I would design a microservices architecture using Express.js by creating loosely coupled services that communicate over HTTP or message queues. Key considerations include service discovery, load balancing, API versioning, and error handling to ensure resilience and scalability.

In a scalable microservices architecture, each service should encapsulate a specific business capability and expose a RESTful API using Express.js. This allows for independent development, deployment, and scaling of services. Service communication can be done via synchronous HTTP calls or asynchronous messaging through a message broker, depending on the use case and latency requirements. It's crucial to implement service discovery to dynamically route requests to instances of services, especially in a cloud-native environment. Load balancing ensures that traffic is efficiently distributed across instances, and API versioning allows for seamless upgrades without breaking existing clients. Additionally, robust error handling and fallback mechanisms are necessary to enhance the system's resilience against failures. Tools like Circuit Breaker can help manage this complexity effectively.

To handle a large number of concurrent database connections in an Express.js application, I would use a connection pooling strategy in combination with an ORM or query builder. This allows for reusing existing connections and minimizes the overhead of establishing new ones, thus improving performance while monitoring and tuning database queries to avoid bottlenecks.

Connection pooling is critical in high-concurrency applications as it limits the number of active connections to the database, which not only enhances performance but also prevents overwhelming the database server. Each connection in the pool can be reused across multiple requests, reducing latency and resource consumption. Additionally, using an ORM like Sequelize or a query builder like Knex can streamline database interactions, but it’s vital to ensure that queries are optimized and indexed appropriately to avoid slowdowns. It’s also important to handle error cases gracefully, like retrying transactions on failures, and to incorporate monitoring tools to track connection utilization and query performance over time.

Edge cases can arise with connection limits imposed by the database or the pool itself. For instance, if the application faces a sudden spike in traffic, requests might get queued if connections are fully utilized. Implementing robust error handling and fallbacks, such as returning appropriate error messages or utilizing caching strategies, can help manage user experience in such scenarios. Furthermore, as the application scales, reviewing and potentially increasing connection limits based on usage patterns becomes essential.