Convert SOAP SimpleOrder api requests to new REST api

we are trying to upgrade from SOAP SimpleOrder api requests to new REST api and can not find appropriate api for the following old SOAP request:
"ccAuthService_run", "recurringSubscriptionInfo_subscriptionID", "ccCaptureService_run" request. What new REST api call or calls should we use instead?

Request parameters used in SOAP service reference NVPTransactionProcessorClient.RunTransaction method:

var requestParameters = new Dictionary<string, string>
{
{"ccAuthService_run", "true"},
{"merchantID", MerchantId},
{"merchantReferenceCode", order.Id},
{"purchaseTotals_grandTotalAmount", amount},
{"purchaseTotals_currency", order.Price.Currency.Code},
{"recurringSubscriptionInfo_subscriptionID", subscriptionId},
{"ccCaptureService_run", "true" }
};

Start by reviewing the repository's C# REST samples and the listed SOAP parameters, focusing on authorization, recurring subscription, and capture operations. Determine which REST call or calls replace the combined request and document the mapping for the supplied merchant, amount, currency, and subscription values. Done means the replacement operation or sequence is identified clearly.