Use of Differential Equations in Modeling

Circadian RhythmsBy Dr. Nathaniel J. Kingsbury

Friday, October 24, 2014, 10:00 a.m.Southwick Hall, Room 401

In this seminar, I will…

Explore the biology of circadian rhythms and provide motivation for modeling them

Show the importance of differential equations in modeling circadian rhythms

Present results and conclusions from active research

Circadian Rhythms: It’s Night and Day

Circadian=24-hour cycle; Your biological clock Controls your sleep and other patterns Found in most life forms Is genetic Must be flexible Systems biologists can describe them

using differential equations

Maladies of Poor Circadian Rhythms

Elderly suffer in particular: Sleep loss and early

wake times1

Poor mood, poor memory, cognitive decline2

Linked to accidents, other health problems, and mortality3

1Buysse D. et. al. (2005) Circadian patterns of sleep, sleepiness, and performance in older and younger adults. Sleep 28:1365–13762 Grandner, M. et. al. (2012) Age and sleep disturbances among American men and women: data from the US Behavioral Risk Factor Surveillance System. Sleep 35:395–406

3 Ancoli-Israel S, Alessi C (2005) Sleep and aging. Am J Geriatr Psychiatr 13:341–3434http://over40fitnessguide.com/wp-images/tired-elderly.jpg, Accessed April 23, 2014

4

The Suprachiasmatic Nucleus (SCN) The brain can be divided by region, and

each region has a distinct function The SCN is one of the best examples of

this

https://angelosscienceportfolio.files.wordpress.com/2013/04/regions_of_the_brain_and_their_functions.jpg, Accessed April 23, 2014https://a248.e.akamai.net/media.pinterest.com.s3.amazonaws.com/736x/e5/59/1a/e5591a7d78e177db8d6a80d5168123cb.jpg, Accessed April 23, 2014

SCN

The Suprachiasmatic Nucleus (SCN): An experiment

Mice Population 1 Mice Population 2

Lights were on from 5am-5pm Lights were on from 5pm-5am

Exercised at 5pm Exercised at 5am

Lights were off for 24h; rhythm is preserved

Lights were off for 24h; rhythm preserved

SCN was surgically removed; rhythm is lost

SCN was surgically removed, rhythm is lost

SCN from Population 1 was transplanted into Population 2

Continued to exercise at random times

Got rhythm from Pop 1, exercised at 5pmAdapted from: Sujino, M. et al. (2003) Suprachiasmatic nucleus grafts restore circadian

behavioral rhythms of genetically arrhythmic mice. Curr. Biol. 13, 664–668

More Experimental Techniques:Bioluminescence

Freeman, et. al. “GABA Networks Destabilize Genetic Oscillationsin the Circadian Pacemaker.” Neuron 78, 799–806, 2013.

More experimental techniques:Microelectrode arrays

200µmFreeman, et. al. “GABA Networks Destabilize Genetic Oscillations in the Circadian Pacemaker.” Neuron 78, 799–806, 2013.

Why Model

Systems biologists can use models to describe an entire complex network in entirety

Experiments are time and energy intensive

Models can be used to validate phenomena found during experiment

Models can develop hypotheses testable in a lab

Limit Cycle Oscillators

Strogatz, Steven H. "Exploring complex networks." Nature 410.6825 (2001): 268-276.

Types of Networks

Strogatz, Steven H. "Exploring complex networks." Nature 410.6825 (2001): 268-276.

Model Network vs. Experimental Network

Making the Network

Network (Graph) Adjacency matrix

Circadian Rhythm Model

21 components, 21 ODEs Modeled for each cell within the network Represent the core molecular clock

DNA mRNA

Protein

Hexokinasehttps://en.wikipedia.org/wiki/File:Hexokinase_ball_and_stick_model,_with_substrates_to_scale_copy.png, Accessed May 1, 2014

+

-

Biological Oscillations

If A B; positive feedback; A B If A B; negative feedback; A B Repressilator example: A,B, and C are all

molecules present inside a bacterial cell A B, B C, C A

Pro

tein

s per

cell

time (minutes)

A—B —C —

Neurotransmitters connect the network

GABA (γ-aminobutyric acid): inhibitory; reduces firing rate

VIP (vasoactive intestinal peptide): excitatory; stimulates transcription of Period gene

Types of model manipulation: light entrainment

Entrainment of the network to light-dark cycles. Phase shifts (simulates jet

lag) Length of daylight period

We are very interested in learning what is important for resynchronization to this kind of phase shift

Days

time of day (h)0 12 24

Basic Output Example

To speed up or slow down?

12:00 am 9:00am

AdvancersSwitchers (w/GABA)Delayers

ConclusionsSystems biology: modeling complex

biological systems Models of circadian rhythms all employ ODEsMy model closely simulates tissue topology,

cell machinery, and signalingGoal of my research is to find and

communicate hypotheses that may be tested experimentally

My model helps describe how the brain works!