various factors among topics of different dimensions and calculate the correlation coefficient between topics.As the spread of social hot events is usually a dynamic process, individuals participating in the discussion of events in the network will enter and exit, so it is necessary to consider the increase and withdrawal mechanism of nodes in the network and study the phenomenon of multi-dimensional public opinion polarization in the dynamic network.However, there are still some deficiencies in this paper, which need further study:


Dreaming is a special topic to investigate with a scientific approach. Its main characteristic is to be difficult to access and to observe which prevents many experimental approaches from being possible or successful  in the sleep preceding a dream report , or on the same topic ], show that the results of Siclari et al. (At a larger scale, the concerns raised in this commentary point to the worrying limitations of the current international scientific publications system whose top one priority seems to be drifting more and more away from scientific soundness, reliability and originality. The case presented here also highlights the always necessary need of theoretical framework and thinking to inform and ground experimental work (e.g., Valli and Revonsuo, The author confirms being the sole contributor of this work and has approved it for publication.The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Thermally stabilized and subsequently carbonized nanofibers are a promising material for many technical applications in fields such as tissue engineering or energy storage. They can be obtained from a variety of different polymer precursors via electrospinning. While some methods have been tested for post-carbonization doping of nanofibers with the desired ingredients, very little is known about carbonization of blend nanofibers from two or more polymeric precursors. In this paper, we report on the preparation, thermal treatment and resulting properties of poly(acrylonitrile) (PAN)/poly(vinylidene fluoride) (PVDF) blend nanofibers produced by wire-based electrospinning of binary polymer solutions. Using a wide variety of spectroscopic, microscopic and thermal characterization methods, the chemical and morphological transition during oxidative stabilization (280 °C) and incipient carbonization (500 °C) was thoroughly investigated. Both PAN and PVDF precursor polymers were detected and analyzed qualitatively and quantitatively during all stages of thermal treatment. Compared to pure PAN nanofibers, the blend nanofibers showed increased fiber diameters, strong reduction of undesired morphological changes during oxidative stabilization and increased conductivity after carbonization. The production of carbon nanofibers (CNFs) based on carbonized electrospun nanofibers has received increasing attention in recent years, owing to the cost efficiency of electrospinning and ongoing development of new commercial applications ,2. Due tPoly(acrylonitrile) (PAN) is a commonly used precursor for the production of CNFs via electrospinning followed by oxidative stabilization and carbonization ,22. OxidDue to its good electrochemical stability and affinity to electrolyte solutions, poly(vinylidene fluoride) (PVDF) has recently received significant attention for its potential as a precursor for CNFs and their potential application in lithium-ion batteries ,60,61,62Although the chemical processes involved in the stabilization and carbonization of pure PAN have been studied for over 60 years, practically nothing is known about the mechanisms in blend fibers and the interaction of two or more polymers in them. The application of such blend fibers is extremely promising and an obvious upgrade for many applications of nanofibers. A major reason why the advantages of blend fibers are rarely utilized in functional applications is that the basic processes are less well understood.In this work, we report on the preparation, carbonization and resulting properties of PAN/PVDF blend nanofibers produced by wire-based electrospinning of binary polymer solutions in DMSO. This blend is of high interest since opposite to blending PAN with gelatin or other biopolymers, which degrade below typical stabilization temperatures , it offeNanofibers were produced by the wire-based electrospinning machine Nanospider Lab  on a polypropylene nonwoven collector substrate. The following spinning parameters were used for the production of nanofibers: high voltage of 60 kV, resulting in a typical current of 0.03 mA; nozzle diameter of 0.9 mm; carriage speed of 100 mm/s; distance from electrode to collector 240 mm; distance from ground electrode to collector 50 mm; process time 20 min; and temperature 24 °C and relative humidity 32% in the spinning chamber.Three different polymer solutions of PAN  and PVDF  in DMSO  were used for electrospinning: (a) a relatively low polymer concentration of 12 wt% PAN and 3 wt% PVDF (referred to as PAN 4:1 PVDF); (b) a relatively high polymer concentration of 15 wt% PAN and 5 wt% PVDF (referred to as PAN 3:1 PVDF); and (c) a reference of 16 wt% PAN (referred to as PAN), which is a commonly used concentration for electrospinning PAN from DMSO. These concentrations are the result of preliminary trials and have been selected according to their apparent spinnability. The blend ratios were chosen based on prior experiments, showing that PAN:PVDF blends of 1:1 or 2:1 were not or hardly spinnable, while higher PAN contents resulted in nanofiber mats quite similar to pure PAN.The nanofibers were stabilized in a muffle furnace B150 , approaching a typical stabilization temperature of 280 °C at a heating rate of 1 °C/min in air, followed by isothermal treatment for 1 h. This procedure was found well suited for oxidative stabilization of pure PAN nanofibers . For subMorphological investigations of the nanofibers were performed with a confocal laser-scanning microscope (CLSM) VK-8710  and by a helium-ion microscope (HIM) Orion Plus . HIM images were taken at an acceleration voltage of 34.8 kV and a current of 1.2 pA. For charge compensation in secondary electron detection, an electron flood gun was used during imaging.The amplitude-sensitive eddy current method was used to measure the thickness of the nonwovens with a FISCHERSCOPE MMS PC2 from Helmut Fischer . The current in a coil around a ferrite core of the probe generates a high-frequency magnetic field, which induces eddy currents in the substrate. Their strength depends on the distance between the probe and the substrate, i.e., the thickness.Thermo-gravimetric analysis (TGA) and differential scanning calorimetry (DSC) were carried out with a Hi-Res TGA 2950 Thermo-gravimetric Analyzer from TA Instruments  and a DSC 3 device by Mettler-Toledo , respectively. Both heating rates and atmospheres followed the aforementioned stabilization and carbonization procedure.13C MAS NMR measurements. An magic angle spinning (MAS) probe for rotors with a diameter of 4 mm was used; the spinning frequency was 7 kHz. Data acquisition was carried out at 25 °C, using single pulse excitation and 1H decoupling. A spectral width of ±250 kHz, 2048 time domain data points, a 90° pulse duration of 3.5 μs, a recycling delay of 5 s and 2048 scans were used for 13C data acquisition. The adamantane signal at 29.5 ppm was used as an external chemical shift reference. The chemical shifts reported have an error of ±0.1 ppm.A 300-MHz Apollo spectrometer by Tecmag  equipped with a wide-bore Oxford magnet was used for −1. Each spectrum was averaged over 32 scans and corrected for atmospheric noise.Fourier transform infrared spectroscopy in attenuated total reflection (ATR-FTIR) was conducted on a FT/IR-4100 spectrometer by JASCO  with a diamond ATR crystal, which results in a common penetration depth of about 1.7 µm, depending on angle and wavenumber. The spectra cover a frequency range from 4000 to 700 cmα irradiation, a Sphera electron analyzer with a resolution of 0.9 eV, and an emission angle of 20°. The probe area from which information is obtained is about 2 mm in diameter. Quantitative evaluation was based on peak integration in OriginPro2020. The atomic fraction was calculated from C 1s, O 1s, N 1s, and F 1s peak areas and their respective relative sensitivity factors published by Wagner et al. [X-ray photoelectron spectroscopy (XPS) was performed in an Omicron Multiprobe ultra high vacuum system  using monochromatic Al Kr et al. .α peaks of light elements such as carbon, oxygen, nitrogen and fluorine. Additionally, the X-ray signal was mapped to a secondary electron image of individual blend nanofibers generated by the Helios Nanolab 600. For this purpose, the nonwovens were glued to a silicon wafer via conductive carbon tape, sputtered with a 10 nm gold layer and mounted on the sample stage.Investigations on the chemical composition of the treated and untreated nanofibers were performed with energy dispersive X-ray spectroscopy (EDX) in a FEI Helios Nanolab 600 dual beam focused ion beam electron microscope . The machine is equipped with a multichannel analyzer to detect the characteristic X-ray spectrum emitted by the sample upon irradiation with high-energy electrons. The measurements were performed on an area of 200 µm × 200 µm at an acceleration voltage of 20 kV, which is sufficient to pick up the KImpedance measurements were conducted with a Novocontrol broadband dielectric spectrometer . The carbonized nonwovens were cut into small discs of 20 mm diameter and placed between two gold electrodes in a Novocontrol BDS1200 sample cell. The mounting stage of the cell was removed and the electrodes were connected to BNC cables through custom-built electrical connections. The BNC cables were connected to the analyzer through a Novocontrol ZG4 test interface (two-wire mode). The temperature was controlled by an Espec SH-242 climate chamber. A 100 Ω reference sample (Novocontrol) was used to test the connections.From a broad span of spinnable PAN/PVDF polymer solutions, two concentration ratios between PAN and PVDF were chosen, 3:1 and 4:1, respectively. Since the carbonization of PAN fibers has been intensively investigated since the 1950s and is very well understood today, PAN is considered the reference polymer in this study. The aim was to investigate the chemical and morphological influences of blending with a second polymer (PVDF). Pure PAN nanofibers spun from a 16 wt% solution served as a reference. While there are many different methods with regard to process gases, heating rates and maximum temperatures, we opted for a well-established process route.First, the macroscopic appearance of the nanofibers deposited as nonwovens was examined. The HIM images in Although the CLSM images in The HIM images show that all as-spun nanofibers are relatively straight, have very few membranous regions and show typical beads, which are often observed in electrospinning with DMSO or other slowly evaporating solvents ,70. FiguA comparison of the CLSM and HIM images shows that highly magnified images, which are common in this field to examine the fiber topology and diameter distribution, lack essential information about the homogeneity on a more macroscopic scale. Additional high-resolution images take time and effort and are often rejected or at least not demanded by reviewers. Therefore, this is a problem that is often not sufficiently addressed in the literature or is dismissed with the undocumented assurance of representativeness of micrographs, bringing along reproducibility issues . The comDespite an increase in the fiber diameter, a reduction in the thickness of the nonwoven fabric is observed, as shown in The polymer concentration in the spinning-solution is not necessarily representative of the polymer concentration in the resulting blend nanofiber nonwoven. In fact, as shown in Since the mass losses during carbonization of pure stabilized PAN of 16.5% and pure PVDF of 66% are now known, the contribution of the two polymers to the resulting total residual mass can be calculated, as shown in Since TGA measurement curves as well as the quality of thermal treatment also depend on the sample geometry, which differs from the samples treated in the furnace, it is important to note that this can only be considered an approximation. Furthermore, these calculations do not take into account the geometry of the fibers or nonwovens, which could possibly have an influence on TGA measurements. How accurate this calculation method is should be determined by comparison with other quantitative measurement methods in further studies.The aromatization of PAN is an exothermic process , which cc(t) is the actual crystallinity of the sample, ΔHm (≈41 J/g) is the heat of melting, determined by integration of the crystallite melting peak and ΔH100% (≈105 J/g) is the heat of melting for a theoretical 100% crystalline PVDF sample [DSC measurements have shown a crystallite melting peak temperature of 171 °C and a crystallinity of about 39% for pure PVDF powder, calculated as follows:F sample . The insF sample .The thermal decomposition of PVDF can be seen in the DSC curve as a steep exothermic peak towards the end of the carbonization phase. As the inset for high temperatures in 13C NMR spectra of as-spun and carbonized nanofibers. These spectra are not fully relaxed and intensity ratios are not quantitative. The main peaks in the spectra of the as-spun samples, as shown in 13C NMR signals are expected. The one of the CH2 group (δ) is found as an additional peak at about 42 ppm, whereas the one of the CF2 group (ε) overlaps with the PAN resonance at 120 ppm and can be recognized as a broadening of the upper part of this signal. These results confirm that PVDF is incorporated into the as-spun nanofibers as expected.13C peaks between 100 and 160 ppm. All of these cyclic structures contain nitrogen atoms. Such highly cyclized structures, which contain nitrogen atoms, are probably present in the carbonized nanofibers. Note the absence of 13C signals in the aliphatic range between 0 and 50 ppm. This is a strong indication that PVDF is no longer present as a linear polymer after carbonization, at least not in larger quantities. The reason for that is probably that PVDF decomposes during thermal treatment. Due to the poor signal-to-noise ratio, potential differences between the three samples cannot be distinguished.As shown in −1 and a carbonyl (C=O) stretching peak at 1728 cm−1, which is an indicator of both residual DMSO [2 at 2935 and 1454 cm−1, respectively, can be seen [−1 represent the symmetrical stretching of the CF2 group, the asymmetrical stretching of C–C–C and the C–F stretching, respectively, that are commonly attributed to PVDF [−1 and the CH2 peak at 2935 cm−1 disappear completely and new aromatic C=C, C=N imine and C–N heterocycle peaks at 1585, 1362 and 808 cm−1, respectively, emerge, clearly indicating the formation of a nitrogen containing ladder-structure [−1 where the C–F stretching vibration is expected to show a strong, broad signal , diffuses to the fiber surface . It then decomposes there during the incipient carbonization (as shown by TGA and NMR) and then partially remains in the fiber surface (as shown by the XPS and EDX). The remaining fluorine content of the resulting CNF is also reflected in a significant increase in conductivity with increasing PVDF concentration in the initial spinning-solution, an effect, which is stronger for the 3:1 blend than for the 4:1 blend, making the former more suitable for applications, in which conductivity is relevant. Further investigations will show at which carbonization temperatures the fluorine content will be fully decomposed. In addition, investigations applying previous chemical stabilization of the PVDF component can be used to investigate whether the overall carbon yield is increased in this case, taking into account that, while studies of other groups show that chemical stabilization is not necessary, it may still be useful to optimize the carbonization result.The investigations contribute to a better understanding of the molecular processes during the thermal treatment of blend nanofibers and exemplify possibilities and challenges in material analysis with regard to these processes. The enrichment of CNF with desired constituents by spinning binary polymer solutions could represent an efficient alternative to the subsequent doping of nanofibers by post-treatment, thus enhancing their functionality in electronic devices and other applications.


Drosophila hyperplastic disc (hyd) gene is the ortholog of mammalian tumor suppressor EDD, which is implicated in a wide variety of cellular processes, and its regulation is impaired in various tumors. It is a member of the highly conserved HECT family of E3 ubiquitin ligases, which directly attach ubiquitin to targeted substrates. In early works, it was shown that Drosophila Hyd may be a tumor suppressor because it is involved in the control of imaginal-disc cell proliferation and growth. In this study, we demonstrated that Hyd is also important for the regulation of female germ cell proliferation and that its depletion leads to additional germline cell mitoses. Furthermore, we revealed a previously unknown Hyd function associated with the maintenance of germ cells’ viability. A reduction in hyd expression by either mutations or RNA interference resulted in large-scale germ cell death at different stages of oogenesis. Thus, the analysis of phenotypes arising from the hyd deficiency points to Hyd’s role in the regulation of germline metabolic processes during oogenesis.The  Drosophila melanogaster hyperplastic disc gene (hyd) has been classified as a tumor suppressor gene owing to the overgrowth phenotype of imaginal disc cells in mutant backgrounds   have been found in a number of common human cancers. The hyd gene, just as EDD, encodes a large protein (approximately 300 kDa) that is a member of the highly conserved family of E3 ubiquitin ligases containing the HECT domain, which mediates specific recognition of substrate proteins and their targeting by ubiquitin (The kgrounds . It is aisplay’) . Impairebiquitin . Ubiquitbiquitin . Throughbiquitin .Drosophila development. Null-alleles of hyd are lethal at the larval stage, and temperature-sensitive alleles induce imaginal-disc hyperplasia and adult gonadal defects leading to sterility (Hedgehog (Hh) and Decapentaplegic (Dpp) in the eye and wing discs. Loss of hyd function induces ectopic expression of both genes, resulting in disc cell overgrowth . The anterior region of each ovariole is the germarium, which includes stem cells and early germline cells (GCs) going through a series of mitotic divisions. In the posterior of the germarium, 16 daughter GCs are surrounded by a monolayer of somatic follicle cells creating an ECh. After leaving the germarium, the ECh moves along the ovariole, gradually developing into a mature oocyte. According to the size and morphology of the ECh, oogenesis can be roughly divided into 14 stages . We believe that the function of Hyd in oogenesis is not related to the regulation of cell death directly. Being an E3 ubiquitin ligase, it is involved in ubiquitination of the protein substrates responsible for the metabolism and biosynthetic activity of GCs. A dysfunction of this mechanism probably causes cell death due to a deficit of resources.Here, we present a study of the Hyd function in Drosophila stocks were raised at 25°C on standard cornmeal medium. We used Bloomington stocks: ri–1 hyd15 e1/TM3, Sb1kni (3718) and 1 w1118; PBac{3HPyy + C017/TM3, Sb1 Ser1}hyd (16256) as a source of mutant alleles, w1118; P{w + mC = PTT-GA}Pabp2 GFP protein trap strain was used as a germline nuclei marker: (48-1) kindly provided by A. Debec .All hyd-RNAi -y 1sc∗v1;P{TRiP.HMS00343}attP2 (32352); osk-GAL4 - w1118; P{osk-GAL4:VP16}F/TM3, Sb1 (44242); nos-GAL4 - w1118; P{w+mC = GAL4:VP16-nos.UTR}CG6325MVD1 (4937); 7023-GAL4 – y1 w∗; P{GawB}109-30/CyO GAL4 (7023); 7024-GAL4 – y1 w∗; P{w + mW. hs = GawB}109-39/TM3,Sb1 (7024); 36287-GAL4 36287 w∗; P{w+mW.hs = GawB}GR1.We used the following strains for RNA interference: hyd mRNA were assigned using method of qPCR. Total RNA preparation, reverse transcription (RT) and qPCR analyses were performed using Trizol (Invitrogen), Superscript III (Invitrogen), and SYBR green kits (Syntol) following the manufacturer’s recommendations. The following primers were used: hyd-specific RT-HYD-Fw-5′-ACGCCAGGATTTGGTTTA CTT and RT-HYD-Rev-5′-TTCGCAGTCGGTAGATGGGA, RpL32-specific RPL32-F-5′-TAAGCTGTCGCACAAATGG and RPL32-R-5′-AGGAACTTCTTGAATCCGGTG as a reference gene  could be associated with a deficiency in the hyd gene product.To determine how this hetero-allelic combination affects the level of hydC017/hyd15 females were found to be sterile and laid only a single egg, which did not develop. The gonads in such females mainly contained reduced ovarioles with a small number of EChs or without them at all  or contained stand-alone germline cysts  in larval ovaries and germarium and differentiated GCs in mid-oogenesis.Immunostaining of a GC marker, the Vasa protein, showed that most of the ne cysts . Mutant hydC017/hyd15 ovaries also contained multi-nuclear EChs  cells. UAS hyd-RNAi strains and Oregon R were used as control.The association of cell death with a decrease in the hyd-RNAi in follicular cells did not lead to any phenotypic changes in the ovaries, oogenesis abnormalities, or a decrease in fertility. Only a combination of UAS-hyd-RNAi with a germline-specific driver, nanos-GAL4 or oskar-GAL4, resulted in massive cell death and ovarian atrophy, which were similar to the phenotypic manifestation of the hyd mutations under study.Implementation of Nanos-GAL4 is expressed in primordial GCs starting from embryogenesis. Accordingly, in nanos-GAL4/UAS-hyd-RNAi females, GC death occurred before the adult stage. In adult females, almost all the germline turned out to be atrophied, and the formed ovaries consisted only of somatic cells .The ogenesis . Before me stage . EChs, gDrosophila oogenesis and allows to save energy and resources eliminating defective or unnecessary EChs. Dying EChs are easily identified by abnormal condensation and subsequent fragmentation of chromatin, which are features of apoptotic cell death  that terminate to divide and specialize in two directions: several cells interact with a newly formed niche and become germline stem cells, whereas the remaining cells begin to differentiate and become cystoblasts  (mcm10 (its product acts in DNA replication)    , mcm10 (ication) , γ-tubulaterial)  and vasaermline) . The samermline) . Nonethed to die . On the d to die , in contoskar-GAL4/UAS-hyd-RNAi ovaries through middle oogenesis. EChs containing Hyd-deficient GCs did not progress through the oogenesis mid-stage checkpoint and degraded completely in early vitellogenesis. It is known that this checkpoint is activated in response to adverse stimuli or physiological and developmental disorders  via ubiquitination for proteasomal degradation of its target PP2Ac (TORC1-associated ɑ4 phosphoprotein). Increased EDD expression in human breast cancer cells in vitro promotes TORC1 signaling, which activates the synthesis of an anti-apoptotic protein promoting drug resistance. On the contrary, a knockdown of EDD arrests cancer cell proliferation decreases their viability and increases apoptosis  and with many factors necessary for the synthesis and modification of proteins and RNA and for Golgi and endoplasmic-reticulum functioning . NonetheSome studies on the somatic tissue in imaginal discs have shown that Hyd is a negative regulator of Hh signaling. Hyd-deficient flies display eye disc overgrowth due to increased Hh activity . In oogehyd mutants, is also observed during dysregulation of the timely degradation of mitotic cyclins: cyclins A, B and E , which is an E3 ubiquitin ligase. In these cases, cyclin E accumulation, entry into the S phase and doubling of the cell number are observed (effete gene (encoding E2 ubiquitin-conjugating enzyme UbcD1) (encore (coding for a protein interacting with the proteasome and Cyclin E) (slmb (coding for an E3 ubiquitin ligase)  , encore yclin E)  or slmb  ligase) .Recent research has shown that the stabilization of CycA expression during mitotic cystoblast divisions is controlled by Bam, which acts together with deubiquitinase Otu . EarlierIt is currently difficult to determine what other factors may be associated with Hyd in this context. The list of potential interactors contains several proteins responsible for cell cycle control . On the Drosophila Hyd in oogenesis and germ cell development. We demonstrated that Hyd is essential for timely regulation of germline cyst mitosis and for the maintenance of germ cell viability. Because Hyd is an E3 ubiquitin ligase, it contributes to cellular processes through ubiquitination of its substrate proteins. In the future, it is necessary to identify these proteins and determine their germline-specific functions in order to understand which signaling pathways and mechanisms mediate Hyd’s involvement in oogenesis control.In this article, we describe a previously unknown function of The original contributions presented in the study are included in the article/ND, YG, and SF designed and conducted the experiments, analyzed the data, wrote and prepared the manuscript. EUB provided obtaining and analysis of electron microscopic data. EMB analyzed the data. All authors contributed to the article and approved the submitted version.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.