## NaPoWriMo (National Poetry Writing Month)

This coming month, April 2022, I am planning to participate in National Poetry Writing Month, and I will be writing a poem a day in response to prompts posted online. This is my first time participating and I am excited for the challenge. I will update this post with my daily poems.

*The italicized text gives the context and prompt for each day

DAY 0: Emily Dickinson Inspired Poem with Humor/Irony

To be in a room full of people yet still alone –  The warm closeness coexists with frigid emotional distance.

DAY 1: A Prose Poem that is a story about the body

CW: Eating Disorders/Body Image

Last year, when I saw her approach me, I examined the way her flesh bulged above her hips, the way her breasts draped over her ribcage like the comforter over the side of my bed. “Moti ho gayi. Khao mat,” I commanded, and she complied until she was back home at night after all her friends had left, and without the judgmental eyes looming over her, she headed right for the stash of protein bars and sugar-infused cereal, and she sat in a corner on the tiles of the bathroom floor and devoured bite after bite until it was time to throw the empty boxes into the recycle chute, and she cried and cried until the veins bulged in her eyes like raisins, and the salt-water stained her smooth, flushed cheeks, and I told her “Nikaalo.” I stared at the disgusting bulges on her skin, the fibrous white marks on her arms, thighs, belly, under her armpits until the nausea was too much for me to take, and she retched over the toilet and coughed until the smell was no longer bearable, and there was nothing left in her throat but stomach acid. Then, she glanced at me with eyes glistening and fresh tears streaming down her cheeks, and I nodded approvingly, and she rinsed and repeated, day after day. But this year, when we meet, I notice, instead, the glint of curiosity in her eye and the dimple in her right cheek and the cascade of shiny waves of her mermaid hair flowing down past her hips, her strong legs that allow her to run and her sturdy shoulders that allow her to bend the water she swims through, and the soft curves that could beget a new life if she so chose. I could have zeroed in on the bulges or the stretch marks, but this year, I am learning to be more kind.

DAY 2: Poem based on the definition of the word funny: FUNN-Y: “The -Y at the end of FUNNY is an old English suffix meaning full of or having the qualities of.”

After it happened, I stopped laughing. I still went through the motions of opening my mouth and deliberately letting out sounds that mimicked the involuntary expressions of joy from people around me, but the sound never reached my eyes.

I used to tell jokes, loads of them, just for fun, simply to make others around me laugh, to see the crinkles in the corners of their eyes and feel the warmth that I had spread to them. But I stopped telling jokes and stopped receiving them – they bounced off my ears like light hitting a mirror because the world no longer felt like a fun place. Because I didn’t see the purpose of fun anymore.

When she asked me how things had changed after increasing the dose of my medication, at first, I hesitated. I knew there was a change, a new spring in my step, a new air of lightheartedness, and less time spent wallowing in my own tears, but when I finally found the words to described the change, it came down to simply this: “The pills’ve made me funny again.”

DAY 3: An Attempt at a Glossa: A Poem that responds to another poem

This poem uses each line in another poem as the last line of the stanza. This poem I wrote is in response to the following lines in the lyrics of the song “We’ll Never Have Sex” by Leith Ross:

You look perfect, you look different

If I said you could never touch me

You’d come over and say I looked lovely

Day after day, I listen

As you compare yourself to other women

You don’t think you measure up to their standards

But I think you’re enough because you are you

You look perfect, you look different.

You’re there for me through thick and thin

When you say you’ll be there, you’ll be there

When you’re busy, you tell me you’ll be a while

I don’t wait by the phone; I know you’ll be back

We can sit in silence devoid of tense awkwardness

Between moments of closeness, we also carve out space

Before lovers, our friendship was the foundation

And I don’t doubt that you would stay

If I said you could never touch me.

You are the standard and I refuse to compromise

Because I know it’s what I deserve

So for now, I wait and rejoice in solitude,

Learning to self soothe, so that when the time comes,

If I ever manage to want you without needing you,

You’d come over and say I looked lovely.

DAY 4: A Poem in the Form of Poetry Writing Prompts

1. Go into the kitchen and turn the gas on the stove.
2. Put out a frying pan and drizzle some olive oil.
3. Finely chop a clove of garlic.
4. When the pan is hot, drop the minced garlic into the sizzling oil.
5. Write a poem about the sounds and smells that fill the room.
6. Write about how your senses and emotions process the anticipation of an unrealized meal.

DAY 5: A Poem About A Mythical Creature Doing Something Unusual or Unexpected

Today, she floats deeper in the sea, watching her sisters from a distance as they lure men from the ships to the water with their irresistible, saccharine melodies. She swishes her tail back and forth, glistening eyes bobbing up and down above the water as she holds herself in place. She finds a pocket of warmth in the endless expanse of saltwater, cups her hands and leads it to her mouth, tilting her chin up as the water floods her dry mouth. She lets out a stream of gargles, before spitting it back into the ocean, expelling the virus that causes her throat to form a coat of mucus and makes her voice so hoarse that no sailor would ever come near her. She rinses and repeats for as many days as it takes for the raspiness to escape her tunes, and then she can return to her sisters, COVID-19 antibodies in tow.

DAY 6: Acrostic Poem with the First Words of Each Line is Part of a Phrase

IT’LL be a miracle if I ever

HAPPEN to find the love of my life

WHEN the era of meet-cutes seems over. Today, as an adult, if

YOU want to find love, especially as a queer person, you have to go on apps or at

LEAST make a conscious effort to leave the house if you

EXPECT to meet single and available, interested and interesting people, but

IT can be exhausting and hard, especially during a global pandemic that oscillates between complete and partial lockdowns.

DAY 7: A Poem That Argues Against a Common Phrase

“If they wanted to, they would.”

Sometimes, I want to,

But I’m too tired to get out of bed,

I’m too busy with responsibilities I can’t avoid,

I’m too bogged down with existential dread,

I’m barely able to remember to eat,

I’m worried that maybe you don’t want to,

That I’m burdening you with my presence,

That you’re only keeping the pretense of our connection

Because you’re afraid to say “no.”

DAY 8: A Poem About My Alter Ego

Someone who isn’t afraid to say what’s on her mind,

Not concerning herself with being perceived as kind,

Someone who is social and eloquent and loud,

Someone who doesn’t hesitate to let you know they’re proud.

I AM HERE, she declares as she enters the room.

Heads turn and the voices of others drown out.

She is assertive, vivacious, and the life of the party.

Her energy commands you as if to say: ATTENTION ON ME.

DAY 9: An Attempt at a Nonet

Nothing made me realize my own growth

more than arriving face-to-face

with just what I used to crave

pining, desiring,

choosing to turn

away, no

second

glance.

DAY 10: A Love Poem

Platonic love is the true romance

ignored by poets and movies,

because it’s much more exciting to describe a rush

than a slow-growing fondness,

much easier to describe the intensity of a crush,

the spike of anticipation of all they could be

rather than the stable, even boring familiarity that blooms over years

of sitting together and doing nothing.

But there is something so beautiful and pure

about genuine platonic friendship and its characteristic comfort;

your friends, who have nothing to offer,

not the spike of adrenaline, not sex, not exclusivity,

but just the space to be authentic, messy, and untethered

to the anxiety, uncertainty, and inherent ephemerality

of attraction and romantic love.

DAY 11: A Poem About Something Large

My dog weighs just under twenty pounds,

The smallest member of my family.

When I first picked her up from the shelter,

she was just four pounds and quieter than pindrops,

and yet, when I carried her into a coffee shop,

a man approached me and said,

“That’s a tiny dog, but she has a BIG heart.”

And over the past seven years, time and time again,

living with little Lily has confirmed

the way she bounces to the door when I come home,

even abandoning treats in favor of a greeting,

the way she curls next to the bathroom door until I come out,

or the way she senses my sadness and licks my tears away,

nothing is as unquantifiably large and limitless

as the patience, loyalty, and pure love of a dog.

DAY 12: A Poem About Something Small

Hydrogen,

The smallest atom on the periodic table,

One proton, one electron, no neutrons.

Add one neutron to get deuterium,

and add two to get tritium,

both isotopes of hydrogen itself.

Adding or taking electrons gives a charged form of hydrogen,

and adding or taking neurons changes the mass.

Only adding protons changes the identity of Hydrogen,

Hydrogen is present in many compounds,

including water, carbohydrates, proteins, and fats.

So strange to think something so small

makes up the glue that binds

everything as we know it.

DAY 13: A Poem About Optimism

I think the key to optimism,

contrary to what one might assume,

is not to have faith that everything will go according to plan,

for the expectations built to the point of distance from reality are often the root of our pain as they crash down.

Rather, the key to optimism is the conviction

that whatever does happen,

regardless of whether or not it is what we envisioned,

there is something to be gained from it.

Thus, one is not tethered to any unreliable, everchanging circumstances,

but rather the conviction that whatever our circumstances are,

they are nothing beyond our capacity to either endure or change.

DAY 14: A Poem About the Opening Scene of the Movie of Your Life

The opening scene of the movie of my life

starts with a pan above the 5-freeway in La Jolla,

with the vibrant turquoise and white freeway signs showing the exit,

La Jolla Village Dr,

and on the bridge running across, above the freeway, reads:

University of California San Diego.

My alma mater, a few hundred miles and hours from where I was born,

it was here that my life began, along with the grieving process

of over twenty years spent pretending to be someone else.

DAY 15: A Poem About Something You Have Absolutely No Interest In

A seemingly innocent exchange begins

setting my preferences to “interested in women” and swiping.

The matches start to come in

and I feel a hit of validation at the thought

that these women I find aesthetically pleasing upon first glance

are interested in starting a conversation with me too.

“Hi, gorgeous,” a message pops in my inbox,

followed by a string of heart-eyed and fire emojis.

But after a few innocuous exchanges,

the inevitable surfaces:

“My boyfriend and I are looking for a third. Are you down to play with us?”

The high from the validation drops like the steepest waterfall,

and I resist the urge to reply

“There is absolutely nothing that interests me less.”

To be clear, I’m not opposed to something casual,

Something with a man or even polyamory.

What ruffles my feathers is the disrespect,

the assumption that my sexuality alone

determines how willing I am to lend my body

for the consumption of a man and a woman,

roots of heteronormative society’s ideal nuclear family,

simply to be discarded when they no longer have any use for it.

DAY 16: An Attempt at a Curtal Sonnet

I long to live a day without worry

A day devoid of deadlines approaching

A day where all the tasks are completed

An hour, a minute, a second, just one,

Where I don’t have to answer anyone.

I long to clear my list of tasks today,

But as the clock approaches the PMs,

The list seems to only grow even longer,

To-Do’s swirling around, vortices in my head,

Haunting me, even when I go off to bed,

For now, it seems endless.

DAY 17: A Poem That Is A Stream of Consciousness Starting With Dogs

Lily is my best friend in the whole wide world,

I might go as far as to say the best dog in the whole wide world,

But some might, understandably, protest that I’m biased.

She is a dog, but she behaves like a cat;

Rather than clinging to me, her attachment is more subtle,

She often protests when I attempt to give her a cuddle,

And yet she never strays far from my side.

There are times when she gets in a playful mood

And her eyes have a laser focus as she zeros in

At the ball, the bone, the toy, or the treat,

And she completes any task you throw at her,

Propelling herself forward or upward, her legs four coiled springs just released,

Hurling her long body in the direction of the target without a second thought.

Sometimes, I wonder if there is something to be learned

From this laser focus on an object,

Whether my unending questions of What? Why? How? hinder my progress,

If people who are motivated to continue in the rat race of capitalism

Simply by the anticipation of the carrot it dangles,

Growing further and further away as you approach,

Just as zero seems to grow further away each time you divide epsilon,

The endpoint is merely a concept, but not a tangible, achievable reality.

But perhaps it is easier to deal with the strife of chasing

Than the agony of questioning whether there is anything to chase.

DAY 18: Five Answers to the Same Question

I’ve always wanted to go the academic route, and nothing has changed.

The market sucks right now, so I might settle for any teaching position I get.

I’m actually looking at scientific illustration or intersections of science and art.

I’m open to literally anything.

Do you seriously think between the pandemic and climate change, our society is even going to survive the next few years?

DAY 19: A Poem That Starts With a Command

I saw you

and I know you saw me

and I know you saw me see you

but we haven’t spoken in over a year

and even when circumstances brought us

in close proximity in the past,

we were never close,

never exchanging anything beyond

pleasant formalities.

I have things to do

and places to be

and you likely do too (though I wouldn’t know),

so please, spare me the emotional energy

from a fake “how are you?”

and a false promise to “catch up”

on a friendship

that never even crossed the start line.

DAY 20: A Poem That Anthropomorphizes Some Kind of Food

Chips are that food that I don’t particularly crave;

Clearly they aren’t quite the paragon of health,

But even the taste isn’t one that particularly entices me,

And when offered the choice between chips and crackers, my answer is clear.

But when there is a plate of chips sitting on a table in my vicinity,

Or a general bag of chips thrown in an event’s complimentary mealbox,

I will inevitably chase chip after chip with another chip down my throat,

Devouring every last morsel.

If chips had the ability to scroll through therapy infographics on Instagram,

If they came across some overused misattributed spiritual quote such as

“Never allow yourself to prioritize someone who treats you like an option,”

I imagine any self-respecting bag of chips

would make the executive decision

To stop allowing themselves to be consumed

By someone who only chooses them out of boredom.

DAY 21: A Poem that asks you to recall someone you were once close to but no longer in touch with, a job you once had but no longer do, and a piece of art that is stuck with you over time, ending with an answerable question.

Sometimes, I wonder if you ever think of me, if you dare to google my name and see all I’ve done since that Tuesday afternoon in March 2013 – how far I’ve come and how much I’ve grown, but then I remember that if you cared, you would have reached out. You would have never let me go, You would have never abandoned me without a word after telling me, unsolicited, that I could tell you anytime I needed support when I felt suicidal, that I could count on you. That we were like family.

That monotonous, painful summer of 2013, I drove to my 9-5 babysitting job, choosing surface streets over freeways because I’d just gotten my license, stopping at every traffic light along Moorpark Street, turning a twenty-minute commute into an hour, with nothing to fill my emptiness but the scorching sun and the blaring ratio, 104.3.

You didn’t have to cut me off.

You treat me like a stranger.

Now you’re just somebody that I used to know.

The lyrics of Gotye’s Somebody that I Used to Know stuck in my mind like a tough stain on a white shirt, They pounded on my brain, forcing me to acknowledge the feelings I didn’t want to accept.

Gotye was likely singing about a messy breakup with a girlfriend, and you weren’t my girlfriend…and maybe that’s why you felt justified in leaving me without the closure that a romantic breakup would provide. I can acknowledge that there are reasons that I’ll never understand, why you chose to cut me off despite our close relationship – you have every right to, and you don’t owe me any explanation. But as someone who was my best friend, my sole confidante, my shoulder, my trusted listening ear – and also, I thought, an open book about your own fears and insecurities – I know with time and distance, after high school, our bond wouldn’t be the same, wouldn’t be as strong, but I never expected it to end up like this, leaving me reflecting on the past three years, ruminating on every word I said, wondering exactly what mistake I made that made you change your mind about how “special” I was to you.

At the age of eighteen, you taught me everything I knew about love, friendship, acceptance, and pain, both by what you said and what you didn’t say. The lessons you told me about resilience and bouncing back from mistakes, about not expecting myself to be infallible, but using those mistakes as a springboard for growth – I had to apply those very lessons to the pain and shame I felt of losing you at a time I most needed the friend that you promised you’d be. I blamed myself that the one person I’d poured out my heart and soul and vulnerabilities to – and you assured me that I wasn’t “dumping” too much – was the only one who couldn’t bear my presence enough to tell me why you couldn’t talk to me. It made me question whether there was something wrong with me, if all my other friends would leave the same abrupt way you did. Scared to trust, scared to open my heart to someone new in fears that I was too high maintenance, too needy, too clingy, that my mental illness would scare them off – that they would go from being just a text away to blocking me on all social media in just a couple days with no explanation.

At one point, I’d have been dying to know what you’d think of me now that I’ve grown, now that I’ve found the will to live and I don’t need you anymore, whether you’d want to be friends again. But as I’ve taken the role of being the confidante, the shoulder, the friend to many others who depended on me, I realized that what we had was never true friendship or love, because I would never treat someone I love that way. I’ve realized that boundaries can be kind and that it’s better to be honest about any limitations in my ability to provide support, to learn to say “no” than to say “yes” to someone who depends on me just to avoid the discomfort of telling something that they might not want to hear. Ultimately, the lack of respect and communication hurts more than a loving “no.”

I’ve learned that closure can never come from the same person who made me seek it; it has to come from myself. And for me, closure came from realizing that I didn’t need closure from you to go on.

So I don’t care whether you google my name, whether you’d be proud of the person I am now. I’ve mustered up the courage to forgive myself, and to open my heart again to new friendships, knowing that there’s no way to guarantee that they’ll last, but choosing to risk it anyways.

Is there any way to avoid pain, loss, and disappointment? Will I continue the pattern of subconsciously seeking out friends and partners that remind me of you, that remind me of my mother, just to relive the trauma of being emotionally abandoned by someone I trust and depend on and hoping for a different outcome? I can never know for sure, but what I do know is that I used to seek people like you, to fill the void in my heart that the loss of our friendship left, and now I’m making an honest effort to seek people more like me. Because I know that genuine friendship is worth the risk. And whether or not you’d be proud of me, for that, I’m proud of myself.

DAY 22: A Poem that uses repetition

When I was young, I used to question everything.

Every phrase uttered by my mom, dad, grandma, or aunt was followed by “How come?”

“How Come?” was so notorious that my aunt donned me with the nickname “Ms. How Come.”

For every “How Come?”, my mom seemed to have an answer – a deceptively simple one.

I thought the path to adulthood would be like the driving test at Legoland- linear, with clear instructions, and easily transferable knowledge from parent to child.

I carried “Ms. How Come” to my high school Chemistry class, questioning everything we learned until my teacher admitted that once we got to college, we’d learn that most of what we learned was a lie anyway.

“They’re just lies to make things simple enough to learn at this stage,” she explained.

In college, I first learned the phrase “All models are wrong, but some are useful.”

Could it be that all I’d been taught in school was just a model, just an attempt to make sense of things beyond comprehension? A desperate search for patterns within utter chaos?

As an adult, I’ve realized that the distinction between childhood and adulthood is yet another useful lie to make things simple – while the official cutoff is eighteen years from birth, the real boundary is murky, fuzzy, and variable.

As adults, we eventually come to accept things as they come to us, settling into an easy familiarity and answering children’s questions with deceptively simple explanations.

But it’s not clear whether adults are closer to knowing “the truth.”

Sometimes, finding “the truth” requires questioning the useful lies we’ve been told to keep things simple, and doing so requires the wisdom to ask “How come?”

DAY 23: A Short and Snappy Poem

We’re quick

to call others

brainwashed,

our friends and family

seemingly sucked into

religion,

cults and MLMs,

failing to recognize

how we were so

brainwashed

that seeing the

very structures

that tether us

reflected

back to us:

ideologies,

personal biases,

groupthink and hierarchical corporate structures,

and we invent

a name,

brainwashed,

that we tack onto others

and not to ourselves.

DAY 24: A Poem with a “Hard-Boiled Simile”

When I started taking antidepressants,

I learned I couldn’t drink,

which for some might feel like a death sentence,

but for me, it was an excuse not to pretend to enjoy

downing clear liquids

that taste like the smell of nail polish remover.

DAY 25: A Poem in which a woman appears who represents or reflects the area in which you live

Every day I spend

shut up in my apartment

telling myself I will work

and failing to do so,

feeling guilty,

not only for not doing the work

but also for not taking a conscious, guiltless break.

The woman of the waves comes to visit me in my dreams,

Blowing from the Pacific,

over the sand of the beach,

across PCH,

up the flimsy, sandy cliffs,

through the park and the grass patches soaked in dog urine,

across Main Street,

through First, Second, and Third Street Promenade,

and past the library,

all the way up to my patio glass window.

She knocks on the glass,

the cold of the night spreading remnants of air that fade in seconds.

“You forgot to visit me,” she mouths through the glass.

Another day and night of my eighteen-month lease passes

without taking advantage of my proximity to the beach.

DAY 26: A Poem about an Epic/Extended/Homeric Simile

My mind is like a planet,

Orbiting around the sun,

Only there are many suns competing for the same planet,

And the planet jumps from sun to sun,

From orbit to orbit,

Sometimes staying longer and sometimes making a quick transition,

Each time returning to the same, familiar, repetitive path around each sun,

Unable to break free from the cycles

Of cycling around a center outside itself.

DAY 27: An Attempt at a Duplex

The scariest thing to learn

Is that you are the only one you can rely on.

On days, someone might let an ear,

For years, you might share space with another.

Another day might come when that connection ends,

And you learn to reclaim the space as yours.

You might share them with others, but they’ll always be yours alone.

Alone is how you’ll spend most of your life,

Even when you live with others, there will be moments of distance.

Distance from some might drive you closer to others,

And one day, you learn that there was never “the one.”

One person will never truly fulfill you in every way, and that, for me, is

The scariest thing to learn.

DAY 28: A Concrete Poem

they

are shaped

like pears because

all the particles of liquid

are rushing to reach the center

of gravity, but they can’t all be at

the same place at the same time, and

and there are intermolecular forces th-

at bind the molecules to one another,

forming a smooth surface, but there

are a few that fall behind, like strag-

glers in a race, forming the cone-

like protrusion on top.

Sensitivity

and a curse.

Sensitivity allows you

to see past people’s smiles,

“How are you, really?”

It allows you to be attentive

to the most minute of details,

To craft the most compelling songs,

to compose the most vibrant paintings,

touching others

by capturing the essence of human emotion.

Sensitivity also makes you vulnerable

to the most disproportionate anxiety,

rendering you reactive

upon detecting the most minute change in tone,

the most subtle shift in energy,

the quietest cry for help.

Sensitivity can drain you,

flood you,

overwhelm you,

and the only thing that helps

is setting boundaries,

while taking care that they don’t turn into impenetrable walls,

preventing you from receiving the very information

that is the source of your energy.

DAY 30: At Attempt at a Cento: A Poem made up of lines taken from other poems

Today I don’t feel like doing anything,

My room is a tank, I’m a fish

The muscles in our legs aren’t used to all the walking

I’m laying on the floor

All day, staring at the ceiling, making

friends with the shadows on my wall.

Feels like I’m buried yet I’m still alive.

Some kind of madness swallowing me whole.

Sometimes I want to disappear.

Hold on, feeling like I’m heading for a breakdown.

Tomorrow might be good for something

Because there’s beauty in the breakdown.

The lines in this poem are taken from song lyrics in The Lazy Song (Bruno Mars), Strangemirror (Shyamala), Waste (Foster the People), affection (BETWEEN FRIENDS), If I Ever Feel Better (Phoenix), Unwell (Matchbox Twenty), Madness (Muse), Houdini (Foster the People) and Let Go (Frou Frou).

And that’s a wrap for NaPoWriMo 2022! I’m glad I was able to finish the challenge and respond to all 30 prompts on time (though it took much longer for me to type them up here). One thing I found myself having trouble with at first was trying to water down my individual experiences to make my work more relatable for those who may or may not know me or share my identities, but I think I ended up preserving at least some of my individual experiences, and I will continue to unlearn this as I find my own voice! I also would like to get better at meter and writing poetry through more imagery rather than writing ideas literally, but I think this was a good start and I’m glad I tried this!

## Network Dynamics, Biophysics, and Mental Illness

[latexpage] This past fall was my first quarter of graduate school, and one of our core courses was Deterministic Models in Biology. For our final project, we chose a quantitative biology paper on a topic of our interest and presented on it to the class. The paper I chose was a review paper, Psychiatric Illnesses as Disorders of Network Dynamics by Daniel Durstewitz, Quentin J.M. Huys, and Georgia Koppe. My undergraduate research focused on the dynamics of neurons at the molecular level, and this paper helped me connect it to specific characteristics of mental illnesses.

This paper proposes that since observable cognitive and emotional states rely on the underlying dynamics of neuronal networks, we should use Dynamical Systems Theory (DST) to characterize, diagnose, and develop therapeutic strategies for mental illness.

The central idea of DST is that there is a set of differential equations that evolve in time. A set of dynamical equations could look as follows:

$\frac{dx_1}{dt} = \dot{x_1} = f_1(x_1, … , x_M, t; \boldsymbol{\theta} )$
$\frac{dx_2}{dt} = \dot{x_2} = f_1(x_1, … , x_M, t; \boldsymbol{\theta})$
$\vdots$
$\frac{dx_M}{dt} = \dot{x_M} = f_M(x_1, … , x_M, t; \boldsymbol{\theta})$

The variables $x_1, x_2, … x_M$ represent the dynamical variables such as voltage or neural firing rate. These equations describe how each of these variables change over time. $\boldsymbol{\theta}$ represents parameters, fixed values that are properties of the system that do not change over time.

We define a fixed point as the point at which the derivatives of all of the variables are equal to 0. Fixed points are stable if activity converges towards them, and unstable if activity diverges from them. Stable fixed points are called attractors. We can define the basin of attraction as the set of points from which activity converges towards the attractor.

The figure below shows an example of a phase plane, a representation of a space spanned by the two variables of a system. Note that it is possible to use dimensionality reduction methods to obtain visual representations for higher dimensional systems. The arrows show the activity of the system. The blue and orange curves represent nullclines, and along each of these curves, the derivative of one of the variables is 0. The green line represents the barrier between the two basins of attractions. It is possible to cross over this barrier as a result of either external influences or random fluctuations.

I will discuss some basic neuroscience before going into the dynamics of mental illnesses. There are many ion currents that pass through a neuron membrane such as sodium, potassium, and calcium. The dynamics of these ions are driven by electrochemical gradients. Spiking activity occurs when there is a rapid influx of sodium ions, producing the spike followed by an efflux of potassium ions, returning the membrane potential to the threshold potential.

We can think of a neuron membrane as a capacitor, where positive and negative charges are accumulated on either side. The current is the rate of charge flowing per time, $I = \frac{dq}{dt}$, and the charge of a capacitor is defined as q = CV. The current through the membrane is this $I_m = C_m \frac{dV_m}{dt}$. We can think of this system as the circuit shown below:

Because of charge conservation, the sum of the currents across the capacitor and each of the resistors must be 0. In mathematical terms, this is $C_m \frac{dV_m}{dt} = -\sum_i I_i$.

If we approximate each of these currents as ohmic, they will satisfy Ohm’s law, V = IR, meaning that the current is proportional to the difference between the membrane voltage and the threshold voltage by a factor of 1/R, or in other words, the conductance.

If the conductance were constant over time, these would be linear. However, the conductance depends on the proportion of ion channels that are open and the proportion of channels that are closed, called the gating variables. For example, a sodium current can be described as

$I_{Na} = g_{max}m^3h(V_m – E_{Na})$

In this system, m and h are the gating variables, and they vary from 0 to 1, and $g_{max}$ is the maximal conductance.

We can think of the dynamical equations for the gating variables as the result of a mass equation. Consider the reaction

$Closed \rightleftharpoons Open$

Suppose $\alpha$ is the rate of opening of a channel, or the forward reaction above, and $\beta$ is the rate of closing, the reverse reaction above, and both of these rates depend on the voltage. If m represents the proportion of channels that are open, the derivative over time is equal to the  forward rate times the concentration of reactants minus the reverse rate times the concentration of products. In other words:

$\frac{dm}{dt} = \alpha(V_m)(1-m) – \beta (V_m)m$

Another form of this dynamical equation commonly seen in the literature is:

$\frac{dm}{dt} = \frac{m_{\infty}(V_m) – m}{\tau_{Na}(V_m)}$

$\tau_{Na}$ is the voltage-dependent time constant, and $m_{\infty}$ is the steady-state proportion of open channels as a function of voltage.

The dynamical equation for voltage for the simple NaKL model is as follows:

$\frac{dV}{dt} = g_{Na}m^3h(E_{Na}-V) + g_K n^4 (E_K -V) + g_L (E_L – V) + I_{inj}C^{-1}$

Neuronal networks are the result of multiple neurons connected to one another through synapses. Pre-synaptic neurons deliverer chemicals, called neurotransmitters, to post-synaptic neurons. Some neurotransmitters are excitatory, such as NMDA (N-Methyl-D-aspartic acid), meaning they increase the likelihood of spiking activity, and others are inhibitory, such as GABA (gamma-aminobutyric acid), meaning that they decrease the likelihood of spiking activity. To describe the networks of neuronal networks, each individual neuron has a voltage equation as illustrated above, with additional terms relating to its synaptic currents. These currents depend on the synaptic conductance, the difference between the membrane voltage and the threshold voltage, the strengths of the synaptic connections, and the fraction of open channels for each receptor. The dynamical equation for the fraction of open channels usually depends on properties of the presynaptic neuron.

So far, the variables we have been considering have been the voltage and the gating variables. In order to discuss the dynamics of mental illness, we must think about another important variable: firing rate. This simply describes the rate of voltage spikes over time. Below is an example of a phase plane, where the vertical axis is the average firing rate of inhibitory neurons, and the horizontal axis is the average firing rate of excitatory neurons.

In this system, the fixed points can be thought of as memories or goal-states, and we can use this system to consider the effects of the underlying dynamics on working memory or decision making. Increasing the depth of the basin of attraction can have the effect of increasing the stability of the state, while flattening the basin of attraction reduces the stability of the state.

This paper highlights the key role of dopamine in altering these attractor dynamics. Stimulating the D1 dopamine receptors has the effect of increasing firing activity of both excitatory (NMDA) and inhibitory (GABA) neurons. This alters the parameters of the system, in particular, the strengths of synaptic connections, over time. As a result, the basins of attraction are deepened, and the state is more stable and robust to external perturbations or noise fluctuations.

Stimulation of the D2 dopamine receptors has the opposite effect, flattening the basins of attractions. These flat attractor landscapes could lead to disorganized or spontaneous thoughts that can be experienced as hallucinations that are characteristic of schizophrenia. This can also explain the high distractibility in attention-deficit hyperactive disorder (ADHD). On the other hand, Obsessive Compulsive Disorder (OCD), a disorder characterized by rumination, invasive and recurrent obsessions and compulsions, can be linked to deep basins of attractions that are robust to potential distractors. Major Depressive Disorder characterized by a coexistence of rumination and a negative mood with lack of concentration and distractibility, and one can think of it as an imbalance between multiple attractor states.

The main point this review paper aims to illustrate is that in order to characterize and develop treatments for mental illnesses, one must consider the underlying network dynamics. The suggested role of dopamine in altering the depth of basins of attractions suggest that we might try to target the dynamics of schizophrenia patients, for example, through dopaminergic drugs.

I found the process of reading this review paper and the sources it cited extremely helpful for me in improving my understanding of neurons, neuronal networks, biophysics, and nonlinear dynamics, and linking my previous understanding of neurons to cognitive processes, something that I had not fully understood before. Because the review paper goes over the general information, I read many of the papers it cited to find the basis behind some of its claims. However, I still do not clearly understand the mechanism behind the changes in the attractor dynamics. I would like to learn more about how the parameters are changed, and how these changes, in turn, alter the attractor landscapes.

At this point, I believe that the connection between these dynamics and mental illnesses as presented in this paper seems rather speculative. However, I think that as more data is collected and analyzed, and further models are developed to understand the dynamics of neuronal networks, we can glean more insight towards understanding and developing treatments for mental illnesses.

References:

Durstewitz, D., Huys, Quentin J. M., Koppe, Georgia. (2018). Psychiatric Illnesses as Disorders of Network Dynamics. doi: https://arxiv.org/pdf/1809.06303.pdf

Durstewitz, D. (2009). Implications of synaptic biophysics for recurrent network dynamics and active memory. Neural Networks, 22(8), 1189-1200.

Durstewitz, D., Seamans, J. K. (2008). The dual-state theory of prefrontal cortex dopamine function with relevance to catechol-o-methyltransferase genotypes and schizophrenia. Biological Psychiatry, 64(9), 739-749.

Durstewitz, D. (2006). A few important points about dopamine’s role in neural network dynamics. Pharmacopsychiatry, 39(S 1), 72-75.

Izhikevich, E. M. (2007). Dynamical Systems in Neuroscience: MIT Press.

Johnston, Daniel, Wu, Samuel Miao-Sin . (2001) Foundations of Cellular Neurophysiology. MIT Press.

Rolls, E. T., Loh, M., Deco, G. (2008). An attractor hypothesis of obsessive-compulsive disorder. European Journal of Neuroscience, 28(4), 782-793. doi: 10.1111/j.1460-9568.2008.06379.x

Strogatz, S. H. (2018). Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering: CRC Press.

## Introduction

I am a first-year grad student in California, and I decided to create this blog to document some of my experiences on this path working towards becoming a scientist. I would like to use this page as a record of some of my ideas in research, as well as some personal reflections about research, classes, teaching experiences, social experiences, and pursuing hobbies.

My department, Biomathematics, is a small basic science research department within the school of medicine. It focuses on theoretical, computational, and statistical modeling in biology and biomedicine. My research interests are in neuroscience, and the project I have been starting to work on this year focuses on applying tools from physics and applied mathematics to model neuronal networks.

I started college as a chemistry major, but after a while, I realized that while I loved the theoretical side of chemistry, experiments were very much not my strong suit. I changed my major to mathematics/applied science, which allowed me to take theoretical chemistry classes along with a set of courses in applied mathematics. I have always found myself interested in neuroscience, and in my last two years of undergrad, I worked in a research group that studied neurons and neuronal networks from the perspective of theoretical biophysics. There, I picked up a lot of skills in programming and applied mathematics. More than anything, I learned how to find the background information I need for a given task, which has been tremendously helpful transitioning into graduate school.

Aside from curiosity, my main motivation to study neuroscience comes from a desire to improve our understanding of the brain and mental health from a quantitative perspective. Mental health diagnoses are often based on self-reported qualitative data such as questionnaires, which are imprecise and very susceptible to bias. I believe that a greater understanding of the brain and cognitive processes from a theoretical perspective could not only better inform diagnosis and therapeutic intervention, but could reduce the stigma surrounding mental illness. Mental illnesses such as depression, anxiety, attention-deficit hyperactive disorder (ADHD), and obsessive-compulsive disorder (OCD) are often not taken as seriously as physical illness. As a result, many people suffer in silence and do not seek the treatment they need. A greater understanding of the mechanistic aspects of cognitive disorders is, I believe, a step towards recognizing the biological basis of mental illnesses and validating the health concerns of those affected. It motivates me to think about this as a long term goal, and that my studies in science are not only for my own benefit, but towards the benefit of society as a whole.

During my free time, I like finding content on the internet, in the form of blogs, art, and youtube videos. Since school is obviously a large part of my life, I like content about college and graduate school. I have found some content about life as a STEM student in graduate school, and I have felt a sense of inspiration and motivation from watching others working towards their research goals while simultaneously pursuing their hobbies. However, since my field, the interface between biology and mathematics, is relatively new, I rarely find content from students who are studying similar things that I can relate to. So I decided that if it doesn’t already exist, why not create it?

I believe it will be helpful for me to have a record of my progress in learning the material I need to know for my research, and writing things out in a pedagogical way would probably aid my own understanding of the things I’m learning. I also think that it will help me hold myself accountable, not only for my research progress, but also towards personal goals and hobbies, such as drawing and painting, swimming, dance, making new friends, and putting myself out there in the queer community.

It is likely that this blog will mostly be for my own record, and maybe some of my friends who might be interested in what I am doing. However, part of the reason I found it difficult to identify with other people in STEM is that I am often surrounded by peers who are very different from me. I have often benefitted from meeting other women, people of South Asian origin, and queer people in my field, and I know from my own experience how important representation is. I would love to know if anyone relates to any part of my experience, so please do not hesitate to contact me.

Here’s to a fruitful new year, and I am excited to begin this new journey.