At the microscale, bacteria, viruses and other cellular organisms face fundamental challenges to propel: swimming in viscous liquids requires asymmetric stroke patterns to break the time reversal symmetry, while surface motility or motility in viscoelastic media requires a quite different approach. Often it is essential that the cells react to external signals (nutrients, poison, stress, temperature, light...). Their size iforbids instantenuous sensing of gradients, bacteria thus evolved clever intra-cell signaling pathways for, e.g., chemotactic motility [1]. E.coli run-and-tumble swimming patterns [2] driven by flagella enable chemotaxis and evading predators in liquids. On solid surfaces, P. aeruginosa perform twitching through extension-attachment-retraction cycles of type IV pili (TFP) [3], which seem to have a role in Pil-Chp chemotaxis [4], mechanotaxis [5] etc. More exotic forms of motility include the "wrap" mode of P. aeruginosa [6] where the flagellar hook buckles, wrapping the filament around the cell body to randomize reorientation and enhance environmental exploration efficiency, H. pylori’s screw-like propulsion to penetrate mucus-like yield-stress fluids [7], or Pseudomonas putida intermittent "run-stop" motility [8] with escape times from tissues following a power-law distribution. 

Microbial motility is typically driven by nanoscale organelles powered by molecular motors, such as flagella, TFP or cilia. Direct observation of dynamics of these filaments is challenging, especially TFP which is only about 2 nm thick. Recent progress in observation techniques for observing TFP activities in situ [9-12] is promising, but the microscopic mechanical information is still limited, and physical modeling [13-16] is practically essential to better understand the mechanisms of single cell motility. For instance, recent data-driven Bayesian modeling approach [16] infered biomechanical properties of TFP that are difficult to extract from direct observational methods. Important insight comes from molecular assembly modeling, fluid dynamics, out-of-equilibrium statistical physics and active matter [17]. For further progress, integrated approach is required: generating good quality experimental data and simulatin/AI tools to interprete and analyze them.

Microbial  self-organizing behaviors, i.e. collective motility such as swarming, pattern and biofilm formation is essential for their environmental adaptation and survival. Bacterial populations can move on self-generated trails via cell communication [18] and can form biofilms [19], ring-like, branched, and striped spatial patterns [20]. Classical pattern formation theories (e.g. Turing mechanism) typically focus on linear instabilities emerging near a homogeneous steady state under fixed boundary conditions, while in living systems pattern formation is coupled with spatial expansion. The formation of patterns at expanding fronts is influenced by environmental heterogeneity, growth-induced structural remodeling, and competition between motility mechanisms [21]. Such systems are generally far from thermodynamic equilibrium, posing significant challenges for theoretical analysis [22]. 

We eventually want to combine understanding of motility mechanisms and complex biological interactions in noisy and varying environments [23-25] to predict and control collective behaviour and evolutionary survival strategies of microbal populations. Through understanding the non-equilibrium characteristics underlying biological principles governing bacterial organization and pattern formation, we will ultimately enable the rational design and construction of diverse synthetic bio-patterns. Research progress is only viable by interdisciplinary approaches integrating biology, chemistry, data science and physics.