Inhibitory synapses can control a neuron's firing rate and also control supralinear dendritic integration. It is not known how inhibitory synapses can learn to perform these functions using only signals available locally at the synaptic site. We study an inhibitory plasticity rule based on the Bienenstock-Cooper-Munro theory in multicompartment models of striatal projection neurons, and show that it can perform these two functions. The rule uses local voltage-gated calcium concentration in the dendrites to regulate inhibitory synaptic strength. We show that, for rate-coded inputs, the rule can achieve precise control of neuronal firing rate after changes in excitatory input rate or excitatory synaptic strength. Additionally, for sparsely-coded inputs that activate localized synaptic clusters in a single dendrite, the rule can either allow or inhibit the evoked evoked supralinear dendritic responses, or equalize their amplitude. Finally, we demonstrate the use of learning to inhibit supralinear dendritic integration for solving the nonlinear feature binding problem (NFBP), in tandem with a simple excitatory plasticity rule. We conclude by discussing why the collateral inhibitory synapses between striatal projection neurons could contribute to solving the NFBP with this plasticity rule. ### Competing Interest Statement The authors have declared no competing interest.

This study investigates the computational potential of single striatal projection neurons (SPNs), emphasizing dendritic nonlinearities and their crucial role in solving complex integration problems. Utilizing a biophysically detailed multicompartmental model of an SPN, we introduce a calcium-based, local synaptic learning rule dependent on dendritic plateau potentials. According to what is known about excitatory corticostriatal synapses, the learning rule is governed by local calcium dynamics from NMDA and L-type calcium channels and dopaminergic reward signals. In order to devise a self-adjusting learning rule, which ensures stability for individual synaptic weights, metaplasticity is also used. We demonstrate that this rule allows single neurons with sufficiently nonlinear dendrites to solve the nonlinear feature binding problem, a task traditionally attributed to neuronal networks. We also detail an inhibitory plasticity mechanism that contributes to dendritic compartmentalization, further enhancing computational efficiency in dendrites. This in silico study highlights the computational potential of single neurons, providing deeper insights into neuronal information processing and the mechanisms by which the brain executes complex computations.

Synaptic plasticity has been shown to occur when calcium, flowing into the synapse due to incoming stimuli, surpasses a threshold level. This threshold level is modifiable through a process called metaplasticity. Some neurons, such as the striatal projection neurons, use different sources of calcium as the signal for synaptic strengthening (long-term potentiation, LTP) or weakening (long-term depression, LTD), resulting in them having two thresholds for inducing plasticity. In this study, we show opposite and complementary roles of metaplasticity in these two thresholds for inducing LTP and LTD on learning how to solve the linear and nonlinear feature binding problem (FBP and NFBP). In short, metaplasticity in one threshold (e.g. LTD) allows synaptic plasticity of the opposite type (e.g. LTP) to be properly expressed. This happens because metaplasticity in the LTD threshold protects strengthened synapses from weakening, thus allowing them to persistently increase during learning (and encode learned patterns). Similarly, metaplasticity in the LTP threhsold prevents weakened synapses from strengthening, thus allowing them to persistently decrease. Metaplasticity in both thresholds is necessary when synapses are clustered and the neuron needs to rely on supralinear dendritic integration for learning.

Plateau potentials are a critical feature of neuronal excitability, but their all-or-none behavior is not easily captured in modeling. In this study, we investigated models of plateau potentials in multi-compartment neuron models and found that including glutamate spillover provides robust all-or-none behavior. This result arises due to the prolonged duration of extrasynaptic glutamate. When glutamate spillover is not included, the all-or-none behavior is very sensitive to the steepness of the Mg2+ block. These results suggest a potentially significant role of glutamate spillover in plateau potential generation, providing a mechanism for robust all-or-none behavior across a wide range of slopes of the Mg2+ block curve. We also illustrate the importance of the all-or-none plateau potential behavior for nonlinear computation with regard to the nonlinear feature binding problem.

Plateau potentials are a critical feature of neuronal excitability, but their all-or-none behavior is not easily captured in modeling. In this study, we investigated models of plateau potentials in multi-compartment neuron models and found that including glutamate spillover provides robust all-or-none behavior. When glutamate spillover is not included, the all-or-none behavior is very sensitive to the steepness of the Mg block. These results suggest a potentially significant role of glutamate spillover in plateau potential generation, providing a mechanism for robust all-or-none behavior across a wide range of slopes of the Mg block curve. We also illustrate the importance of the all-or-none plateau potential behavior for nonlinear computation with regard to the nonlinear feature binding problem.

Adenylyl cyclases (ACs) play a key role in many signaling cascades. ACs catalyze the production of cyclic AMP from ATP and this function is stimulated or inhibited by the binding of their cognate stimulatory or inhibitory Gα subunits, respectively. Here we used simulation tools to uncover the molecular and subcellular mechanisms of AC function, with a focus on the AC5 isoform, extensively studied experimentally. First, quantum mechanical/molecular mechanical free energy simulations were used to investigate the enzymatic reaction and its changes upon point mutations. Next, molecular dynamics simulations were employed to assess the catalytic state in the presence or absence of Gα subunits. This led to the identification of an inactive state of the enzyme that is present whenever an inhibitory Gα is associated, independent of the presence of a stimulatory Gα. In addition, the use of coevolution‐guided multiscale simulations revealed that the binding of Gα subunits reshapes the free‐energy landscape of the AC5 enzyme by following the classical population‐shift paradigm. Finally, Brownian dynamics simulations provided forward rate constants for the binding of Gα subunits to AC5, consistent with the ability of the protein to perform coincidence detection effectively. Our calculations also pointed to strong similarities between AC5 and other AC isoforms, including AC1 and AC6. Findings from the molecular simulations were used along with experimental data as constraints for systems biology modeling of a specific AC5‐triggered neuronal cascade to investigate how the dynamics of downstream signaling depend on initial receptor activation.

Neuroscience incorporates knowledge from a range of scales, from single molecules to brain wide neural networks. Modeling is a valuable tool in understanding processes at a single scale or the interactions between two adjacent scales and researchers use a variety of different software tools in the model building and analysis process. Here we focus on the scale of biochemical pathways, which is one of the main objects of study in systems biology. While systems biology is among the more standardized fields, conversion between different model formats and interoperability between various tools is still somewhat problematic. To offer our take on tackling these shortcomings and by keeping in mind the FAIR (findability, accessibility, interoperability, reusability) data principles, we have developed a workflow for building and analyzing biochemical pathway models, using pre-existing tools that could be utilized for the storage and refinement of models in all phases of development. We have chosen the SBtab format which allows the storage of biochemical models and associated data in a single file and provides a human readable set of syntax rules. Next, we implemented custom-made MATLAB® scripts to perform parameter estimation and global sensitivity analysis used in model refinement. Additionally, we have developed a web-based application for biochemical models that allows simulations with either a network free solver or stochastic solvers and incorporating geometry. Finally, we illustrate convertibility and use of a biochemical model in a biophysically detailed single neuron model by running multiscale simulations in NEURON. Using this workflow, we can simulate the same model in three different simulators, with a smooth conversion between the different model formats, enhancing the characterization of different aspects of the model.

Striatal projection neurons (SPNs) in the basal ganglia gradually increase their firing rate during movement initiation. Arkypallidal neurons in globus pallidus briefly increase their firing rate upon a Stop signal, which cues movement cancellation. This increase potentially leads to the suppression of movement-related activity in striatum by inhibiting SPNs. However, this brief inhibition from arkypallidal neurons may be too short to completely prevent the gradual firing rate increase in SPNs. Here, we investigated the impact of the brief inhibition on the gradual increase in a multi-compartmental model of a SPN. We reproduced the movement-related firing pattern in the SPN model neuron by brief clustered excitation added to a baseline, subthreshold excitation. This brief clustered excitation evoked a dendritic plateau potential leading to a long-lasting depolarization at the soma, which enhanced the somatic excitability and evoked spikes upon the baseline excitation that was formerly subthreshold. A brief inhibition, representing arkypallidal stop responses, applied on the dendritic site where the clustered excitation was present, suppressed the somatic depolarization and attenuated the movement-related activity similar to the firing pattern observed in rats for successful action suppression. We conclude that arkypallidal Stop responses can suppress movement-related activity in the striatum by suppressing the dendritic plateau potentials.

Long-term potentiation and depression of synaptic activity in response to stimuli is a key factor in reinforcement learning. Strengthening of the corticostriatal synapses depends on the second messenger cAMP, whose synthesis is catalysed by the enzyme adenylyl cyclase 5 (AC5), which is itself regulated by the stimulatory Gαolf and inhibitory Gαi proteins. AC isoforms have been suggested to act as coincidence detectors, promoting cellular responses only when convergent regulatory signals occur close in time. However, the mechanism for this is currently unclear, and seems to lie in their diverse regulation patterns. Despite attempts to isolate the ternary complex, it is not known if Gαolf and Gαi can bind to AC5 simultaneously, nor what activity the complex would have. Using protein structure-based molecular dynamics simulations, we show that this complex is stable and inactive. These simulations, along with Brownian dynamics simulations to estimate protein association rates constants, constrain a kinetic model that shows that the presence of this ternary inactive complex is crucial for AC5's ability to detect coincident signals, producing a synergistic increase in cAMP. These results reveal some of the prerequisites for corticostriatal synaptic plasticity, and explain recent experimental data on cAMP concentrations following receptor activation. Moreover, they provide insights into the regulatory mechanisms that control signal processing by different AC isoforms.

A b s t r a c t: In this article we propose a model for the spread of two types of information in networks. The model is a natural generalization of the epidemic susceptible-infective-susceptible(SIS) model. The two information types have different attractiveness, which affects the nodes' decision on which information type to adopt when both arrive at a node in the same time step. At difference with results from other authors, the model shows simultaneous existence of the two information types in the stable state. We give approximations for the average number of nodes informed with each information type at the end of the spreading process when nodes have high degree.

Many contagions spread over various types of communication networks and their spreading dynamics have been extensively studied in the literature. Here we propose a general model for the concurrent spread of an arbitrary number of contagions in complex networks. The model is stochastic and runs in discrete time, and includes two widely used mechanisms by which a node can change its state. The first, termed the spontaneous state change mechanism, describes spontaneous transition to another state, while the second, termed the contact-induced state change mechanism, describes acquiring other contagions due to contact with the neighbors. We consider reactive discrete-time spreading processes of multiple concurrent contagions where time steps are of finite size without neglecting the possibility of multiple infecting events in a single time step. An essential element for making the model numerically tractable is the use of an approximation for the probability that a node transits to a specific state given any set of neighboring states. Different transmission probabilities may be present between each pair of states. We also derive corresponding continuous-time equations that are simple and intuitive. The model includes many well-known epidemic and rumor spreading models as a special case and it naturally captures spreading processes in multiplex networks.

In this paper, a novel model for opinion dissemination over network is suggested so that market penetration activities can be described. The model assumes the existence of two different products, one of which is always considered first and the supporters' (or users') opinions are allowed to propagate among individuals of the population. This is to describe the dynamics of market penetration of a particular product, by gaining the market share of its competitor or attracting new users, even the competitor is with higher reputation. From the simulation results, it is found that the product with lower preference can still obtain a non-zero fraction of market share in many cases, when a small-world network is considered. Some level of clustering in the network facilitates the adoption of the product, while increasing randomness undermines its existence. The simulations also show the importance of the users' remembrance of a product and the communication effectiveness in related to market penetration.

We propose a metric for vulnerability of labeled graphs that has the following two properties: (1) when the labeled graph is considered as an unlabeled one, the metric reduces to the corresponding metric for an unlabeled graph; and (2) the metric has the same value for differently labeled fully connected graphs, reflecting the notion that any arbitrarily labeled fully connected topology is equally vulnerable as any other. A vulnerability analysis of two real-world networks, the power grid of the European Union, and an autonomous system network, has been performed. The networks have been treated as graphs with node labels. The analysis consists of calculating characteristic path lengths between labels of nodes and determining largest connected cluster size under two node and edge attack strategies. Results obtained are more informative of the networks’ vulnerability compared to the case when the networks are modeled with unlabeled graphs.

An alternate model for rumor spreading over networks is suggested, in which two rumors (termed rumor 1 and rumor 2) with different probabilities of acceptance may propagate among nodes. The propagation is not symmetric in the sense that when deciding which rumor to adopt, nodes always consider rumor 1 first. The model is a natural generalization of the well-known epidemic SIS (susceptible-infective-susceptible) model and reduces to it when some of the parameters of this model are zero. We find that preferred rumor 1 is dominant in the network when the degree of nodes is high enough and/or when the network contains large clustered groups of nodes, expelling rumor 2. However, numerical simulations on synthetic networks show that it is possible for rumor 2 to occupy a nonzero fraction of the nodes in many cases as well. Specifically, in the Watts-Strogatz small-world model a moderate level of clustering supports its adoption, while increasing randomness reduces it. For Erdos-Renyi networks, a low average degree allows the coexistence of the two types of rumors. In Barabasi-Albert networks generated with a low $m$, where $m$ is the number of links when a new node is added, it is also possible for rumor 2 to spread over the network.

A novel model for information (rumor) spreading over networks is suggested, in which two difierent kinds of information, one of which is always considered flrst, may propagate among the nodes. The model is a natural generalization of the well-known epidemic SIS (susceptible-infective-susceptible) model, and reduces to it when some of the parameters of this new model are zero. We flnd that the preferred information type 1 is heavily promoted when the degree of nodes is high enough and/or when the network contains large clustered groups of nodes, expelling information type 2. In particular, the information type 1 is dominant when the average degree in Erdos-Renyi graphs is increased, the cliquish neighborhoods in Watts-Strogatz small-world networks are increased, and the number of links m, when a new node is added, in Barabasi-Albert networks is increased. On the other hand, simulations show that it is possible for information type 2 to occupy a nonzero fraction of the nodes in many cases as well. Speciflcally, in the Watts-Strogatz small-world model some level of clustering facilitates its adoption, while increasing randomness undermines it. For Erdos-Renyi networks, a low average degree allows the coexistence of the two types of information. In Barabasi-Albert networks generated with a small m, it is also possible for information type 2 to spread over the network.