server.R

library(shiny)
library(tidyverse)

genes <- c('A','B','C')
expression <- cbind(rbind(10,100,50),genes) %>% data.frame()
colnames(expression) <- c('Expression','Gene')

shinyServer(function(input, output, session) {
  updateSelectizeInput(session, 'Gene', choices = genes, selected=c('A','C'), server = TRUE)
  
  output$boxPlot <- renderPlot({
    input$pan_button
    isolate({
      input.gene <- input$Gene
      plot_data <- expression %>% filter(Gene %in% input.gene)
      ggplot(plot_data, aes(x=Gene,y=as.numeric(as.character(Expression)))) + geom_bar(stat='identity') + ylim(0,100)
    })
  })  
})

ui.R

library(shiny)

fluidPage( actionButton('pan_button','Re-draw Plot!'),
           selectizeInput('Gene',strong('Gene:'), choices = NULL, selected='ABCA4'), 
           plotOutput('boxPlot'))