For this build we will be taking advantage of sentinel weapon buffs, warframe buffs, and arcanes to maximize the amount of damage that the weapon can inflict. Against popular belief, testing out multiple arcane and mod combinations on this specific weapon against status resistant enemies and bosses such as the Archons and Specters created some interesting insights on the weapon.

Headshot Powerhouse:
The [Synapse] is one of the few weapons capable of using both corrosive and viral damage to rip apart any enemy. Due to the perfect accuracy of this weapon even when reducing the accuracy statistic, headshot kills are also both easy to make in large enemy encounters and to keep buffs from resetting. The Primary Deadhead Arcane not only provides increased damage per headshot kill, but also increases the headshot damage multiplier. Combined with [Galvanized Scope] and [Bladed Rounds] for increased critical chance and critical damage on headshot kills while aiming, this maximizes the capability of the weapon when combined with additional warframe abilities, mods, and arcanes. With both [Galvanized Scope] and [Point Strike], the [Synapse] can obtain orange criticals consistently with the combined critical multiplier of 18x. Infected clip and Rime Rounds can combine with the corrosive on the weapon to create a corrosive/viral weapon while keeping the numbers closer in line with each other for a more even status proc experience. By equipping all of the vigilante mods onto a sentinel weapon, we can push the critical capabilities for a 20% chance of performing over 300% critical chance for red criticals and the combined critical multiplier of 27x. With [Vigilante Supplies] not being needed on the weapon itself, we can choose to either add [Primed Rifle Ammo Mutation] for better ammo supply or [Sinister Reach] for the added beam distance. Lastly, we can pair the weapon with a Warframe using subsumed [Rhino] Roar on a strength build to increase the faction damage value of the weapon along with the Arcane Acceleration and Arcane [Rage] Arcanes providing a constant 90% increased rate of fire to speed up damage per second and the additional 240% increased damage on landing a headshot that pairs well with [Galvanized Scope]. While I originally thought to remove [Serration] due to the amount of additional increased damage buffs present, upon further testing [Serration] continued to be the optimal choice when combined with all additional buffs present.

positives and negatives:
This weapon as is will melt almost anything instantly under level 400. While this is significantly more powerful than any other build I have worked on for the [Synapse], this build also requires both headshots and multiple headshot kills before the weapon capabilities become noticeable on bosses. In certain situations or during bosses such as archons and high level specters, while the total possible damage may be much higher, the need to stop shooting bosses to find enemies to keep buffs active is situational and harder to consistently occur depending on team members or mission requirements. Note that neither corrosive or viral can stagger enemies making for an easier time focusing on headshots with this setup and in not focusing on slash procs like [Hunter Munitions], this build is both still fully usable on enemies immune to status procs and you wont be fighting over headshot kills with your own slash procs.

With a Riven:
If you have a riven, my recommendation would be to remove [Bladed Rounds] for a riven that contains critical damage. If you have a Riven with both critical chance and critical damage, upon testing with multiple rivens and mod/arcane combinations, I would recommend removing [Galvanized Scope] for [Heavy Caliber]. After a long amount of testing, [Heavy Caliber] seemed to provide the most noticable increase in this specific case. You can also equip the [Verglas] to your sentinel with increased status mods and swap primary deadhead for primary [Frostbite] depending on what you have on your riven. Primary [Frostbite] can be activated from the sentinel weapon allowing you to keep the rest of the build intact. This can modify the above build from requiring the original headshot kills and hits to be much more accessible while dropping the total possible damage output moderately.