The success of human civilization is rooted in our ability to cooperate by communicating and making joint plans. We study how artificial agents may use communication to better cooperate in Diplomacy, a long-standing AI challenge. We propose negotiation algorithms allowing agents to agree on contracts regarding joint plans, and show they outperform agents lacking this ability. For humans, misleading others about our intentions forms a barrier to cooperation. Diplomacy requires reasoning about our opponents’ future plans, enabling us to study broken commitments between agents and the conditions for honest cooperation. We find that artificial agents face a similar problem as humans: communities of communicating agents are susceptible to peers who deviate from agreements. To defend against this, we show that the inclination to sanction peers who break contracts dramatically reduces the advantage of such deviators. Hence, sanctioning helps foster mostly truthful communication, despite conditions that initially favor deviations from agreements. Artificial Intelligence has achieved success in a variety of single-player or competitive two-player games with no communication between players. Here, the authors propose an approach where Artificial Intelligence agents have ability to negotiate and form agreements, playing the board game Diplomacy. Systems based on artificial intelligence (AI) control a growing part of our lives, from personal assistants to high-stake decisions such as authorizing loans or automated job market screening4. Cooperation and negotiation are central to AI11, and AI systems already affect human trade and negotiation through algorithmic trading and bidding16. It is thus imperative that we endow our AI systems with the tools to coordinate and negotiate with others18.Coordination, cooperation and negotiation play a key role in our everyday lives, from small-scale problems such as safely driving on roads and scheduling meetings to large-scale efforts such as international trade or mediating peace. A key driver to the success of humans as a species is our ability to cooperate with others21 led to successes in Chess22, Go23, Poker24, control25, and video games27. However, the majority of such work deals with two-player games that are fully competitive (zero-sum), which are mathematically easier to analyze28, but cannot capture alliance formation and negotiation. Similarly, work on games where agent goals are fully aligned30, or two teams of agents engaged in a competition32, lacks the need to negotiate. In contrast, many real-life domains require negotiation as the goals of participants only partially align. These domains exhibit tensions between cooperation and competition35, making them harder to tackle using AI agents37. Communication has a key role in such settings as it enables us to share beliefs, goals and intents with others, allowing us to negotiate, form alliances and find mutually beneficial agreements10.Game playing has been a focus area of AI since its inception. Progress on search, reinforcement learning, and game theory38 is a prominent 7-player board game that focuses on communication, cooperation and negotiation. An introduction to the rules of Diplomacy is given in Supplementary Note 21 to 1064 legal actions per turn, and an immense game tree size of 1090039; for comparison, Chess has fewer than 100 legal actions per turn, with a game tree size of 10123. The heart of Diplomacy is the negotiation phase occurring before entering moves, where players communicate trying to agree on the moves they are about to execute.Diplomacy41. The standard version is Press Diplomacy, which includes a negotiation phase prior to each move phase. In human games this takes place through conversations in natural language: players may converse privately by stepping into another room, or through a private chat channel when playing online. For AI, researchers have proposed computer-friendly negotiation protocols42, sometimes called Restricted-Press.These properties make Diplomacy a key AI challenge domain for negotiation and alliance formation in a large-scale realistic mixed-motive setting. AI approaches for Diplomacy have been researched since the 1980sA much simpler version is No-Press Diplomacy, where direct communication between players is not allowed, eliminating the negotiation phase. We contrast No-Press and Press Diplomacy in Fig. 46, and falling far behind human performance (both with and without communication). Paquette et al. achieved a breakthrough in game performance47, training a neural network called DipNet to imitate human behavior based on a dataset of human games. While DipNet has defeated previous state-of-the-art agents by a wide margin, it only handles No-Press Diplomacy, employing no communication or negotiation. Recent work improved the performance of such agents using deep reinforcement learning39 or deep regret matching49, but still without communication or negotiation. Our Contribution: We leverage Diplomacy as an abstract analog to real-world negotiation, providing methods for AI agents to negotiate and coordinate their moves in complex environments. Using Diplomacy we also investigate the conditions that promote trustworthy communication and teamwork between agents, offering insight into potential risks that emerge from having complex agents that may misrepresent intentions or mislead others regarding their future plans.Many AI approaches for Diplomacy were proposed through the years, mostly relying on hand-crafted protocols and rule-based systems39, and augment them to play Restricted-Press Diplomacy by endowing them with a communication protocol for negotiating a joint plan of action, formalized in terms of binding contracts. Our algorithms agree on contracts by simulating what might occur under possible agreements, and allow agents to win up to 2.5 times more often than the unaugmented baseline agents that cannot communicate with others. Human cooperation is impeded by the potential impact of breaking agreements or misleading others about future plans51. We use Diplomacy as a sandbox to study how the ability to break past commitments erodes trust and cooperation, focusing on ways to mitigate this problem and identifying the conditions for honest cooperation. We find that artificial agents face a similar problem as humans regarding breaches of trust: communities of communicating agents are susceptible to peers that may deviate from agreements. When agreements are non-binding, an agent may agree on one course of action in a turn but choose an action violating this agreement in the next turn. We refer to such agents as deviators, and show that even deviators that select their actions using simple algorithms win almost three times as often as peers that never break their contracts. To defend against this, we endow agents with the inclination to retaliate when agreements are violated, and find that this sanctioning behavior dramatically reduces the advantage of deviators. When the majority of the agents sanction peers that break agreements, simple deviators win less frequently than agents that always abide by their contracts.We consider No-Press Diplomacy agents trained to imitate human gameplay and improved using reinforcement learningFinally, we consider how a deviator may optimize its behavior when playing against a population of agents that sanction peers that break agreements, and find that the deviator is best-off adapting its behavior to very rarely break its agreements. Such sanctioning behavior thus helps foster mostly-truthful communication among AI agents, despite conditions that initially favor deviations from agreements. However, sanctioning is not an ironclad defense: the optimized deviator does gain a slight advantage over the sanctioning agents, and sanctioning is costly when peers break agreements, so the population of sanctioning agents is not completely stable under learning.We view our results as a step towards evolving flexible communication mechanisms in artificial agents, and enabling agents to mix and adapt their strategies to their environment and peers. Our work offers two high-level insights. Firstly, algorithms that reason about the intents of others and employ game-theoretic solutions allow communicating agents to outperform peers through better coordination, even under simple interaction protocols. Secondly, the ability of participants to break from prior agreements is a barrier hindering cooperation between AI agents; however, even in complex environments, simple principles such as negatively responding to the breach of agreements help promote truthful communication and cooperation.39, discussed in the section “The sampled best responses procedure”. This method constructs neural networks capturing a policy which maps the board state to the game action to be taken, and a value network which predicts the win probabilities of the agents. We provide these agents with a protocol for negotiating bilateral agreements regarding the actions they would take.Our proposed method takes non-communicating agents trained for No-Press Diplomacy, and augments them with mechanisms for negotiating a joint plan of action with peers. To obtain the initial non-communicating agents we use existing reinforcement learning agentspi, pj who must act in a state s, we denote by Ai(s), Aj(s) the respective sets of actions the agents may take. A potential contract D is a pair D =  where Ri ⊆ Ai is the restricted subset of actions each side may take under the contract; an action a ∈ Ai⧹Ri is one that violates the contract D. One type of contract D =  is where Ri consists of a single action: Ri = {ai} where ai ∈ Ai(s), meaning that agent pi commits to taking the action ai next turn. Two contracts D1 = D2. Figure We first consider binding agreements, where agents who agree on a joint plan cannot deviate from it later. We view a contract as a restriction over the actions each of the agents may take in the future. For simplicity we focus only on contracts relating to the upcoming timestep. Given two agents entclass1pt{miniman agents P = {p1,…,pn} about to take simultaneous actions. We consider two general protocols for reaching pairwise agreements regarding future actions. The Mutual Proposal protocol places restrictions on the actions both sides may take. The Propose-Choose protocol enables both sides to agree on each taking a specific move.A protocol is a set of negotiation actions through which agents may communicate and agree on contracts. We consider a set of pi, pj ∈ P has only a single possible contract between them, depending on the state; we call the specification of this the contract type. Each agent pi ∈ P may propose, to each of the remaining agents, to enter into the contract specified by the contract type. We denote the proposal of agent pi to pj as Di→j: if pi does not propose to enter into a contract with pj, this is denoted as pi violates the peace with agent pj if one of the pi’s units attempts to move into a province occupied by pj or enter or hold a supply center owned by pj, or to assist another unit to do so. The Peace Contract D =  between pi and pj is defined by Ri and Rj containing only the actions that do not violate the peace between pi and pj.Under this protocol every pair of agents pi proposes to pj as Di→j. We say a contract D involves agent pi if D is either a contract D = Di→j that pi proposed to another agent pj or if D is a contract D = Dj→i that some other agent pj proposed to pi. In the choose phase, each agent pi may choose only one contract D that involves them out of all the contracts on the table. Denote the contract chosen by pi as pi and pj choose Di→j or both choose Dj→i). In our experiments we enhance the protocol slightly, allowing each player pi in the Choose phase to either only choose a contract Di→j or Dj→i for some pj, or to optionally also indicate that they are willing to accept either of Di→j, Dj→i; when both pi, pj indicate that they are willing to accept both Di→j, Dj→i but rank these two contracts in a different order, we select one of the two contracts randomly. We use the Propose-Choose protocol with contracts that completely specify what each unit of each side would do the next turn, i.e., a contract D = . Each agent could potentially propose n − 1 contracts and could potentially receive n − 1 contracts, so an agent pi who wishes to reach an agreement with pj is competing with the other agents to get pj to choose their contract. If an agent proposes a contract that is mostly beneficial to itself, the other agent is unlikely to choose that contract. Hence, agents must reason about which contracts others are likely to accept.This protocol consists of two stages: a Propose phase where each agent may propose a single contract to each other agent, and a Choose phase where each agent selects one of the contracts involving them . We refer to contracts proposed in the first phase as contracts On The Table. We denote the contract that We summarize the negotiation algorithms, with full details in the “Methods” section. We propose a method called Restriction Simulation Sampling (RSS) for the Mutual Proposal protocol, and a method called Mutually Beneficial Deal Sampling (MBDS) for Propose-Choose. We evaluate these on Diplomacy using Peace contracts for RSS and contracts fully specifying the next turn moves for MBDS, but our methods generalize to other contract types ” section.Our methods identify mutually beneficial deals by simulating how the game might unfold under various contracts. We use the Nash Bargaining Solution (NBS) from game theory55. Multiple approaches have been proposed for constructing policy and value functions for Diplomacy, such as imitation learning47 or regret minimization48; we use functions trained via reinforcement learning39. Following this training, these functions are held fixed throughout the experiments . Our methods simulate what might occur in the next turn by sampling from various policies, such as the unconstrained policy of the underlying No-Press Diplomacy agent, or a constrained policy that agent pi must follow after agreeing to a contract D = . This approach is illustrated in Fig. Unfortunately, directly calculating expected utilities through game simulation and finding the optimal NBS contract are computationally intractable: the game may unfold in many ways as players may take many possible actions, and there may be a vast space of potential contracts to search through. We address these difficulties through a Monte-Carlo simulation, sampling from the space of potential future states using policy and value functions, which are common machinery in the AI literature39, and select actions from it using the same algorithm (the Sampled Best Response procedure39 described in the “The sampled best responses procedure”) section. However, only the negotiators are able to communicate: negotiators interact via the RSS method in the Mutual Proposal protocol, or via MBDS in the Propose-Choose protocol . Diplomacy has seven players, so we consider k communicating agents and 7 − k non-communicators for k ∈ {1,2,…,6}. Figure We show that augmenting agents with our negotiation mechanism allows them to outperform baseline non-communicating agents lacking this mechanism. Both the negotiators and the baseline use the same policy function obtained using reinforcement learning38 . Much more importantly, in many real-life settings we can also not assume that agreements are binding—people may agree to act in a certain way, then fail to meet their commitments later on. To enable cooperation between AI agents, or between agents and humans, we must examine the potential pitfall of agents strategically deviating from agreements, and ways to remedy this problem. Diplomacy is a board game that can serve as a sandbox, i.e., an abstract analog to real world domains, enabling us to explore this topic.A key limitation of our results in the “Negotiating with binding agreements” section is the implicit assumption that agreements are binding—once an agent has agreed to a contract, they do not deviate from it. We now lift this assumption, and consider agents who may agree to a contract in one turn and deviate from it the next. This serves multiple purposes. First, a key feature of the rules of Diplomacy is that agreements made during the negotiation phase are not binding49 such as the non-communicating baseline39). We call the agents of the section “Negotiating with binding agreements” Baseline Negotiators as they operate assuming agreements are binding. We consider Deviator Agents which overcome Baseline Negotiators by deviating from agreed contracts. The “Baseline negotiatiors are defeated by deviators who break contracts” section discusses Simple Deviators and Conditional Deviators, and shows they outperform the Baseline Negotiators. The “Mitigating the deviation problem: defensive agents” section considers Defensive Agents, such as the Binary Negotiators and Sanctioning Agents, which deter Deviators from breaking contracts while retaining the advantages stemming from communication. It also describes the Learned Deviator, a Deviator optimized against a population of Defensive Agents, showing that it learns to rarely break its contracts. The full algorithms appear in the “Methods” section). Our Defensive Agents reproduce human behaviors of ceasing to trust peers who break promises or sanctioning such deviations, inspired by work on the Evolution of Cooperation57  is reached, a Baseline Negotiator pi only selects actions in Ri, which do not violate the contract. In contrast, the Simple Deviator forgets the contract, and always samples actions from the unconstrained policy (possibly selecting ones that violate the contract). Conditional Deviators are more sophisticated, and optimize their actions assuming that peers who accepted a contract would act according to it. Similarly to Simple Deviators, when no deal has been agreed, a Conditional Deviator pi selects actions from the unconstrained policy. However, when a deal D =  is agreed on with another player pj, the Conditional Deviator considers multiple actions it might take . For each such action, it performs multiple simulations of the next turn, by sampling actions for pj from the policy constrained by the contract, reflecting the assumption that pj would honor the agreement and thus refrain from taking an action a ∉ Rj. The Conditional Deviator uses its average value in the sample to estimate the expected next turn utility for each candidate action, selecting the action that maximizes this expected value. The Deviator agents are fully described in the section “Deviator Agent algorithms”.We first show the advantage that Deviator Agents obtain by breaking contracts. Simple Deviators behave as if no contract was accepted even when agreements are reached. When a contract k Deviator agents playing against 7−k Baseline Negotiators, for k ∈ {1,2,…,6}. Figure We evaluate the relative performance of Baseline Negotiators and Deviators. Figure Communication allows Baseline Negotiators to outperform non-communicators, but the section “Baseline negotiatiors are defeated by deviators who break contracts” shows they are vulnerable to Deviators who gain the upper hand by breaking contracts. We overcome this problem using Defensive Agents that respond adversely to deviations. We consider Binary Negotiators that cease to communicate with agents who have deviated, and Sanctioning Agents who modify their goal to actively attempt to lower the deviator’s value. We also consider Learned Deviators, which learn when to activate the deviator behavior mode ; these agents learn to break agreements very rarely, making the vast majority of communication in the game truthful.pi accepts a deal D =  with a counterpart agent pj, they examine the move that pj executes the next turn. If pj deviates from the agreement , they modify their behavior for the remainder of the game. We consider two responses to deviations: Binary Negotiators and Sanctioning Agents.Defensive Agents deter deviations by negatively responding to them. Defensive agents initially act identically to the Baseline Negotiators, but when a defensive agent pj who deviates from an agreement by ignoring any communication from them until the end of the game. Following a deviation, a Binary Negotiator stops making any proposals to the deviator, and declines all proposals from the deviator .Binary Negotiators respond to a peer pi responds to a deviation by a peer pj by selecting actions so as to lower the deviator pj’s reward. A Baseline Negotiator pi evaluates actions sampled from the policy π by performing simulations yielding possible future states pj’s probability of winning α ≥ 0 controls the relative importance placed on the two goals, with α = 0 reflecting no sanctioning  and α = 1 reflecting equal importance on lowering the Deviator’s utility. As α → ∞, the Sanctioning Agent focuses solely on making the deviator lose the game, without regard to its own odds of winning the game  agreed to with another player pj: the approximate immediate deviation gain ϕi(s) reflecting the immediate improvement in value pi can gain by deviating from D, and the remaining opponent strength ψi(s) reflecting the ability of the other agents to retaliate against pi should pi deviate from a contract. Given the state and the contracts agreed to by pi, both of these features can be computed using the value and policy functions.A Learned Deviator tϕ, tψ. They behave as a Baseline Negotiator, respecting all agreed contracts, until the first turn where the state s is one such that ϕ(s) > tϕ and ψ(s) < tψ. Then, they switch their behavior to that of the Conditional Deviator. Any two thresholds tϕ, tψ result in different Deviator behavior and winrate against a population of 6 Sanctioning agents. Full details regarding how the features ϕ(s), ψ(s) are computed and tuned to maximize the winrate against Sanctioning agents are given in the section “Learned Deviator”. Figure A Learned Deviator waits until a turn where the immediate gains from deviation are high enough and the ability of the other agent to retaliate is low enough, and only then deviates from an agreement. Such agents are parametrized by two thresholds Even under the strongest parameter settings for the Learned Deviator, it only has a slight advantage, winning 1.7% more often than the Sanctioning agents with the Mutual Proposal protocol (1.0% for Propose-Choose). The average turn in which the Learned Deviator indeed deviates from an agreed contract is 82 , while the average number of turns in games where deviations occurred is 101 . This indicates that the Learned Deviator adapts to break contracts quite late in the game. In the few games where the Learned Deviator does break its agreements, it often wins: 53.1% of the time for Mutual Proposal and 52.6% for Propose-Choose  of the contracts it had agreed to; by optimizing its behavior against a population of Sanctioning agents it adapts to honor the vast majority of its contracts, making the communication in these games almost entirely truthful.58, we consider agents working in teams, each trying to counter the strategies of other teams. We take agents trained using reinforcement learning and augment them with a protocol for agreeing future moves. Our agents identify mutually beneficial deals by simulating future game states under possible contracts.We consider mechanisms enabling agents to negotiate alliances and joint plans. Similarly to recent work38 is a decades-long AI challenge, and we hope that this work will inspire future research on problems of cooperation. Diplomacy makes an exceptional testbed: it has simple rules but high emergent complexity, and an immense action space43 which has recently been tackled using deep learning48 (future work could of course uncover other successful approaches). Communication adds another important layer of complexity. Game theory offers powerful tools for analyzing games such as Diplomacy and for constructing agents. In particular, solving for a subgame perfect equilibrium or applying repeated game analysis7 could be useful for building capable agents. However, the large action space in Diplomacy results in an incredibly large game tree size, which impedes game theoretic analysis (see Supplementary Note 52), and address computational barriers using a Monte-Carlo simulation of potential future game trajectories.In terms of broader impact, Diplomacy51. Similarly for AI agents in Diplomacy, when agreements are non-binding, an agent may promise to act one way during negotiation but act in a different way later. Our objective was to understand the conditions that foster truthful cooperation between artificial agents, and our results offer insight into some of the risks that arise with complex agents that can misrepresent intentions. We find that similarly to humans, cooperation is jeopardized by the ability of agents to break prior agreements. The “Baseline negotiatiors are defeated by deviators who break contracts” section shows that while Baseline Negotiators outperform silent agents due to increased cooperation, they are susceptible to peers who make false promises regarding future actions. We mitigate this risk by endowing agents with the inclination to retaliate against such deviations.Our results highlight the difficulty in establishing cooperation due to deviation from agreements. For humans, the potential to break promises or mislead others hinders cooperation, requiring people to decide whether they can trust others59 and different people may have different expectations regarding the behavior of artificial Diplomacy agents60. Recent methods recover human-like play through regularization61. We have not incorporated such regularization: after the policy network is learned from imitating human play, further training is based entirely on reinforcement learning.Strong Diplomacy AI gameplay may differ from human play62. It’s striking that our Learned Deviators follow a similar strategy: they adapt to typically follow through on their promises for long periods of time, breaking agreements only when the gains are high enough and when their opponents are left less capable of retaliating for the deviation. We strived to create a rich representation of the Diplomacy game, recreating its dilemmas relating to strategic communication. One possible cause for the strategic similarity is that Diplomacy was designed such that deviating from agreements can be beneficial when the opponent would find it difficult to respond. In other words, Diplomacy, even under the restricted communication protocols we considered, has a strategy space where such a behavior can be an effective way to win, so both humans and our Learned Deviator exhibit it.Humans playing Diplomacy sometimes employ a strategy of keeping promises until a crucial deviation late in the gameThe “Sanctioning dramatically reduces the advantage of deviation” section shows that when a population of agents are inclined to sanction broken agreements, they are resistant to deviators; when the proportion of retaliating agents is high enough, constant deviations from agreements are not beneficial as the long term negative consequences of the retaliation outweigh the immediate gains from the deviation. Even Learned Deviators, who optimize their choice of when to deviate against Defensive agents, rarely deviate from agreements. Hence, sanctioning peers who break contracts can foster more truthful communication among AI agents.57).Learned Deviators do gain a slight advantage against Defensive agents, and when many agents deviate from agreements sanctioning deviations becomes more costly. Hence, Sanctioning agents may themselves start deviating from agreements, and if the sanctioning behavior proves to be costly, the Sanctioning agents may cease sanctioning deviators. In Supplementary Note 64, or relying on a judicial system to provide remedies for the breach of contracts65. Future work could investigate how to implement such mechanisms for AI agents, similarly to earlier work on deterring deviations in dynamic coalition formation settings, for instance keeping track of peer behavior over multiple interactions or leveraging indirect reciprocity and tagging68.Such issues have been studied in the literature on the evolution of cooperation, and for simpler games researchers noted that additional mechanisms might be required to support sustained cooperation, such as having repeated interaction. Similarly for Diplomacy, to avoid a population of learning agents gradually becoming less cooperative one might need to employ additional mechanisms. Repeating the interaction and playing multiple games of Diplomacy against the same opponents could increase the incentives for cooperative behavior. Further, we focused on sanctioning, but humans rely on diverse solutions to deter deviating from agreements such as employing trust and reputation systemsOne limitation of our methods is that we took initial agents trained for No-Press Diplomacy, then augmented them with negotiation algorithms. This means that the action strategy, coming from the base agent, was designed separately from the communication and negotiation strategies. Future work might build stronger agents through better methods for co-evolving the action and communication strategies, allowing the agent’s play to capture even more of the strategic richness that arises in human play. Our work has further limitations  and “Negotiating with non-binding agreements” .πi: S × Ai →  mapping any game state to a distribution over actions, with the probability of taking action a ∈ Ai in state s denoted as πi, and a state-value function π to refer to policies πi for each player pi. Various methods were proposed for constructing policy and value functions in Diplomacy49. Our experiments in “Results” use policy and value networks trained by first imitating human gameplay on a dataset of human Diplomacy games, then applying reinforcement learning to improve agent policies39 (available at https://github.com/deepmind/diplomacy). Hence, the value and policy functions we use are based on both learning from human data and applying reinforcement learning, but our algorithms can work with any such functions. We denote sampling an action a in state s for agent pi from the policy πi as a ~ πi(s). Given a contract D =  we can restrict the policies πi, πj to respect the limitations expressed in the contract, yielding a policy pi where the probability of pi taking action a in state s is:Our methods use policies πi and a restricted action set Ri ), one can sample an action ai from Ri . Similarly, we denote by pj which respects the contract’s restriction Rj.Note that given a neural network capturing a policy πi or a constrained policy a be a vector of agent actions T be the transition function of the game, taking the current state s and the action profile a and returning the resulting next game state. Finally, let Q = V).A key building block in our methods is to simulate what might occur in the next turn when players follow various policies, such as the unconstrained policy pi trying to select an action in a state s and playing with agents Pi− = {p1,…,pi−1,pi+1,…,pn} who follow the respective policies πi− = . Each policy in πi− may be for instance the unconstrained policy π or alternatively πj may be a policy D =  that agent pj had agreed with some agent pk. By ai− ~ πi− we denote sampling actions for the players Pi− from these respective policies πi−. We denote the full action profile combining the action ai for pi and the actions ai− for the players Pi− as . By applying the joint action value function Q) we arrive at an estimate of each player’s value if pi takes the action ai; we can consider this as a conditional action value function Consider a player ai for pi and aj for pj as , and the resulting pairwise conditional action value function as We can also extend this to two players: we denote the action profile combining Vi, we can estimate pi’s value for taking an action ai as the expected value pi in the next game state, with the expectation taken over the actions of the other agents sampled from their respective policies πi−:Given a value function M partial action profiles profile that consists of actions for all players except pi). We use the sample Ai− to get a Monte-Carlo estimate for agent pi’s expected value when taking action ai, by calculating pj’s value Vj)) when pi takes an action ai in a similar way. We use the notation Consider sampling a list of pi considering a contract D = . When pi, pj select actions under this contract they use the respective policies π, we consider the policy profile k ∉ {i,j} we have pi’s value by taking the expected value in the next game state, with the expectation taken over all agents’ actions when sampled from their respective policies in πD:Consider a player A of full action profiles a1,…,aM ~ πD . Averaging over these, we obtain the value estimate We can obtain a Monte-Carlo estimate of the agents’ values. We take a sample ai for player pi and an action aj for player pj, for example in order to evaluate a contract D = . In such situations, we may evaluate pi’s value by taking their expected value in the next game state, over the actions of the other agents as sampled from their respective policies πi, j}−{. This yields the following value:We use a similar calculation for the Propose-Choose protocol, when considering the combined effect of an action Ai, j}−{ consisting of actions for all players except {pi,pj}: pi, pj. Given an action ai for agent pi and an action aj for pj, each such element This expectation is taken over many actions, so we approximate this using a Monte-Carlo simulation. We consider a sample 39. In the “Negotiators outperform non-communicating agents” section, we use agents produced under this approach as our baseline non-communicating agents. The neural policy iteration works by taking a current behavior policy network π, and applying an improvement operator aimed at generating actions that are better than those in this underlying policy. Many game trajectories are then generated using this improved policy. Given these games a new policy neural network A recent method for constructing No-Press Diplomacy agents starts with a policy which mimics human gameplay (imitation learning), then gradually improves this policy using a neural policy iteration process39, called Sampled Best Response (SBR for short), as we use it as a building block for our negotiating agents (see the recent paper39 for further details about SBR and using it to derive Diplomacy RL agents). SBR selects the action of player i in state s as follows. SBR first samples many candidate actions i from the policy πb to produce the actions of the other agents, either using the same network as πc or a previous generation policy.We briefly describe the improvement operator used for No-Press Diplomacycj, SBR simulates the possible behavior of other players by taking a sample A of partial action profiles 39 is given in Algorithm 1.To evaluate the quality of Algorithm 1 Sampled Best Response.s, the Baseline Negotiator pi is free to choose any legal action from its unconstrained policy ai = SBRIn the following sections, we describe the algorithms for the Baseline Negotiator of the section “Negotiating with binding agreements”, including RSS and MBDS. We first describe the action phase, as it is the same for both protocols. If no agreement has been reached during the negotiation phase in state Di,j =  was agreed, it places a restriction Ri that the Baseline Negotiator respects. If Ri contains only a single action that pi may take under the contract, the Baseline Negotiator simply selects that action. If multiple actions are allowed under Ri, the Baseline Negotiator selects an action by applying SBR on a restricted policy pj would also respect the agreement and select actions from the restricted policy ai = SBRIf a contract Our negotiation algorithm for the Mutual Proposal protocol, called RSS, is based on applying SVE to contrast what might occur when a contract is agreed and when it is not agreed.Di,j =  an agent may propose to another, such as a Peace contract in Diplomacy. Under the Mutual Proposal protocol an agent pi must decide whether to extend an offer to each of the other agents. When deciding whether agent pi would make a proposal Di,j to agent pj, RSS uses SVE to estimate the expected value to pi in two cases: (1) assuming that pi does not reach an agreement with pj, and (2) assuming pi and pj agree on the contract Di,j = . The full RSS method, given in Algorithm 2, compares agent utilities between these cases.We consider the case where there is a single contract Algorithm 2 Restriction Simulation Sampling.pi and pj are free to select any action, so we use the unrestricted policies πi and πj for pi and pj. RSS makes the simplifying assumption that no other agent would reach any agreements , so we also use the unrestricted policies π for all the other agents. Hence, the case of not having an agreement is evaluated by applying SVE with the policy profile π, so actions for all players p1, …, pn are sampled from their respective unconstrained policies π1, …, πn.For the first case, where no agreement is reached, both Di,j =  is reached between pi, pj, both pi, pj may only choose actions in the respective action sets Ri, Rj, so we use the restricted policies pi and pj respectively. Similarly to the no agreement case, we make the simplifying assumption that no further contracts between other agents have been agreed, so we can reuse the actions for the other players P⧹{i,j} as used in the SVE procedure for the no-agreement.In the second case, where an agreement pi and pj; to get these, we reuse the constraint-satisfying actions from the no-agreement SVE, resampling only those actions which fall outside of Ri and Rj. For instance, for a Peace contract, the resampling for pi, pj is done by rejecting actions that violate the peace. We do so to reduce the variance in the estimate of the difference between values in the agreement and non-agreement case.To estimate values in the case of reaching an agreement we also require samples from pi in the case of no agreement, and by pi in the case of an agreement D = . If pi expects to achieve more utility when the contract is agreed, so they propose it to pj, and otherwise they refrain from proposing it.We denote by 53. Given a space s =  in S yielding respective utilities d1,d2), and a disagreement outcome Our negotiation algorithm for the Propose-Choose protocol is MBDS. It decides which contracts to propose during the Propose phase, and which contracts to choose during the Choose phase. It generates and selects contracts seeking mutually beneficial deals. In order to choose between possible contracts, we used the Nash Bargaining Solution (NBS) from game theory52.NBS is the only bargaining solution concept that satisfies certain fair bargaining axioms, producing a negotiation outcome that’s mutually advantageous relative to the no-agreement outcomeNBS guarantees Pareto optimality, meaning negotiators never select a contract if they can find an alternative contract that guarantees both sides higher utility than the chosen agreement, independence of units of measure, meaning switching to an equivalent utility representation other than winrates does not result in a change in the chosen contracts, and symmetry, meaning that if the space of possible contracts is symmetric in the winrates it allows, then the chosen agreement would yield both sides the same winrate.These properties of the NBS are important for our Diplomacy agents, as they guarantee that agreements are chosen so as to maximize the win probabilities of both sides and provide robustness to our choice of measuring utility in terms of winrate improvements. Further, these properties mean that negotiators attempt to choose balanced contracts that both sides may agree on, rather than choosing contracts that prefer one side over the other, which would make it more difficult to agree.Approximating the Nash Bargaining Solution (NBS): When applying NBS to the Propose-Choose setting, one reasonable interpretation is to consider the disagreement utility as the win probability of the sides assuming no contract is agreed (with both sides selecting actions from their unconstrained policy), and to consider the utility under a contract as the win probabilities of the sides assuming the contract is signed (with both sides selecting actions from the constrained policies under the contract).21 to 1064 legal actions per turn39, and the space of possible contracts grows quadratically in the size of the legal actions set . Hence, it is intractable to exhaustively search through the space of contracts, or to exactly compute expected win probabilities under a contract. In addition, the interpretation of disagreement utility as assuming no contract is signed by either side is flawed: either side may instead sign a contract with a different peer. We overcome these difficulties using a sampling approach, and by simulating the negotiation process of other agents.However, Diplomacy has more than two agents and combinatorially large action spaces, and agent policies are stochastic. Diplomacy has an enormous action space of 10pi could offer to pj. The candidate contracts Ci for pi and Cj for pj, and looking at the Cartesian product Ci × Cj = {: ci ∈ Ci, cj ∈ Cj} of these actions, i.e., all possible combinations of the candidate actions for the two sides. The candidate actions for the sides are generated by sampling many actions K ranked by a metric that combines both pi’s and pj’s expected utility under the actions , and an additional scaling factor ci is a weighted sum of pi’s utility and pj’s utility: β < 1 reflects the degree of emphasis on the utility of the partner to whom the contract is offered; low values of β reflect emphasizing actions that lead to a high utility for the proposer, and high values of β emphasize actions that lead to a high utility for the proposee.We consider these action profiles B of M action profiles for all players from πb, and using SAVE to select selfishly-best actions pi’s and pj’s values in the case where no deal is made: The scaling factor pj, the proposer pi must consider and balance two factors relating to the resulting agent utilities (winrates): (1) the value that pi stands to gain should the contract be agreed on, and (2) the likelihood of pj agreeing to the contract, which is determined by the value pj stands to gain should the contract be agreed.When deciding about which of the contracts in 52, which reflects reasonable bargaining axioms69. We compute the Nash Bargaining Score in Algorithm 3, which relies on qi, qj which are used as estimates of the no-deal baseline values that the gains are relative to. The values qi, qj indicate what values pi and pj may expect to obtain in the absence of a deal between them.We combine these two factors by using the Nash Bargaining SolutionAlgorithm 3 Nash Bargaining Score.pi and pj are free to choose any legal action. Hence, we assume they would choose the best actions πc. As in SBR, we take the simplifying assumption that that the remaining agents P⧹{pi,pj} would not form agreements amongst themselves, and hence would simply choose actions from their policy πb. Seeking to estimate the next state values for this case, we use the STAVE algorithm described earlier, defining When there is no agreement, both pi and pj can reach without a deal between them, as either side may be able to do better by making a deal with another player. To estimate this we use an iterative approach akin to other iterative negotiation methods70 and described in Algorithm 4.The initial no-deal estimates may not fully represent the values Algorithm 4 BATNA Update by Internal Dynamic Bargaining Simulation.pi considers their action with regard to each partner pj, it contrasts its no-deal baseline with pj with the best alternative deal from among the remaining players P⧹{pi,pj}. We apply a damping factor κ to avoid oscillations in partner choice. Using the updated baselines, MBDS proposes to each partner the deal with the highest score. The full procedure for the Proposal phase is given in Algorithm 5.Algorithm 4 simulates an iterative process of updating beliefs regarding the contracts that might be agreed between all agents, and the resulting estimates of the values all agents might obtain. In each iteration, we examine each pair of players, and assume the deal they would select is the one with the highest Nash Bargaining Score over the current baseline estimates. Further, the update assumes that when each player Algorithm 5 Mutually Beneficial Deal Sampling Proposal.pi examines the set of contracts involving pi, and computes the Nash Bargaining score for each one using the baseline values from the Proposal phase. If some Nash Bargaining scores are positive, it considers the partners with whom such deals are possible, selecting the partner with whom the highest-score deal is most favorable to itself. If not, it simply selects the deal most favorable to itself from among those that are estimated to be preferable to the no-deal baseline with their respective counterpart.MBDS applies the same ranking during the Choose phase. In this phase, each agent must choose from amongst the contracts that are On The Table for them, selecting a single partner to agree a contract with. MDBS for a target agent Lastly, for the chosen deal, MBDS evaluates and indicates whether both deals with the chosen counterpart would be acceptable, by comparing their estimated values with the no-deal BATNA. The full MBDS method for the Choose phase is given in algorithm 6.Algorithm 6 Mutually Beneficial Deal Sampling Choice.Deviators are agents who may deviate from deals they have agreed to. In the following sections, we fully describe the Simple Deviators and Conditional Deviators of the section “Negotiating with non-binding agreements”. Simple Deviators enter into deals in a way that is identical to the Baseline Negotiators, but even when a deal is agreed on they select their action directly from the unconstrained SBR policy, as if no deal was agreed. Conditional Deviators also enter into deals identically to Baseline Negotiators, but when selecting their action in turns when a deal has been reached, they attempt to maximize their reward under the assumption that the other side would honor the deal.During the negotiation phase, Simple Deviators behave identically to the Baseline Negotiator. Simple Deviators only behave differently to Baseline Negotiators during the action phase.s, if no deal has been reached for a Baseline Negotiator pi, this Baseline Negotiator selects an action ai = SBRpi agreed to deals j1,…,jk then the Baseline Negotiator pi selects an action ai = SBRDuring the action phase in state pi always selects an action from the unconstrained policy ai = SBRpi has agreed on a deal D =  with another player pj, during the action phase it still chooses an action which does not necessarily respect the constraint Ri, and doesn’t assume that pj will respect the constraint Rj.In contrast to a Baseline Negotiator, a Simple Deviator Similarly to the Simple Deviators, during the negotiation phase the behavior of a Conditional Deviator is identical to that of a Baseline Negotiator. Conditional Deviators only behave differently to Baseline Negotiators during the action phase.pi selects an action in the same way as the Baseline Negotiator, i.e., using the SBR logic: sampling a set Bi− of M partial action profiles, sampling N candidate actions from the unrestricted policy D =  has been agreed between a Conditional Deviator pi and some other player pj, the Conditional Deviator attempts to maximize its gain under the assumption that the other side would respect their end of the deal; again we use a sample Bi− of M partial action profiles, but in this sample we select the action for any deal partner pj from the restricted policy pj would behave according to the restriction of the contract. We consider the top candidate action sampled from the unconstrained policy pi has agreed to, by taking a sample of candidate actions pi had agreed to. The top ranked action that does not violate pi’s agreements is c* exceeds that of c*; otherwise, when a deviation is not deemed profitable, it selects the top contract-respecting action When no deal has been agreed, a Conditional Deviator Algorithm 7 Conditional Deviator Action Selection for pi.pi has deviated from a deal with pj at a certain point in a game, pj will never again reach an agreement with pi in that game. Thus, a deviator agent pi playing against a defensive agent pj only has a single opportunity to deviate from an agreement with them in a game. Hence, it makes sense to pose the issue of optimizing the behavior of a deviator pi as identifying the point in the game where it is best to deviate from an agreement with some defensive agent pj. We simplify the problem further by having the Learned Deviators consider only two features of the current state s and contract D =  agreed with a peer pj. The first is the approximate immediate deviation gain pi can gain by deviating from D. The second is the strength of the other agents that pi may turn against itself should pi deviate from a contract. In Diplomacy, the win probability of a player pi in a state s is closely correlated with the number of units (or supply centers) that this player has, and how well positioned they are to attack other players. These characteristics of the state are also closely correlated with the ability of that player to retaliate against an attack from another player. In other words, when a player pi considers deviating from an agreement with player pj, they should be more worried regarding player pj’s retaliation when pj has a high win probability  in the resulting state. Thus, we derive a measure ψ from two considerations. One is that if none of the partners with whom a contract has been made is strong, pi may more safely deviate. The other is that if one of the partners is very dominant among the non-pi players, then that partner may be mostly incentivized to reduce pi’s value to begin with, and so pi doesn’t have as much to lose by triggering its retaliation. Thus, with c*, s, B, and Di,j as defined in Algorithm 7, we define We describe our approach for training a deviator agent that learns the optimal state in which to deviate from a contract when playing a population of other agents . Consider that the defensive agents of the section “Mitigating the deviation problem: defensive agents” modify their behavior following any deviation from a previous agreement, and starting from that point they persist with their negative behavior towards the deviator for the remainder of the game; if pi parameterized by two thresholds tϕ, tψ. It follows the Baseline Negotiator behavior (as though ϕ < 0 in Algorithm 7) until the first turn where ϕ > tϕ and ψ < tψ. Then, the agent switches its behavior to that of the Conditional Deviator. In other words, this Deviator waits until a turn where the immediate gains from deviation are high enough and the ability of the other agent to retaliate is low enough, and only then deviates from an agreement. In our experiments the thresholds tϕ, tψ are tuned by applying a simple grid search over the space of parameters  with a counterpart agent pj, it examines the behavior of the counterpart pj in the following action phase. If pj deviates from the agreement by taking a disallowed action aj ∉ Rj, it changes its behavior towards this deviator for the remainder of the game. We now fully describe the Binary Negotiators and Sanctioning agents discussed in the section “Negotiating with non-binding agreements”.Defensive agents are designed to deter others from deviating from agreements, while still retaining the advantage negotiation skills afford over non-communicating agents; they shun Deviators, or work as a group to repel them by negatively responding to deviations so as to reduce the gains from such deviations. Defensive agents act identically to the Baseline Negotiator agents described in detail in the “Baseline Negotiator algorithms” section, but change their behavior when another agent deviates from an agreement made with them. When a defensive agent pj by ceasing all communication with pj for the remainder of the game. In the Mutual Proposal protocol this means never proposing any contract to pj and hence never agreeing on any contract with pj for the remainder of the game, and in the Propose-Choose protocol this means never choosing any contract proposed by or to pj, hence never agreeing a contract with pj for the remainder of the game. This is done via an additional check on lines 8 and 17 of Algorithm 6.Binary Negotiators respond to a deviation of pi takes a more active role when responding to a deviation by player pj. Following such a deviation, the Sanctioning agent pi modifies its behavioral goal so as to attempt to lower the deviator pj’s reward in the game.A Sanctioning agent pi in the next state when taking action a as pj against player pi, we consider the modified score pi’s utility and the negative of player pj’s utility, where the parameter α controls the degree of importance placed on lowering player pj’s utility.The standard SBR procedure, Algorithm 1 described in the section “The sampled best responses procedure”, estimates the expected value for player pi selects actions identically to the Baseline Negotiator of the section “Baseline Negotiator algorithms” until a deviation occurs by a peer pj. Following this point and until the end of the game, the Sanctioning Agent turns to selecting the actions maximizing the perturbed score pi, the negative utilities are combined to form pj, the Sanctioning agent pi optimizes for a perturbed score that represents a combination of maximizing the win probability of pi and minimizing the win probability of the deviator pj.A Sanctioning Agent Supplementary InformationPeer Review File


We then study the impact of these additional degrees of freedom on viral wrapping. We find that cells with an optimal density of filamentous extracellular components (ECCs) are more likely to be infected as they uptake the virus faster and use relatively less cell surface area per individual virus. At the optimal density, the cell surface folds around the virus, and folds are faster and more efficient at wrapping the virus than crumple-like wrapping. We also find that cell surface bending rigidity helps generate folds, as bending rigidity enhances force transmission across the surface. However, changing other mechanical parameters, such as the stretching stiffness of filamentous ECCs or virus spikes, can drive crumple-like formation of the cell surface. We conclude with the implications of our study on the evolutionary pressures of virus-like particles, with a particular focus on the cellular microenvironment that may include filamentous ECCs.Nanoparticles, such as viruses, can enter cells via endocytosis. During endocytosis, the cell surface wraps around the nanoparticle to effectively eat it. Prior focus has been on how nanoparticle size and shape impacts endocytosis. However, inspired by the noted presence of extracellular vimentin affecting viral and bacteria uptake, as well as the structure of coronaviruses, we construct a computational model in which  Viruses are relatively simple in structure as they consist of a container and genetic material. The container material ranges from solid-like proteins to fluid-like lipids , 2. For Since the contents of a virus are minimal, in order to replicate, viruses must enter cells to hijack their biological machinery. Viruses enter cells via multiple pathways. Two of the dominant pathways for coronaviruses are membrane fusion, and endocytosis , 13. In both the cell-like construct and the virus-like construct contain their own filamentous structures protruding from their surfaces and study the impact of these additional degrees of freedom on viral wrapping. Indeed, much research has focused on how the size and shape of the virus impact viral wrapping [outside of a cell assist in viral wrapping?Following our initial mostly experimental study of how extracellular vimentin impacts viral uptake , here, wwrapping –24 with wrapping . In addiwrapping . Filamenwrapping , 28. HowTo begin to answer the above question, we have organized the manuscript as follows. We first present the computational model with several simplifying assumptions. The first is that the cell surface is modeled as a deformable sheet with bending and stretching energy costs, representing the underlying cell cortex supporting the lipid bilayer. Second, as extracellular vimentin is our main filamentous protein candidate, vimentin selfassembles into filamentous, hierarchical structures whose tetramers are six times longer than the thickness of a cell membrane . There iTo understand the role of the filamentous structures on the outside of both a cell and a virus on viral uptake, we model viral wrapping via coarse-grained Brownian dynamics simulations. Here are the relevant players and how they are incorporated into the model and their respective interactions with the other players.rij is the distance between nearest neighbors and lo is the edge length of the equilateral triangle. Bending rigidity is introduced in the surface with a spring interaction between second nearest neighbors rik is the distance between second nearest-neighbors and We model the cell surface as a deformable sheet, as shown in Again, we are modeling the cell surface as a deformable sheet. With this assumption, we can also explore local, nontrivial shapes of the underlying cortex, which, in turn, drives the plasma membrane shape. On the other hand, since earlier work demonstrates that the head domain of vimentin can also associate with a plasma membrane , we willθlmn is the angle between three consecutive particles in co-receptors and rij is the distance between nearest neighbor and σo is the diameter of a ECC particle. Finally, we assume that these filamentous extracellular components are bound to the cell cortex just beneath the lipid bilayer [The filamentous ECCs are semiflexible polymers also modeled as particles connected with springs, as shown in  bilayer , 40, 41.A short receptor is placed in the middle of the cell surface and is the same as the ECC receptor with different values for ro is the equilibrium distance found by the triangulation. This construction of a deformable, elastic virus surface, with ultimately filamentous structures emanating from it, is a simplifying assumption as viruses with spike proteins typically consist of fluid-like containers but, nonetheless, provides a starting point for the modeling.The deformable virus surface is initialized by generating particles on a sphere. The particles are arranged in a Fibonacci sequence. We then implement a Delaunay triangulation to identify the edges between these particles. All particles on the sphere are connected with a harmonic spring potential σo is the particle’s diameter. We place the spikes on the virus’s surface such that the typical distance between two neighboring spikes is between 3–15 nm, the range found in experiments [Spikes are two particles joined by harmonic springs, as shown in eriments , 44.ro is the equilibrium distance. The receptor is made up of four particles connected via harmonic spring and has some bending rigidity.The virus is connected to the primary receptor via a harmonic spring interaction, rij is the distance between ith top spike particle and the jth top ECC particle, and σo is the diameter of the particle, orVirus spikes and extracellular components may interact via specific binding domains and charge interactions , 37, 45. domains , 46, we  domains . Thus, oKSoft−Repulsion is the strength of the soft repulsion, rij is the distance between the centers of two particles, and σo is the diameter of a particle. The repulsion force acts only when the distance between particles is lower than the diameter of the particle, orAll components of the model have volume exclusion due to soft-core repulsion given by ri is the position of an ith particle, ξ(t) is the Gaussian white noise to simulate thermal fluctuations and follows < ξ(t) >= 0 and < ξi(t)ξj(t′) >= 0. The sum of conservative forces on the ith particle ith particle coordinate We implement Brownian dynamics to quantify the dynamics of the model. The equation of motion is given by μs, and one force unit is 10−1pN. All simulation quantities are expressed in terms of these basic units. We run the total simulation with dt 10−4 for 108 simulation steps or 50 ms and recording positions at each 25 μs. Total run time is comparable to the typical viral endocytosis time[kBT. Since bending rigidity is encoded in the second nearest-neighbor springs, multiplying that spring constant with the area of the triangle made up of those springs, with side Our Brownian dynamics simulation is a coarse-grained simulation. All simulation quantities are normalized via length, time, and force scales. We can convert simulation quantities to biologically relevant quantities by the following definitions: one unit simulation length is defined as 10 nm, one unit simulation time is 1osis time, 49. To The simulation box contains up to 8624 particles. Each particle has a diameter of 10 nm. Since the typical size of the virus is 10s-100s of nanometers and the cell size is usually at the scales of 10 s of micrometers, thus virus interacts only a small part of the cell surface. So, we simulated only a small patch of the cell surface of size 550 nm×480.6 nm, which is made up of 1444 particles. The cell surface boundary is free in our simulations. Each ECC has a length of 40 nm, which is in the range of many cell surface proteins , 52 and A.−3 nm−2. ECC coverage of 100 % corresponds to the area density of 5.4 ×10−3 nm−2.We first investigate the effects of varying extracellular components (ECC) and the virus spike density on wrapping. We altered the cell surface coverage by the ECCs from 20 percent to cover it fully and varied the spike numbers from 25 to 200 spikes. In To quantify the wrapping behavior, we define virus wrapping as the ratio of the surface area covered via a cell surface divided by the whole surface area of the virus, as shown in not lead to higher virus wrapping. Virus wrapping is maximum at the medium coreceptors density, where virus spikes have enough coreceptors to interact with those around them and have enough space between spikes not to invoke shielding effects. Thus, we found an optimal percent coverage of cell surface coreceptors for maximal wrapping. The notion of an optimal percent coverage for maximal wrapping is a rather reasonable one if one considers effective cell surface bending rigidity that depends on such a quantity. More specifically, as the ECC percent coverage increases, the sheet stiffens such that the sheet eventually can no longer wrap around the viral. At lower ECC percent coverage, some stiffening of the sheet gives rise to a more coordinated wrapping, which we explore in more detail in the next subsection.We find non-monotonic behavior for the wrapping as a function of the percentage of coverage of extracellular components for 200 spikes, as shown in B.Next, we investigate the cell surface bending rigidity’s role in viral wrapping. Since there exists heterogeneity in the structure and mechanics of the cell cortex, as viruses invade cells, they may encounter different cellular surface rigidities, which may affect the rate of its uptake. In R, centered at the center of mass of the virus. Starting with the highest spike on the virus that is adhered to an ECC, we construct a cylinder around the virus and identify all the cell surface particles in this cylinder for a given radius. As these particles are a part of a triangulated lattice, we see the total surface area of the cell surface inside the cylinder by adding up all the triangle areas inside the cylinder. Here, the radius of cylinder R sets how close or far from the virus we find the surface area. To arrive at a dimensionless area, we divide the obtained surface area by the total area of the sheet. We cannot have a large value of R compared to the virus radius as there is a finite amount of cell surface; by taking too small R, on the other hand, we may miss some of the data. Therefore, R is 1.5 times of radius of the virus or 150 nm. For other radii, we studied the quantification, and it is robust for a range of R. Please see P as well as the cell surface area A inside the cylinder. We then define a dimensionless quantity called shape index as Given that we have two general types of wrapping configurations that the cell surface takes on, crumple-like wrapping and fold-like wrapping, how do we distinguish between the two types? We say “crumple-like” because the crumpling is very localized near the virus, unlike the crumpling of a sheet of paper, for example . QuantifIn Furthermore, we plotted the cell surface shape index as a function of ECC percent coverage and cell surface bending rigidity in C.We now explore the dynamics of viral wrapping. From From We also investigate the virus’s engulfing velocity to further understand the role of folds and crumples in viral uptake. We plotted the virus velocity in the z-direction, or perpendicular with respect to the cell surface, see D.−2pN/nm. The attraction between spikes and ECC with low stretching cost energy makes them more accessible to each other, leading to many attachments between them. Even though we have a significant number of spikes connected to coreceptors, the cell surface does not form a fold but a crumple. This is because these low- stretching strength coreceptors cannot transfer enough force to the cell surface to make a more coordinated fold. On the other hand, in 2pN/nm, which is enough to generate forces to fold the cell surface around the virus. Thus, we found that an optimal ECC percent coverage determined for one set of mechanical parameters does not ensure efficiency that virus wrapping can always be achieved. The stretching rigidity of spikes and filaments on the cell surface also constrains the formation of folds.In this subsection, we investigate the effects of the mechanical properties of spike and ECC on viral wrapping. Indeed, filaments on the cell surface have varied mechanical properties depending on the type of filament. Therefore, we vary the stretching strength of coreceptors and virus spikes on viral uptake. Given this additional mechanical variation, we ask the question, is the optimal percent coverage of coreceptors always guaranteed a fold? To answer this question, we maintain the percent coverage of coreceptors at 40%, which yielded maximal virus wrapping, as shown in We vary the stretching strength of spike and coreceptors up to four orders of magnitude given in −2pN/nm and vary the coreceptors stretching strength from 10−2pN/nm to 102 pN/nm. We observe that changing coreceptors stretching strength does not contribute much to the virus wrapping behavior as it just increases with time having similar trends for all coreceptor’s stretching strength values. On the other hand, from 2pN/nm, we see that low coreceptor stretching values are associated with wrapping slowly and get less virus wrapping than for high coreceptor stretching strength. This is because, with the higher stretching strength of the spike and coreceptor, the cell surface folds, leading to the faster wrapping of the virus.We also examine the time series analysis to understand how the fold and crumple formation mechanism changes due to the stretching strength of spike and coreceptors. In We demonstrate that having optimal coreceptors percent coverage is not enough for efficient wrapping via folds. Coreceptors and spikes also require a threshold stretching strength above which the cell surface folds to achieve more wrapping. We also investigate the effects of the bending rigidity of filamentous ECCs and virus spikes. Bending rigidity does not impact the cell surface morphologies as stretching. See Our study suggests that cells whose surfaces are optimally populated with filamentous protein structures acting as coreceptors are more likely to be infected as they uptake the virus faster and use relatively less cell surface area per individual virus so that more virus-like particles can be uptaken. At the optimal percent coverage, the cell surface makes folds around the virus, and folds are faster and more efficient at wrapping the virus than crumple-like wrapping. Our study also finds that cell surface bending rigidity helps generate folds, as bending rigidity enhances force transmission across the surface. We also conclude that such an optimal percent coverage does not always ensure a fold formation, as changing mechanical parameters, such as the stretching stiffness of the ECC or the virus spikes, can drive the crumple-like formation of the cell surface.There has been much work exploring the role of viruses or nanoparticle spikes and how their mechanical properties affect endocytosis. However, these studies treat receptors as sticky particles on the cell surface without any degree of freedom , 56–60. The earlier experimental finding that extracellular vimentin enhances SARS-CoV-2 uptake is intriguing , 19. It We have assumed that the virus-like particle is already attached via a small receptor to the cell surface and quantified viral wrapping. However, it would also be interesting to study how the cellular microenvironment affects the trajectory of a nanoparticle to find that initial receptor in terms of search strategy . We have1


The relationship between transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and the amount of virus present in the proximity of a susceptible host is not understood. Here, we developed a within-host and aerosol mathematical model and used it to determine the relationship between viral kinetics in the upper respiratory track, viral kinetics in the aerosols, and new transmissions in golden hamsters challenged with SARS-CoV-2. We determined that infectious virus shedding early in infection correlates with transmission events, shedding of infectious virus diminishes late in the infection, and high viral RNA levels late in the infection are a poor indicator of transmission. We further showed that viral infectiousness increases in a density dependent manner with viral RNA and that their relative ratio is time-dependent. Such information is useful for designing interventions. Quantifying the relationship between SARS-CoV-2 dynamics in upper respiratory tract and in aerosols is key to understanding SARS-CoV-2 transmission and evaluating intervention strategies. Of particular interest is the link between the viral RNA measured by PCR and a subject’s infectiousness. Here, we developed a mechanistic model of viral transmission in golden hamsters and used data in upper respiratory tract and aerosols to evaluate key within-host and environment based viral parameters. The significance of our research is in identifying the timing and duration of viral shedding, how long it stays infectious, and the link between infectious virus and total viral RNA. Such knowledge enhances our understanding of the SARS-CoV-2 transmission window. The studies . The oth studies .To model infectious virus shedding into the environment, we extended the upper respiratory tract model to account for infectious virus titer and total viral RNA emitted into aerosols. Within-host and aerosol model fitting showed that infectious virus titers get released into the air immediately after inoculation with peak shedding 21–37 hours after inoculation in males and 3–5 hours in females. Infectious viral shedding ends faster in females compared to males, with virus in aerosols losing replication-competency by 2.5–4.1 days post infection in females and 3.7–5.6 days post inoculation in males. The predicted loss of virus infectivity in aerosols before day six is consistent with experimental observations that have shown lack of transmission to naive hamsters co-housed with hamsters infected six days prior .2 and 108 RNA/TCID50 in the first five days following infection, wider than in other studies [Our models and data herein predict that viral RNA persists in both upper respiratory tract and in aerosols long after replication-competent virus stops being detected, with RNA values staying above detectable levels at least a week after the infectious virus is lost. While in public health setting a SARS-CoV-2 diagnostic is determined by PCR assays, RNA levels are not always indicative of virus infectivity, with PCR specificity for detecting replication-competent virus decaying as the cycle threshold (Ct) values increase –32, 32.  studies , 12. We  studies . These e studies , 32, 34, studies .50 ratio. The turning point where viral infectiousness starts to saturate is study dependent, with differences due to experimental settings.We have also investigated the population level relationship between the amount of RNA and the amount of infectious virus in a sample and found that the infectious virus increases in a density-dependent manner with the viral RNA, as suggested by previous work , 24. TheT(0) = 107 epithelial cells/ml, as in influenza [p. We can obtain the same results for any other initial number of susceptible epithelial cells, as long as the p × T0 is fixed at the current estimates. We assumed that both infectious virus clearance and RNA degradation rates are known, with infectious virus clearance set at influenza levels c + d = 10 per day (corresponding to life-span of 2.4 hours) and the degradation rate set arbitrarily at d = 1 per day (corresponding to life-span of one day). Using sensitivity analysis we have found that changing the clearance rates to c + d = 15 and c + d = 5 does not influence the results (not shown). In all instances, however, the RNA degradation needs to be small, d = 1 or smaller, to explain the differences between infectious virus and viral RNA decay. Moreover, we had to include an additional removal of the aerosol infectious virus, which we assumed was due to infectious viral inactivation due to the elements, which we set at d1 = d = 1 per day. We have also considered that all neutralized virus leads to RNA production. Further information is needed to determine the biological processes leading to increased degradation of infectious virus in aerosols compared to upper respiratory tract and those leading to the persistence of RNA in upper respiratory tract and aerosols after infectious virus is lost. Lastly, due to limited aerosol data in the females (with some subjects having just one data point above the limit of detection) we could not properly identify sex-specific differences and excluded this group from some of the analyses.Our study has several limitations. We assumed that the initial target population is nfluenza . This chIn conclusion, we have developed a within-host and aerosol model for SARS-CoV-2 infection in golden hamsters and used it to investigate the dynamics of viral RNA and infectious virus titers in URT and aerosols. We validated the models against data and used it to determine the temporal relationship between infectious virus, viral RNA and the probability of a nearby host getting infected. The results can guide interventions.S1 Text(PDF)Click here for additional data file.


In Myanmar, yellow mosaic and leaf curl diseases caused by whitefly-transmitted begomoviruses are serious problems for vegetables such as tomatoes and peppers. To investigate the incidence of begomoviruses in Myanmar between 2017 and 2019, a field survey of tomato and pepper plants with virus-like symptoms was conducted in the Naypyitaw, Tatkon, and Mohnyin areas of Myanmar. Among the 59 samples subjected to begomovirus detection using polymerase chain reaction, 59.3% were infected with begomoviruses. Complete genome sequences using rolling circle amplification identified five begomovirus species: tomato yellow leaf curl Thailand virus (TYLCTHV), tomato yellow leaf curl Kanchanaburi virus (TYLCKaV), tobacco leaf curl Yunnan virus (TbLCYnV), chili leaf curl Pakistan virus (ChiLCV/PK), and tobacco curly shoot Myanmar virus (TbCSV-[Myanmar]). Excluding the previously reported TYLCTHV, three begomoviruses  were identified in Myanmar for the first time. Based on the 91% demarcation threshold of begomovirus species, TbCSV-[Myanmar] was identified as a new species in this study. Among these, ChiLCV/PK and TbCSV-[Myanmar] were the most predominant in tomato and pepper fields in Myanmar. Identification of begomovirus species may be helpful for predicting the origin of viruses and preventing their spread. Begomovirus in the family Geminiviridae) are serious problems in the cultivation of various vegetable crops ) . Among tSolanum lycopersicum) and pepper (Capsicum annuum) plants belong to the family Solanaceae and are major vegetable crops in tropical and sub-tropical regions of the world. In Myanmar, during the year 2017/18, tomatoes and peppers (dried) were cultivated on 103,000 and 108,000 hectares with a total production of 1,157,000 and 130,000 metric tons, respectively . In general, tomato and pepper production are severely affected by various viral diseases. Begomovirues are the major group of pathogens that cause yellow mosaic and leaf curl disease. At least 36 distinct species of begomovirus, including TYLCV, have been identified from tomato and pepper plants in southeast and east Asia  isolates, we used seven recombination analysis methods: RDP, GENECONV, BootScan, MaxChi, Chimaera, SiScan, and 3Seq in the RDP v4.101  program . The par


Geminiviridae) are a major group of emerging plant viruses worldwide. The knowledge of begomoviruses is mostly restricted to crop plant systems. Nevertheless, it has been described that non-cultivated plants are important reservoirs and vessels of viral evolution that leads to the emergence of new diseases. High-throughput sequencing (HTS) has provided a powerful tool for speeding up the understanding of molecular ecology and epidemiology of plant virome and for discovery of new viral species. In this study, by performing earlier metagenomics library data mining, followed by geminivirus-related signature single plant searching and RCA-based full-length viral genome cloning, and based on phylogenetic analysis, genomes of two isolates of a novel monopartite begomovirus species tentatively named Galium leaf distortion virus (GLDV), which infects non-cultivated endemic plant Galium mexicanum, were identified in Colima, Mexico. Analysis of the genetic structure of both isolates (GLDV-1 and GLDV-2) revealed that the GLDV genome displays a DNA-A-like structure shared with the new world (NW) bipartite begomoviruses. Nonetheless, phylogenetic analysis using representative members of the main begomovirus American clades for tree construction grouped both GLDV isolates in a clade of the monopartite NW begomovirus, Tomato leaf deformation virus (ToLDeV). A comparative analysis of viral replication regulatory elements showed that the GLDV-1 isolate possesses an array and sequence conservation of iterons typical of NW begomovirus infecting the Solanaceae and Fabaceae families. Interestingly, GLDV-2 showed iteron sequences described only in monopartite begomovirus from OW belonging to a sweepovirus clade that infects plants of the Convolvulaceae family. In addition, the rep iteron related-domain (IRD) of both isolates display FRVQ or FRIS amino acid sequences corresponding to NW and sweepobegomovirus clades for GMV-1 and GMV-2, respectively. Finally, the lack of the GLDV DNA-B segment  confirmed the monopartite nature of GLDV. This is the first time that a monopartite begomovirus is described in Mexican ecosystems, and “in silico” geometagenomics analysis indicates that it is restricted to a specific region. These data revealed additional complexity in monopartite begomovirus genetics and geographic distribution and highlighted the importance of metagenomic approaches in understanding global virome ecology and evolution.Begomoviruses (Family  Geminiviridae family with over 520 species constitute the major group of emerging plant viruses affecting a multitude of important vegetable and fiber crops and causing significant economic losses in many countries located in tropical and subtropical regions of the world , Becurtovirus, Begomovirus, Capulavirus, Curtovirus, Eragrovirus, Grablovirus, Mastrevirus, Topocuvirus, Turncurtovirus, Citlodavirus, Maldovirus, Mulcrilevirus, Opunvirus, and Topilevirus, according to its genome organization, host range, insect vector, and phylogeny  and ecologically more successful genus in the entire virosphere infecting a wide range of dicotyledonous plants (Tomato yellow leaf curl virus (TYLCV) was introduced into the Americas in the early 1990s, indigenous NW tomato-infecting monopartite begomoviruses including Tomato leaf deformation virus (ToLDeV) in Ecuador and Peru (Tomato mottle leaf curl virus (ToMoLCV), Tomato leaf curl purple vein virus in Brazil (Tomato twisted leaf virus (ToTLV) in Venezuela (Corchorus yellow vein Cuba virus (CoYVCUV) infecting the non-cultivated plant Corchorus siliquosus  in Cuba  from China (accession number: MH602265) was selected for further analysis. The SPLCV-like signature was used as a template to design a primer set  using the PrimerSelect  software. For identification of plants harboring the SPLCV-like signature, a total of 49 plants belonging to nine families  from the Colima state sample collection , yielding one fragment of 2.7 kb and two fragments of 1.8 and 0.9 kb. The three fragments were cloned into a pGreen 0029 vector  program. The comparisons of complete circular genomes and their individual open reading frames (ORFs) were performed with MEGA 7.0 software  with φ-29 DNA polymerase  as described previously . The res9 vector  and transoftware  and compsoftware  with Bowsoftware  using ther 9.0.2 2.3 and protein motifs analyzed manually. Recombination analysis was performed with the RDP4 program  isolates (GLDV-1 and GLDV-2) were constructed as previously described  (New England BioLabs) following the manufacturer’s instructions. Then, the fragments were ligated with a monomeric copy of a full-length viral genome released with BamHI from the corresponding monomeric construct to yield GLDV-1 1.6mer and pG-GLDV-2 1.6mer constructs. In each cloning step, positive clones were verified by enzymatic digestion. Positive partial dimeric clones were transformed into Agrobacterium tumefaciens GV3101 strain by electroporation  in a Gene PulserXCell (Bio-Rad) apparatus.Infectious begomovirus partial dimeric clones of escribed . A fragmAgrobacterium tumefaciens strains harboring partial dimeric constructs were grown and inoculated as previously described , Hybrid Maya. The plants were agroinoculated in the four-leaf stage by stem puncture and leaf infiltration, maintained for 4 days in a bioclimatic chamber, BINDER, at 24oC under long-day conditions (16/8 light/darkness), and, after that, transferred to a greenhouse. Symptoms were documented weekly, and samples of non-inoculated new emerging apical leaves were collected 21 days post-inoculation (dpi). Begomovirus molecular detection was performed by PCR using Galium leaf distortion virus (GLDV)-specific primers recognizing both viral isolates, designed to amplify a fragment of viral intergenic regions . Infection assays were performed in three independent biological replicates of 3-4 plants each.For inoculation of GLDV-derived infectious clones, escribed . Plant sMH602265). SPLCV is an OW monopartite begomovirus belonging to a sweepovirus clade, and to date, monopartite begomoviruses have not been reported in Mexico. In order to identify plants harboring the putative begomovirus associated with SPLCV-like signature, a specific primer set, SP-Like-F/SPLike-R (expected amplicon: 232 bp), was used for molecular detection. A total of 49 plants belonging to nine families, Amaranthaceae (1), Asteraceae (3), Convolvulaceae (4), Cucurbitaceae (2), Malvaceae (28), Nyctaginaceae (4), Rubiaceae (2), Solanaceae (4), and Vervenacea (1) from the Colima state sample collection, were individually analyzed by PCR. The expected amplicon (232 bp) was detected in one sample corresponding to the Galium mexicanum species belonging to the Rubiaceae family (data not shown) collected in Tecomán, Colima, Mexico , and the resulting concatemers were digested independently with BamHI and SacI, yielding one fragment of 2.7 kb and two fragments of 1.8 and 0.9 kb, and two independent clones of each fragment were fully sequenced. The assembly and sequence comparison showed two putative full-length genomes of 2,656 and 2,658 bp from ∼2.7-kb cloned fragments sharing 91.34% sequence identity between them. Additionally, the alignment of 1.8- and 0.9-kb fragments using full-length genome-1  and full-length genome-2  sequences as a reference resulted in ∼100% homology with genome-1 of one 1.8-kb fragment and one 0.9-kb fragment. Similarly, the remaining two fragments of 1.8 and 0.9 kb, showed ∼100% homology with genome-2. These data show that SacI fragments (1.8 and 0.9 kb) are split forms of the full-length genome. Nucleotide sequences of both genomes were compared with the begomovirus database of NCBI using the BLASTn algorithm. The 2,656- and 2,658-bp genomes showed 79.88 and 79.2% identity with the DNA-A of the NW begomovirus Tomato leaf deformation virus (ToLDeV), isolate PA10-S9 (Accession number: JX501506.1), and Sida mosaic Bolivia virus (SiMBoV) (Accession number: KJ742421.1). To identify the putative cognate DNA-B segment, total DNA from Galium mexicanum positive sample was used as a template for PCR using two sets of universal degenerate primers BC1-290-for/BV1-470-rev and BC1-290-rev/BV1-310-for  is proposed. Hereafter, GLDV-1  and GLDV-2 . Both sequences were submitted in GenBank . To validate the obtained data and determinate the geographic distribution of GLDV across agro-ecological interfaces in the Northern Pacific Mexico region, RCA-cloned GLDV-1 and GLDV-2 genome sequences were aligned with the complete metagenomic data from Galium leaf distortion virus (GLDV) in the original sampling region, 12 samples of Gallium mexicanum showing leaf distortion and foliar chlorosis symptoms were collected in Tecomán, Colima in 2021 -specific primers (IR GLDV-F/IR GLDV-R), resulting in 8 out of the 12 plants being positive for GLDV infection  collected in ecosystems surrounding cultivated areas  located in seven states of the Northern-Pacific Mexico region . The asssymptoms . Afterwa-310-for , yieldin-310-for , suggest-310-for , the 2,6 in 2021  and testnfection . FurtherMungbean yellow mosaic India virus (MYMIV) and monopartite Tomato yellow leaf curl virus (TYLCV) OW begomoviruses (Bean golden mosaic virus (BGMV) and the monopartite Tomato leaf deformation virus (ToLDeV) NW begomovirus. Additionally, in the complementary strand sense (overlapping with the AV1 gene), both GLDV-1 and GLDV-2 encode an ORF corresponding to the AC5 gene conserved in different NW (BGMV and ToLDeV) and OW Mungbean yellow mosaic India virus (MYMIV) begomoviruses. Intriguingly, the GLDV-2 isolate encodes an ORF putatively encoding the AC6 gene in a complementary strand sense partially overlapped with the AV1 gene, which is syntenically conserved in some OW monopartite begomoviruses belonging to the sweepovirus clade including SPLCV. Finally, both GLDV isolates possess an intergenic region (IR) containing the nonanucleotide TAATATTAC conserved in the Geminiviridae family located in a predicted stem-loop structure, which marks the origin of geminiviral DNA replication (Abutilon mosaic virus (AbMV) Brazil is a clade, Tomato leaf deformation virus (ToLDeV), and squash clades) available in the GenBank database showed that GLDV-1 and GLDV-2 are placed in the ToLDeV clade together with Boerhavia yellow spot virus (BoYSV)  . ToLDeV Tomato leaf deformation virus (ToLDeV) and Boerhavia yellow spot virus (BoYSV), belonging to the same GLDV clade] confirmed the high divergence of GLDV isolates compared with their closest relatives from Latin America   . To idenFabaceae family infecting NW bipartite begomovirus BGMV-GT , which possess the same iteron arrangement with TGGAG consensus. Left IRs of ToLDeV, BoYSV, and GLDV-2 display an arrangement of two directed and one inverted iteron conserved among different lineages of NW begomoviruses. ToLDeV possesses direct CGGTG/TGGAG and reverses CGGTG iteron cores similar to NW bipartite begomovirus Bean golden mosaic virus  infecting the Fabaceae family with CGGTG consensus, whereas BoYSV shows direct TGGAG/TGGAG and reverse TGGAG iteron cores similar to NW bipartite begomovirus Tomato golden mosaic virus Guatemala strain TGMV-GT infecting the Solanaceae family with TGGAG consensus. Intriguingly, in spite of GLDV-2 showing an iteron arrangement conserved among NW begomoviruses, the direct TGGTG/TGGGG and reverse TGGTG iteron sequences are shared with OW begomovirus Ipomea yellow vein virus (IYVV) belonging to the sweepovirus clade and infecting the Convolvulaceae family, showing OW begomovirus iteron arrangement (three directed iteron up-stream TATA box and one iteron down-stream TATA box) with sequence consensus TGGTG , Tomato leaf deformation virus(ToLDeV), and Boerhavia yellow spot virus (BoYSV) FKIN and FRLQ IRD motifs shared with BGMV-BZ and TGMV-GT, respectively, whereas GLDV-2 shows the IRD FRIS motif shared with IYVV , FLTFP in two genera (Opunvirus and Mulcrilevirus), and interestingly, OW begomoviruses belonging to the sweepovirus clade, SPLCV, IYVV, and SPLCCNV, and both GLDV isolates showed FITYP consensus including the substitution of Isoleucine (I) instead Leucine (L) in the second position of Motif I FLTYP conserved in begomovirus genera  contains replication-associated iterated elements (iterons) that are virus-specific, whereas the right IR contains transcriptional regulatory elements of the AV1/CP gene  . An analus TGGTG . On the us TGGTG  similar us TGGTG . The gemus TGGTG . A compaith IYVV , which iith IYVV , and theith IYVV . Motif Ie family , as reves genera . The rems genera . Altoget4 showed a different phosphorylation pattern between AC2 proteins (Tomato yellow leaf curl virus (TYLCV) and Tomato golden mosaic virus (TGMV) AC3 proteins (Tomato leaf deformation virus (ToLDeV) and Boerharvia yellow spot virus (BoYSV) (ToLDeV clade), and with other NW begomoviruses according to those with full-length genome-based phylogeny  in three independent experiments. Nicotiana benthamiana plants inoculated with GLDV-1 displayed symptoms such as stunting and severe leaf curling, and were PCR-positive , whereas plants inoculated with the GLDV-2 isolate remained predominately asymptomatic 21 dpi and, nonetheless, showed 50% infectivity by PCR molecular detection (6/12 plants)  . On the  plants) . These rGeminiviridae family with single-stranded DNA genomes, particularly Begomovirus genera, are the major group of emerging plant viruses  according to the current ICTV demarcation criteria were discovered by data mining of our previous reported metagenomic data  is the reservoir of GLDV. Non-cultivated plants belonging to the Rubiaceae family, such as Galium mexicanum, are ranked as the third most important group of plants used in traditional ethno-medicine in Mexico  in 2021 showed that GLDV is currently established in these ecosystems surrounding cultivated areas, warning about a possible viral spillover to crops. Interestingly, the sequence of the amplicons obtained with specific primers is related to the GLDV-1 isolate, suggesting better fitness in such an environment. Recently, georeferenced metagenomics, (geometagenomics), has precisely linked individual sequence reads to plant hosts from which they were obtained and spatial arrangement of these hosts, enabling to study impacts of host diversity, host spatial variations, and environmental conditions on plant virus diversity and prevalence (Geminiviridae family (Tomato yellow leaf curl virus (TYLCV) genome are expressed and play a role during viral infection, implying that the repertoire of geminiviral proteins can be expanded (Tomato leaf deformation virus (ToLDeV). The phylogenic relationship of GLDV with a monopartite begomovirus and lack of cognate DNA-B  suggested that GLDV possesses a monopartite nature. Interestingly, a recombination analysis using both isolates of GLDV and all reported sequences of NW begomovirus DNA-A genomes did not render significant results, suggesting that GLDV parental sequences have not been currently discovered. A comparative gene-by-gene analysis of GLDV sequences showed that both isolates share high homology in AV1 and AC1 coding regions , in agreement with the conservation of these genes in the Geminiviridae family, followed by the AC4 gene . On the other hand, divergent regions were observed, including the left IR (85% nucleotide identity), AC2, AC3, and AC5 (< 89% amino acid similarities), and analyzed more in detail. The IRs of geminiviruses contain transcription and replication-associated elements, whose arrangement and consensus are conserved in OW and NW linages. The left IR (relative to stem-loop structure) contains replication-associated iterated elements (iterons) that are virus-specific, whereas the right IR contains transcriptional regulatory elements of the AV1/CP gene  , and two direct and one inverted iterons for the GLDV-2 present in a Tomato golden mosaic virus Guatemala isolate (TGMV-GT)). However, a GLDV-1 iteron consensus (TGGAG) is shared with NW begomovirus BGMV-GT, and, intriguingly, a GLDV-2 iteron consensus (TGGTG) is shared with OW begomovirus Ipomea yellow vein virus (IYVV) belonging to the sweepovirus clade and infecting the Convolvulaceae family. Sweepoviruses are monopartite and infect Ipomoea species worldwide, and they phylogenetically belong to a branch distinct from the OW and NW begomovirus linages; this branch seems to represent one of the earliest points of divergence in Begomovirus genera  will be necessary to validate the function of predicted different phosphorylation patterns. The alignment of GLDV-1 and GLDV-2 AC3/REn proteins, followed by secondary and tertiary structure prediction, showed that both proteins share different regions of helices and sheets in the N-terminal and central regions. However, a different sheet structure is observed in the C-terminal region between both isolates, and this change is correlated with changes in the spatial tertiary structure of proteins. AC3 is a viral replication enhancer, and its function is controlled by direct protein-protein interactions with host factors including retinoblastoma-related protein (pRBR) and proliferating cell nuclear antigen (PCNA), and viral protein autointeractions between AC1 and AC3 gene products (Tomato leaf deformation virus (ToLDeV) clade and with other NW begomoviruses according to those with full-length genome-based phylogeny. Additionally, the amino acid alignment of AC5 proteins of members of the ToLDeV clade showed that AC5 proteins are encoded by 84 amino acids (AAs) for GLDV-1 and 106 AAs for GLDV-2, and contains the conserved Gemini AC5-1 domain. The AC5 gene is conserved in different NW and OW begomoviruses ranging from 83 to 225 AAs and displaying one or two domains (Gemini AC5-1 and Gemini-AC5-2), and has been described as a pathogenicity determinant and gene silencing suppressor. However, in some cases, mutagenic analyses have shown that this gene is a cryptic gene that lacks functionality (Nicotiana benthamiana and tomato (Solanum lycopersicum) plants using GLDV-1 and GLDV-2 agroinfectious clones and analyzed 21 dpi. In Nicotiana benthamiana, GLDV-1 induced strong symptoms such as stunting and severe curling in all inoculated plants, which remained present until the late infection stage (35 dpi), whereas GLDV-2 inoculation resulted in predominantly an asymptomatic phenotype, and only an initial step of infection in several plants a minor symptom was observed. On the other hand, inoculation of both GLDV isolates in tomato plants resulted in an asymptomatic phenotype 21 dpi. The infectivity efficiency determined by PCR molecular detection showed that GLDV-1 presents 100 and 60% of infectivity in Nicotiana benthamiana and tomato, respectively, and that GLDV-2 presents 50 and 0% infectivity in Nicotiana benthamiana and tomato, respectively. These results corroborate the monopartite nature of GLDV and the differential infection capability of viral isolates previously predicted at the molecular level. In spite of both GLDV isolates displaying an iteron arrangement conserved in NW begomovirus linages, their iteron consensus is divergent. A GLDV-1 iteron consensus (TGGAG) is shared with NW begomovirus, whereas a GLDV-2 iteron consensus (TGGTG) is shared with OW begomovirus belonging to the sweepovirus clade. Thus, it is possible that differences in pathogenicity and virulence between GLDV isolates (at least in the host tested in this study) could be related to specific replicative adaptations influenced by Rep binding affinity to corresponding iterons and/or with host proviral factors. However, we cannot rule out a putative individual or the combinatorial role of divergent genes  in viral replication and evasion of host defense by gene silencing suppression or other molecular mechanisms. It is canonically assumed that new world (NW) begomoviruses are bipartite (Tomato leaf deformation virus (ToLDeV) in Ecuador and Peru (Tomato mottle leaf curl virus (ToMoLCV) and Tomato leaf curl purple vein virus in Brazil (Tomato twisted leaf virus (ToTLV) in Venezuela (Corchorus yellow vein Cuba virus (CoYVCUV) infecting the non-cultivated plant Corchorus siliquosus  in Cuba  . The lefs genera , suggests genera . To inits genera . GLDV-1 e family , showinge family , and 116e family  did not e family . Howeverppressor , and it ppressor . In vitrproducts . Directeionality  and remaipartite . Howeverand Peru , Tomato n Brazil , and Tomenezuela . Recentl in Cuba  was repohttps://www.ncbi.nlm.nih.gov/genbank/, OL689630; https://www.ncbi.nlm.nih.gov/genbank/, OL689631.The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found below: EG-R, ER-N, JM-L, and NL-L: conceptualization. EG-R, ER-N, and JM-L: formal analysis, methodology, and writing . JM-L: funding acquisition and resources. EG-R and ER-N: investigation. ER-N, JM-L, NL-L, and EA-C: supervision. EG-R, ER-N, JM-L, NL-L, and EA-C: writing (review and editing). All authors have read and agreed to the published version of the manuscript.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.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.