Harvard neuroscientist Venkatesh N. Murthy has a sunny second-floor office on Divinity Avenue, where he is a professor in Harvard’s Department of Molecular and Cellular Biology. In one corner is a set of weights and a soccer ball — both untouched in over a year, he said, because of an intensely busy schedule.

There’s a stack of jazz CDs — the 43-year-old Murthy is a fan, and admits to playing jazz guitar badly — and there’s a white board covered with arcane scrawls about his specialty: how brain cells connect with one another.

It’s a specialty involving vast numbers. There are an estimated 100 billion neurons in the average 3-pound human brain. Connecting them are as many as 10 trillion synapses, the circuitlike chemical pathways that link neurons to one another. “The power of higher brain areas,” said Murthy, “is in numbers.”

The numbers give neurons and the brain immense computational power, he said. In turn, the brain’s plasticity (functional flexibility) comes in part from synapses that can be big, small, weak, strong — a range of variations in the trillions.

Finding out how synapses grow, fire, modify, and break is important work. The synaptic impulses that link neurons are vital; they transform brain activity into motion by delivering messages from the brain and spinal cord to muscles and organs.

Yet the actual mechanisms of synaptic connectivity, at the cellular level, are “largely mysterious,” said Murthy — “Venki” to his friends. He has been at Harvard since 1999, arriving from postdoctoral work at the prestigious Salk Institute for Biological Studies. Only in the past decade, said Murthy, have scientists “begun to draw a reasonable cartoon” of how synapses work — how they grow, load up with the right chemicals, pass on information, communicate with one another, and get recycled.

Better understanding of how synapses work could one day have profound implications for the treatment of diseases affected by neural impulses. Included are Parkinson’s, autism, depression, and schizophrenia. (Mutations in certain genes tied to synaptic function have been linked to schizophrenia, whose genetic origins are an interest of Murthy’s.)

He and his research team are using the brains of mice to model how synapses work. Specifically, they are taking real-time pictures of the way synapses light up in a region of the brain called the olfactory bulb, where odor information is processed.

Eventually, they’ll explore the way synapses are altered by experience in a deeper and more complex region of the brain called the cortex.

In the meantime, the olfactory bulb as a model offers many advantages. It’s close to the surface of the skull, eliminating the need for imprecise and invasive probes. And it’s a sensory system — meaning that it has a known set of responses to known stimuli. A smell produces a predictable reaction within a discrete location of the brain.

But observing and measuring synaptic connectivity even in the accessible and transparent olfactory system is a technical challenge. For one, neurons are tiny, measured in millionths of a meter — each about 10 microns across. For another, their related synapses fire in transient bursts, covering just fractions of a second.

So Murthy and his researchers have built recording and measurement gear from scratch. In several labs there are combinations of powerful multiphoton microscopes; optical microscopy arrays that record synaptic firing and download it into computers as images; and machines that deliver sequential odor stimuli in precise doses to the noses of rodents.

In one lab, one such olfactometer sprouts 100 tubes, each capable of measuring out precise puffs of smell from synthetic chemicals. (Some of the odors are familiar, like camphor and spearmint. Most are synthetic chemicals known to light up the olfactory center.) The odor signals go to a mouse, whose cascade of changing brain reactions are captured on a computer screen.

In his office, Murthy presses a few buttons on his laptop. A video appears, showing a rodent skittering around a tiny box blanketed with an odorant-soaked paper towel. Attached to the mouse’s head is an array of hairlike flexible wires a meter long. They transmit, in real time, images of the mouse’s reaction to odor stimulation.

The skittering rodent is breaking scientific ground. So will the mouse soon to run in place atop a rotating plastic ball, in a laser-based measuring device being constructed in another Murthy lab. Ordinarily, observing synaptic activity is done in anesthetized animals, not ones that are alert, awake, and reacting to their surroundings.

In his first years at Harvard, Murthy continued his Salk Institute experiments, studying synaptic activity in vitro by watching how nerve cells from the hippocampus, isolated in a Petri dish, react to stimuli. That’s good for understanding the “detailed mechanisms” of synapse biochemistry, he said. But there’s no substitute for in vivo research — looking at “synapses during the actual behavior in the actual animal,” said Murthy. “We want to understand [synaptic connectivity] in the context of the real thing.”

Natural experiments like this, in monkeys, occupied Murthy when he was a doctoral student in physiology and biophysics at the University of Washington, Seattle.

Murthy’s doctoral thesis on nerve impulses in the cortex was a hit in the scientific press. He and co-researchers observed that a pattern of coherent (or synchronous) brain activity occurred more frequently during novel untrained behavior. The hypothesis: This mode of activity may coordinate multiple regions of the brain during complex behaviors that require attention. His dissertation, said Murthy, “is still my most-cited paper, and also my oldest in neuroscience.”

The India-born researcher admits to having taken — in academic terms — a rather eccentric path to get to where he is. His father was an engineer from a family of engineers, and Murthy himself — a gifted student — landed a coveted spot as an undergraduate in mechanical engineering at the Indian Institute of Technology in Chennai (Madras) in his native South India.

India’s seven Indian Institutes of Technology, including the one in Chennai, consider around 100,000 applications a year; 4,000 of these applicants are admitted.

“Once you get in, it’s hard not go there,” he said of the school — where his graduating class (1986) produced two other current Harvard professors: Ananth Raman (Harvard Business School) and L. Mahadevan (Harvard University School of Engineering and Applied Sciences).

He took a master’s degree in bioengineering in Washington, “but I was still writing equations and solving them for someone else,” said Murthy. “I still didn’t understand what science meant — trying to understand how something works, asking the questions, then finding the solutions.”

He transferred to the doctoral program in biophysics and physiology. At age 25, said Murthy, he was finally ready to explore science fully, including his first course work in biology.

By the time he left Seattle, he had settled on his life’s work, a cellular-level analysis of neurons. Salk “was the best I could have done,” said Murthy — a multidisciplinary immersion in how synapses work. Synaptic transmission “is an elementary event, (common) to all animals,” he said, calling it a still-mysterious arena of “exquisite regulation.”

At home in Newton, Mass., there’s exquisite regulation of a sort too. The onetime graduate school soccer player and touring bicyclist is getting a workout raising his two daughters (Sophie, 4, and Sonia, 1) with his biologist wife Meredith, a biotech clinical trials specialist. Murthy is between two busy worlds — long hours of research and deep hours of child care.

Luckily, there is coffee. An espresso machine ticks away in the anteroom to his office, where graduate students catch a bite and read. “I admit,” said Murthy, fussing with a china mug, “to being slightly addicted.”